Iron-Based Superconducting Thin Films (Springer Series in Materials Science, 315) 3030751309, 9783030751302

Citation preview

Springer Series in Materials Science 315

Silvia Haindl

Iron-Based Superconducting Thin Films

Springer Series in Materials Science Volume 315

Series Editors Robert Hull, Center for Materials, Devices, and Integrated Systems, Rensselaer Polytechnic Institute, Troy, NY, USA Chennupati Jagadish, Research School of Physics and Engineering, Australian National University, Canberra, ACT, Australia Yoshiyuki Kawazoe, Center for Computational Materials, Tohoku University, Sendai, Japan Jamie Kruzic, School of Mechanical & Manufacturing Engineering, UNSW Sydney, Sydney, NSW, Australia Richard M. Osgood, Department of Electrical Engineering, Columbia University, New York, USA Jürgen Parisi, Universität Oldenburg, Oldenburg, Germany Udo W. Pohl, Institute of Solid State Physics, Technical University of Berlin, Berlin, Germany Tae-Yeon Seong, Department of Materials Science & Engineering, Korea University, Seoul, Korea (Republic of) Shin-ichi Uchida, Electronics and Manufacturing, National Institute of Advanced Industrial Science and Technology, Tsukuba, Ibaraki, Japan Zhiming M. Wang, Institute of Fundamental and Frontier Sciences - Electronic, University of Electronic Science and Technology of China, Chengdu, China

The Springer Series in Materials Science covers the complete spectrum of materials research and technology, including fundamental principles, physical properties, materials theory and design. Recognizing the increasing importance of materials science in future device technologies, the book titles in this series reflect the state-of-the-art in understanding and controlling the structure and properties of all important classes of materials.

More information about this series at http://www.springer.com/series/856

Silvia Haindl

Iron-Based Superconducting Thin Films

123

Silvia Haindl WRHI Tokyo Tech Institute of Innovative Research Tokyo Institute of Technology Yokohama, Kanagawa, Japan

ISSN 0933-033X ISSN 2196-2812 (electronic) Springer Series in Materials Science ISBN 978-3-030-75130-2 ISBN 978-3-030-75132-6 (eBook) https://doi.org/10.1007/978-3-030-75132-6 © Springer Nature Switzerland AG 2021 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Dedicated to kb

Preface

The semimetallic Fe-pnictides and Fe-chalcogenides, which are also known as ‘Fe-based superconductors’, constitute a new class of unconventional superconductors with maximum critical temperatures ranging 55–60 K (and up to 75 K in 1uc FeSe/SrTiO3 ). Their appearance during 2008 and the following years has caused an intense excitement in condensed matter physics. Since then, we have witnessed a dynamic development in material synthesis, material analysis and theoretical description. The purpose of this monograph is to provide an updated overview of the various activities and results in thin film research of Fe-based superconductors. The progress in the growth and study of Fe-based superconducting thin films manifested itself in the first superconducting LaO1 x Fx FeAs films prepared by a two-stage process, the successful application of pulsed laser deposition in the growth of Ba (Fe1 x Cox )2 As2 and FeSe1 x Tex films, the establishment of different film growth techniques in the synthesis of the Fe-oxyarsenides LnO1 x Fx FeAs (Ln = La, Nd, Sm), various other Fe-pnictides and Fe-chalcogenides, and, notably, the growth of FeSe monolayers as well as FeSe/Bi2 Se3 heterointerfaces by molecular beam epitaxy. Not only most recent contributions in the engineering of ultrathin films and heterointerfaces but also ongoing efforts in improving thin film properties for applications demonstrate that we enter a lively field that is still full of surprises! This monograph was originally planned as a follow-up project after finishing the first comparative review on Fe-based superconducting thin films in 2014 [1]. Its intention is not only to provide a thematic introduction for graduate students but also to offer a structured and commented data collection for thin film engineers and scientists working in the field. Readers will be able to quickly identify the state of knowledge and its relevant resources for Fe-based superconducting thin films with respect to growth techniques or investigated properties. This monograph also includes several topics, which are typically omitted in the past published surveys. Having a great interest in interfaces, ideas for an interface atlas came up, in which the experimentally available data on different film/substrate combinations are referenced systematically. It became quickly clear that such a compilation goes beyond the content that is usually found in review articles. Attention is drawn to vii

viii

Preface

several perspectives with more clarity, such as the difference between Fe-chalcogenides as van der Waals materials and Fe-pnictides as polar compounds and the importance of the control of the film/substrate interface. The monograph is organized into six chapters. After an introduction to the materials and physics of Fe-based superconductors (Chap. 1), there are two main chapters: Thin film growth of Fe-based superconductors (Chap. 2) contains technical details of thin film engineering, systematically sorted by growth methods and compounds. Most resources cover the dominantly applied techniques in the growth of Fe-based superconductors: pulsed laser deposition and molecular beam epitaxy. However, this monograph describes also many other and less applied engineering routes applied to Fe-pnictide and Fe-chalcogenide films. Thin film studies under focus (Chap. 6) summarizes various contributions of thin film studies under a specific topic, including vortex physics, superconductor-to-insulator transitions, electronic phase diagrams, metastable compounds, FeSe monolayers, Fe-based superconducting thin films in high magnetic fields, electromagnetic and spectroscopic thin film studies and finally irradiation experiments. Three additional chapters are devoted to the analytical characterization of Fe-pnictide and Fe-chalcogenide thin films, the analysis of their surfaces (Chap. 3), the film/substrate interface analyzed by transmission electron microscopy (Chap. 4) and the growth and analysis of multilayers and heterostructures (Chap. 5). According to the large and growing amount of literature resources, the overview cannot be complete but offers the main trends in thin film engineering of Fe-based superconductors and the most relevant literature. Finally, I am deeply grateful to Sara Kate Heukerott, Editor at Springer, who has provided initial support, as well as to all other members of the editorial office. Although no funding for this monograph was provided by WRHI Tokyo Institute of Technology as well as the German Research Foundation (DFG), I want to mention that their support made a continuous work on the topic of Fe-based superconducting thin films possible. Agustín Conde-Gallardo, Carlo Ferdeghini and Makoto Takahashi are gratefully acknowledged for providing images, which demonstrate film growth synthesis in their labs, Takahiko Kawaguchi and Hiroshi Ikuta are gratefully mentioned as previous project partners within one of my DFG projects. I also would like to thank several previous colleagues and co-authors, in particular Erik Kampert and the supportive team at High Magnetic Field Laboratory at Dresden-Rossendorf (HLD-HZDR: member of the European Magnetic Field Laboratory), Martin Kidszun, Fritz Kurth, Sebastian Molatta, Andreas Reisner, Tom Thersleff and Elke Reich as well as Rudolph Hübener, Dieter Kölle and Reinhold Kleiner for their encouragement and fruitful discussions over the past years. Last but not the least, I want to thank Yoshinori Muraba and Joonho Bang for their help with translations of Japanese and Korean sources and Sergey Nikolaev and Tianping Ying for fruitful discussions. Tübingen, Germany/Tokyo, Japan

Silvia Haindl

Preface

ix

Reference [1] Haindl, S., Kidszun, M., Oswald, S., Hess, C., Büchner, B., Kölling, S., Wilde, L., Thersleff, T., Yurchenko, V.V., Jourdan, M., Hiramatsu, H., Hosono, H.: Thin film growth of Fe-based superconductors: from fundamental properties to functional devices. A comparative review. Rep. Prog. Phys. 77, 046502 (2014)

Contents

. . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

1 1 3 9 11 13 19

2 Thin Film Growth of Fe-Based Superconductors . . . . . . . . . . . 2.1 Pulsed Laser Deposition . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.2 PLD of Fe-Chalcogenides . . . . . . . . . . . . . . . . . . . . 2.1.3 PLD of Fe-Pnictide Compounds with ThCr2 Si2 Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.4 PLD of Fe-Oxyarsenides with ZrCuSiAs Structure . . 2.2 Molecular Beam Epitaxy . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.2 MBE-Growth of Fe-Chalcogenide Thin Films . . . . . 2.2.3 Fabrication of Fe-Chalcogenide Monolayers . . . . . . 2.2.4 Alkali-Metal Evaporation on Ultrathin FeSe Films . . 2.2.5 Fe-Chalcogenides/Topological Insulators (TIs) . . . . . 2.2.6 MBE-Growth of Fe-Pnictides . . . . . . . . . . . . . . . . . 2.3 Other Thin Film Growth Methods . . . . . . . . . . . . . . . . . . . 2.3.1 Two-Stage Synthesis with Postdeposition Annealing 2.3.2 Selenization Methods for FeSe Film Growth . . . . . . 2.3.3 Magnetron Sputtering of Fe-Chalcogenides . . . . . . . 2.3.4 Metal-Organic Chemical Vapor Deposition . . . . . . . 2.3.5 Electrodeposition of FeSe and LiFeAs . . . . . . . . . . 2.3.6 Other Wet Chemical Deposition Processes for FeSe . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . .

. . . .

. . . .

. . . .

27 28 28 34

. . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . .

52 60 66 66 69 72 79 80 83 93 95 100 102 109 114 124 129

1 Introduction to Fe-Based Superconductors . . . . . . . . . . . 1.1 Discoveries and the ‘Iron Age’ in Superconductivity . 1.2 Compounds and Crystal Structures . . . . . . . . . . . . . 1.3 Iron (Fe) and Superconductivity . . . . . . . . . . . . . . . 1.4 Electronic Bands and Fermi Surfaces . . . . . . . . . . . . 1.5 Nematicity, Magnetism and Superconductivity . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

xi

xii

Contents

. . . . . . . . . . . . .

. . . . . . . . . . . . .

. . . . . . . . . . . . .

149 149 149 152 159 160 160 163 169 169 171 173 181

4 The Film/Substrate Interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Substrates in Thin Film Growth of Fe-Based Superconductors . 4.1.1 The Role of the Substrate . . . . . . . . . . . . . . . . . . . . . . 4.1.2 Buffer and Seed Layers . . . . . . . . . . . . . . . . . . . . . . . 4.1.3 Fe-Chalcogenide Film/Substrate Interfaces . . . . . . . . . . 4.1.4 Selected Fe-Pnictide Film/Substrate Interfaces . . . . . . . 4.2 Interface Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1 Misfit Dislocations . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.2 FeSe and FeSe1 x Tex on TiO2 and TiO2 -Terminated SrTiO3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.3 Interface Models for Fe-Chalcogenides on LaAlO3 and MgO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.4 Heterointerfaces with Fe-Pnictides . . . . . . . . . . . . . . . 4.3 TEM Interface Atlas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.1 Fe-Chalcogenide Thin Film/Substrate Interfaces . . . . . . 4.3.2 Fe-Pnictide Thin Film/Substrate Interfaces . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . .

. . . . . . . .

189 189 189 193 198 202 206 206

3 Growth, Microstructure and Surfaces . . . . . . . . . . . . . . . 3.1 In-Situ Film Growth Monitoring . . . . . . . . . . . . . . . 3.1.1 LEED . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.2 RHEED . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.3 HEPD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Thin Film Texture and Crystal Quality . . . . . . . . . . . 3.2.1 Texture and In-Plane-Alignment of Grains . . 3.2.2 Out-of-Plane-Alignment and Rocking Curves 3.3 Growth Modes, Surface Structure and Morphology . . 3.3.1 Polar Surfaces . . . . . . . . . . . . . . . . . . . . . . . 3.3.2 Growth Modes of Vapor Deposited Films . . . 3.3.3 Examples of Surface Studies . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . .

. . . . . . . . . . . . .

. . . . . . . . . . . . .

. . . . . . . . . . . . .

. . . . . . . . . . . . .

. . . . . . . . . . . . .

. . 208 . . . . . .

. . . . . .

210 211 212 214 223 228

. . . .

. . . .

235 235 240 243

5 More Interfaces: Multilayers and Heterostructures with Fe-Based Superconductors . . . . . . . . . . . . . . . . . . . . . . 5.1 FeSe1 x Tex -Based Multilayers . . . . . . . . . . . . . . . . . . . . 5.2 New Platforms: Interfaces Between FeSe (FeTe) and TIs 5.3 BaFe2 As2 -Based Heterointerfaces . . . . . . . . . . . . . . . . . 5.4 Secondary Phase Formation and Artificially Introduced Nanoparticles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . 248 . . . . . . 250

6 Thin Film Studies Under Focus . . . . . . . . . . . . . . . . . . . . . . 6.1 Vortex Matter in Thin Films . . . . . . . . . . . . . . . . . . . . . 6.1.1 Vortex Motion . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1.2 Berezinskii-Kosterlitz-Thouless (BKT) Transition

. . . .

. . . .

. . . .

. . . .

. . . .

. . . .

. . . .

. . . .

. . . .

. . . .

253 253 253 258

Contents

6.1.3 Critical Currents and Vortex Pinning . . . . . . . . . . . . . 6.1.4 The Role of Grain Boundaries . . . . . . . . . . . . . . . . . . 6.2 Superconductor-to-Insulator (SIT) Transitions . . . . . . . . . . . . . 6.2.1 Granular and Crystalline FeSe Films . . . . . . . . . . . . . . 6.2.2 Electrostatic Doping in EDLT/FeSe Films and SIT . . . 6.3 Electronic Phase Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.1 FeSe1 x Tex and FeSe1 x Sx . . . . . . . . . . . . . . . . . . . . . 6.3.2 FeSe and K-Coated FeSe Surface . . . . . . . . . . . . . . . . 6.3.3 Ba(Fe1 x Cox )2 As2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.4 BaFe2 As2 /SrTiO3 Superlattices . . . . . . . . . . . . . . . . . . 6.4 Metastable Compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5 The Tc Boost in FeSe Monolayers . . . . . . . . . . . . . . . . . . . . . 6.5.1 Fermi Surface, Topology and Energy Gap . . . . . . . . . . 6.5.2 Charge Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5.3 Interfacial Electron-Phonon Coupling . . . . . . . . . . . . . 6.5.4 Vortices and Andreev Bound States . . . . . . . . . . . . . . 6.6 High Magnetic Field Studies . . . . . . . . . . . . . . . . . . . . . . . . . 6.6.1 Fe-Chalcogenide Thin Films in High Magnetic Fields . 6.6.2 Fe-Pnictide Thin Films in High Magnetic Fields . . . . . 6.7 Electromagnetic Properties, Superconducting Gaps and Fermi Surfaces from Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . 6.7.1 DC Transport and Response to Low Frequency Fields . 6.7.2 Radio Frequency and Microwave Techniques . . . . . . . 6.7.3 Optical (IR/THz) Spectroscopy . . . . . . . . . . . . . . . . . . 6.7.4 Photoelectron Spectroscopies . . . . . . . . . . . . . . . . . . . 6.7.5 Point-Contact Spectroscopy . . . . . . . . . . . . . . . . . . . . 6.8 Irradiation and Implantation . . . . . . . . . . . . . . . . . . . . . . . . . . 6.8.1 Laser Light Irradiation of and Ion Implantation in FeTe Films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.8.2 Irradiation and Implantation Effects in FeSe1 x Tex Films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.8.3 Irradiation of Fe-Pnictide Thin Films . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

xiii

. . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . .

260 277 282 282 284 287 287 291 293 294 295 298 300 304 306 309 309 313 315

. . . . . . .

. . . . . . .

317 317 322 325 338 342 348

. . 351 . . 353 . . 355 . . 359

Appendix A: Chronological Survey of Selected Publications . . . . . . . . . . 381 Appendix B: Space Groups and Brillouin Zones . . . . . . . . . . . . . . . . . . . 383 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387

Acronyms

2D 3D AAS AEM AES APT ARPES CBD CSD CVD DC DMFT EDS or EDX EELS EIES EPMA FESEM FIB FWHM HAADF HEPD HGPTS HR-STEM HR-TEM HV IBAD ICP ICP-MS IR LDA

2-dimensional 3-dimensional Atomic Absorption Spectroscopy Auger Electron Microscopy Auger Electron Spectroscopy Atomic Probe Tomography Angle-Resolved Photoemission Spectroscopy Chemical Bath Deposition Chemical Solution Deposition Chemical Vapor Deposition Direct Current Dynamical Mean-Field Theory Energy Dispersive X-ray Spectroscopy Electron Energy Loss Spectroscopy Electron Impact Emission Spectroscopy Electron Probe Micro-Analysis Field Emission Scanning Electron Microscopy Focused Ion Beam Full width half maximum High-Angle Annular Dark-Field High-Energy Positron Diffraction High Gas Pressure Trap System High-Resolution Scanning Transmission Electron Microscopy High-Resolution Transmission Electron Microscopy High vacuum Ion Beam Assisted Deposition Inductively-Coupled Plasma Inductively-Coupled Plasma Mass Spectrometry Infrared Local Density Approximation

xv

xvi

LEED MBE ML MO MOCVD PCARS PCS PES PLD QCM QPI RABiTS RBS RF RHEED RSM SEM SQUID SSRM STEM STM STS TEDS TEM THz TI TRHEPD UHV UPS WDS XAS XPS XRR

Acronyms

Low-Energy Electron Diffraction Molecular Beam Epitaxy Monolayer Magneto Optics Metalorganic Chemical Vapor Deposition Point Contact Andreev Reflection Spectroscopy Point Contact Spectroscopy Photoemission Spectroscopy Pulsed Laser Deposition Quartz Crystal Microbalance Quasi-Particle Interference Rolling Assisted Biaxially Textured Substrates Rutherford Backscattering Spectrometry Radio frequency Reflection High-Energy Electron Diffraction Reciprocal Space Mapping Scanning Electron Microscopy Superconducting Quantum Interference Device Scanning Spreading Resistant Microscopy Scanning Transmission Electron Microscopy Scanning Tunneling Microscopy Scanning Tunneling Spectroscopy Transmission Energy Dispersive X-ray Spectroscopy Transmission Electron Microscopy Terahertz Topological insulator Total-Reflection High-Energy Positron Diffraction Ultra high vacuum Ultraviolet Photoelectron Spectroscopy Wavelength Dispersive Spectroscopy X-ray Absorption Spectroscopy X-ray Photoelectron Spectroscopy X-ray Reflectivity

Chapter 1

Introduction to Fe-Based Superconductors

1.1 Discoveries and the ‘Iron Age’ in Superconductivity The announcement of superconductivity below a critical temperature of Tc = 26 K in the F-substituted Fe-oxypnictide compound LaOFeAs by Yoichi Kamihara et al. in February 2008 excited researchers of superconductivity worldwide [1]. Suddenly, a new class of materials with a potential comparable to the cuprate high-temperature superconductors became available. This accidental discovery by a young post-doc happened in the search for novel transparent oxide semiconductors and should be dated back to 2006, where in a publication on LaOFeP the ‘new class’ of superconductors (i.e. F-substituted Fe-oxypnictides) was already announced [2], but details remained covered due to a patent application. Insight is offered by the discoverer in [3, 4]. Superconductivity in LaOFeP below Tc = 3.2 K was originally found in 1996 by Barbara Zimmer [5], but was documented only in her Ph.D. thesis [6] and not in a journal publication [7]. Furthermore, many quaternary Fe-oxyarsenides were synthesized already in Wolfgang Jeitschko’s group before 2008 [8], however, their electronic properties at low temperatures remained unexplored. Kamihara’s new achievement was electron doping of the compound by F-substitution and its investigation at low temperatures. While superconductivity in LaOFeP received only little attention in 2006, the much higher Tc in F-substituted LaOFeAs was exceeded within only two months by research groups from Hefei, Beijing, and Hangzhou [9–13]: The critical temperature in F-substituted Fe-oxyarsenides could be raised up to 56 K by means of rare-earth (RE) substitution. This extremely fast validation of superconductivity by independent laboratories confirmed that these materials were not ‘unidentified superconducting objects’ (USOs) [14] and fueled expectations that Tc could reach liquid nitrogen temperatures. The media hype around the new superconducting materials promised an ‘iron age’ [15], a pun that should describe a termination of the dominance of cuprates in high-temperature superconductivity. However, to date the maximum Tc © Springer Nature Switzerland AG 2021 S. Haindl, Iron-Based Superconducting Thin Films, Springer Series in Materials Science 315, https://doi.org/10.1007/978-3-030-75132-6_1

1

2

1 Introduction to Fe-Based Superconductors

within the Fe-oxypnictide and related Fe-pnictide or Fe-chalcogenide compounds remained below ∼75 K. The immediate hype was also accelerated by the active usage of the ‘arXiv’ [16], a pre-print server that stores uploaded manuscripts and enforces circulation by open access. In the meantime, the synthesis of the new superconductors that contain Fe was also started at European and American laboratories and the number of so called ‘Fe-based’ compounds surprisingly multiplied. The new class of superconductors turned out to be much larger: Dirk Johrendt’s group at the University of Munich announced superconductivity with a critical temperature of 38 K in K-substituted BaFe2 As2 , a compound that also contains Fe2 As2 layers in its structure similar to the Fe-oxypnictides [17]. A complete substitution resulting in KFe2 As2 , however, lowered Tc by a factor of 10. Similar to Fe-oxypnictides, the ternary arsenide BaFe2 As2 , first synthesized in 1980 [18], allows chemical substitution at all crystallographic sites, i.e. for the alkaline earth metal, for the transition metal and for the pnictogen ion. Accordingly, Co-substituted BaFe2 As2 and LaFeAsO were both found with superconducting transitions at 22 K and 14.3 K, respectively [19, 20]. Several projects focused on chemical substitution or the synthesis of more anisotropic compounds with the aim of increasing the superconducting transition temperature further. Another route followed the reduction of structural complexity. As a result, LiFeAs (known since 1968 [21]) was announced as superconductor with Tc = 18 K at the end of June 2008 by Xian Cheng Wang et al. [22]. Two weeks later, superconductivity was verified below 8 K in the binary Fe-chalcogenide compound FeSe (first synthesized in 1933 [23]) at Academia Sinica Taiwan [24]. It turned out quickly, that the common crystallographic structure of all new compounds, the [Fe2 X2 ] (X = As, P or Se, Te) layers, are responsible for the electronic properties including superconductivity. Materials with this layered structure constituted the term ‘Fe-based superconductors’. In spring 2008 thin film growth experiments on the F-substituted Fe-oxyarsenides started independently by at least two research laboratories. Their results appeared on the arXiv pre-print server in August 2008. Pulsed laser deposition (PLD), which was chosen for the first film growth experiments, soon manifested crucial limitations when dealing with volatile elements like F. Because F was not transferred from the target to the heated substrate, the as-grown films neither contained F nor showed a superconducting transition. Though epitaxial growth of LaOFeAs thin films on MgO and (La,Sr)(Al,Ta)O3 substrates could be achieved, only the undoped ‘parent’ compound was obtained [25]. At the same time, Elke Backen et al. applied a two-stage process that based on a room-temperature deposition of the material, in order to prevent F losses, and a subsequent ex-situ post-annealing of the granular precursor film [26]. This method established the first successful growth of superconducting LaOFeAs films and was adapted later to other compounds with highly volatile elements, such as (Ba1−x Kx )Fe2 As2 , H-substituted SmOFeAs and others (see Sect. 2.3.1). Thin film synthesis followed for Co-substituted SrFe2 As2 , yet announced in August 2008 on the arXiv pre-print server [27]. PLD of ternary Fe-pnictide compounds as well as FeSe turned out to be less complicated than that of Fe-oxyarsenides.

1.1 Discoveries and the ‘Iron Age’ in Superconductivity

3

As a result, Co-substituted BaFe2 As2 , FeSe and other Fe-chalcogenide thin films appeared in 2009. A list of important publications on thin film synthesis in chronological order can be found in Appendix A. Reports on non-superconducting FeSe, Fe-Se (and FeTe) films can also be found before 2008 and various examples for the growth of Fe-chalcogenide films are summarized in Sect. 2.3. The binary FeSe has been synthesized by far more methods than other related compounds of the Fe-based superconductor family. However, Fe-based superconductors are generally grown by physical vapor deposition methods such as PLD and molecular beam epitaxy (MBE), which are summarized in Sects. 2.1 and 2.2. At the begin of 2012 the claim of stabilizing high-temperature superconductivity in a 1 uc FeSe (‘monolayer’) initiated an exciting development [28]. The large energy gaps measured in-situ by scanning tunneling microscopy (STM) indicated corresponding transition temperatures of 60 K and higher (Sects. 2.2.3 and 6.5). The activities around 1 uc FeSe opened a new research front towards interface engineering in ultrathin films and heterostructures that include surface doping by alkali metal atoms (Sect. 2.2.4) or the synthesis of FeSe/Bi2 Se3 (FeTe/Bi2 Te3 ) heterointerfaces between Fe-chalcogenides and chalcogenide topological insulators (TIs) (Sects. 2.2.5 and 5.2). The two-dimensional superconducting state in monolayers or at interfaces brought additional controversies about the Cooper pairing mechanism in Fe-based superconductors. Their fundamental difference in Fermi surface topology through the entire disappearance of the hole pockets remained a topical question. Early results for Fe-chalcogenide thin films were reviewed in [29, 30]. A first comparative overview [31] provided an introduction into the fast growing research area based on selected important issues for functional thin film growth. Many further review articles cover specific topics on fabrication, properties and the application potential of Fe-based superconducting thin films, for example, notes on Fe-pnictide thin film growth by UHV PLD [32], the application of PLD and MBE in the growth of Fe-based superconductors [33–35], and prospects for device fabrication and the application potential [36–38]. FeSe monolayers and their interfaces are summarized in [39–44] discusses ex-situ transport measurements on FeSe monolayers. Recent surveys on FeSe films and monolayers are also found in [45–47]. Recommended introductions about Fe-based superconductors are edited by Nan-Ling Wang, Hideo Hosono and Pengcheng Dai [48] and by Johnson et al. [49].

1.2 Compounds and Crystal Structures For the variety of Fe-chalcogenides and Fe-pnictides categorized as Fe-based superconductors the [Fe2 X2 ] layers constitute a common structural feature of their unitcells. These layers are built up by a square lattice of Fe2+ ions (with short Fe–Fe distances ∼2.75 ± 0.1 Å) that are tetrahedrally coordinated either to chalcogen ions (X2− = S2− , Se2− , Te2− ) or pnictogen ions (X3− = As3− , P3− ), respectively (Fig. 1.3). Each unit cell contains two inequivalent Fe2+ ion lattice sites as well as two inequivalent X2− ion sites, one above and one below the Fe plane (Fig. 1.2a).

4

1 Introduction to Fe-Based Superconductors

Fig. 1.1 Schematic level structure for Fe-pnictides after lifting of the degeneracy of the Fe 3d orbitals due to the tetrahedral crystal field and an additional distortion with tetragonal (lattice) symmetry (without hybridization and spin-orbit coupling)

By making use of the glide-mirror symmetry, band structures can be described on a reduced unit cell with only one Fe2+ ion (and one X2− ion), which corresponds to a larger (unfolded) Brillouin zone in reciprocal space (Appendix B). The four X anions around Fe2+ describe four ligands in a tetrahedral complex and result in a crystal field splitting of the 3d orbital into a top t2g level with 3-fold degeneracy (dx y , d yz , dx z ) and a bottom eg level with 2-fold degeneracy (dx 2 −y 2 , d3z 2 −r 2 or ‘dz 2 ’). The further breaking of the orbital degeneracy within both levels originates from the tetragonal lattice symmetry and can be slightly different for different Febased superconductors. Figure 1.1 represents the situation in Fe-pnictides, whereas in Fe-chalcogenides the d yz and dx z levels are energetically above dx y . The total crystal field splitting is in the order of ΔCF = Δt ≈ 100–200 meV. The degeneracy of the d yz and dx z levels is further split in an orthorhombic environment and by spin orbit interaction ΔSO ≈ 20 meV. Fe-based superconductors are thus multi-orbital electron systems, governed by the Fe 3d states at the Fermi level. These states are responsible for the electronic properties (see Sect. 1.4). Hybridization effects between Fe 3d and As 4 p states affect most strongly the d yz and dx z orbitals. Variations in the bonding lengths and bonding angles of the corner-sharing FeX4 tetrahedra (or anion heights, h) sensitively affect the band structure [50] and also the electronic properties, as it will be discussed later (Fig. 1.2b, c). For the moment, we will focus on the different structures of Fe-based superconductors that are often designated according to their stoichiometry as ‘11’, ‘111’, ‘1111’ and ‘122’ compounds. An overview of the different crystallographic structures of Febased superconductors can be found in [51, 52]. In general, distinct bonding regimes are encountered in all structures: within the [Fe2 X2 ] layers, the chemical bonding is of

1.2 Compounds and Crystal Structures

5

Fig. 1.2 a 2-Fe and 1-Fe unit cells (real space) indicated within the (square) Fe-plane. Anions above and below the Fe-plane are indicated by different color. b [Fe2 X2 ] (mono)layer with important structural parameters: anion height h and c 2-fold and 4-fold X-Fe-X bonding angles α and β with basic formulas. z M and z X are the Wyckoff position coordinates of Fe2+ and X anions, h is the anion height above the Fe2+ plane, a and c are the lattice parameters of the tetragonal unit cell, and M¯X denotes the bonding length between Fe2+ and X as shown in c

Fig. 1.3 Structures of the main compounds of Fe-based superconductors grown as thin films: Differences between Fe-chalcogenides (e.g. FeSe) and Fe-pnictides (e.g. LiFeAs, LaOFeAs and BaFe2 As2 )

6

1 Introduction to Fe-Based Superconductors

a mixed covalent/metallic nature. A predominant covalent bonding is found between Fe and As, whereas Fe–Fe bonds are metallic. Between the layers (along the c-axis direction) chemical bonding is strongly determined by the valence of the chalcogen ion (X2− ) and the pnictogen ion (X3− ), respectively. In 11 Fe-chalcogenides, the [Fe2 X2 ]0 layer with compensated charge results in a van der Waals bonding along the c-axis lattice direction. The tetragonal 11 Fe-chalcogenides are, therefore, layered van der Waals compounds, which are of particular interest in thin film synthesis (see Sects. 4.1.3 and 5.2). In the Fe-pnictides, however, the [Fe2 X2 ]2− layers become negatively charged in the presence of pnictogen ions which leads to an ionic bonding. The tetragonal 111, 1111 and 122 Fe-pnictide compounds are, therefore, stabilized by ionic forces along the c-axis direction. The positively charged spacer (charge donation) layers are composed of alkali metal ions such as Li+ or Na+ (in 111) and alkaline earth metals such as Ca2+ , Sr2+ or Ba2+ (in 122). The quaternary Fe-oxpnictides (1111 compounds) can be described by an alternating stacking of [Fe2 X2 ]2− and [Ln2 O3 ]2+ with Ln = lanthanide. Apart from some exceptions (FeSe, LiFeAs), the parent compounds are non-superconducting. Chemical substitution possible at all lattice sites can lead to charge carrier doping. This is called direct doping when the substitute is within the [Fe2 X2 ] planes, indirect doping when the substitute is in a spacer layer. Latter does not induce chemical disorder in the [Fe2 X2 ] planes and usually leads to higher critical temperatures. For example, the maximum Tc is 39 K in K-substituted BaFe2 As2 (indirect hole doping) compared to 26 K in Co-substituted BaFe2 As2 (direct electron doping), or 55 K in F-substituted SmOFeAs (indirect electron doping) compared to 17 K in Co-substituted SmOFeAs (direct electron doping). 11 Compounds The binary compound FeSe shows dimorphism of an anti-PbO-type structure (space group: P4/nmm) and a NiAs-type structure (space group: P6 3 /mmc) as first noted by Gunnar Hägg and Anna-Lisa Kindström in 1933 [23]. While the hexagonal FeSe phase (a = 3.519 Å; c = 5.684 Å) is a ferrimagnet up to ∼400 K, tetragonal FeSe with anti-PbO-type structure (a = 3.689 Å; c = 5.854 Å) undergoes a structural transition to an orthorhombic FeSe phase (space group: Cmma) below 90–100 K and shows a superconducting transition temperature at Tc ≈ 8 K, as reported by Fong-Chi Hsu et al. in 2008 [24]. The prefix ‘anti’ in anti-PbO-type structure denotes the reversal of anion/cation sites in FeSe compared to PbO. Fe and Se occupy the Wyckoff positions 2a {coordinates (0, 0, 0) and (1/2, 1/2, 0)} and 2c {coordinates (0, 1/2, z Se ) and (1/2, 0, z¯ Se )}. It is the simplest Fe-based superconducting compound and only formed by a stacking of [Fe2 Se2 ] layers. Monolayers (1 uc) FeSe (Fig. 1.2) with a 8–9 times higher Tc than bulk FeSe play an important role in the thin film research. They are extremely air sensitive and require in-situ characterization or must be protected by a cover layer. The stability range of the tetragonal FeSe phase lies within 1 at.% and its thermal decomposition is at 730 K [53]. Apart from a stoichiometry close to 1:1, the Fe-Se phase diagram is rich in other phases as well, for example Fe3 Se4 , FeSe2 and

1.2 Compounds and Crystal Structures

7

Fe7 Se8 [54]. None of these phases were reported to be superconducting. Substitution of the anion site by other chalcogenide ions yields FeSe1−x Tex or FeSe1−x Sx with tetragonal unit cells (space group: P4/nmm) (see also Sect. 6.3.1). A considerable fraction of thin film activities are devoted to these compounds. The binary FeTe (or Fe1+x Te) adopts a defective Cu2 Sb-type structure (space group: P4/nmm), which is similar (but not isostructural) to the PbO-type structure. It was, therefore, suggested, that the Cu2 Sb structure type (Fe2 As) should be regarded as the fundamental parent, which most structure types of Fe-based superconductors can be related to. Bulk lattice parameters are given as a = 3.656 Å and c = 6.515 Å. The excess Fe ions are found at interstitial crystallographic sites. Besides the structural difference, the electronic and magnetic properties of FeTe are distinct from FeSe. A simultaneous structural and magnetic transition from a tetragonal, paramagnetic phase into a monoclinic (space group: P21 /m), antiferromagnetic (spin density wave) phase occurs at ∼70 K. FeTe and oxygenated FeTe can be found in several thin film studies. Recently, interest in topological superconductivity has initiated studies of FeTe/Bi2 Te3 interfaces and even a topological phase in monolayer FeSe1−x Tex was predicted [55]. 111 Compounds LiFeAs with either a small Li or a small Fe excess was first reported by Robert Juza and Klaus Langer in 1968 [21]. Since 2008 [22] it became a well investigated representative of the ternary, equiatomic (111) Fe-pnictide, that crystallizes in the PbClF-type structure with a = 3.791 Å and c = 6.107 Å (space group: P4/nmm), which is related to the Cu2 Sb structure. Thin film growth of the 111 compounds has played only a marginal role. On the one hand, the volatile character of Li challenges its incorporation into films that are grown by vapor deposition methods. On the other hand, LiFeAs is extremely sensitive against moisture and its hydrolytic decomposition must be avoided by vacuum or Ar atmosphere. Material synthesis thus requires either an UHV environment with in-situ analytical investigations or appropriate encapsulation and protection of the thin film sample. 1111 Compounds A filled version of the PbClF-type structure leads to the ZrCuSiAs-type structure (space group: P4/nmm), that was described in 1974 by Vancliff Johnson and Wolfgang Jeitschko [56]. The quaternary 1111 Fe-oxyphosphides were first mentioned in [7], Fe-oxyarsenides with LnOFeAs (Ln = lanthanide) were then synthesized in 2000 [8]. Ln, O, Fe and As occupy the Wyckoff positions 2c {coordinates (0, 1/2, z Ln ) and (1/2, 0, z¯ Ln ) with z Ln ≈ 0.14}, 2a {coordinates (0, 0, 0) and (1/2, 1/2, 0)}, 2b {coordinates (0, 0, 1/2) and (1/2, 1/2, 1/2)} and 2c {coordinates (0, 1/2, z As ) and (1/2, 0, z¯ As ) with z As ≈ 0.65}, respectively. After the discovery of superconductivity in F-substituted LaOFeAs [1], they became famous representatives of the ZrCuSiAs structure type. Their stability is guaranteed by ionic bonding and a charge transfer between the layers [57]. Among the Fe-pnictides, the electron doped, F-substituted Fe-oxyarsenides have the highest superconducting transition temper-

8

1 Introduction to Fe-Based Superconductors

atures upon lanthanide substitution (55–58 K). They play an important role in thin film fabrication because of their promising superconducting properties such as high upper critical field and high critical current densities. Between 140–180 K, the undoped parent compound LnOFeAs undergoes a combined structural and magnetic phase transition from tetragonal, paramagnetic to orthorhombic, antiferromagnetic (spin density wave). The low temperature crystallographic phase adopts the space group Cmma. 122 Compounds The 122 Fe-pnictide compounds crystallize in the tetragonal ThCr2 Si2 -type structure (space group: I4/mmm), which commonly appears for ternary intermetallics. BaFe2 As2 , first synthesized in 1980 [18], is one of the most investigated compounds in the study of Fe-based superconductors. Its bulk lattice parameters are a = 3.96 Å and c = 13.04 Å. The Wyckoff positions for Ba, Fe and As are 2a {coordinates (0, 0, 0)}, 4d {coordinates (0, 1/2, 174) and (1/2, 0, 1/4)}, and 4e {coordinates (0, 0, z As ) and (0, 0, z¯ As ) with z As ≈ 0.36}. The As-As distance along the c-axis direction is ∼3.57 Å which maintains a layered sequence of Ba2+ and [Fe2 As2 ]2− with ionic character. At 140 K, a combined structural and magnetic transition from a paramagnetic, tetragonal (space group I4/mmm) phase to an antiferromagnetic (spin density wave) phase with an orthorhombic lattice (space group Fmmm) occurs. The large possibility of substitutions at all crystallographic sites generates a large number of 122 Fe-pnictide superconductors. Upon substitution of Ba2+ by Sr2+ and Ca2+ , the As-As distance decreases and can lead to the formation of covalent As-As bonds and a collapsed tetragonal structure in CaFe2 As2 or under pressure. The c-axis shortens with the substitution of Fe2+ by other transition metal ions (Co2+ , Ni2+ , Cu+ ). Electron-doped Sr(Fe1−x Cox )2 As2 , hole doped (Ba1−x Kx )Fe2 As2 and various electron doped BaFe2 As2 compounds were synthesized as thin films. In particular, benchmarks for technological applications were achieved in Co- and P-substituted BaFe2 As2 thin films. Other Compounds The family of Fe-pnictides and Fe-chalcogenides is not restricted to the above mentioned stoichiometries. However, thin film growth is yet mainly dealing with 11, 122 and 1111 compounds. Besides rare activities in LiFeAs thin film growth, the synthesis of a Tl1−x Fe1.6 Se2 and a Li1−x Fex OHFeSe film will also be mentioned. Tl1−x Fe1.6 Se2 is known since 1978 [58] and was described with a defective ThCr2 Si2 -type struc2+ ture. √ shown that there is a vacancy-ordering on the Fe lattice forming a √ It was 5a × 5a sublattice [59]. The structure is also described as descendant from a Tl2 Fe4 Se5 (‘245’) phase. TlFe1.6 Se2 orders antiferromagnetically below ∼430– 560 K and becomes superconducting upon charge carrier doping with Tc ≈ 32 K. Li1−x Fex OHFeSe (or ‘FeSe-11111’) is an intercalated Fe-chalcogenide with maximum superconducting transition temperatures of 40–43 K. It has been synthesized

1.2 Compounds and Crystal Structures

9

by a hydrothermal method only [60]. Similar to the Fermi surface topology of 1 uc FeSe/SrTiO3 , the intercalated Li1−x Fex OHFeSe also has no hole pocket around Γ [61].

1.3 Iron (Fe) and Superconductivity The simultaneous occurrence of superconductivity with high critical temperatures and the presence of magnetic ions appears counterintuitive. The transition element Fe constitutes a well known ferromagnet with a Curie temperature of TC = 1043 K. The possibility that conventional Cooper pairs (with an intrinsic diamagnetism in the so-called Meissner state) coexist with ferromagnetic ordering of magnetic moments in Fe or Fe-containing compounds was ever since regarded as excluding phenomena. Rather unspectacular, Bernd Matthias noticed the absence of superconductivity in ferro- as well as in antiferromagnetic transition metals such as Cr, Mn, Fe, Co and Ni: ‘Stay away from magnetism,’ was one of his generalized observations for the prediction of new superconductors, known as Matthias rules [62, 63]. Superconductivity generally sets in with the formation of Cooper pairs that are composed of two  close to the Fermi level, E F , with opposite momenta and  electrons opposite spins: k↑ , −k↓ (‘singlet’). Within the conventional BCS theory, named after John Bardeen, Leon N. Cooper and John R. Schrieffer, the interaction between the two electrons is mediated by lattice vibrations, i.e. phonons (see Sect. 1.5). A generalized description of Cooper pairs in ‘dirty’ superconductors refers to two time-reversed electronic states, known as Anderson’s theorem [64]. Any parallel alignment of spins (e.g. spin polarization in ferromagnets) thus reduces the number of superconducting electron pairs. Moreover, though conventional Cooper pairs can be robust against non-magnetic impurities, the addition of magnetic (spin-flip) scattering centers in a superconductor causes a destruction of Cooper pairs and can be noted in a significant suppression of Tc . The origin of ferromagnetism in metallic Fe has been controversially discussed for many decades emphasizing either an itinerant view, a quantum fluctuation model of the magnetic moments or a localized view. In general, ferromagnetism is a result of the collective behavior of the distributed charges and spins in a system and sensitively depends on lattice symmetries. In an isolated Fe2+ ion the 3d electronic states are filled according to Pauli’s exclusion principle and Hund’s rules, which are result of the quantum mechanical exchange interaction. This results in four unpaired electrons, a total spin S = −2 (a total angular momentum of L = 2) and a spin polarization of 4 μB , with μB = e/2m e = 9.274×10−24 Am2 the Bohr magneton (Fig. 1.4). At surfaces and in bulk configurations, crystal field splitting effects becoming dominant (ΔCF > ΔSO ) and the angular momentum is almost quenched. The magnetic moment per Fe2+ ion then depends mainly on the spin moment, which is 2.5–3.0 μB on surfaces or 2.2 μB in bulk iron. In Fe-based superconductors, the spin magnetic moment per Fe2+ ion ranges from 0.25 μB (in Fe-oxypnictides) to 2.5 μB (in 245 Fe-chalcogenides).

10

1 Introduction to Fe-Based Superconductors

Fig. 1.4 Energy levels of Fe2+ : According to the Hund’s rules the 3d states are filled in order to maximize  the total spin S = i si . Electrons are denoted by their spin

Studies on Fe have demonstrated that the magnetic ordering can be modified by experimental conditions. For example, antiferromagnetic order was found in small crystallites of face-centered cubic (fcc) γ -Fe, produced after a quench from high temperatures to a metastable state [65]. Other extreme conditions included the application of high external pressures upon which a transition from α-Fe to paramagnetic ε-Fe occurs. In 1979 Erich Peter Wohlfarth argued that Fe could become a superconductor under high pressure and he wrote: ‘Superconductivity in any form of iron would, of course, be an interesting phenomenon since other forms of this metal order magnetically’ [66]. Pressures of at least 13 GPa are needed in order to transform bcc Fe into a hexagonal lattice and destroy the ferromagnetic order. The experimental evidence for superconductivity in ε-Fe with a maximum Tc ≈ 2 K at 20 GPa was provided by Katsuya Shimizu et al. in 2001 [67]. In the above experiment the exchange interaction between Fe 3d electronic states was modified by the application of external pressure and superconductivity appeared with the suppression of ferromagnetism, possibly in vicinity of an antiferromagnetic instability. It was thus argued that spin fluctuations mediate the Cooper pairing in hcp Fe under pressure [68, 69]. Yet experimentally unrealized is the idea of using epitaxial strain in order to synthesize a nonmagnetic and metastable simple cubic phase of Fe for which superconductivity was predicted below Tc ≈ 10 K [70]. Within the last two decades, numerous experiments demonstrated how the magnetism of Fe overlayers can be tuned by different nonmagnetic substrates and antiferromagnetic ordering was found in Fe overlayers on W(001) [71] and on Ir(001) [72].

1.3 Iron (Fe) and Superconductivity

11

Fe-based superconductors can be viewed as a two-dimensional (2D), slightly distorted, square lattice of Fe2+ ions embedded between chalcogen or pnictogen ion layers, that shows an antiferromagnetic order in its ground state. Superconductivity arises after suppression of the antiferromagnetic long range order either by external pressure or by chemical substitution (leading to charge carrier doping and/or chemical pressure). Upon optimal conditions, Tc up to 55–58 K can be reached in the Fe-oxyarsenides. In the extreme limit of 1 uc FeSe on a SrTiO3 substrate, a gap in the density of states is noticed even at temperatures of 65–75 K. Although a complete theoretical (microscopic) description of Fe-based superconductors has not been established by now, many important aspects of the electronic structure, the Fermi surface topology and the electronic properties of these novel materials have been studied during the last decade and will be covered in the following two sections.

1.4 Electronic Bands and Fermi Surfaces Fe-pnictides and Fe-chalcogenides have a typical semimetallic band structure with a small overlap ( n e ) or electron-conductivity (n e > n h ). Latter compounds are said to be hole- (or electron-) doped. An increase in the number of hole-like (electron-like) charge carriers is usually obtained by chemical substitution, where a rigid band shift is assumed to be valid in first approximation. When the number of charge carriers remains unchanged, the substitution is called isovalent, for example in P-substitution of BaFe2 As2 . Extreme cases of charge carrier doping may lead to a qualitatively different FS topology. In KFe2 As2 , the Fermi level (E F ) lies deep in the hole-like and below the electron-like bands (Fig. 1.5c, d). In contrast, monolayer or 1 uc FeSe films grown by MBE on pretreated SrTiO3 substrates are heavily electron doped with only the electron-like FS sheet (Fig. 1.5e, f). Band structure and FSs were calculated initially for LaOFeP using density functional theory (DFT) [73] and later for LaOFeAs [50, 74], BaFe2 As2 and LiFeAs [75], and the binary Fe-chalcogenides [76]. Correlations were first addressed by

12

1 Introduction to Fe-Based Superconductors

Fig. 1.5 a Schematic semimetallic band dispersion (E(k)) along Γ -M with hole-like and electronlike bands in the paramagnetic ground state. The band overlap is indicated by dashed horizontal lines. b Corresponding Fermi surface topology. c, d Case of a heavily hole-doped compound. e, f Case of a heavily electron-doped compound

dynamical mean-field theories in [77–79]. A special case is 1 uc FeSe, which was studied in a series of works [42, 80–82]. Reference [83] discusses correlation effects for an electron-doped FeSe monolayer; electron transfer from the substrate into the monolayer is theoretically investigated in [84, 85]. STM investigations of the band structure in 1 uc FeSe/SrTiO3 at the Γ point have also revealed an additional electron pocket 75 meV (140 meV) above the Fermi level (hole pocket) [86]. This observation tells that the system could host a topologically nontrivial phase, if the band structure can be adequately tuned. Indeed, a nontrivial FS topology (2D Z2 ) and band inversion was predicted and observed in FeSe0.5 Te0.5 [87]. For 1 uc FeSe1−x Tex band inversion was predicted to be driven by the anion height [55].

1.5 Nematicity, Magnetism and Superconductivity

13

1.5 Nematicity, Magnetism and Superconductivity The electronic properties of Fe-pnictides and Fe-chalcogenides, in particular the appearance of magnetism and superconductivity, are determined by the Fe 3d orbitals at the Fermi surface. Their multiorbital nature distinguishes the materials from simple metals. Within these ‘correlated metals’, electronic correlations have been described as moderate to strong, with the possibility for a simultaneous presence of electrons with itinerant as well as localized character in different orbitals. Such an orbitalselective Mott phase, where one of the electronic bands becomes Mott-localized, has been proposed for FeSe [88]. For Fe-pnictides, the electronic correlations are seen mainly as a result of magnetic exchange correlations or Hund’s (rule) coupling between electrons of different orbitals [89] rather than from Coulomb-type interactions within the same orbital. The 1111 Fe-oxypnictides are closest to the itinerant limit, whereas in 122 and 111 Fe-pnictides the electronic correlations are stronger, although these compounds are still metallic. In general, Hund’s (rule) coupling was not only proposed to be the decisive factor for correlation effects, but also accounts for the presence of local magnetic moments (even at high temperatures), the magnetic long range order (at low temperatures), a reduced conductivity [90, 91] or the potential to drive the metallic state towards an orbital selective Mott phase [92]. The Fe-chalcogenides show the strongest electronic correlations due to a strong Hund’s (rule) coupling as well as a strong Coulomb repulsion between electrons, and as mentioned above, they have been placed in the vicinity of a Mott-transition. Although a variety of FS topologies appear in different bulk and monolayer Fechalcogenides, a universal tendency for an orbital selective Mott phase was claimed: the many-body renormalization of the electron effective mass is m  /m b ≈ 20 for the 3dx y orbital, compared to ≈ 3 for 3dx z and 3d yz orbitals [93]. Recent calculations propose that the absence of magnetic long range order in the ground state of bulk FeSe is a result of reduced interorbital charge fluctuations and enhanced crystal field splitting, whereas 1 uc FeSe films on SrTiO3 should theoretically display magnetic ordering [94]. A recent experiment [95] claimed the existence of a checkerboard antiferromagnetic order at low temperatures (T = 500 mK). Moreover, the monolayer Fe-chalcogenide is a special case, where magnetic fluctuations become stronger by the reduced dimensionality and the proximity to the SrTiO3 substrate [96]. It is, therefore, not surprising that the multiorbital character has also an effect on the paramagnetic state. Latter shows an unconventional linear increase of the susceptibility with temperature and the presence of itinerant and localized magnetic moments that are strongly fluctuating. When the temperature is decreased, most Fe-pnictides and Fe-chalcogenides undergo symmetry breaking transitions. At first, rotational (point group) symmetry is broken in a structural/nematic transition (sometimes denoted as Tstruct ), which manifests itself by a small lattice distortion and an asymmetric change in dx z and d yz orbitals, respectively. The low-temperature phase is, therefore, structurally described by an orthorhombic unit cell, with an orthorhombic distortion, (a − b)/(a + b), in the order of 10−3 . The reduction of rotational symmetry from C4 (invariance under a rotation by 90◦ ) to C2 (invariance under a rotation

14

1 Introduction to Fe-Based Superconductors

by 180◦ ) is coined ‘nematic transition’ (Fig. 1.7a). The nematic phase is characterized by an in-plane anisotropy of electronic properties, for example, the resistivity. Possible scenarios in the theoretical description of the nematic state include spin fluctuations, orbital ordering, or Pomeranchuk instabilities of the FS [97]. An increased nematic transition temperature was found in FeSe thin films by ARPES (see [98, 99] and Sect. 6.7.4), however nematicity was suppressed in monolayer FeSe. The interplay between nematicity and superconductivity is not yet solved, but it was suggested that both are competing phenomena in 1 uc FeSe/SrTiO3 . Scanning tunneling microscopy (STM) on FeSe films has revealed a stripe-type charge ordering beneath the nematic state, which could explain the lack of superconductivity in FeSe films thicker than a monolayer [100]. Decreasing the temperature further, also translational symmetry is broken in most compounds and they undergo a phase transition from (the unconventional) paramagnetic phase to a long range antiferromagnetic ordering of the magnetic moments below a Néel temperature, TN . The itinerant picture explains the antiferromagnetic ordering as cooperative phenomenon with the formation of an energy gap—or spin density wave (SDW) gap—due to band folding, which was experimentally found in neutron scattering experiments [101]. The SDW is induced in the electronic band structure by FS nesting. FS nesting appears when larger parts of disconnected sheets can be brought into an overlap by adding a momentum QSDW (nesting vector). This applies to Fe-based superconductors, where a large overlap is generated due to the similar size of hole and electron FSs. This transition to the antiferromagnetic state is found with decreasing temperature at TN ≈ 120–140 K in LnOFeAs (Ln = La or rare earth), TN ≈ 130–140 K in BaFe2 As2 or TN ≈ 200–220 K in SrFe2 As2 . The undoped parent compounds are, therefore, SDW semimetals down to their ground state at T = 0. However, the SDW state does not develop a fully gapped electronic band structure (Fig. 1.6a). A mean-field analysis of the SDW ground state demonstrated the presence of nodes in the SDW gap function (stable Dirac nodes protected by inversion symmetry) and residual FS pockets [102]. The existence of small FS pockets in the SDW ground state of BaFe2 As2 was proven by quantum oscillations [103], Dirac cones were found in ARPES measurements [104] (Fig. 1.6b). The localized picture, on the other hand, operates with a super-exchange interaction between the spin moments that originate from the Fe2+ ions (μ ≈ 0.25–1μB in Fe-pnictides and up to 2.5μB in 11 Fe-chalcogenides). The magnetic properties of Fe-pnictides and Fe-chalcogenides can be found summarized in [105–107]. Superconductivity in the Fe-based superconductors is believed to be intimately connected to the antiferromagnetic phase, not only by competition but also by the presence of antiferromagnetic spin fluctuations that give rise to an unconventional Cooper pairing mechanism. This is because of the dual role of Fe 3d electrons for magnetism and superconductivity. However, the antiferromagnetic long range order has to be sufficiently weakened by charge carrier doping, pressure or strain, in order to promote superconductivity. The interplay between antiferromagnetism, superconductivity and nematic order is reflected in the electronic phase diagram, where regions of coexistence were found. This coexistence occurs at an atomic scale,

1.5 Nematicity, Magnetism and Superconductivity

15

Fig. 1.6 a Nodal SDW ground state (two energy bands) in a reduced BZ. (Reprinted with permission from Fig. 3b in [102]. © (2009) by the American Physical Society.) b Schematic Dirac cone at the -point between Γ and M. The color indicates the distance from . (Reprinted with permission from Fig. 4a in [104]. © (2010) by the American Physical Society)

as first noted in [108]. Reviews about superconductivity in Fe-based superconductors are provided in [109–111]. Conventional superconductors are described by the BCS theory. It provides a microscopic explanation for the measured superconducting transition temperature   1 (1.1) kB Tc = 1.13ωD exp − , λ with λ = V · N (E F ), where kB , ωD , V , and N (E F ) denote the Boltzmann constant, the Debye (cut off) frequency, an electron-ion interaction potential and the density of states at the Fermi level, respectively. The dimensionless parameter λ is called the electron-phonon coupling constant and (1.1) describes the superconducting transition temperature in the weak-coupling regime (λ  1). In the conventional BCS superconductor the screening of the Coulomb repulsion between two electrons with   opposite momenta and opposite spin, k↑ , −k↓ , is due to an electron-phonon interaction. This conventional scenario was early ruled out for Fe-based superconductors based on density functional calculations that show that the electron-phonon interaction cannot account for the high transition temperatures [76, 112]. Results from the isotope effect have been controversial. In addition, the role of N (E F ) for the superconducting mechanism has not been entirely clarified. For example, based on local density approximation (LDA) calculations, N (E F ) ≈ 2 states·uc−1 ·eV−1 was found for bulk as well as for monolayer FeSe, despite their large difference in Tc [42]. It is largely accepted that a microscopic theory of superconductivity in Fepnictides and Fe-chalcogenides will have to incorporate an orbital degenerate multiband model and Cooper pairing mediated by antiferromagnetic spin fluctuations through a generalized electron-boson interaction (possibly in the strong coupling regime). As a direct consequence, model Hamiltonians, H = H0 + Hint , have to

16

1 Introduction to Fe-Based Superconductors

Fig. 1.7 a Reduction of the rotational symmetry from C4 to C2 in the transition from a tetragonal (square plane) to orthorhombic (rectangular plane) lattice. b Proposed universal electronic phase diagram for Fe-based superconductors. The diagram is based on K- and Co-substituted BaFe2 As2 for hole- and electron-doped compounds; KFe2 As2 in the extreme hole-doped limit and K1−x Fe2−y Se2 in the extreme electron-doped limit. Adapted from Fig. 1b in [117]. c Regions of Fermi liquid (below dashed light green line) and non-Fermi liquid behavior in the electronic phase diagram. The spin freezing transition is indicated by a dark green line. (Adapted by permission from Nature Publishing Group: Fig. 3c in [118], © (2012))

sum over five orbitals in H0 as well as in the interaction part which include intra- and interorbital Coulomb repulsions, U , U , as well as Hund’s (rule) coupling and pair hopping contributions, J , J . In addition, the pairing interaction becomes orbitaldependent. Antiferromagnetic spin fluctuations are currently dealt as the hottest candidate among the mechanisms that mediate Cooper pairing. They enter the pairing interaction via the dynamical susceptibility, χ(k, ω). If the FeSe monolayers on SrTiO3 could or should be treated the same way, is questionable. A pump-probe experiment on an FeSe thin film has rediscussed the possibility of a complex interplay of electron-phonon and electron-electron interactions [113] and a recent survey discusses an interfacial (or ‘cooperative’) electron-phonon coupling based on surface phonons of SrTiO3 [46]. Here, it was demonstrated that a single-band Hamiltonian can capture essential features of high-temperature superconductivity in 1 uc FeSe/SrTiO3 (see Sect. 6.5.3). However, the phonon contribution to Cooper pairing remained an open issue and it was early pointed out that the high transition temperatures found in monolayer FeSe cannot easily be explained [114]. Ideas of a composite/cooperative Cooper pairing mechanism arose where a primary mechanism is boosted by a secondary one [115], or, even more exotic is a recent proposal of a topological superconducting state [116] (see Sect. 6.5.1). Similar to the cuprates, a universal electronic phase diagram with an apparent electron/hole-symmetry was proposed for the Fe-based superconductors [117]. The diagram is shown in Fig. 1.7b. Common to most Fe-based superconductors is a dome-like superconducting phase with an underdoped region (with increasing Tc ), a maximum Tc at optimally doping and an overdoped region (with decreasing Tc ). The electronic phase diagram has been studied widely for thin films (Sect. 6.3). It has to be specified that the symmetry of the phase diagram for Fe-pnictides is restricted

1.5 Nematicity, Magnetism and Superconductivity

17

Fig. 1.8 Tc as a function of a bonding angle α (adapted with permission from Fig. 7 in [120]; © (2008) The Physical Society of Japan), or b anion height (adapted from Fig. 1 in [122]; © (2010) IOP Publishing. Reproduced with permission. All rights reserved.) c Tc and density of states at the Fermi level as function of anion height. (Adapted with permission from Fig. 13 in [42]; © Uspekhi Fizicheskikh Nauk 2016)

to indirect hole doping. Mn- or Cr-substitution of BaFe2 As2 did not result in a superconducting phase. In addition, there are subtle differences between hole- and electron-doped compounds with respect to electron correlations revealing non-Fermi liquid properties with increasing hole doping [118, 119] (Fig. 1.7c). A spin freezing transition at the boundary between Fermi liquid and non-Fermi liquid behavior would account for a low conductivity in the normal state. Much has been studied about the relationship between the specific geometry of the FeX4 tetrahedra (and the X-Fe-X bonding angle) and the superconducting properties. It was shown (Fig. 1.8a–c) that the superconducting transition temperature, Tc , peaks sharply at a bonding angle of a regular tetrahedron, α = 109.47◦ , or a corresponding anion height parameter [120–122]. Some insight is provided by growing metastable (Ba1−x Lax )Fe2 As2 thin films (Sect. 6.4). A theory of superconductivity in these novel compounds has not been established yet and several important issues, such as pairing mechanism or order parameter symmetry are under debate. The superconducting order parameter in the Fe-based superconductors is strongly connected to the geometry of the FeX4 tetrahedra and the FS topology. A so-called s± order parameter symmetry was first proposed and is consistent for Cooper pairing mediated by spin-fluctuations [123]. The s± state of the superconducting order parameter can be viewed as s-wave symmetries of the superconducting gaps around the individual hole- and electron-like FS pockets, Δ1,2 eiφ1,2 , but with a phase difference of π (i.e. ‘sign change’) between them: φ2 = φ1 + π or, when writing the order parameter as a function of k-space, sgn(Δ(k + QSDW )) = −sgn(Δ(k)). Many theoretical investigations of the pairing interaction based on models using a random phase approximation (RPA) method or a fluctuation exchange (FLEX) approximation in the weak coupling regime have supported the s± -scenario. Experimental evidence for such a sign-changing order parameter comes from the observation of a neutron spin scattering resonance [124]. Nevertheless, this scenario is challenged by several other proposals, most prominently, s++ symmetry for superconductivity without phase dif-

18

1 Introduction to Fe-Based Superconductors

Fig. 1.9 Different order parameter symmetries for Fe-based superconductors for one, two, and three FS pockets. The different colors represent superconducting order parameters Δ j exp iφ j ( j = 1, 2, 3)

ference and mediated by orbital fluctuations [125]. Evidence for a nodeless d-wave order parameter [126] has been recently proposed for 1 uc FeSe/SrTiO3 [127]. More complex pairing symmetries including s + is and frustration in models for three FS pockets [128] have been discussed as well (Fig. 1.9). Theoretical modeling has been and still is motivated by finding a universal description for unconventional high-temperature superconductors [110, 129]. Although Febased superconductors share some similarities with the cuprate high-temperature superconductors as well as with conventional multiband superconductors, such as MgB2 , they are fundamentally different (Table 1.1). MgB2 is a two-band BCS superconductor, where Cooper pairing originates from a retarded electron-phonon interaction. The behavior is well understood by the BCS theory and its extensions to two bands [130, 131]. In contrast, an unconventional pairing mechanism is responsible for high-temperature superconductivity in the cuprates. Fe-based superconductors have a strong multiband (and multiorbital) character, show presence of spin fluctuations, strong magnetoelastic coupling, and an unusual Cooper pairing sym-

1.5 Nematicity, Magnetism and Superconductivity

19

Table 1.1 Fe-based superconductors in comparison with cuprates and MgB2 MgB2 Fe-based Cuprates superconductors Tc (K) sc layers sc states near E F Unit cell Undoped ground state sc gaps Cooper pairing Year of discovery a In

39 – B 2pσ , B 2pπ Hexagonal Metal 2 Conventional 2001

8–58, ≤ 75a Fe2 X2 (X = As, Se) Fe 3d Tetragonal afmc semimetal Up to 5 Unconventional 2006; 2008

90–150b CuO2 Cu 3d x 2 −y 2 (O 2pσ ) Orthorhombic afmc Mott insulator 1 Unconventional 1986

FeSe monolayers; b under pressure; c antiferromagnetic

metry. Their unconventional pairing mechanism is believed to be mediated by an electron-electron or a generalized electron-boson interaction. Although their transition temperatures do not reach liquid nitrogen temperatures, they might also bear an application potential.

References 1. Kamihara, Y., Watanabe, T., Hirano, M., Hosono, H.: Iron-based layered superconductor La[O1−x Fx ]FeAs (x = 0.05 − 0.12)with Tc = 26 K. J. Am. Chem. Soc. 130, 3296 (2008) 2. Kamihara, Y., Hiramatsu, H., Hirano, M., Kawamura, R., Yanagi, H., Kamiya, T., Hosono, H.: J. Am. Chem. Soc. 128, 10012 (2006) 3. Kamihara, Y.: A private story, discovery of iron-based high Tc superconductors. The Nihon Butsuri Gakkaishi (Butsuri) 66, 753 (2011) 4. Kamihara, Y.: A private story, discovery of iron-based high Tc superconductors II. TEION KOGAKU (J. Cryogen. Superconduct. Soc. Jpn.) 52, 383 (2017) 5. Jeitschko, W., Zimmer, B.I., Glaum, R., Boonk, L., Rodewald, U.C.: ZrCuSiAs-type phosphide oxides: TbRuPO, DyRuPO, the series LnOsPO (Ln = La, Ce, Pr, Nd, Sm), and ThAgPO. Z. Naturforsch. 63b, 934 (2008) 6. Zimmer, B.: Darstellung und Charakterisierung ternärer Phosphide und quaternärer PhosphidOxide der Seltenerdelemente und des Thoriums mit Übergangsmetallen. Westfälische Wilhelms-Universität Münster: PhD thesis (1996) 7. Zimmer, B.I., Jeitschko, W., Albering, J.H., Glaum, R., Reehuis, M.: The rare earth transition metal phosphide oxides LnFePO, LnRuPO, and LnCoPO with ZrCuSiAs type structure. J. Alloys Compounds 229, 238 (1995) 8. Quebe, P., Terbüchte, L.J., Jeitschko, W.: Quaternary rare earth transition metal arsenide oxides RTAsO (T = Fe, Ru, Co) with ZrCuSiAs type structure. J. Alloys Compounds 302, 70 (2000) 9. Chen, X.H., Wu, T., Wu, G., Liu, R.H., Chen, H., Fang, D.F.: Superconductivity at 43 K in SmFeAsO1−x Fx . Nature 453, 761 (2008) 10. Ren, Z.A., Lu, W., Yang, J., Yi, W., Shen, X.-L., Li, Z.-C., Che, G.-C., Dong, X.-L., Sun, L.-L., Zhou, F., Zhao, Z.-X.: Superconductivity at 55 K in iron based F-doped layered quaternary compound Sm[O1−x Fx ]FeAs. Chin. Phys. Lett. 25, 2215 (2008)

20

1 Introduction to Fe-Based Superconductors

11. Ren, Z.A., Yang, J., Lu, W., Yi, G., Che, G.C., Dong, X. L., Sun, L. L., Zhao, Z. X.: Superconductivity at 52 K in iron based F doped layered quaternary compounds Pr[O1−x Fx ]FeAs. Mat. Res. Innov. 12, 105 (2008) 12. Wang, C., Li, L., Chi, S., Zhu, Z., Ren, Z., Li, Y., Wang, Y., Lin, X., Luo, Y., Jiang, S., Xu, X., Cao, G., Xu, Z.: Thorium-doping-induced superconductivity up to 56 K. EPL 83, 67006 (2008) 13. Wen, H.-H., Mu, G., Fang, L., Yang, H., Zhu, X.: Superconductivity at 25 K in hole-doped (La1−x Srx )OFeAs. EPL 82, 17009 (2008) 14. Owens, F.J., Poole, C.P., Jr.: The New Superconductors. Selected Topics in Superconductivity, pp. 168–169. Springer, Boston (2002) 15. Choi, C.Q.: A new iron age. Sci. Am. 298, 25 (2008) 16. http://arxiv.org/, see statistics at http://arxiv.org/help/stats 17. Rotter, M., Tegel, M., Johrendt, D.: Superconductivity at 38 K in the Iron Arsenide (Ba1−x Kx )Fe2 As2 . Phys. Rev. Lett. 101, 14731 (2008) 18. Pfisterer, M.; Nagorsen G.: Zur Struktur ternärer Übergangsmetallarsenide. Z. Naturforsch. 35b, 703 (1980) 19. Sefat, A.S., Huq, A., McGuire, M.A., Jin, R., Sales, B.C., Mandrus, D., Cranswick, L.M.D., Stephens, P.W., Stone, K.H.: Superconductivity in LaFe1−x Cox AsO. Phys. Rev. B 78, 104505 (2008) 20. Sefat, A.S., Jin, R., McGuire, M.A., Sales, B.C., Singh, D.J., Mandrus, D.: Superconductivity at 22 K in co-doped BaFe2 As2 crystals. Phys. Rev. Lett. 101, 117004 (2008) 21. Juza, R., Langer, K.: Ternäre Phosphide und Arsenide des Lithiums mit Eisen, Kobalt oder Chrom im Cu2 Sb-Typ. Zeit. anorg. allg. Chemie 361, 58 (1968) 22. Wang, X.C., Liu, Q.Q., Lv, Y.X., Gao, W.B., Yang, L.X., Yu, R.C., Li, F.Y., Jin, C.Q.: The superconductivity at 18 K in LiFeAs system. Solid State Commun. 148, 538 (2008) 23. Hägg, G., Kindström, A.L.: X-ray investigation of the system iron-selenium. Z. Phys. Chem. B 22, 453 (1933) 24. Hsu, F.-C., Luo, J.-Y., Yeh, K.-W., Chen, T.-K., Huang, T.-W., Wu, P. M., Lee, Y.-C., Huang, Y.-L., Chu, Y.-Y., Yan, D.-C., Wu, M.-K.: Superconductivity in the PbO-type structure α-FeSe. PNAS 105, 14262 (2008) 25. Hiramatsu, H., Katase, T., Kamiya, T., Hirano, M., Hosono, H.: Heteroepitaxial growth and optoelectronic properties of layered iron oxyarsenide. LaFeAsO. Appl. Phys. Lett. 93, 162504 (2008) 26. Backen, E., Haindl, S., Niemeier, T., Hühne, R., Freudenberg, T., Werner, J., Behr, G., Schultz, L., Holzapfel, B.: Growth and anisotropy of La(O, F)FeAs thin films deposited by pulsed laser deposition. Supercond. Sci. Technol. 21, 122001 (2008) 27. Choi, E.-M., Jung, S.-G., Lee, N.H., Kwon, Y.-S., Kang, W.N., Kim, D.H., Jung, M.-H., Lee, S.-I., Sun, L.: In situ fabrication of cobalt-doped SrFe2 As2 thin films by pulsed laser deposition with excimer laser. Appl. Phys. Lett. 95, 062507 (2009) 28. Wang, Q.-Y., Li, Z., Zhang, W.-H., Zhang, Z.-C., Zhang, J.-S., Li, W., Ding, H., Ou, Y.-B., Deng, P., Chang, K., Wen, J., Song, C.-L., He, K., Jia, J.-F., Ji, S.-H., Wang, Y.-Y., Wang, L.L., Chen, X., Ma, X.-C., Xue, Q.-K.: Interface-induced high-temperature superconductivity in single unit-cell FeSe films on SrTiO3 . Chin. Phys. Lett. 29, 037402 (2012) 29. Li, Q., Si, W., Dimitrov, I.K.: Films of iron chalcogenide superconductors. Rep. Prog. Phys. 74, 124510 (2011) 30. Mele, P.: Superconducting properties of iron chalcogenide thin films. Sci. Technol. Adv. Mater. 13, 054301 (2012) 31. Haindl, S., Kidszun, M., Oswald, S., Hess, C., Büchner, B., Kölling, S., Wilde, L., Thersleff, T., Yurchenko, V. V., Jourdan, M., Hiramatsu, H., Hosono, H.: Thin film growth of Fe-based superconductors: from fundamental properties to functional devices. A comparative review. Rep. Prog. Phys. 77, 046502 (2014) 32. Haindl, S., Kidszun, M., Kampert, E.: Iron pnictide thin films: synthesis and physics. Phys. Stat. Sol. B 254, 1600341 (2017)

References

21

33. Haindl, S., Hanzawa, K., Sato, H., Hiramatsu, H., Hosono, H.: In-situ growth of superconducting SmO1−x Fx FeAs thin films by pulsed laser deposition. Sci. Rep. 6, 35797 (2016) 34. Sakoda, M., Iida, K., Naito, M.: Recent progress in thin-film growth of Fe-based superconductors: superior superconductivity achieved by thin films. Supercond. Sci. Technol. 31, 093001 (2018) 35. Wang, L.-L., Ma, X.-C., Chen, X., Xue, Q.-K.: Molecular beam epitaxy and superconductivity of stoichiometric FeSe and Kx Fe2−y Se2 crystalline films. Chin. Phys. B 22, 086801 (2013) 36. Gurevich, A.: Challenges and opportunities for applications of unconventional superconductors. Ann. Rev. Condens. Matter Phys. 5, 35 (2014) 37. Pallecchi, I., Eisterer, M., Malagoli, A., Putti, M.: Application potential of Fe-based superconductors. Supercond. Sci. Technol. 28, 114005 (2015) 38. Shimoyama, J.: Potentials of iron-based superconductors for practical future applications. Supercond. Sci. Technol. 27, 044002 (2014) 39. Huang, D., Hoffman, J.E.: Monolayer FeSe on SrTiO3 . Ann. Rev. Condens. Matter Phys. 8, 311 (2017) 40. Lee, D.-H.: Routes to high-temperature superconductivity: a Lesson from FeSe/SrTiO3 . Ann. Rev. Condens. Matter Phys. 9, 261 (2018) 41. Peng, R., Xu, H.-C., Feng, D.-L.: In-situ spectroscopic studies and interfacial engineering on FeSe/oxide heterostructures: insights on the interfacial superconductivity. Chin. Phys. B 24, 117902 (2015) 42. Sadovskii, M.V.: High-temperature superconductivity in FeSe monolayers. Phys. Usp. 59, 947 (2016) 43. Wang, L., Ma, X., Xue, Q.-K.: Interface high-temperature superconductivity. Supercond. Sci. Technol. 29, 123001 (2016) 44. Ying, X., Jian, W.: Direct evidence of high temperature superconductivity in one-unit-cell FeSe films on SrTiO3 substrate by transport and magnetization measurements. Chin. Phys. B 24, 117404 (2015) 45. Geng, X., Yi, J.: The development of high-temperature superconductors and 2D iron-based superconductors. In: Hong, N. H. (ed).: Nano-sized Multifunctional Materials: Synthesis, Properties and Applications, pp. 117–145. Elsevier (2019) 46. Xu, X., Zhang, S., Zhu, X., Guo, J.: Superconductivity enhancement in FeSe/SrTiO3 : a review from the perspective of electron-phonon coupling. J. Phys.: Condens. Matter 32, 343003 (2020) 47. Yang, H., Feng, Z.-P., Lin, Z.-F., Hu, W., Qin, M.-Y., Zhu, B.-Y., Yuan, J., Jin, K.: Preparation and characterization of high-quality FeSe single crystal thin films. Acta Phys. Sinica 67, 207416 (2018) 48. Wang, N.-L., Hosono, H., Dai, P. (eds.): Iron-based Superconductors: Materials, Properties and Mechanisms. CRC Press, Taylor & Francis Group (2013) 49. Johnson, P.D., Xu, G., Yin, W.-G. (eds.): Iron-Based Superconductors. Springer [Springer Series in Materials Science 211] (2015) 50. Vildosola, V., Pourovskii, L., Arita, R., Biermann, S., Georges, A.: Bandwidth and Fermi surface of iron oxypnictides: covalency and sensitivity to structural changes. Phys. Rev. B 78, 064518 (2008) 51. Johrendt, D., Hosono, H., Hoffmann, R.-D., Pöttgen, R.: Structural chemistry of superconducting pnictides and pnictide oxides with layered structures. Z. Kristallogr. 226, 435 (2011) 52. Martinelli, A.: Crystallochemistry of Fe-based superconductors: interplay between chemical, structural and physical properties in the Fe(Se, Te) and 1111-type systems. J. Supercond. Nov. Magn. 28, 1103 (2015) 53. Schuster, W., Mikler, H., Komarek, K.L.: Transition metal chalcogen systems, VII.: The iron selenium phase diagram. Monatsh. Chem 110, 1153 (1979) 54. Okamoto, H.: The Fe-Se (iron-selenium) system. J. Phase Equilib. 12, 383 (1991) 55. Wu, X., Qin, S., Liang, Y., Fan, H., Hu, J.: Topological characters in Fe(Te1−x Sex ) thin films. Phys. Rev. B 93, 115129 (2016)

22

1 Introduction to Fe-Based Superconductors

56. Johnson, V., Jeitschko, W.: ZrCuSiAs: A “filled” PbFCl type. J. Solid State Chem. 11, 161 (1974) 57. Pöttgen, R., Johrendt, D.: Materials with ZrCuSiAs-type structure. Z. Naturforsch. 63b, 1135 (2008) 58. Klepp, K., Boller, H.: Ternäre Thallium-Übergangsmetall-Chalkogenide mit ThCr2 Si2 Struktur. Chemical Monthly [Monatshefte für Chemie] 109, 1049 (1978) 59. Häggström, L., Verma, H.R., Bjarman, S., Wäppling, R., Berger, R.: Magnetic properties of TlFe2−x Se2 . J. Solid State Chem. 63, 401 (1986) 60. Lu, X.F., Wang, N.Z., Wu, H., Wu, Y.P., Zhao, D., Zeng, X.Z., Luo, X.G., Wu, T., Bao, W., Zhang, G.H., Huang, F.Q., Huang, Q.Z., Chen, X. H.: Coexistence of superconductivity and antiferromagnetism in (Li0.8 Fe0.2 )OHFeSe. Nat. Mater. 14, 325 (2015) 61. Zhao, L., Liang, A., Yuan, D., Hu, Y., Liu, D., Huang, J., He, S., Shen, B., Xu, Y., Liu, X., Yu, L., Liu, G., Zhou, H., Huang, Y., Dong, X., Zhou, F., Liu, K., Lu, Z., Zhao, Z., Chen, C., Xu, Z., Zhou, X.J.: Common electron origin of superconductivity in (Li, Fe)OHFeSe bulk superconductor and single-layer FeSe/SrTiO3 films. Nat. Commun. 7, 10608 (2016) 62. Matthias, B.: Superconductivity in the periodic system. Prog. Low Temp. Phys. 2, 138 (1957) 63. Pines, D.: Superconductivity in the periodic system. Phys. Rev. 109, 280 (1958) 64. Anderson, P.W.: Theory of dirty superconductors. J. Phys. Chem. Solids 11, 26 (1959) 65. Abrahams, S.C., Guttman, L., Kasper, J.S.: Neutron diffraction determination of antiferromagnetism in face-centered cubic (γ ) iron. Phys. Rev. 127, 2052 (1962) 66. Wohlfarth, E.P.: The possibility that ε-Fe is a low temperature superconductor. Phys. Lett. 75A, 141 (1979) 67. Shimizu, K., Kimura, T., Furomoto, S., Takeda, K., Kontani, K., Onuki, Y., Amaya, K.: Superconductivity in the non-magnetic state of iron under pressure. Nature 412, 316 (2001) 68. Jarlborg, T.: Spin fluctuations, electron-phonon coupling and superconductivity in nearmagnetic elementary metals - Fe Co. Ni Pd. Phys. C 385, 513 (2003) 69. Mazin, I.I., Papaconstantopoulos, D.A., Mehl, M.J.: Superconductivity in compressed iron: role of spin fluctuations. Phys. Rev. B 65, 100511(R) (2002) 70. Freeman, A.J., Continenza, A., Massidda, S., Grossman, J.C.: Structural and electronic properties and possible superconductivity in simple cubic Fe. Phys. C 166, 317 (1990) 71. Kubetzka, A., Ferriani, P., Bode, M., Heinze, S., Bihlmayer, G., von Bergmann, K., Pietzsch, O., Blügel, S., Wiesendanger, R.: Revealing antiferromagnetic order of the Fe monolayer on W(001): spin-polarized scanning tunneling microscopy and first-principles calculations. Phys. Rev. Lett. 94, 087204 (2005) 72. Kudrnovský, J., Máca, F., Turek, I., Redinger, J.: Substrate-induced antiferromagnetism of a Fe monolayer on the Ir(001) surface. Phys. Rev. B 80, 064405 (2009) 73. Lebègue, S.: Electronic structure and properties of the Fermi surface of the superconductor LaOFeP. Phys. Rev. B 75, 035110 (2007) 74. Singh, D.J., Du, M.-H.: Density functional study of LaFeAsO1−x Fx : a low carrier density superconductor near itinerant magnetism. Phys. Rev. Lett. 100, 237003 (2008) 75. Singh, D.J.: Electronic structure and doping in BaFe2 As2 and LiFeAs: density functional calculations. Phys. Rev. B 78, 094511 (2008) 76. Subedi, A., Zhang, L., Singh, D.J., Du, M.H.: Density functional study of FeS, FeSe and FeTe: electronic structure, magnetism, phonons, and superconductivity. Phys. Rev. B 78, 134514 (2008) 77. Aichhorn, M., Pourovskii, L., Vildosola, V., Ferrero, M., Parcollet, O., Miyake, T., Georges, A., Biermann, S.: Dynamical mean-field theory within an augmented plane-wave framework: assessing electronic correlations in the iron pnictide LaFeAsO. Phys. Rev. B 80, 085101 (2009) 78. Anisimov, V.I., Korotin, Dm. M., Korotin, M.A., Kozhevnikov, A.V., Kuneš, J., Shorikov, A.O., Skornyakov, S.L., Streltsov, S.V.: Coulomb repulsion and correlation strength in LaFeAsO from density functional and dynamical mean-field theories. J. Phys.: Condens. Matter 21, 075602 (2009)

References

23

79. Haule, K., Shim, J.H., Kotliar, G.: Correlated electronic structure of LaO1−x Fx FeAs. Phys. Rev. Lett. 100, 226402 (2008) 80. Nekrasov, I.A., Pavlov, N.S., Sadovskii, M.V., Slobodchikov, A.A.: Electronic structure of FeSe monolayer superconductors. Low Temp. Phys. 42, 891 (2016) 81. Nekrasov, I.A., Pavlov, N.S., Sadovskii, M.V.: On the origin of the shallow and “replica” bands in FeSe monolayer superconductors. JETP Lett. 105, 370 (2017) 82. Nekrasov, I.A., Pavlov, N.S., Sadovskii, M.V.: Electronic structure of FeSe monolayer superconductors: Shallow bands and correlations. J. Exp. Theor. Phys. 126, 485 (2018) 83. Qiu, D.Y., Coh, S., Cohen, M.L., Louie, S.G.: Comparison of GW band structure to semiempirical approach for an FeSe monolayer. Phys. Rev. B 101, 235154 (2020) 84. Zheng, F., Wang, Z., Kang, W., Zhang, P.: Antiferromagnetic FeSe monolayer on SrTiO3 : the charge doping and electric field effects. Sci. Rep. 3, 2213 (2013) 85. Xu, M., Song, X., Wang, H.: Substrate and bend bending effects on monolayer FeSe on SrTiO3 (001). Phys. Chem. Chem. Phys. 19, 7964 (2017) 86. Huang, D., Song, C.-L., Webb, T.A., Fang, S., Chang, C.-Z., Moodera, J.S., Kaxiras, E., Hoffman, J.E.: Revealing the empty-state electronic structure of single-unit-cell FeSe/SrTiO3 . Phys. Rev. Lett. 115, 017002 (2015) 87. Wang, Z., Zhang, P., Xu, G., Zeng, L.K., Miao, H., Xu, X., Qian, T., Weng, H., Richard, P., Fedorov, A.V., Ding, H., Dai, X., Fang, Z.: Topological nature of the FeSe0.5 Te0.5 superconductor. Phys. Rev. B 92, 115119 (2015) 88. Craco, L., Laad, M.S., Leoni, S.: Low-temperature metal-insulator transition in the electrondoped iron chalcogenide FeSe superconductor. EPL 91, 27001 (2010) 89. Haule, K., Kotliar, G.: Coherence-inhcoherence crossover in the normal state of iron oxypnictides and importance of Hund’s rule coupling. New J. Phys. 11, 025021 (2009) 90. Georges, A., de’Medici, L., Mravlje, J.: Strong correlations from Hund’s coupling. Annu. Rev. Condens. Matter Phys. 4, 137 (2013) 91. Yin, Z.P., Haule, K., Kotliar, G.: Kinetic frustruation and the nature of the magnetic and paramagnetic states in iron pnictides and iron chalcogenides. Nat. Mater. 10, 932 (2011) 92. de Medici, L., Hassan, S.R., Capone, M., Dai, X.: Orbital-selective Mott transition out of band degeneracy lifting. Phys. Rev. Lett. 102, 126401 (2010) 93. Yi, M., Liu, Z.-K., Zhang, Y., Yu, R., Zhu, J.-X., Lee, J.J., Moore, R.G., Schmitt, F.T., Li, W., Riggs, S.C., Chu, J.-H., Lv, B., Hu, J., Hashimoto, M., Mo, S.-K., Hussain, Z., Mao, Z.Q., Chu, C.W., Fisher, I.R., Si, Q., Shen, Z.-X., Lu, D.H.: Observation of universal strong orbital-dependent correlation effects in iron-chalcogenides. Nat. Commun. 6, 7777 (2015) 94. Moon, C.-Y.: Strong enhancement of magnetic order from bulk to stretched monolayer FeSe as Hund’s metals. NPJ Comput. Mater. 6, 147 (2020) 95. Qiao, S., Zhang, P., Ding, H., Zhang, S., Liang, L., Zhang, Z., Long, X., Chen, X., Lu, J., Wu, J.: Fingerprint of checkerboard antiferromagnetic order in FeSe monolayer due to magneticelectric correlation. Mat. Today 41, 44 (2020) 96. Shishidou, T., Agterberg, D.F., Weinert, M.: Magnetic fluctuations in single-layer FeSe. Commun. Phys. 1, 8 (2018) 97. Fernandes, R.M., Chubukov, A.V., Schmalian, J.: What drives nematic order in iron-based superconductors? Nat. Phys. 10, 97 (2014) 98. Shen, B., Feng, Z.-P., Huang, J.-W., Hu, Y., Gao, Q., Li, C., Xu, Y., Liu, G.-D., Yu, L., Zhao, L., Jin, K., Zhou, X.J.: Electronic structure and nematic phase transition in superconducting multiple-layer FeSe films grown by pulsed laser deposition method. Chin. Phys. B 26, 077402 (2017) 99. Zhang, Y., Yi, M., Liu, Z.-K., Li, W., Lee, J.J., Moore, R.G., Hashimoto, M., Nakajima, M., Eisaki, H., Mo, S.-K., Hussain, Z., Devereaux, T.P., Shen, Z.-X., Lu, D.H.: Distinctive orbital anisotropy observed in the nematic state of a FeSe thin film. Phys. Rev. B 94, 115153 (2016) 100. Li, W., Zhang, Y., Deng, P., Xu, Z., Mo, S.-K., Yi, M., Ding, H., Hashimoto, M., Moore, R.G., Lu, D.-H., Chen, X., Shen, Z.-X., Xue, Q.-K.: Stripes developed at the strong limit of nematicity in FeSe film. Nat. Phys. 13, 957 (2017)

24

1 Introduction to Fe-Based Superconductors

101. de la Cruz, C., Huang, Q., Lynn, J.W., Li, J., Ratcliff, W., II., Zarestky, J.L., Mook, H.A., Chen, G.F., Luo, J.L., Wang, N.L., Dai, P.: Magnetic order close to superconductivity in the iron-based layered LaO1−x Fx FeAs systems. Nature 453, 899 (2008) 102. Ran, Y., Wang, F., Zhai, H., Vishwanath, A., Lee, D.-H.: Nodal spin density wave and band topology of the FeAs-based materials. Phys. Rev. B 79, 014505 (2009) 103. Harrison, N., Sebastian, S.E.: Dirac nodal pockets in the antiferromagnetic parent phase of FeAs superconductors. Phys. Rev. B 80, 224512 (2009) 104. Richard, P., Nakayama, K., Sato, T., Neupane, M., Xu, Y.-M., Bowen, J.H., Chen, G.F., Luo, J.L., Wang, N.L., Dai, X., Fang, Z., Ding, H., Takahashi, T.: Observation of Dirac cone electronic dispersion in BaFe2 As2 . Phys. Rev. Lett. 104, 137001 (2010) 105. Lumsden, M.D., Christianson, A.D.: Magnetism in Fe-based superconductors. J. Phys.: Condens. Matter 22, 203203 (2010) 106. Mannella, N.: The magnetic moment enigma in Fe-based high temperature superconductors. J. Phys.: Condens. Matter 26, 473202 (2014) 107. Tranquada, J.M., Xu, G., Zaliznyak, I.A.: Magnetism and superconductivity in Fe1+y Te1−x Sex . J. Phys.: Condens. Matter 32, 374033 (2020) 108. Laplace, Y., Bobroff, J., Rullier-Albenque, F., Colson, D., Forget, A.: Atomic coexistence of superconductivity and incommensurate magnetic order in the pnictide Ba(Fe1−x Cox )2 As2 . Phys. Rev. B 80, 140501 (2009) 109. Johnston, D.C.: The puzzle of high temperature superconductivity in layered iron pnictides and chalcogenides. Adv. Phys. 59, 803 (2010) 110. Scalapino, D.J.: A common thread: the pairing interaction for unconventional superconductors. Rev. Mod. Phys. 84, 1383 (2012) 111. Stewart, G.R.: Superconductivity in iron compounds. Rev. Mod. Phys. 83, 1589 (2011) 112. Boeri, L., Dolgov, O.V., Golubov, A.A.: Is LaFeAsO1−x Fx an electron-phonon superconductor? Phys. Rev. Lett. 101, 026403 (2008) 113. Gerber, S., Yang, S.-L., Zhu, D., Soifer, H., Sobota, J.A., Rebec, S., Lee, J.J., Jia, T., Moritz, B., Jia, C., Gauthier, A., Li, Y., Leuenberger, D., Zhang, Y., Chaix, L., Li, W., Jang, H., Lee, J.-S., Yi, M., Dakovski, G.L., Song, S., Glownia, J.M., Nelson, S., Kim, K.W., Chuang, Y.-D., Hussain, Z., Moore, R.G., Devereaux, T.P., Lee, W.-S., Kirchmann, P.S., Shen, Z.-S.: Femtosecond electron-phonon lock-in by photoemission and x-ray free-electron laser. Science 357, 71 (2017) 114. Li, B., Xing, Z.W., Huang, G.Q., Xing, D.Y.: Electron-phonon coupling enhanced by the FeSe/SrTiO3 interface. J. Appl. Phys. 115, 193907 (2014) 115. Li, Z.-X., Wang, F., Yao, H., Lee, D.-H.: What makes the Tc of monolayer FeSe on SrTiO3 so high: a sign-problem-free quantum Monte Carlo study. Sci. Bull. 61, 925 (2016) 116. Hao, N., Shen, S.-Q.: Topological superconducting states in monolayer FeSe/SrTiO3 . Phys. Rev. B 92, 165104 (2015) 117. Basov, D.N., Chubukov, A.V.: Manifesto for a higher Tc . Nat. Phys. 7, 272 (2011) 118. Werner, P., Casula, M., Miyake, T., Aryasetiawan, F., Millis, A.J., Biermann, S.: Satellites and large doping and temperature dependence of electronic properties in hole-doped BaFe2 As2 . Nat. Phys. 8, 331 (2012) 119. Liebsch, A., Ishida, H.: Correlation-induced spin freezing transition in FeSe: a dynamical mean field study. Phys. Rev. B 82, 155106 (2010) 120. Lee, C.H., Iyo, A., Eisaki, H., Kito, H., Fernandez-Diaz, M.T., Ito, T., Kihou, K., Matsuhata, H., Braden, M., Yamada, K.: Effect of structural parameters on superconductivity in fluorinefree LnFeAsO1−y (Ln = La, Nd). J. Phys. Soc. Jpn. 77, 083704 (2008) 121. Lee, C.H., Kihou, K., Iyo, A., Kito, H., Shirage, P.M., Eisaki, H.: Relationship between crystal structure and superconductivity in iron-based superconductors. Solid State Commun. 152, 644 (2012) 122. Mizuguchi, Y., Hara, Y., Deguchi, K., Tsuda, S., Yamaguchi, T., Takeda, K., Kotegawa, H., Tou, H., Takano, Y.: Anion height dependence of Tc for the Fe-based superconductor. Supercond. Sci. Technol. 23, 054013 (2010)

References

25

123. Mazin, I.I., Singh, D.J., Johannes, M.D., Du, M.H.: Unconventional superconductivity with a sign reversal in the order parameter of LaFeAsO1−x Fx . Phys. Rev. Lett. 101, 057003 (2008) 124. Christianson, A.D., Goremychkin, E.A., Osborn, R., Rosenkranz, S., Lumsden, M.D., Malliakas, C.D., Todorov, I.S., Claus, H., Chung, D.Y., Kanatzidis, M.G., Bewley, R.I., Guidi, T.: Unconventional superconductivity in Ba0.6 K0.4 Fe2 As2 from inelastic neutron scattering. Nature 456, 930 (2008) 125. Kontani, H., Onari, S.: Orbital-fluctuation-mediated superconductivity in iron pnictides: analysis of the five-orbital Hubbard-Holstein model. Phys. Rev. Lett. 104, 157001 (2010) 126. Kuroki, K., Onari, S., Arita, R., Usui, H., Tanaka, Y., Kontani, H., Aoki, H.: Unconventional pairing originating from the disconnected Fermi surfaces of superconducting LaFeAsO1−x Fx . Phys. Rev. Lett. 101, 087004 (2008) 127. Ge, Z., Yan, C., Zhang, H., Agterberg, D., Weinert, M., Li, L.: Evidence for d-wave superconducting in single layer FeSe/SrTiO3 probed by quasiparticle scattering off step edges. Nano Lett. 19, 2497 (2019) 128. Chubukov, A.: Pairing mechanism in Fe-based superconductors. Annu. Rev. Condens. Matter Phys. 3, 57 (2012) 129. Chubukov, A., Hirschfeld, P.J.: Iron-based superconductors, seven years later. Phys. Today 68, 46 (2015) 130. Moskalenko, V.A.: Superconductivity in metals with overlapping energy bands. Fiz. Met. Metalloved. 8, 503 (1959) [Phys. Met. Metallogr. 8, 25 (1959)] 131. Suhl, H., Matthias, B.T., Walker, L.R.: Bardeen-Cooper-Schrieffer theory of superconductivity in the case of overlapping bands. Phys. Rev. Lett. 3, 552 (1959)

Chapter 2

Thin Film Growth of Fe-Based Superconductors

Traced from the literature output, the last decade has witnessed substantial efforts in the control and optimization of conditions for the thin film growth of Fe-based superconductors. Today, several hundred publications are devoted to Fe-chalcogenide or Fe-pnictide thin films and several research groups were stimulated by the avalanche of new superconducting compounds which were synthesized during 2008–2009 and the following years. The growth of Fe-based superconductor thin films, consequently, explored new scientific territory. An exception is the binary FeSe, for which first thin film synthesis dates back to the 1970s. In addition, the largest number of different film preparation techniques can be found applied in the growth of FeSe films. Apart from this exception, the growth of Fe-based superconducting thin films is clearly dominated by the state-of-the-art physical vapor deposition methods of pulsed laser deposition (PLD) and molecular beam epitaxy (MBE). Both methods turned out to be most efficient based on the number of successfully grown compounds and the number of publications. In addition, both methods were predominantly employed by the majority of research groups involved in the growth of Fe-based superconducting thin films, whereas other methods were often only employed by one or two research groups. To mention some examples: (1) Metal-organic chemical vapor deposition (MOCVD) of Fe-oxyarsenides combined with a post-growth annealing in a twostage process, sputter deposition of Fe-chalcogenides or electrodeposition of FeSe can be still regarded as niche activities. (2) The growth of thick films from the melt or LiFeAs film synthesis were basically singular events. (3) Chemical solution deposition is practically unexplored for Fe-pnictides, and seems not yet promising for FeSe film growth. Table 2.1 summarizes the current status of different thin film growth methods in the synthesis of Fe-chalcogenide and Fe-pnictide superconductors: (1) physical vapor deposition methods like PLD, MBE and sputter deposition; (2) chemical vapor deposition such as MOCVD; (3) electrochemical methods like electroplating; (4) © Springer Nature Switzerland AG 2021 S. Haindl, Iron-Based Superconducting Thin Films, Springer Series in Materials Science 315, https://doi.org/10.1007/978-3-030-75132-6_2

27

28

2 Thin Film Growth of Fe-Based Superconductors

Fig. 2.1 a PLD setup (Courtesy of Carlo Ferdeghini, SPIN Institute of National Research Council (CNR), Genova.) b Schematic PLD setup with laser, optical components (aperture, mirrors, lenses), and the main vacuum chamber, where the deposition takes place. Target and substrate positions as well as the plume formation are indicated. c Plasma plume inside UHV chamber

two-stage processing routes that involve a vapor deposition and a post-deposition heat treatment comparable to solid phase epitaxy (SPE); (5) other methods including less commonly applied deposition and coating methods.

2.1 Pulsed Laser Deposition 2.1.1 Overview Pulsed laser deposition (PLD) is a film growth method that is based on a laser induced ablation process, where atoms, ions and particle clusters are ejected from an irradiated target surface and generate a highly directional and dense plasma plume inside a vacuum chamber (Fig. 2.1). The plasma plume is directed towards a substrate on which the film condenses. The method, first demonstrated five years after the invention of the ruby laser by Howard M. Smith and Arthur Francis Turner in 1965 [1], benefited strongly from the development of laser technology during the 1970s and 1980s. PLD became popular after the first deposition of YBa2 Cu3 O7−δ thin films [2]. Laser Specifications For the ablation of material PLD makes use of high power pulsed lasers. Usual power densities (also called laser intensities) are in the range of 107 –108 Wcm−2 . The important laser parameters that influence the initial process of the laser-target interaction are: laser energy density, ε, laser wavelength, λ, and pulse duration, τ . The energy density or energy per unit area (also called fluence) is given in Jcm−2 and the required values for a spot on the target surface are between 1 and several Jcm−2 . Laser wavelengths in PLD range from the ultra-violet (UV) to the near infrared (NIR) and must be absorbed by the target material. The optical absorption coefficients of the target material are decisive for the choice of the laser wavelength. In addition,

2.1 Pulsed Laser Deposition

29

Table 2.1 Different film growth methods applied for Fe-chalcogenides and Fe-pnictides (●) and in combination with a post-deposition heat treatment defining a two-stage process ( & ■) PLD

MBE

Sputtering

Fe-chalcogenides 11

FeSe Mg:FeSe FeTe Fe(Se1−x Tex )

/

Fe(Te1−x Sx ) Fe(Se1−x Sx ) 245

Tl1−x Fe1.6 Se2

11111

(Li1−x Fex )OHFeSe

Fe-pnictides 111

LiFeAs

122

CaFe2 As2 Ca(Fe1−x Cox )2 As2 Sr(Fe1−x Cox )2 As2 (Sr1−x Kx )Fe2 As2 (Sr1−x Lax )Fe2 As2 BaFe2 (As1−x Px )2 Ba(Fe1−x Crx )2 As2 Ba(Fe1−x Cox )2 As2 Ba(Fe1−x Nix )2 As2 Ba(Fe1−x Rux )2 As2 (Ba1−x Lax )Fe2 As2 (Ba1−x RE x )Fe2 As2 (Ba1−x Kx )2 As2 KFe2 As2

1111

LaOFeAs La(O1−x Fx )FeAs LaO(Fe1−x Cox )As (La1−x Smx ) (O1−x Fx )FeAs Gd(O1−x Fx )FeAs NdOFeAs Nd(O1−x Fx )FeAs NdO(Fe1−x Cox )As SmOFeAs Sm(O1−x Fx )FeAs Sm(O1−x Hx )FeAs SmO(Fe1−x Cox )As

/

MOCVD Twostage process

Electro- Other chemi- methods cal

30

2 Thin Film Growth of Fe-Based Superconductors

Fig. 2.2 Variety of lasers with wavelengths ranging from UV to NIR used in the growth of different Fe-based superconductors and related compounds (target compositions)

the laser light interacts with the plasma plume. Shorter wavelengths are commonly favored because they are less strongly absorbed by the generated plasma and thus result in larger ablation rates [3]. Appropriate lasers for the PLD process of Febased superconductors are either Nd-doped yttrium aluminium garnet Y3 Al5 O12 (Nd:YAG) solid state lasers or excimer lasers (Fig. 2.2). Both laser types are used for the ablation of semimetallic Fe-pnictide and Fe-chalcogenide targets. Table 2.2 lists different lasers with their specifications and their use for the deposition of Febased superconductors. No serious restriction in the choice of laser wavelength in the range of 193–1064 nm was yet reported. Failed attempts were mentioned only for the use of an excimer laser in the ablation of 1111 Fe-oxyarsenides [4], but the reason is unclear. In contrast, an excimer laser was successfully used in the ablation of a La(O1−x Fx )FeAs target with material transfer to a substrate held at room-temperature in a two-stage process [5]. In Nd:YAG crystals the rare earth (RE) impurity ions serve as active laser medium. It is optically pumped by a flash-lamp. The energy level scheme for Nd:YAG is well investigated [6]. The fundamental wavelength is 1064 nm corresponding to the most probable electron transition from the 4 F3/2 to the 4 I11/2 state. Second harmonic generation (i.e. frequency doubling, 2ω) leading to a wavelength of 532 nm, and third (3ω) and fourth (4ω) harmonic generation are technically possible. The laser wavelength can thus be tuned from the NIR to UV. The repetition rates in Nd:YAG

2.1 Pulsed Laser Deposition

31

Table 2.2 Laser specifications and use in thin film growth of Fe-chalcogenides and Fe-pnictides: laser medium, wavelength (λ), maximum pulse energy per pulse (E), FWHM of the pulse duration (τ ) and target compositions used in PLD for Fe-based superconductors Laser λ (nm) E (mJ) τ (ns) Compounds (target compositions) ArF KrF

193 248

500 1000

XeCl Nd:YAG(3ω) Nd:YAG(2ω)

308 355 532

300 100 200

20 5–8 5–8

1064

450

5–8

Nd:YAG

10 25–30

FeSe1−x Tex , Ba(Fe1−x Cox )2 As2 FeSe, FeSe1−x Tex , Tl1−x Fe1.6 Se2 , Ba(Fe1−x TM x )2 As2 (TM = Cr, Co, Ni, Ru), BaFe2 (As1−x Px )2 , Sr(Fe1−x Cox )2 As2 , KFe2 As2 FeSe, FeTe, FeSe1−x Tex FeSe, Mg:FeSe, FeSe1−x Tex Fe(Te1−x Sx ), AE(Fe1−x Cox )2 As2 (AE = Ca, Sr, Ba), BaFe2 (As1−x Px )2 , (AE 1−x Lax )Fe2 As2 (AE = Sr, Ba), (Ba1−x RE x )Fe2 As2 (RE = Ce, Pr, Nd), LaOFeAs, SmOFeAs, LaOFe1−x Cox As, SmOFe1−x Cox As FeSe1−x Tex , Ba(Fe1−x Cox )2 As2

lasers are usually fixed to 10 or 20 Hz. A drawback of Nd:YAG lasers is the limited lifetime of their excitation source (flash-lamp). The Gaussian beam profile of the laser beam leads to less uniformly ablated material and a blurred crater edge that can result in larger errors in the estimation of the energy density on the target surface. Excimer lasers are gas lasers where the active laser medium consists of diatomic gas molecules of noble gases (X2 ), halogens (H2 ) or noble gas-halogen dimers (XH). Commercially available of the latter are ArF, KrF and XeCl. The advantages of excimer lasers lie in their short wavelength (UV), a high maximum pulse energy and a variable repetition rate (1–200 Hz). They are disadvantageous in their high operating costs. Typical pulse durations are in the range of 1–10 ns and the maximal pulse energies can be up to 1000 mJ high. Due to a sharp beam profile the ablation spot on the target surface has a well-defined edge enabling a more uniform ablation compared to Nd:YAG lasers [7]. Stoichiometric Transfer Since 2008 PLD of Fe-based superconductors was performed under different conditions. In the majority of studies the growth chamber provided at least a high vacuum (HV) or an ultra-high vacuum (UHV) environment with base pressures in the range of 2×10−10 to 10−5 mbar. Very few studies tested higher pressures or Ar background gas, pAr . FeSe1−x films were grown up to pAr = 3×10−1 mbar [8]. FeSe1−x Tex films were also grown under vacuum conditions of 10−3 mbar [9] and even up to pAr = 1 mbar [10, 11]. Deposition of SmOFeAs films under H atmosphere (H2 as well as rf-generated H up to pH = 1.2×10−4 mbar) was tested in order to induce electron

32

2 Thin Film Growth of Fe-Based Superconductors

doping, however, so far all in-situ attempts for a H-substitution failed [12]. Similar observations were made for the deposition of SmOFeAs in N2 atmosphere: No incorporation of N into the 1111-phase could be found. The stoichiometric transfer of material from the target to the substrate is often acknowledged as one of the major advantages in the PLD process. Unfortunately, stoichiometric transfer is not fully guaranteed for volatile species with their strong tendency of vaporization. The volatility of elements (or substances) is quantified by their vapor pressure. Some elements with high vapor pressures belong to the constituents of the Fe-based superconductors as pointed out in [13] and a violation of the stoichiometric transfer can appear during (i) the absorption of laser light in the target, (ii) the plume expansion, and finally, (iii) the nucleation and film growth [14]. PLD of Fe-based superconductors is, therefore, severely challenged by the difficulty to control the stoichiometric transfer of typical dopants that induce high temperature superconductivity like K (in BaFe2 As2 ) or F (in Fe-oxyarsenides). The growth of LiFeAs thin films using PLD is yet still unrealized. Experiences with PLD under UHV conditions have noted the failure in transferring the dopant to the heated substrate when working with a (Ba1−x Kx )Fe2 As2 or with a F-substituted SmOFeAs target. In contrast, a reduced transfer of F− ions from an ablated LaO1−x Fx FeAs target onto a substrate at room temperature was confirmed [5]. Similarly, a loss in the transfer of K+ ions was also noted in the ablation of a KFe2 As2 target without heating of the substrates [15]. Apart from specific dopants, chalcogens and pnictogens also tend to evaporate at high temperatures. For example, Te- and S-deficiency was noted in Fe-Te-S films [16]. In general, actual Se- and Te-contents in Fe(Se1−x Tex ) films as well as As- and P-contents in BaFe2 As2 films can deviate from the nominal target composition. The conventional approach in the compensation of material loss during PLD uses intentionally off-stoichiometric targets enriched with the volatile element. Target composition adjustments were reported for the As-content in the deposition of SrFe2 As2 and BaFe2 As2 films [17–19] as well as for Te in the deposition of FeTe films [20, 21] or FeTex S y films [22]. A FeSe0.55 Te0.55 target with small excess in both of the chalcogens was used in [23]. The laser fluence is another essential parameter in PLD. On the one hand, a too low laser fluence results in the preferential thermal evaporation of volatile components in the target rather than in a stoichiometric material ablation. The ablation regime appears above a certain threshold energy density. Threshold energies for the laser pulse in the ablation of Ba(Fe0.92 Co0.08 )2 As2 were estimated from plume formation for different laser wavelengths between 193 and 1064 nm [24]. It was found that the threshold pulse energy increases with decreasing wavelength: 10–20 mJ (Nd:YAG), 50 mJ (KrF), 115 mJ (ArF). On the other hand, a too high laser fluence increases the energies of ablated ions that contribute more effectively in preferential sputtering of the most volatile component [14]. For example, in the deposition of KFe2 As2 on unheated substrates the chemical composition of the films varied with laser fluence in the range of 1.7–4.3 Jcm−2 [15]. In the growth of Fe-chalcogenide thin films laser fluences in the range of 0.74–10 Jcm−2 are found in literature, while the actual film composition remains often undetermined. A similar high spread in laser fluence

2.1 Pulsed Laser Deposition

33

of 3–10 Jcm−2 can also be noticed in the growth of BaFe2 (As1−x Px )2 thin films [25, 26]. A stoichiometric growth condition demands the adatoms to arrive in a stoichiometric ratio on the substrate surface. The adsorption processes involve accommodation and sticking of the adatoms on the substrate surface as well as their mobility. Important parameters are (i) deposition rates, (ii) substrate temperature, (iii) the roughness of the substrate (or buffer) surface and its coverage. As for all vapor deposition methods it is important to reduce residual gas and substrate contamination before film growth, which can be achieved well by working in UHV and heating the substrate in-situ before film growth to several hundred degrees (◦ C). Different diffusivities of light and heavy elements or the preferred re-evaporation of volatile species influence phase formation processes on the substrate. The reported substrate temperatures range from 200 to 1300 ◦ C. Table 2.3 summarizes selected parameters used in PLD of different compounds. Generally, lower substrates temperatures are common for PLD of 11 Fe-chalcogenides compared to Fe-pnictides: • The 11 Fe-chalcogenide superconductors are typically deposited below a substrate temperature of 500 ◦ C. Initially a few references suggested higher temperatures [8, 27]. A natural limit of the substrate temperature during deposition is given by the strong tendency for re-evaporation and a vanishing sticking rate, which was tested for FeSe to be TS = 800 ◦ C [28]. It was furthermore noted that re-evaporation affects the FeSe1−x Tex film thickness at 550 ◦ C [11]. • In contrast to Fe-chalcogenides, phase formation for 122 Fe-pnictides is observed only at substrate temperatures above 600 ◦ C and epitaxial growth is typically achieved above 650 ◦ C. The temperature range for epitaxial growth is 650–850 ◦ C in the growth of Ba(Fe1−x Cox )2 As2 . TS = 1050 ◦ C is the highest substrate temperature for which 122-type Fe-pnictide film growth was reported [26]. The upper limit of the substrate temperature is mainly given by the stoichiometric imbalance that favors the growth of impurity phases (especially Fe) and accounts for a gradual loss in epitaxy, too. In general, films grown by PLD are often not purely single-phase. For PLD growth of 1111 Fe-oxyarsenides substrate temperatures of 750–870 ◦ C are required and the optimal growth window for epitaxy and reduced amount of impurity phases is small. Two further parameters are important in PLD: (i) the distance between target and substrate, dTS , and (ii) the repetition rate of the laser pulses. Both affect the film growth rate, the film growth mode and also the final roughness of the film surface. Reported target-substrate distances, dTS , are 35 and 40 mm in PLD of FeSe1−x Tex thin films [9, 42], 44–55 mm in PLD of FeSe, FeTe and FeSe1−x Tex films [11, 29, 33, 43–47], and 60 mm in PLD of FeSe1−x Tex films [48]. dTS = 40–70 mm was used in the growth of FeTe0.8 S0.2 films [49]. In PLD of BaFe2 As2 distances varied from 30 mm [24, 50], 40 mm [51], 45 mm [19] to 50–55 mm [39, 40]. BaFe2 (As1−x Px )2 films were grown with a dTS = 50–70 mm [25, 52], while dTS = 25–30 mm for the deposition of 1111 Fe-oxyarsenides, such as SmOFeAs [41]. Typical repetition rates

34

2 Thin Film Growth of Fe-Based Superconductors

Table 2.3 Comparison of PLD growth parameters for selected Fe-chalcogenides and Fe-pnictides: base pressure ( p), substrate temperature (TS ), fluence (ε) and laser repetition rate (rate) Substrate

p (mbar)

TS ( ◦ C)

ε (Jcm−2 )

Rate (Hz)

Refs.

MgO

10−5

250–500

5–6

2

[29]

LaAlO3

10−8

400–550

1.3

10

[30]

CaF2

10−6

280

–

10

[31]

Various

–

320

5–6

2

[32]

Various

10−6

380

–

–

[28]

Various

10−5

610

1.15

48

[27]

Various

3×10−6

620

10

2

[8]

CaF2

10−9

550

2

3

[21]

Various

4×10−7

540

10

4

[20]

SrTiO3

5×10−9

450

2

3–10

[33]

Glass

10−6

400

–

5

[34]

TlFe1.6 Se2

CaF2

10−7

600

10

10

[35]

Sr(Fe1−x Cox )2 As2

(La,Sr)(Al,Ta)O3

10−7

600–700

1.5

10

[36]

LaAlO3

10−6

770–820

1.15

48

[17]

5×10−9

800–850

1.7–4.3

10

[37]

CaF2

10−7

700

–

9

[38]

Various

6×10−6

720

3.1

29.1

[39]

Various

10−9

700

3–5

20

[40]

MgO

10−7

80

10

10

[25]

MgO

5×10−9

1050

3

10

[26]

LaOFeAs

MgO

10−7

780

1.5

10

[4]

SmO1−x Fx FeAs

CaF2

10−8

860

2.15

10

[41]

Compound FeSe

FeTe FeSe0.5 Te0.5

Ba(Fe1−x Cox )2 As2 (La,Sr)(Al,Ta)O3

BaFe2 (As1−x Px )2

are 10 Hz when working with Nd:YAG lasers. Different repetition rates for excimer lasers are found to be in the range of 2–10 Hz in the growth of 11 Fe-chalcogenides and 2–20 Hz in the growth of 122 Fe-pnictides. Occasionally, higher repetition rates of ∼29 and 48 Hz can be found, resulting in higher growth rates (Table 2.4).

2.1.2 PLD of Fe-Chalcogenides FeSe Pulsed laser deposited FeSe thin films with a tetragonal unit cell were first reported during 2009 [8, 28, 29, 55]. FeSe grows with a predominant (001)-orientation on a variety of substrates. Under certain deposition conditions epitaxial growth is found. The lattice mismatch of ∼12% between FeSe and MgO substrates is very large. Domain matching epitaxy was, therefore, suggested first in [45] with m:n = 8:7

2.1 Pulsed Laser Deposition

35

Table 2.4 Growth rates (GR) of different Fe-based superconductors grown by PLD Compound Substrate TS (◦ C) GR (Ås−1 ) Refs. FeSe FeSe FeSe FeSe FeTe FeSe0.5 Te0.5 FeSe1−x Tex FeTe1−x Sx Ba(Fe1−x Cox )2 As2 BaFe2 (As1−x Px )2 Sr(Fe1−x Cox )2 As2 SmOFeAs

LaAlO3 Various SrTiO3 Various MgO LaAlO3 MgO Various (La,Sr)(Al,Ta)O3 MgO LaAlO3 , Al2 O3 CaF2

400 350 400 610 380 550 300 400 850 1050 770–820 860

0.08–0.11 0.22 0.38 50–60 0.28 0.06–0.2 0.3–0.7 0.14–0.56 2.8–3.8 2.0–4.0 30–40 0.6

[30] [44] [53] [27] [28] [54] [13] [22] [24] [26] [17] [41]

Fig. 2.3 Domain matching epitaxy in FeSe/MgO(100): a 11 uc FeSe along 10 uc MgO as found in [58]. Previously suggested ratios with b 8 uc FeSe along 7 uc MgO for FeSe(001) out-of-plane orientation and c 7 uc FeSe along 11 uc MgO for a FeSe(101) out-of-plane orientation. Images in b and c are reprinted from Fig. 3 in [45], © (2019) with permission from Elsevier

36

2 Thin Film Growth of Fe-Based Superconductors

(Fig. 2.3). Here, m is the number of FeSe unit cells and n is the number of MgO unit cells along the interface. Evidence for domain matching epitaxy can be extracted from high-resolution transmission electron microscopy (HR-TEM) on a 1 uc FeSe film grown by MBE in [56], however with a ratio of m:n = 11:10, which reduces the strain of the FeSe layer to 1.3% in-plane tensile strain (see Sect. 4.3). A recent reinvestigation of the FeSe/MgO interface prepared by PLD has confirmed domain matching epitaxy with ratios of m:n = 11:10, 10:9 and 9:8 in accordance with theoretical predictions [57] and confirmed that the interface is chemically heterogeneous containing regions with Fe diffusion into the substrate [58]. FeSe films deposited on MgO(100) can also contain two different growth domains with mutually rotated epitaxial relations [29]: one domain grows apparently cube-on-cube with (001)[100]FeSe  (001)[100]MgO , the second domain grows 45◦ in-plane-rotated with (001)[110]FeSe  (001)[100]MgO . FeSe film growth on MgO(100) may reveal further complexities as demonstrated by a recent study [45], where two different crystallographic phases, (001)-oriented tetragonal FeSe and (101)-oriented hexagonal Fe7 Se8 were detected in the films. Their appearance was studied upon the variation of substrate temperature, laser fluence and target composition (Cu alloying). Highly oriented or epitaxial FeSe films with (001)[100]FeSe  (001)[100]S are often reported on other cubic oxide substrates (S) with smaller lattice mismatch for deposition temperatures below 500 ◦ C. The crystallographic orientation can change with higher temperatures. In [8] FeSe1−x films were grown at very high substrate temperatures of 610–630 ◦ C on LaAlO3 substrates. Microstructure and surface morphology changed between 610 ◦ C (smooth films with secondary phases), 620 ◦ C (films with a coarse surface) and 630 ◦ C (smooth surface with cracks along [100]S and [010]S ). Similar high substrate temperatures were also used in [27], where an orientation relation of (101)FeSe1−x  (001)S , was found on SrTiO3 and Al2 O3 substrates. In both growth studies the films were Se-deficient, FeSe1−x , but superconducting with a maximum Tc = 11.5 ± 0.5 K near x = 0.11 ± 0.01. The same orientation was observed in non-deficient FeSe films on MgO(100) for deposition temperatures of 550 ◦ C and laser fluences of 3.4 Jcm−2 [45], which suggests that high substrate temperatures may be responsible for the deviation from the (001)-orientation of the film grains. This result is in agreement with another early study [55], where the change in the preferential growth orientation of FeSe films on MgO(100) from (001) to (101) was described with increasing sub-

2.1 Pulsed Laser Deposition

37

strate temperature: Films deposited at TS = 320 ◦ C are (001)-oriented, while films deposited at TS = 500 ◦ C are (101)-oriented. Despite the different texture, similar FeSe lattice constants (a = 3.78 Å and c = 5.54 Å) were found, however, only the film deposited at 500 ◦ C showed a complete superconducting transition above 2 K. It was further demonstrated, that (101)-oriented FeSe thin films undergo a structural transition (from tetragonal to orthorhombic) below ∼80 K, whereas the structural transition was suppressed in purely (001)-oriented FeSe indicating a stronger interaction between film and substrate lattice [55]. Another interesting result is the suppression of the superconducting transition in FeSe/MgO(100) for film thicknesses below 280 nm [29], which was attributed to an enhanced ‘substrate strain’-effect for thinner films. Tensile strain seems to be disfavorable for superconductivity in FeSe. A superconducting transition in a FeSe film of only 18 nm in thickness on MgO was achieved after post-annealing [59], but remained yet unreproduced in independent studies. Reference [28] suggested the use of lower deposition temperatures ∼380 ◦ C in the growth of FeSe in order to avoid the appearance of its hexagonal modification (with NiAs-type structure) above 450 ◦ C, the accumulation of impurity phases and predominant re-evaporation at very high temperatures of 800 ◦ C. The vanishing sticking coefficients define an upper limit in substrate temperature for FeSe growth. The c-axis lattice parameters of the films (5.49–5.52 Å) were close to a bulk reference (5.518 Å) and did neither correlate with the lattice mismatch (between FeSe and LaAlO3 , SrTiO3 or MgO) nor with the film thickness (50, 100, 200 nm). Films with the smallest c-axis lattice parameter did not become superconducting above 2 K. Again, it was concluded, that superconductivity in FeSe is suppressed by tensile strain. Lower substrate temperatures of 320 ◦ C were used in [32] with the idea to extend film deposition to substrate materials that do not tolerate high temperatures. Consequently, (001)-oriented FeSe films could also be grown on Si and amorphous SiOx . A further decrease of deposition temperatures to 280–300 ◦ C was reported in the growth of FeSe films on CaF2 (100) substrates [31, 60]. At present, PLD of FeSe films is carried out at substrate temperatures of ∼300 ◦ C. As mentioned above, in the fabrication of electric double layer transistors (EDLT) based on FeSe (Sect. 6.2.2), FeSe films with film thicknesses of 10–20 nm were additionally annealed. The originally non-superconducting films became superconducting after in-situ annealing at 450 ◦ C for 30 min [59, 61, 62]. The substrate temperature has not only an influence on film texture and orientation, but also on the surface morphology. In [30] the growth of FeSe thin films with a thickness of 40 nm on LaAlO3 (100) were investigated in a temperature range of TS = 100–600 ◦ C. All films were epitaxially grown. Their c-axis lattice parameter decreases with increasing TS up to 550 ◦ C. The study also suggested that the thin film crystallinity is better for smaller growth rates (0.11 Ås−1 ) compared to higher growth rates (0.67 Ås−1 ). In addition, the surface morphology inspected by scanning electron microscopy (SEM) changes drastically with substrate temperature. Up to TS = 400 ◦ C the film surfaces were smooth and homogeneous, above this temperature the surfaces became inhomogeneous and rough due to the formation of island

38

2 Thin Film Growth of Fe-Based Superconductors

Fig. 2.4 SEM images of spherical precipitates on the surface of FeSe thin films: a FeSe0.88 /LaAlO3 deposited at 620 ◦ C. (Reprinted from Fig. 3d in [8]; © IOP Publishing.Reproduced with permission. All rights reserved.) b FeSe/LaAlO3 deposited at 400 ◦ C. (Reprinted with permission from Fig. 12 in [30], © (2011) the Authors, Creative Commons Attribution Noncommercial License.) Several studies (for example [45, 58]) confirmed the appearance of particulates in AFM images (not shown here)

structures. Spherical precipitates (particulates) were found on the entire film surface independent of the substrate temperature (Fig. 2.4). Since they appear in general on the surface of any vapor deposited FeSe film (PLD, MBE, sputter-deposition) they are most likely formed by the condensation of Se vapor [63]. A SEM-EDS analysis of such a precipitate can be found in [58]. The chemical composition of FeSe films is in first instance controlled by the target composition, the substrate temperature and the vacuum conditions during deposition. The Se-deficiency in FeSe1−x films deposited at high substrate temperatures above 600 ◦ C on different oxide substrates was 0.1 ± 0.02 examined by energy dispersive X-ray spectroscopy (EDS) [27]. The corresponding Tc,90 varied between 10.5 and 11.7 K. Reference [30] mentioned the variation of doping level with substrate temperature after in-situ film analysis by ultraviolet and X-ray photoelectron spectroscopy (UPS/XPS). Additional influences on the stoichiometry were encountered as well: (1) substrates that react chemically with the FeSe film, and (2) film exposure to air. Surface oxidation of FeSe films was first confirmed by XPS in [32] and induces the chemical reduction of Se. On the other hand, the process of oxidation originating from SrTiO3 substrates caused the formation of Fe3 O4 particles during annealing of FeSe films at temperatures of 500 ◦ C [64]. For Fe-chalcogenide films deposited on CaF2 , a TEM-EDS analysis suggested anion interdiffusion, Se2− ←→ F− [65]. For a discussion of the film/substrate interface see Sects. 4.1.3 and 4.3. In the last decade a variety of tetragonal FeSe or FeSe1−x films with different structural and superconducting properties were fabricated. Investigations of FeSe thin film growth on 12 different substrates (CaF2 , SrF2 , MgF2 , LiF, MgO, SrTiO3 , TiO2 , Nb:SrTiO3 , LaAlO3 , (La,Sr)AlO3 , (La,Sr)(Al,Ta)O3 , and MgAl2 O4 ) has repeatedly noted the absence of a correlation between Tc and the lattice mismatch between FeSe and the substrate, but confirmed a correlation of Tc,on with the c-axis lattice constant of the films [44]. Simultaneously, a strong compression of the a-axis lattice param-

2.1 Pulsed Laser Deposition

39

eter was observed for films grown on CaF2 substrates that show a superconducting transition up to 15.2 K. This sensitivity on structural parameters has been confirmed many times (see also Fig. 1.8). The strong increase in Tc of FeSe films on CaF2 has been attributed to the strain-dependent band dispersion and an increase in the density of states at the Fermi level, N (E F ) [66]. The experiment is discussed in Sect. 6.7.4. In the majority of studies films were deposited under HV or UHV conditions (Table 2.5). In [8] FeSe films were grown under an Ar pressure of pAr = 1–3×10−1 mbar, which did neither contribute to an improvement in the degree of crystallinity nor to the enhancement of Tc compared to vacuum deposition at 3×10−6 mbar. It was noted that superconducting FeSe1−x films could only be grown in a small window of substrate temperatures (610–620 ◦ C at pAr = 10−1 mbar) and the further increase in pressure suppressed the superconducting transition in the resulting films. In the aforementioned study, the highest Tc,on of 11.8 K was obtained under vacuum deposition at 3×10−6 mbar and for LaAlO3 substrate temperatures of 620 ◦ C. Mg:FeSe A single study was devoted to the growth of FeSe thin films with Mg coating [60]. A 120 nm thin FeSe precursor film was first grown on a CaF2 substrate at TS = 300 ◦ C under HV conditions (5×10−6 mbar). Afterwards, Mg was deposited on the as-grown films with varying deposition times (1.5, 3, 10 and 20 min) and probably at the same elevated temperature in order to promote Mg diffusion into the precursor film. FeSe and Mg targets were ablated by a Nd:YAG(3ω) laser with a power output of 2 W. It was speculated that Mg fills the Fe vacancy sites of FeSe and substitutes for Fe2+ . The actual Mg-content (atomic ratio of Mg ions in FeSe) in the resulting films (6.4, 13.1, 26.2 and 75.3%) was measured by EDS. Besides the 00 FeSe reflections, the X-ray diffraction (XRD) pattern of the Mg:FeSe films shows also a number of unindexed peaks of smaller intensity. The c-axis lattice parameter first expands (for a Mg-content of 6.4%) and shrinks again for higher Mg-contents. Furthermore, the intensity of the FeSe reflections varies for the different films. The FeSe precursor film showed a Tc = 10.7 K. With increasing Mg diffusion into FeSe Tc varies with a typical dome-shape and reaches a maximum value of Tc = 13.4 K for a Mg-content of 13.1%. K:FeSe Polycrystalline K0.8 Fe2 Se2 targets were ablated by a Nd:YAG(3ω) laser with a repetition rate of 4 Hz and an energy of 20 mJ/pulse in UHV [69]. The films were deposited on 0.07 wt.% Nb-doped SrTiO3 substrates between 380 and 480◦ C and at a target-substrate distance of 4 cm. An alkali metal dispenser was used as K supply. The resulting epitaxial films were not single phase and contained FeSe coexisting with Kx Fe2−y Se2 (245 phase). The fraction of Kx Fe2−y Se2 increased with decreasing substrate temperature as well as with increasing K supply. An XPS study was performed on the films.

40

2 Thin Film Growth of Fe-Based Superconductors

Table 2.5 PLD growth parameters for FeSe thin films: substrate materials, substrate temperature (TS ), base pressure ( p), fluence (ε) and laser repetition rate (rate). Film thickness (t) and superconducting transition temperature of the films (Tc ) are indicated Substrate

TS (◦ C)

p (mbar) ε (Jcm−2 )

Rate (Hz) t (nm)

Tc (K)

Refs.

CaF2

280

10−6

10

11.4

[31]

CaF2

300

5×10−6

10

20–320

15.1

[67]

LaAlO3

100–600

10−8

10

40

6

[30]

LaAlO3

380

10−6

MgO

250–500

10−5

100–600

2

MgO

320, 500

MgO

350–550

10−9

SrTiO3

400

10−8

1.3

2 5–6

2

[68]

5–6 1.3–3.4

2–10

[29] [55]

10

400

[45]

10

950

5

10–27

2

140

6.8

[32]

50–200

8

[28]

11.8

[8]

7

[53]

Growth studies using various substrates KTaO3 , MgO, SrTiO3

300

LaAlO3 , MgO, Si, a-SiO2 , SrTiO3

320

LaAlO3 , MgO, SrTiO3

380

10−6

LaAlO3 , (La,Sr) (Al,Ta)O3 , SrTiO3

620

3×10−6

BaF2 , CaF2 , MgF2 , LaAlO3 , (La,Sr)AlO3 ,

350

10−7

Al2 O3 , LaAlO3 , 610 (La,Sr)(Al,Ta)O3 ,

10−5

5–6

10

2

[61]

2

20–160

4.75– 15.17

[44]

48

1000– 1800

10.5– 11.7

[27]

(La,Sr)(Al,Ta)O3 , LiF MgAl2 O4 , MgO, Nb:SrTiO3 , SrTiO3 , TiO2 1.15

SrTiO3

FeTe and FeTe:Ox PLD of FeTe has produced non-superconducting films and—in contrast to bulk specimens or crystals—also superconducting films (Table 2.6). The origin of superconductivity in these films has not yet been satisfactorily resolved (see also Sect. 6.3.1). Based on the available data the epitaxial relation between film and substrate can be generalized to

2.1 Pulsed Laser Deposition

41

Table 2.6 PLD growth parameters for FeTe thin films on various substrates: base pressure ( p) substrate temperature (TS ), fluence (ε) and laser repetition rate (rate). Film lattice parameters and the superconducting transition (Tc,on ) are indicated where given Substrate TS ( ◦ C)

p (mbar)

CaF2

300–400

10−5

CaF2

550

10−9

LaAlO3

300–400

10−5

1–10

MgO

300–400

10−5

1–10

MgO

380

7×10−7

MgO

400

10−6

ε Rate (Jcm−2 ) (Hz)

a (Å)

1–10

3.817

3

3.79

2

3.8358

c (Å)

Tc,on (K) Refs. [80]

6.31

[21]

6.275

–

[79]

6.285

–

[79]

6.2734

12

[75] [70]

MgO, 540 LaAlO3 , (La, Sr)(Al, Ta)O3 , SrTiO3

4×10−7

1

4

SrTiO3

300–450

10−4 (O2 ) 3

5

SrTiO3

300–450

2×10−6

5

SiO2 /Si

RT, 220

4×10−8

Glass

400

10−6

3

3.821

6.265

13

6.275

12

5

[73] [73]

5 3

[20]

[46] –

6.2208

12

[71]

[100](001)FeTe  [100](001)S on oxide substrates and [110](001)FeTe  [100](001)S on CaF2 substrates. An exceptional case is again film growth on MgO(100), where FeTe grains of different epitaxial relation with the MgO lattice were found in a transmission electron microscopy (TEM) study [70]. No clear correlation could be traced between the a-axis lattice parameters of the FeTe films and the substrate lattice parameters. (001)-oriented growth of superconducting FeTe films with Tc = 8 K also succeeded on amorphous glass substrates [71]. An accompanying Fe2 TeO5 impurity phase indicated the presence of oxygen inside the films on the glass substrates. For pulsed laser deposited FeTe thin films the highest onset transition temperatures Tc,on = 13 K were reported in [20] for films grown on MgO, SrTiO3 , LaAlO3 and (La,Sr)(Al,Ta)O3 at substrate temperatures of 500–580 ◦ C. The reduced c-axis lattice parameters of the films compared to the bulk value indicated that the film lattice is under tensile stress. Tc,0 was correlated with the Fe-Te-Fe bond angles of the thin films that were larger compared to the non-superconducting reference. A followup neutron scattering study on a stack of 21 superconducting films grown on MgO revealed magnetic long range ordering up to TN = 67 K [72]. The lattice parameters

42

2 Thin Film Growth of Fe-Based Superconductors

Fig. 2.5 Annealing procedure for the preparation of FeTe:Ox films as described in [74]. Films were deposited on MgO(100) or SrTiO3 (100) substrates. Deposition and annealing takes place in O2 atmosphere ( pO2 = 5.6×10−6 mbar)

of the slightly strained films in this study were a = 3.86 Å and c = 6.31 Å. The low superconducting fraction of only 22% of the film volume could indicate a confined superconducting volume close to the film/substrate interface. An independent study claimed that the incorporation of O2− ions into the FeTe film lattice would be vital for superconductivity [73]. The authors compared a thin film grown under high vacuum ( pbase < 2×10−6 mbar) with a Fe1.08 Te:Ox film deposited under an O2 partial pressure pO2 = 10−4 mbar. Latter showed a complete superconducting transition with Tc,0 = 8 K. The attempt to tune the transition temperature via O2− incorporation however failed because O2 partial pressures higher than 10−4 mbar suppressed epitaxial film growth. A third research group announced superconductivity in FeTe films induced by O2 -annealing after film growth (Fig. 2.5) leading to FeTe:Ox with a crystal structure similar to that of FeTe [74, 75]. The O2− uptake during annealing was facilitated by the less dense microstructure of the films. A reversible change between the appearance and absence of superconductivity by alternating vacuum and O2 -annealing procedures was confirmed. For denser films O2− was incorporated during film growth at low O2 partial pressures of pO2 = 5.6×10−6 mbar [74]. The same group also observed emerging superconductivity after the films were exposed to air for more than 2 weeks. The opposite nature of FeTe films (O2− uptake induces superconductivity) and FeSe films (O2− uptake destroys superconductivity) was investigated in more detail by XPS and X-ray absorption spectroscopy (XAS) [76, 77]. In FeTe, both, Fe and Te changed their valence states with O2− incorporation: from Fe0 to Fe3+ and from Te0 to mixed Te0 /Te4+ . After vacuum annealing the valence state of Fe changed from Fe3+ to Fe2+ , whereas that of Te reverses to Te0 . Furthermore, the film surface became Te-deficient with extended exposure to O2 . In FeSe, only Fe changed its valence from Fe0 to Fe3+ after O2 -annealing, whereas Se remained in its Se0 state. The effect of oxygenation of FeTe on superconductivity remains controversially discussed. In a recent study superconductivity could not be induced could not be induced in FeTe single crystals by oxygenation [78]. Non-superconducting FeTe films were grown by PLD on MgO(100) as well as on LaAlO3 (100) substrates at 300–400 ◦ C [79] and on CaF2 substrates at 300 ◦ C [80] and 550 ◦ C [21], respectively. Absence of O-diffusion into the films was stated [79],

2.1 Pulsed Laser Deposition

43

however an oxidized surface layer of 6 nm in thickness was found by TEM analysis in a 25 nm thick FeTe film grown on MgO [81]. The authors argued that the film was exposed to air for a longer time. It is interesting to note that this film developed an incomplete superconducting transition with Tc,on = 11 K approximately 2 months after film growth, which is qualitatively confirming the observations made in [75]. Storage conditions of FeTe films thus need special attention. Similar aging effects were reported in [82] where the temperature dependence of the resistance of Fe1+x Te films changed over time (up to 3 years) and developed an incomplete superconducting transition at 11 K even when the films were stored at 25 ◦ C in dry air inside desiccators. Hall measurements revealed a finite mobility of holes (μh ≈ 2·10−4 m2 V−1 s−1 ) and electrons (μe ≈ 3.5·10−4 m2 V−1 s−1 ) in superconducting FeTe films [81]. In films without superconducting transition the hole mobility vanished, whereas μe increased to 5–7.5·10−4 m2 V−1 s−1 (see Sect. 6.7.1). FeSe1−x Te x Among PLD of 11 Fe-chalcogenides FeSe1−x Tex has been most extensively investigated since 2009. Nd:YAG solid state lasers (2ω, 3ω) as well as different excimer lasers (ArF, Krf, XeCl) were proven suitable for target ablation. (001)-oriented growth and, in most cases, epitaxial growth of FeSe1−x Tex was achieved on a number of oxide substrates [83], fluoride substrates [84], amorphous glass [34, 85], Si-based substrates [86], flexible mica substrates [87], MgO/IBAD-MgO [88] and LaMnO3 buffered metal tapes [89], RABiTS templates [90], invar 36 alloy [91], crystalline Fe buffer layers [48], a-Al2 O3 -buffered metal tapes [71] and on the piezoelectric crystal Pb(Mg1/3 Nb2/3 )0.7 Ti0.3 O3 (PMN-PT) [92, 93]. Selected deposition parameters are summarized in Table 2.8. It was furthermore demonstrated that a CeO2 layer can be grown epitaxially between two FeSe0.5 Te0.5 layers [43]. FeSe1−x Tex thin films were deposited under UHV environment with pbase = 10−9 mbar up to 1 mbar Ar background gas pressure [10, 11]. Vacuum conditions of 10−3 mbar as used in [9] are possibly responsible for the formation of SeO2 and FeO impurities besides Fe. Epitaxial relations between FeSe1−x Tex and oxide or fluoride substrates correspond largely to those found for FeSe and FeTe films. Again, the in-plane texture of films on MgO(100) substrates is more complex and the texture changes with substrate temperature: Nanocrystalline or non-crystalline growth is found at TS = 180 ◦ C, an epitaxial domain with a 45◦ -in-plane rotation of the basal plane with respect to the MgO lattice, i.e. [110](001)Fe(Se,Te)  [100](001)MgO , grows at TS = 280 ◦ C, a mixed texture with two domains of either 45◦ -in-planerotated or cube-on-cube appears at TS = 400 ◦ C, and a pure cube-on-cube epitaxy, i.e.

44

2 Thin Film Growth of Fe-Based Superconductors

Fig. 2.6 a Schematic evolution of texture with substrate temperature TS in FeSe0.5 Te0.5 films deposited on MgO(100) substrates as found in [94]. The different textures are indicated by schematic 360 ◦ in-plane φ-scans of the film (101) reflection with respect to the substrate (101) reflection (arb. intensities). b (101)-pole φ-scans of two FeSe1−x Tex films on MgO(100) with different Tecontent x (arb. intensities). (Data reprinted from Fig. 2 in [96]; © IOP Publishing. Reproduced with permission. All rights reserved)

[100](001)Fe(Se,Te)  [100](001)MgO is found at TS = 500 ◦ C [94]. In [95] the transition between a single preferential orientation and a mixed texture occurs already at TS = 300 ◦ C. Fig. 2.6 represents a schematic and simplified chart of the texture evolution of Fe-chalcogenide thin films on MgO with substrate temperature. Depending on the actual chemical composition of the film, the in-plane texture can vary strongly as indicated by non-vanishing intensity around the (101)-reflections in the φ-scan [96]. The deposition temperature is often optimized to the highest achievable Tc , and rarely to the best crystalline properties as mentioned, for example, in [97]. A nonmonotonic dependence of Tc on the substrate temperature was noted in several growth studies with a maximum Tc for TS = 450 ◦ C on SrTiO3 [33], 400 ◦ C [98] or 300 ◦ C on CaF2 substrates [99] and 300 ◦ C on MgO [95] (Fig. 2.7a). The temperature window for optimal growth can be modified by the introduction of a thin FeSe1−x Tex seed layer. For the subsequent homoepitaxial growth of FeSe1−x Tex the optimal substrate temperature for epitaxial growth could be lowered as shown first in [95]. This method of a combined high and low temperature deposition was later adopted in [91, 100]. Like in FeSe and FeTe thin films, Tc of FeSe1−x Tex thin films can be substantially larger than in bulk or target specimens: Reported values are Tc,on = 16.6 K (CaF2 , [101]), 17 K (SrTiO3 , [33, 102]), 18.15 K (CaF2 , [99]), 21 K (LaAlO3 , [103, 104]), 21 K (CaF2 , [105]), 22 K (CaF2 , [98]) and even 22.3 K (CaF2 , [106]). Films grown on CeO2 -buffered YSZ or on RABiTS also showed Tc,on ∼20 K [90]. For films on MgO a maximum Tc of 19.7 K was found in [95]. Strain and chemical composition (i.e. varying Se/Te-ratio and Fe-content) were discussed as primary reasons for the Tc -enhancement in the films. Several systematic studies have been carried out in order to determine the influence of growth conditions on the film lattice parameters and the superconducting properties, however, there is

2.1 Pulsed Laser Deposition

45

Fig. 2.7 a Variation of the superconducting transition temperature, Tc , with substrate temperature, TS , for film deposition based on nominal FeSe0.5 Te0.5 targets. All studies used a KrF laser for ablation [33, 95, 99]. TS can be reduced for homoepitaxial film growth on FeSe1−x Tex /MgO [95]. The actual thin film composition may deviate from the nominal target composition (see text). b Chemical composition of FeSe1−x Tex films on different substrates from a FeSe0.5 Te0.5 target (indicated by a black dot) in the Fe-Se-Te ternary phase diagram. (Adapted from Fig. 3 in [97])

less information about the variation of the actual film composition with substrate material, temperature and film thickness. Studies, in which the chemical composition of the resulting films was determined by SEM-EDS, wavelength dispersive spectroscopy (WDS) or Rutherford backscattering spectrometry (RBS) are largely in qualitative agreement. All data confirm that the stoichiometric transfer is not fully guaranteed in PLD of FeSe1−x Tex films. Furthermore, even the actual target compositions may already deviate from the nominal values (obtained from the precursor powders). SEM-EDS measurements of the film composition [99] revealed a significant loss of Te at TS = 300 ◦ C (on CaF2 , MgO, LaAlO3 , SrTiO3 ). The Te-content of films deposited at 450 ◦ C even fell below 0.15. Material ablation from a FeSe0.55 Te0.55 target resulted in a final film composition of FeSe0.65 Te0.42 (measured by SEM-EDS), as noted in [107]. The deposition conditions were TS = 350 ◦ C, pbase = 6×10−10 mbar, a target-substrate distance of 60 mm, a repetition rate of 4 Hz, and a laser pulse energy of 80 mJ. Nb-doped SrTiO3 substrates were used. A more detailed study [23] showed that the Se-content increases with substrate temperature and film thickness: Films grown at 250, 350 and 450 ◦ C with a thickness of 100 nm on SrTiO3 from a FeSe0.55 Te0.55 target (nominal composition) have Se-contents of 0.71, 0.74 and 0.86 [23], whereas the Se-contents of 30 nm thin films are 0.5, 0.6 and 0.49. Te-losses were noticed in a recent work [108], in the ablation of a Fe1.05 Se0.5 Te0.5 target. There, the composition of the films grown on LaAlO3 at 350 ◦ C with a repetition rate of 10 Hz was determined by EDS as Fe1.06 Se0.52 Te0.33 or Fe1.05 Se0.55 Te0.35 . Excess Seand reduced Te-contents were reported in [97] for films grown on oxide substrates with the following deposition parameters: TS = 300 ◦ C, pbase = 9×10−7 mbar, a target-substrate distance of 45 mm, a repetition rate of 4 Hz, and a laser pulse energy of 320 mJ. The chemical composition of FeSe1−x Tex thin films deposited on CaF2

46

2 Thin Film Growth of Fe-Based Superconductors

substrates is controversially discussed. In [97, 109] it was recognized that the film stoichiometry on CaF2 substrates has excess Te (and Se-deficiency), a result which also qualitatively differs from previous reports (Fig. 2.7b). Because of the overlap of the Ca K and the Te L edges in films on CaF2 substrates, SEM-EDS was considered to be less appropriate for the determination of the film composition. WDS and RBS were employed in [98], where the actual target composition (FeSe0.39 Te0.61 ) already deviates from the nominal composition (FeSe0.45 Te0.45 ). Thin films grown at 380–460 ◦ C on CaF2 have finally Se-contents of 0.73–0.63. Different sticking coefficients for Se and Te which depend on temperature and on the substrate surface could be one possible explanation for the loss of stoichiometric transfer. An increase of Fe-content and a simultaneous decrease of Se-content with substrate temperature was reported in [98], however it was argued that re-evaporation alone would not account quantitatively for the drastic change of the Se/Te-ratio in the thin film composition. Therefore, a non-stoichiometric plume generation was assumed based on stronger binding energies in FeSe compared to FeTe. A better understanding would definitely require a plume analysis, for example, by a time-offlight mass spectroscopy. It is also important to note that Se diffusion into CaF2 was observed by TEM-EDS resulting in a Se-deficiency in the initial growth stage [80]. Similar observations were made for FeSe thin films where a CaSe layer forms in an interface reaction for films grown on CaF2 [67], which will be discussed in detail in Sect. 4.1.3. Besides the chemical composition, (i.e. the Fe- and Se-/Te-contents), a possible oxidation of the films and its influence on the superconducting properties is another important issue. Oxidation of excess Fe in Fe-chalcogenide films can either occur due to residual O2 from the growth chamber or due to O-diffusion from the substrate. For example, after annealing of as-grown FeSe1−x Tex films at 500 ◦ C, Fe3 O4 nanoparticle formation was observed [64]. Detrimental effects on the superconducting properties of FeSe1−x Tex were noted for annealing procedures at temperatures higher than 90 ◦ C under pO2 = 1.3 mbar [110]. The effect of air-exposure to FeSe1−x Tex films was investigated in [107] by synchrotron radiation photoemission spectroscopy (PES) and XAS. The 100 nm thick film grown on Nb:SrTiO3 (100) with a Tc,on = 15.8 K was exposed to air at room temperature for one month and then re-investigated. Ccontamination at the surface and O-chemisorption were detected. O2− was able to break the Fe-Te bonds and was driving the oxidation of Fe, whereas the Fe-Se bonds stayed unaffected. A Fe2 O3 layer formed at the film surface. The superconducting transition fully disappeared and the temperature dependence of the film resistance developed a negative temperature coefficient. Preferential etching of anions (Se2− , Te2− , O2− ) by high energetic Ar+ ions was noted in [107]. Therefore, Ar-etching can worsen the Fe excess in the Fechalcogenide thin films. After 10 min of Ar-etching (at 1000 V) the Fe/Te-ratio increased to values larger than 2. Fe-chalcogenide thin film growth on amorphous glass substrates is another remarkable topic. These experiments do not only offer a better understanding of the growth of the van der Waals compound, but also test low cost substrates for possible applications. A highly textured film with lattice parameters a = 3.79 Å

2.1 Pulsed Laser Deposition

47

Table 2.7 Superconducting transition temperatures for FeSe1−x Tex films on amorphous glass, Si, and amorphous SiOx . The deposition conditions are: pbase = 10−6 , TS = 400 ◦ C, ε = 3 Jcm−2 . A KrF laser was used for target ablation with a repetition rate of 5 Hz Substrate x Tc,on Refs. a-Al2 O3 /steel a-SiOx /Si Glass Glass Glass Si

0.9 0.9 0.5 0.5 0.9 0.9

10 10.5–12.2 5.5 10 12.3 10.8–12.2

[71] [86] [85] [34, 71] [71] [86]

and c = 5.88 Å could be grown on glass [34]. The ‘semi-epitaxial’ growth was confirmed in cross-sectional and plan-view TEM images. It was noted that a reduced c-axis lattice parameter of the films also occurred without the confinement of FeSe0.5 Te0.5 to the regular surface of a crystalline substrate. Films with Tc,on = 10 K had critical current densities of Jc,sf (4K) = 1.2×104 Acm−2 and Jc (4K, 2T) = 800 Acm−2 (see Sect. 6.1.3). The attempt in growing a FeSe0.5 Te0.5 /CeO2 /FeSe0.5 Te0.5 trilayer with a 7 nm thick CeO2 interlayer on glass did neither result in an improved texture nor in good superconducting properties [85]. HR-TEM images revealed a polycrystalline growth of the intermediate CeO2 layer that prevented a successful transfer of epitaxy like in the trilayers deposited on single crystalline SrTiO3 . The epitaxial variant of the trilayer will be discussed in Sect. 5.1. In contrast, the quality of texture could be maintained after the deposition of an interlayer from a composite FeSe0.5 Te0.5 /CeO2 target. (001)-oriented film growth was also found on an amorphous-Al2 O3 -buffered stainless steel tape [71], on amorphous-SiO2 and on HF-etched Si substrates [86]. Table 2.7 summarizes the growth studies on amorphous substrates and on Si. The initial progress that was made in the PLD of FeSe0.5 Te0.5 thin films enabled their successful growth on flexible metal tapes known as coated conductor technology [88]. The so-called second generation (2G) high-temperature superconducting wires (or coated conductors) were originally developed for YBa2 Cu3 O7−δ and are classified as ion-beam-assisted deposition (IBAD) technique or as the rolling-assisted biaxiallytextured substrate (RABiTS) approach. The IBAD technique, known since the 1980s, is one of the successfully applied routes that generate a biaxially aligned buffer layer for the subsequent epitaxial growth of YBa2 Cu3 O7−δ conductors on stainless steel or Ni-based alloy (Hastelloy, inconel) tapes [111, 112]. In the IBAD process the epitaxial growth of MgO is facilitated by the interaction with an ion beam (700 eV Ar+ ions). The biaxial texture of MgO finally serves as template for epitaxial growth of the superconducting layer. At the begin of 2011 the successful growth of Ba(Fe0.9 Co0.1 )2 As2 films on MgO/IBAD-MgO buffered Hastelloy tapes was announced [113, 114] and motivated the use of MgO/IBAD-MgO-buffered Hastelloy also for the Fe-chalcogenides,

48

2 Thin Film Growth of Fe-Based Superconductors

although no weak-link behavior of grain boundaries in FeSe0.5 Te0.5 was known at that time. FeSe0.5 Te0.5 demonstrated promising superconducting properties, especially for technological applications in high magnetic fields compared with conventional superconductors that are predominantly applied in liquid He: NbTi and Nb3 Sn. A transition temperature of Tc,0 = 10 K and the critical currents larger than 104 Acm−2 at 20 T and 4.2 K could be achieved [88]. A detailed discussion can be found in Sect. 6.1.3. For the fabrication of RABiTS a cube-textured Ni-W alloy is coated with a buffer-layer architecture consisting of Y2 O3 , YSZ and CeO2 layers [115]. In [90] FeSe0.5 Te0.5 film growth on CeO2 -buffered YSZ on RABiTS templates with Tc,on ≈ 20 K and Tc,on ≈ 18 K is discussed. The critical current of FeSe0.5 Te0.5 films on RABiTS was improved by one order of magnitude and reached 105 Acm−2 at 30 T at 4.2 K. Typical parameters for the deposition of FeSe0.5 Te0.5 films in the Brookhaven research group are: pbase = 2×10−7 mbar, TS = 300–450 ◦ C and ε = 3 Jcm−2 [116]. Recently also an uncoated Ni-Fe alloy (invar 36) was employed in the growth of FeSe0.5 Te0.5 conductors [91]. There, a 200 nm thick FeSe0.5 Te0.5 layer was first deposited with 10 Hz repetition rate at 400 ◦ C followed by a second, 250 nm thick FeSe0.5 Te0.5 layer deposited with 3 Hz repetition rate at 200 ◦ C. The laser fluence was 2 Jcm−2 . A strong Ni-diffusion from the invar tape into the film could be detected by Transmission energy dispersive X-ray Spectroscopy (TEDS). In addition, O was detected throughout the film. The growth parameters for various FeSe1−x Tex films are summarized in Table 2.8. FeTe1−x Sx PLD of Fe-Te-S or FeTe1−x Sx (FeTex S y ) films on MgO and SrTiO3 substrates was first reported in [121] and subsequently in [49, 122]. Substrate temperatures were tested in the range from 200 to 600 ◦ C. Optimal temperatures for 50 nm thin films on SrTiO3 (100) and MgO(100) substrates were found to be 300–400 ◦ C leading to epitaxial growth with the epitaxial relationship: [110](001)FeTex S y  [100](001)S . The chemical composition of films deposited at 400 ◦ C were FeTe0.49 S0.13 /SrTiO3 and FeTe0.83 S0.12 /MgO indicating an overall loss in S-content during deposition. The strong Te-deficiency of the film on SrTiO3 could be the result of an interface layer reaction as it had been suggested after TEM investigations [49]. The growth of 120–200 nm thin films of FeTe0.8 S0.2 also revealed different growth rates for the deposition on MgO (faster) and SrTiO3 (slower) as well as a cube-on-cube epitaxy [49]. The FeTe1−x Sx films mentioned above were deposited using a KrF excimer laser. Because of its highly energetic excitation power the authors of [22] believed that it could produce active O2− inside the vacuum chamber and have, therefore, chosen a Nd:YAG(2ω) laser for film deposition. The growth conditions were optimized by lowering the deposition rate from 0.56 to 0.14 Ås−1 . Nevertheless, S and Te deficiencies occurred in the films, mainly caused by re-evaporation. The enrichment

2.1 Pulsed Laser Deposition

49

Table 2.8 PLD growth parameters for the ablation of FeSe1−x Tex : substrate material, substrate temperature (TS ), vacuum pressure ( p), fluence (ε) and laser repetition rate (rate). The resulting critical temperatures (Tc ) are indicated Substrate TS (◦ C) p (mbar) ε (Jcm−2 ) Rate (Hz) Tc,on (K) Refs. Target: FeSe1−x Tex (x ≤ 0.4) CaF2 280 1.3×10−7 Target: FeSe1−x Tex (x = 0.5±0.1) Al2 O3 , 500 8×10−9 MgO, SrTiO3 CaF2 280 10−5 CaF2 300 10−5 CaF2 380–460 2×10−7 CaF2 , 400 10−9 LaAlO3 , MgO CaF2 , 550 5×10−9 LaAlO3 , SrTiO3 CeO2 /YSZ 300–450 2×10−7 Fe/MgO 450 10−10 LaAlO3 350 4×10−6 LaAlO3 380 10−6 LaAlO3 , 550 5×10−9 MgO, SrTiO3 , YSZ LiF 550 5×10−9 MgO 180–500 MgO 300 10−5 PMN-PT 300 3×10−6 PMN-PT 450 10−5 SrTiO3 250–450 6×10−10 SrTiO3 300–450 2×10−7 SrTiO3 300–650 5×10−9 SrTiO3 400 10−4 (O2 ) YSZ 550 5×10−9 Target: Fe0.94 Se0.45 Te0.55 (x = 0.55) CaF2 380–460 2×10−7 Target: FeSe0.3 Te0.7 PMN-PT 275 10−6 Target: FeSe0.1 Te0.9 Mica 400 εopt as well as for d T > Topt and ε < εopt . The upper row shows XRD (Bragg Brentano) for Cu Kα radiation. The lower row shows 1×1 μm2 AFM scans of the individual film surfaces. (Reprinted from Fig. 4 in [163]; © (2018) with permission from Elsevier)

the deposition temperature results in epitaxial growth of the 1111 phase but also in the stabilization of SmAs. Sm2 O3 is also present when the deposition temperature and the energy density on the target surface deviate from the optimal values. The presence of impurity phases and misaligned grains affects the film topography and the surface roughness (Fig. 2.9). The rms roughness increases slightly from 1.2 nm (Fig. 2.9a), 1.3 nm (Fig. 2.9b), 1.4 nm (Fig. 2.9c) to 1.5 nm (Fig. 2.9d). Despite the large lattice mismatch between SmOFeAs and MgO the epitaxial relation is [100](001)SmOFeAs  [100](001)MgO , which could be a result of domain matching epitaxy. A thickness study has indicated pseudomorphic growth for ultrathin films, however with increasing thickness 3D growth becomes dominant [163]. PLD of Fe-oxyarsenides still suffers from low reproducibility, growth studies need further attention.

2.1 Pulsed Laser Deposition

63

Co substitution Film growth studies of LaOFe1−x Cox As and SmOFe1−x Cox As constituted an intermediate step towards mastering an all in-situ PLD process for F-substituted Feoxyaesenides. Compared to LaO1−x Fx FeAs (SmO1−x Fx FeAs) the Co-substituted sister compound has only a maximum Tc of 13 K (17 K), however, in the PLD process (non-volatile) Co can be controlled significantly better than (volatile) F. The stoichiometric transfer of Co from the targets to the films was proven by AES depth profile analysis. Epitaxial films grown on MgO(100) substrates did not show superconductivity down to 2 K, possibly due to tensile strain. PLD of Fe-oxyarsenides remains much more difficult compared to 122 Fe-pnictides. In a recent growth study [164] Cosubstituted Fe-oxyarsenide thin films were deposited on MgO(100), LaAlO3 (100), MgAl2 O4 (100) and CaF2 (100) substrates under the same conditions. Strong XRD intensities of the Fe-oxyarsenide 00 reflections were found on MgO and on CaF2 , whereas only weak 00 reflections of the Fe-oxyarsenide phase appear on LaAlO3 and on MgAl2 O4 . All films contained a small fraction of impurity phases, mainly Fe, FeAs2 , SmAs and Sm2 O3 . The SmOFe1−x Cox As (x = 0.07, 0.15) films show an incomplete superconducting transition below 7.5 and 8.5 K on LaAlO3 and on MgAl2 O4 . The best result was obtained for film growth on CaF2 which only contained an Fe impurity phase and showed a Tc,on = 14.2 K. The resulting films are SmO1−x Fx Fe1−y Co y As due to F-diffusion from the substrate into the film. The upper critical field, μ0 Hc2 , of this film reached 21 T ( c) and 38 T ( ab) at 2 K (Sect. 6.6.2). It was concluded that the superconducting state in the Fe-oxyarsenide films is sensitive to strain. LnO(Fe1−x Cox )As (Ln = La, Sm) with varying x were also deposited successfully on BaFe2 As2 /MgO [41, 165]. It was shown, that Co diffuses from the top into the bottom layer during film deposition at high temperatures of 850 ◦ C. As a result, the originally undoped BaFe2 As2 layer becomes Co-enriched and electrondoped while the Co-content of the LnO(Fe1−x Cox )As layer reduces compared to the Co-content of the target. A superconducting state with Tc = 20.5 K was obtained in a SmO(Fe1−x Cox )As/Ba(Fe1−x Cox )2 As2 and 18.8 K in a LaO(Fe1−x Cox ) As/Ba(Fe1−x Cox )2 As2 bilayer, where the diffused Co-content of the bottom layer was explicitly indicated in the formulas. F Substitution Handling the transfer of volatile elements is challenging for PLD. The conventional approach in the deposition of compounds containing a volatile element advises the enrichment of the target with that element in order to compensate for the losses. According to this approach the target becomes the source for an additional material supply. However, this method also fails for F at high deposition temperatures. Consequently, another source for F supply had to be found, which could be either (i) F-containing gas resulting in a reactive PLD process, or, (ii) the substrate, which induces a chemical reaction or diffusion process, respectively (Fig. 2.10). For an insitu incorporation of F into SmOFeAs during the PLD process the latter method was successfully employed first in 2016 by using alkaline earth fluoride substrates (CaF2 , SrF2 , BaF2 ) [13, 41].

64

2 Thin Film Growth of Fe-Based Superconductors

Fig. 2.10 PLD of compounds with volatile components (adapted after [13]): a Conventional method based on the modification of the target composition: The target (T) is enriched with the volatile component. b Diffusion method: The substrate (S) acts as source for an additional supply of the volatile component. (F) denotes the film and (L) indicates the laser beam

Alkaline earth fluorides belong to the class of ion conductors where the mobility of ionic defects and, therefore the electrical conductivity, is thermally activated. Correspondingly, diffusion of F− anions is activated at high temperatures. Selected studies that have reported interfacial chemical reactions and F diffusion from CaF2 substrates into the as-grown thin film are listed in Table 2.16. Moreover, F diffusion from SmF3 cap layers was also successfully used for electron doping of the MBEgrown SmO1−x Fx FeAs thin films [166, 167]. F-diffusion from a CaF2 cap layer was reported for MBE-grown NdO1−x Fx FeAs thin films at 800 ◦ C [168]. Such a cap layer strategy is typical in the development of MBE-grown Fe-oxyarsenide thin films (see Sect. 2.2.6). There, F-diffusion from CaF2 substrates never seemed sufficiently strong for obtaining superconducting films with high Tc and a complete transition, which may be a result of growth temperatures below 700 ◦ C. The best result was reported in [169] for a MBE-grown SmO1−x Fx FeAs film with Tc,onset ≈ 50 K and a resistive transition width of 9 K. PLD-grown films deposited for 15 min showed similar Tc,onset and transition widths. In general, the deposition of Fe-oxyarsenide thin films by PLD is carried out at temperatures above 800 ◦ C instead, which should result in an enhanced diffusion. At present this diffusion process is not yet fully optimized. Although interfacial reactions between Fe-chalcogenide thin films and CaF2 substrates are also reported (Table 2.16) their growth temperatures of 300–400 ◦ C are too low in order to activate a strong fluorine diffusion process. The formation of CaSe at the film/substrate interface rather points towards a passivation of the CaF2 surface. During PLD of SmO1−x Fx FeAs a passivation of the CaF2 surface could happen with the activated anion interdiffusion process (mainly F− ←→ O2− ), but the possible formation of CaO at the interface was not yet observed experimentally. In a TEMEDS study anion and—to a much smaller content—cation interdiffusion was found

2.1 Pulsed Laser Deposition

65

Table 2.16 Reported reactions between CaF2 substrates and thin films of different compounds Compound Deposition p (mbar) TS ( ◦ C) Interface Analytical Refs. method reaction method YBa2 Cu3 O7−δ FeSe

PLD PLD

160 (O2 ) 6·10−6

800 300

Ba(Fe1−x Cox )2 As2 PLD

10−9

700

SmO1−x Fx FeAs

10−9

650

MBE

F− ←→ O2− XPS CaSe TEMEDS BaF2 TEMEDS − 2− F ←→ O

[170] [67] [134] [169]

at the SmOFeAs/CaF2 interface [171]. Analytical TEM investigations are, however, limited due to the strong reactivity of alkaline earth fluorides with electron beams. The SmOFeAs unit cells grow with a 45◦ -in-plane-rotation with respect to the fluoride unit cell (Fig. 2.11a): [100](001)SmOFeAs  [110](001)CaF2 . PLD-grown SmO1−x Fx FeAs thin films have several peculiarities that originate from the diffusion process. From a technical viewpoint thin film growth is yet restricted to alkaline earth substrates. The superconducting properties of the films reflect the presence of a diffusion gradient resulting in broad resistive transitions and a layered hybrid structure with a higher F-content near the film/substrate interface and a vanishing F-content near the film surface (Fig. 2.11b, c). Based on AES depth profiling and TEM-EDS mapping of a film cross section, F could be detected up to a

Fig. 2.11 a Pole figure for 2θ = 30◦ (Cu Kα). b Typical hybrid structure of PLD-grown SmO1−x Fx FeAs thin films: The F-gradient along the film thickness divides the film in a superconducting and a non-superconducting layer. c Resistive transitions for μ0 H  c = 0, 1, 2, 4, 6 and 8 T. The transition width, Tc = Tc,90 − Tc,10 , is ∼10 K. (Adapted and reprinted with permission from Figs. 2e and 4a in [41]; Reprinted from Fig. 1c in [171]; © IOP Publishing. Reproduced with permission. All rights reserved)

66

2 Thin Film Growth of Fe-Based Superconductors

distance of 10 nm from the substrate into the film, which serves as an estimation of the effective thickness, teff , of the superconducting layer [171]. With a decreasing F-content along the film thickness the top layers of the film are non-superconducting and may even exhibit an antiferromagnetic phase as suggested from the electronic phase diagram for F-substituted Fe-oxyarsenides. The longer the CaF2 substrate is held at high temperatures the larger the F-content in the films. This was proven indirectly by increasing the deposition time from 10 to 15 min which corresponded to an increase of Tc,90 by 10 K (from 32.6 to 42.8 K).

2.2 Molecular Beam Epitaxy 2.2.1 Overview Molecular beam epitaxy (MBE) is a physical vapor deposition method that was developed during the 1960s and 1970s, initially by Alfred Y. Cho and John R. Arthur at the Bell Laboratories [172]. The slow film growth rates in MBE (typically 1 monolayer per second) favor a high control over film thickness and chemical composition as well as doping, a low impurity content and a high reproducibility of film growth once the parameters are found. This made MBE an ideal tool for the growth of semiconductors and heterostructures. Today, MBE has been successfully employed in the growth of various compounds including Fe-based superconducting thin films. MBE uses elemental or molecular beams that are emitted in an UHV environment from sources inside effusion cells or other special cell types, for example, cracker cells and electron-beam evaporators. The material supply is basically controlled by shutters which open and close the cells. The UHV environment (typical pressures in the range of p = 10−10 mbar) is essential for the molecular beams since it ensures a long mean free path of the evaporated species (lmfp ∝ kB T / p), so that they can reach the heated substrate without scattering events. The original Knudsen thermal effusion cell (‘K-cell’) is characterized by a small aperture compared to larger ones of modern effusion cells. The beam intensities should achieve typical growth rates of 0.1–1 Ås−1 . The material that is evaporated (or sublimated) is placed into containers or crucibles made of pyrolytic boron nitride (pBN), graphite, Ta, W, or Al2 O3 . The crucibles are conventionally resistively heated and have an installed thermocouple at the source. Effusion cells operate up to 1400 ◦ C. Their temperature is controlled via a feed-back loop from the thermocouple to the power supply. For the evaporation of sources with low vapor pressure either hightemperature effusion cells or electron-beam evaporators are used (Table 2.17). For example, Fe has a low vapor pressure (8.8×10−5 mbar at 1200 ◦ C). In the growth of Fe-oxyarsenides thin films, Fe is evaporated at temperatures above 1000 ◦ C from effusion cells using Al2 O3 crucibles [173] or effusion cells with an Al2 O3 coated tungsten basket [174]. Cells with pBN were not used, after a reaction of Fe and the crucible was found at temperatures of 900–1000 ◦ C. In the growth of FeSe thin films

2.2 Molecular Beam Epitaxy

67

Table 2.17 Vapor pressures for selected sources at different temperatures and recommended crucible materials Source Vapor pressures (mbar) at Crucible material 300 ◦ C 500 ◦ C 1000 ◦ C K Se Te Li Ba Fe

0.44 0.32 3.6×10−4 1.2×10−6 1.6×10−8

44.5 57.5 1 4.8×10−3 1.9×10−4 700 ◦ C interdiffusion between film and substrate was reported [253]. Films deposited under additional K flux did not contain K when the substrate temperatures were TS > 300 ◦ C. However, a decrease in substrate temperature without readjusting the As flux (i.e. the background As pressure, pAs ) did not produce the 122-phase. It was shown in [176] that for K-substituted films the optimal value of pAs was ∼9×10−8 mbar (Sr1−x Kx Fe2 As2 ) or ∼4×10−8 mbar (Ba1−x Kx Fe2 As2 ) when TS was set to 340 ◦ C in contrast to ∼2.7×10−6 mbar for undoped films. No 122-phase formation was revealed for pAs ≤ 2.7 × 10−8 mbar. It was furthermore noted, that a too high Fe-

2.2 Molecular Beam Epitaxy

85

Table 2.19 Reported growth parameters for SrFe2 As2 , Ba2 As2 and their K-substituted compounds (with x denoting the K-content). The chamber base pressure was p = 1.3×10−9 mbar. Films were ¯ grown on Al2 O3 (1102) substrates Rates (Ås−1 ) pAs (mbar) TS (◦ C) Flux ratios Refs. SrFe2 As2 0.5–0.7 (Fe), 1.2 (Sr) 0.5 (Fe) Sr1−x Kx Fe2 As2 n.a. 0.5 (Fe) BaFe2 As2 0.5 (Fe) 1.4 (Ba), 0.5–0.7 (Fe) Ba1−x Kx Fe2 As2 0.5 (Fe)

2.7×10−6

500

Sr:Fe = 1:2.4

[186]

(2.6–5.3)×10−4

540–600

n.a.

[176]

8×10−8 9.3×10−8

250 340

n.a. n.a.

[186] [176]

4×10−7 4.7×10−7

540–600 580

n.a. Fe:Ba = 2.6:1

[176] [254]

4×10−8

340

Ba:K = 1–x:2x

[176]

flux (Fe:Sr = 2.8:1) resulted in the formation of FeAs impurities [186]. The optimal value of 0.5 Ås−1 minimized the residual resistivity of the films. Best films achieved an onset of superconductivity at Tc,on = 33.2 K (Sr1−x Kx Fe2 As2 ) and 38.3 K (Ba1−x Kx Fe2 As2 ). Degradation of the films in air was prevented by coating them with a toluene-diluted polystyrene resin after removal from the growth chamber. In particular, the characterization of KFe2 As2 films remained difficult and indicated that the selected coating method was not practicable for films with higher K-content. In a further study film growth was extended on different sub¯ films were grown on MgO(100), LaAlO3 (100), and strates: Besides Al2 O3 (1102), SrTiO3 (100) [176]. The c-axis lattice parameters followed Vegard’s law for varying K-content and matched with the reported bulk values. No substrate dependence on the c-axis lattice constant was found. XRD confirmed the (001)-oriented growth, in-plane alignment was confirmed during RHEED monitoring. BaFe2 (As1−x P x )2 Like MBE-growth of K-substituted BaFe2 As2 films, the growth of P-substituted BaFe2 As2 first focused on the search for an appropriate evaporant. The generation of white phosphorus (P4 ) poses a general problem in MBE because, besides its high vapor pressure, it has a number of hazards such as inflammability and toxicity. Therefore, the use of elemental P-sources, that produce P4 -tetramer vapor that condenses inside the growth chamber, should be avoided. In addition, the well known low sticking coefficients of P4 are not favorable for film fabrication [255]. Instead, a P2 -dimer vapor can be supplied from the high-temperature decomposition of GaP. The additional Ga flux, that is controlled by the difference in Ga and P vapor pressures, is small [255], and trap systems for suppressing the Ga flux were developed

86

2 Thin Film Growth of Fe-Based Superconductors

since the 1980s [256]. Modern, commercially available sources include such a trap for separating Ga and delivering a pure P2 beam. MBE growth of BaFe2 (As1−x Px )2 films uses elemental sources of As, Ba, and Fe as well as a GaP source. The first reports on P-substituted BaFe2 As2 thin films produced by MBE can be found in [257], however without practical preparation details. Films were grown in an UHV chamber with base pressure pbase = 10−9 mbar [258]. The P-content in the films was varied by changing the cell temperature. Although As was over-supplied, the excess As was not incorporated in the films. A compositional analysis of the films by EPMA could not detect Ga impurities. The thicknesses of the investigated films was 100 nm (for a growth time of 1 h). Films were grown on LaAlO3 (100) at TS = 700 ◦ C with a (001)-orientation. Two domains, a cubeon-cube and a 45◦ in-plane-rotated orientation appeared resulting in non-epitaxial, multidomain films. Film growth on MgO(100) was carried out at higher substrate temperatures, TS , between 800 and 900 ◦ C. The in-plane texture of the films was better on MgO than on LaAlO3 . Except for the completely substituted BaFe2 P2 film, two domains with different orientation occurred in films with varying P-content. An investigation of the film surface morphology using AFM found a rms roughness of 0.52 nm (on an area of 2 μm × 2 μm) for a film grown on MgO at 850 ◦ C [259]. The fabricated BaFe2 (As1−x Px )2 films on LaAlO3 showed superconductivity in the range of x = 0.15–0.7 with Tc -values comparable to those found in single crystals. For films grown on MgO superconductivity appears already at x = 0.06. Simultaneously, smaller c-axis lattice parameters (and a larger a-axis lattice parameters) were found for the films on MgO compared to the values found in polycrystals. The authors in [258] concluded that the fabricated BaFe2 (As1−x Px )2 films on MgO are under tensile stress and explained the observed shift of the superconducting dome in electronic phase diagram (Tc (x)) by a change in pnictogen height due to strain. A similar shift of the superconducting dome in the Tc (x) electronic phase diagram was previously found for Co-doped BaFe2 As2 thin films deposited on Fe-buffered MgO(100) substrates by PLD [131] (see Sect. 6.3.3). LaO1−x Fx FeAs MBE growth of LaOFeAs with and without fluorine followed the successful growth of NdOFeAs films [260]. Knudsen cells were charged with As, Fe, Fe2 O3 , and LaF3 solid sources. The elemental arsenic source evaporates predominantly As4 molecules. LaF3 has a melting point at 1493 ◦ C and it sublimates as a molecule. Fe2 O3 reduces to Fe3 O4 at temperatures below 800 ◦ C under the loss of oxygen. The vapor pressures were 1.5×10−5 mbar (As), 1.9×10−8 mbar (Fe), 5.4×10−8 mbar (LaF3 ) and 1.6×10−7 mbar (O). Prior to Fe-oxyarsenide film growth, a 200 nm thick GaAs homoepitaxial layer was grown at 610◦ on a GaAs substrate and pretreated in the growth chamber at 630 ◦ C for 10 min in order to remove the native oxide layer. The Fe-oxyarsenide thin film was then grown at a temperature of 650 ◦ C and showed preferential (001)-orientation as well as in-plane texture. After a deposition of 1 h no superconducting transition occurred in the 17 nm thin film. After an increased deposition time of 6 h the films showed Tc,on = 4.5 K. Reference [260] offered a similar explanation as previously given for NdOFeAs thin films: LaF3 may have

2.2 Molecular Beam Epitaxy

87

reacted initially with the GaAs layer to form GaF3 that sublimed at temperatures of 650 ◦ C. Therefore, no F was detected in the thin films. For film growth times of 6 h, LaOF and Fe2 O3 impurities were found. Up to date there no further development in MBE-grown LaO1−x Fx FeAs films. NdO1−x Fx FeAs MBE growth of NdOFeAs [261] and F-substituted NdOFeAs thin films [262–264] was elaborated between 2009 and 2012. For the growth of these multinary compounds Knudsen cells with different sources were used: As, Fe, Fe2 O3 and NdF3 . The cell with elemental As provides predominantly As4 vapor. A release of O2− was expected to take place during the reduction process of Fe2 O3 to Fe3 O4 between a cell temperature of 500 and 800 ◦ C without additional increase in Fe flux, because of the low vapor pressure of Fe3 O4 . F should be supplied from NdF3 . The vapor pressures were determined by an ion gauge beam flux monitor in dependence of the individual cell temperatures. The vapor pressures were 1.5×10−5 mbar (As), 1.9×10−8 mbar (Fe), and 2.7×10−8 mbar (NdF3 ). The optimal conditions were adjusted in two steps: (i) control of the fluxes for the appropriate Nd:Fe ratio, (ii) As and O vapor pressures were adjusted. Initial film growth experiments were carried out on GaAs(100) substrates covered with a 300 nm thick homoepitaxial GaAs layer [261, 262], MgO(100) [263], and on other substrates, for example, CaF2 (100) and LaAlO3 (100) [264]. The GaAs substrate temperature was ∼650 ◦ C. Typical growth rates of the films were 0.042 Ås−1 . FeAs and NdAs were identified as impurity phases for either increased As flux or increased or decreased O flux. NdOF, Fe2 O3 , FeAs, and NdAs impurities were also detected in thicker films grown for more than 4 h, i.e. with a thickness of ∼60 nm [262]. Despite the appearance of impurity phases, thicker films were superconducting with Tc,on = 45 K (75 nm) and Tc,on = 48 K (90 nm). The puzzle was solved by further analytical investigations using EPMA and AES depth profiling (Fig. 2.15): Whereas no F was found in films with thicknesses in the range of 15–60 nm, a NdOF layer was identified on top of the thicker films with a F-diffusion gradient reaching down to the substrate. It was proposed that during the initial film growth F reacts with Ga from the GaAs layer. The formed GaF3 should sublimate immediately. With increasing NdOFeAs film thickness, however, the chance for this reaction decreased. Instead Fig. 2.15 AES depth profile for a NdO1−x Fx FeAs film grown for 6 h by MBE suggesting that a NdOF cap layer formed on top of a NdOFeAs film grown on a GaAs layer. (Reprinted from Fig. 4 in [262], with the permission of AIP Publishing)

88

2 Thin Film Growth of Fe-Based Superconductors

a NdOF layer formed on top of the film. A look on the data suggested that NdOF formation became dominant after a growth time of 4 h. The simultaneous growth of a F-reservoir on top of the NdOFeAs film and the continuous heating activated F-diffusion into the as-grown film. Further development was made in [263]. First, the reaction of F with the GaAs layer was inhibited by changing to MgO substrates. As a result, no Fe-oxyarsenide phase formed when the previously found optimal parameters were used. It was suggested that an oversupply of F was detrimental to the formation of the 1111compound. Since the Nd- and the F flux could not be changed independently when using a NdF3 source, another method had to be found for controlling their individual supply. Elemental Nd sources and Nd2 O3 molecular beams were ruled out because of the fast oxidation and the low vapor pressure, respectively. Since Ga works as a getter for F, an additional Ga flux was supplied during film growth showing that the 1111-compound grows epitaxially on MgO. The epitaxial relation was determined as [110](001)NdOFeAs  [110](001)MgO . No Ga was found in the films up to a vapor pressure, pGa = 10−7 mbar. Restoring of the NdOFeAs film growth was obtained already for pGa = 8×10−8 mbar. At this critical value also the F-content in the films vanished. Consequently, the films were again non-superconducting. Therefore, an additional NdOF layer was grown on top of the NdOFeAs films by continuing the beams from NdF3 and Fe2 O3 sources for 1 h. The thickness of the NdOF layer was 10 nm. Due to the activated F-diffusion into NdOFeAs the films became superconducting and showed a Tc,on = 45 K [263]. The method of depositing an NdOF layer on top of the F-free NdOFeAs film was repeated for film growth on GaAs, LaAlO3 and CaF2 resulting in superconducting films with critical temperatures of Tc,on = 37, 45 and 56 K, respectively [264]. Films grown on CaF2 had the highest critical temperature, the largest c-axis lattice parameter and the smallest a-axis lattice parameter. Parameters and results for NdO1−x Fx FeAs films are summarized in Table 2.20. In [168] the NdOF cap layer was replaced by a CaF2 layer with some changes in the experimental procedure: (i) The O source was changed to He-diluted O2 gas and (ii) a Knudsen cell for the supply of a CaF2 molecular beam was installed. NdOFeAs thin films were grown on MgO(100) at 800◦ with a thickness of 50 nm. Then a 25 nm thin CaF2 layer was grown (with a rate of 0.83 Ås−1 ). Growth temperatures of 800 ◦ C resulted in a very rough surface of CaF2 , which did not change after in-situ annealing at the same temperature for 30 min. When the growth temperature of CaF2 was decreased to 600 ◦ C or 400 ◦ C, followed by an annealing at 800◦ , the surfaces flattened. In contrast, no superconducting transition was recorded when CaF2 was grown at 400 ◦ C, the highest critical temperature was obtained when CaF2 was grown at 800 ◦ C (see Sect. 3.1). A striking feature of the first MBE-grown Fe-oxyarsenide thin films was their bilayer character. The incorporation of F into the films was only possibly by diffusion from either a NdOF cap layer or a CaF2 substrate, as will be discussed in the paragraph below for SmOFeAs films. In [173] MBE-growth of F-substituted

2.2 Molecular Beam Epitaxy

89

Table 2.20 Parameters and results for NdOFeAs and NdO1−x Fx FeAs thin film growth by MBE. Films were grown for 1 h resulting in a thickness of ∼15 nm Substrate TS (◦ C) Vapor pressures a (Å) c (Å) sc Refs. (mbar) 1.5×10−5 (As), 1.9×10−8 (Fe) 2×10−7 (Fe2 O3 ), 2.7×10−8 (NdF3 ) MgO 650 1.5×10−5 (As), 1×10−7 (Ga) With intentionally grown NdOF cap layer:a MgO 650 1.5×10−5 (As), 1×10−7 (Ga) LaAlO3 650 1.5×10−5 (As), 9×10−8 (Ga) 1×10−9 (Fe), 2.7×10−8 (NdF3 ) CaF2 650 Same as above GaAs

a Grown

670

at

610◦

–

8.57

No

[261]

4.023

8.576

No

[263]

3.978

8.533

Yes

[263]

3.943

8.532

Yes

[264]

3.920

8.618

Yes

[264]

for 1 h resulting in a thickness of 10 nm

NdOFeAs films was achieved without a diffusion process from a cap layer. Two factors that limited the direct growth of superconducting films in the previous experiments were identified: (i) Too low growth temperatures reduced the migration rate for the adatoms on the substrate, (ii) a large amount of N2 (in the order of 10−7 mbar) was detected in the growth chamber that originated from pyrolytic boron nitride (pBN) crucibles used in the Fe cell. After increasing the growth temperature to 800 ◦ C, exchanging the pBN crucible into Al2 O3 (reducing N2 to a pressure of 10−10 mbar), and adjusting the Ga:O2 flux ratio, a superconducting film with Tc,on = 37 K was obtained within an extremely small parameter window: pGa ∼1.9×10−7 mbar, pO2 ∼4.5×10−8 mbar. Slightly deviating conditions resulted in impurity phase formation and non-superconducting films. When the pGa was only 1.6×10−7 mbar, the 1111 phase did not grow. The growth conditions were further optimized and Tc,on improved to 50 K. SmO1−x Fx FeAs The first reports on SmO1−x Fx FeAs thin films grown by MBE appeared at the end of 2011 [166, 167, 253] and initially followed strategies of the overlayer method that was previously tested in MBE growth of NdO1−x Fx FeAs films. Analogous to the MBE growth of NdO1−x Fx FeAs the problem of F incorporation has been essential to the MBE-growth of SmO1−x Fx FeAs films, too. It is thus not astonishing, that over the past years experiments with different F sources were performed, beginning with a F-containing cap layer for a diffusion of F into the pristine Fe-oxyarsenide film. This approach was called ‘two-step growth’ in the relevant literature. MBE-growth on the 1111 compounds has then mainly focused to find a ‘one-step growth’ process by finding a F source that supplies the doping agent already during film growth. Besides

90

2 Thin Film Growth of Fe-Based Superconductors

the F supply by F-diffusion from alkaline earth fluorides, the use of molecular beams of SmF3 , FeF2 and FeF3 were investigated. In the early experiments based on a F-containing cap layer, MBE growth of Ffree SmOFeAs films was carried out in an UHV environment (with a base pressure 10−9 mbar) on LaAlO3 (100) at TS = 540–680 ◦ C, and on CaF2 (100), SrF2 (100) and BaF2 (100) substrates at 650 ◦ C. Beams from As, Fe, and Sm element sources were used. Their flux was adjusted by the cell temperature and controlled by electron impact emission spectroscopy (EIES). Fe and Sm growth rates were in the range of 0.25–0.6 Ås−1 and 0.7–1.4 Ås−1 , respectively. Evaporated As contained mostly As4 tetramers and As2 dimers. Its rate was controlled via a quadrupole mass spectrometer and an ionization gauge (noting the background As pressure, pAs ). O2 gas was supplied at a gas flow of 0.1–0.5 sccm. The growth rate of the SmOFeAs films varied between 2.8 and 3.3 Ås−2 (i.e. thicknesses of 100–170 nm for deposition times of 5–10 min). Directly after SmOFeAs film growth, a 20–50 nm thin SmF3 cap layer was grown on the film at the same temperature for 30 min. Phase-pure films could only be produced in a narrow window of O2 partial pressure. For film growth on LaAlO3 at 650 ◦ C a partial pressure of pO2 = ∼10−6 mbar was required to balance the Fe-oxyarsenide formation in favor to the impurity phase formation. A slightly increased partial pressure facilitated the growth of Sm2 O3 and FeAs, whereas SmAs was grown when pO2 was too small. The precise control of the O2 atmosphere turned out to be very important. Formation of SmOFeAs depended also on the cation fluxes: at low Sm rates (0.7 Ås−1 ) the optimal film growth appeared near ∼0.19 sccm O2 , at higher Sm rates (1.4 Ås−1 ) best conditions were reached with ∼0.30 sccm O2 . It was additionally pointed out that a stringent control of the Fe:Sm ratio was needed: Almost no SmOFeAs phase formation was observed for Fe:Sm ≤ 0.9 and Fe:Sm ≥ 1.2. At large ratios SmFeO3 impurity occurred. The optimization was carried out in maximizing the XRD intensity of the SmOFeAs (003) Bragg reflection. Typical impurity phases found in XRD measurements were SmAs, SmOF and SmO0.7 F1.6 . Films grown on BaF2 and SrF2 substrates also contained Sm2 O3 as an impurity phase [265]. The c-axis lattice parameter for films grown on LaAlO3 was 8.50–8.52 Å and similar to the bulk values, however, their crystalline quality was much poorer compared to that of films grown on CaF2 . Nevertheless, a transition temperature of Tc,on = 50 K was reached after capping the film with SmF3 and inducing F-diffusion into SmOFeAs. Among different films on the alkaline earth fluoride substrates the superconducting transition, Tc,on , varied between 42 and 57.8 K (on CaF2 ) and there was also a large spread of c-axis lattice parameters (8.49–8.64 Å) for superconducting films. The c-axis lattice constants were mostly larger compared to that of the bulk phase, indicating that the films were compressed in-plane. Reference [167] also demonstrated that the growth of SmOFeAs on CaF2 substrates could result in superconducting transitions even without the deposition of a SmF3 cap layer. An exemplary comparison is shown in Fig. 2.16 where films were grown at 0.21 sccm O2 flow at an Fe rate of 0.25 Ås−1 at 650 ◦ C with and without a 25 nm thin SmF3 overlayer. Since the only F source is the CaF2 substrate, the experiment showed that there is a non-negligible F-diffusion from the substrate into the film.

2.2 Molecular Beam Epitaxy

91

Fig. 2.16 Comparison of electrical resistivities for SmOFeAs films grown on CaF2 with and without additional SmF3 overlayer. F diffuses from the substrate as well as from the cap layer, which results in the formation of a SmO1−x Fx FeAs film. The c-axis lattice parameters and Tc,on are indicated. (Adapted from Fig. 4 in [167]; © IOP Publishing. Reproduced with permission. All rights reserved)

Subsequent studies have tested SmOFeAs thin film growth on different substrates including r-cut Al2 O3 , YAlO3 (110), MgO(100) [265] and CaF2 -buffered LaAlO3 [169]. The thickness of the SmF3 cap layer was reduced to 20–30 nm. It was found that SmOFeAs films grow in general with a single epitaxial relation to the substrate, except on MgO(100), where additional 45◦ -in-plane-rotated grains appeared together with the cube-on-cube orientation. Another variation included the test of a SmOF cap instead of a SmF3 overlayer. In a comparative experiment, films were deposited on LaAlO3 , CaF2 and Ca2 -buffered LaAlO3 . The CaF2 buffer layer was grown prior to Fe-oxyarsenide deposition at 650 ◦ C. The flux ratio between Sm:SmF3 :Fe = 0.87:0.13:1.45 and the As vapor pressure was pAs = 8.4×10−7 mbar. O2 gas was provided at 0.27 sccm. With these parameters, films on CaF2 -buffered LaAlO3 showed the best result with Tc,on = 52.2 K. The main goal, however, was the incorporation of F into the 1111-phase during film growth (called ‘one-step growth’), not via a diffusion process after film growth. For a ‘one-step growth’ three solid sources were tested (Tables 2.21, 2.22): SmF3 [169], FeF2 [266], and FeF3 [174]. Each source was coevaporated together with As, Fe, and Sm under O2 atmosphere. The use of the rare earth trifluoride, SmF3 , as source resulted in a poor reproducibility, possibly to its stability at a substrate temperature of 650 ◦ C. FeF2 decomposes at 650 ◦ C and its use for Fe-oxyarsenide growth showed improved reproducibility. Moreover, the variation of F-content in

Table 2.21 Comparison of different F sources for effusion cells in MBE: melting temperature (Tm ), deposition temperature (Td ) Source Tm (◦ C) Td ( ◦ C) Reproducibility Comment for film growth SmF3 FeF2 FeF3 a [267]

1306 1020a 1027a

900 650 1 MAcm−2 in self-field and >0.1 MAcm−2 at μ0 H = 10 T. As a consequence, research activities (predominantly for FeSe1−x Tex and Co- or P-substituted BaFe2 As2 compounds) focused on the measurement of the (depinning) critical current densities. This section shows, that Fe-based superconductors compass these benchmarks on single crystalline substrates as well as on flexible metal tapes at liquid He temperatures, but their overall performance yet demands for improvement in high magnetic fields and at higher temperatures. The challenges that are encountered in the engineering of the new superconductors adopt the techniques that were previously developed for cuprate coated conductors and MgB2 thin films, however, at present, Fe-based superconductors are not yet found as commercial materials in superconducting power applications. The most promising advances in the last years include film deposition on CaF2 substrates, CeO2 buffer layers and flexible metal tapes. Critical currents and critical current densities associated with vortex pinning are defined by Bean’s ‘critical state’, where the pinning force, Fp , balances the Lorentz force on the flux line lattice, Jc × B = Jc B sin θ . The critical current densities, Jc , are usually determined as a function of magnetic field and temperature, Jc (B, T ), either by electrical transport measurements or by magnetization measurements. In electrical transport measurements, a DC current, I , is ramped up until a voltage drop occurs. The voltage drop follows a power law

6.1 Vortex Matter in Thin Films

261

Fig. 6.2 a SEM image of a FeSe0.5 Te0.5 nanobridge with w = 800 nm. (Reprinted with permission from Fig. 1c in [49]; © the Authors; Creative Commons CC BY license.) b SEM image of a FeSe0.5 Te0.5 bridges with w = 8 μm with a constriction (red line) smaller than 1 μm. (Reproduced from Fig. 1 in [50] with the permission of AIP Publishing.) c SEM of a FeSe nanobridge with w = 300 nm and schematic presentation of its preparation steps. (Reprinted with permission from The Korean Physical Society and Springer Nature: Fig. 2 in [51]; © (2012).)

U ∝I n ,

(6.5)

and the critical currents, Ic (B, T ), are defined for a corresponding electrical field criterion (typically 0.1–10 μVcm−1 ). Transport measurements are generally carried out on thin film strips or ‘transport bridges’ with a defined cross section given by thickness and width, t × w. Depending on the size they are also called ‘microbridges’ or ‘nanobridges’. Their preparation includes mechanical cutting, photolithography, Ar+ ion etching or wet etching and structuring by FIB using Ga+ ions. Micro- and Nanobridges The fabrication of superconducting nano- and microbridges does not only play an important role in the determination of critical transport currents. They are elements in nanoscale electronic devices, junctions and essential in the design of bolometers. Examples of nanobridges are shown in Fig. 6.2. The dimensions of the bridge and its edges influence the current-voltage-characteristics, especially when the width, w, becomes comparable to or smaller than the penetration depth, λL or when it approaches the Likharev limit of 4.4ξGL (T ) [42]. Damage of the superconducting material in the preparation of the transport bridges can not be avoided completely and results in altered properties (suppression of Tc , increase or decrease of Jc ). For example, the effects of laser and FIB cutting were described as heating, redeposition and injection of milling ions [6]. In [47] etching of a 100 nm thin FeSe0.5 Te0.5 film on MgO by an Inductively-Coupled Plasma (ICP) resulted in a change of Tc (ΔTc ) from a very large value, 17.5 K (1.5 K) to 5.9 K (3.3 K) and a thickness reduction to 30 nm due to overetching. Reference [48] reports a much stronger Tc -suppression after electronbeam lithography Ar+ ion etching of a Ba(Fe1−x Cox )2 As2 /Fe/MgAl2 O4 film protected by a 20 nm thin Au layer on top compared to a Ba(Fe1−x Cox )2 As2 /Fe/MgO film with a 100 nm thin Au protection layer on top. Micro- and nanobridges are required for the determination of depairing currents (Table 6.2). The depairing current is defined as the maximum supercurrent that can be

262

6 Thin Film Studies Under Focus

Table 6.2 Depairing current densities in Fe-based superconductors (extrapolated for T = 0). For c ab comparison, calculated values are given for T = 4.2 K (Jc,dp –Jc,dp ) Compound

Jc,dp (0 K) (MAcm−2 )

Refs.

FeSe FeTe/Bi2 Te3 FeSe0.5 Te0.5 (Ba0.5 K0.5 )Fe2 As2 Ba(Fe1−x Cox )2 As2

52 150

[54] [55]

944 ∼4

[53] [52]

calc (4.2 K) Jc,dp (MAcm−2 )

Refs.

16.7–24.6

[56]

14.5–27.2, 46.5

[52, 56]

carried before the Cooper pairs break apart. For most superconductors, the depairing current densities are in the range of 107 –109 Acm−2 . Within the Ginzburg-Landau theory its temperature dependence is given by Jc,dp (T ) = Jc,dp (0)(1 − T /Tc )3/2 , where φ0 . (6.6) Jc,dp (0) =  3 3π μ0 λ2 (0)ξ(0) Reference [52] documents an early attempt in the assessment of the depairing current density, Jc,dp . The 90 nm thin Ba(Fe1−x Cox )2 As2 film was grown by PLD on (La,Sr)(Al,Ta)O3 and the microbridges had widths of 1 < w < 10 μm. It was shown, that Jc,dp (T ) could be described by the Ginzburg-Landau theory down to temperatures of 0.4Tc , where it reached values of 2–2.5 MAcm−2 . A value of ∼4 MAcm−2 was extrapolated for T = 0. For a (Ba0.5 K0.5 )Fe2 As2 microbridge (w = 2 μm) the depairing current density was experimentally investigated in [53]. The microbridge was prepared from a cleaved sheet of a single crystal that was further thinned down to a thickness of 91 nm by Ar+ ion etching (200 V, 0.25 mAcm−2 ). A value of Jc,dp (35 K) = 10.8 MAcm−2 was measured. Based on a Ginzburg-Landau analysis Jc,dp (0) was estimated to be 944 MAcm−2 . The preparation of nanobridges (w = 300 nm, l = 100 nm) on 1 μm thin FeSe films deposited on Al2 O3 substrates was described first in [51]. After photolithography and Ar+ ion etching, further patterning was carried out using FIB with Ga+ ions (9 pA). Tc,on and Tc,0 were 11 and 6.7 K for the as-grown FeSe film, 10 and 6 K after Ar+ ion etching and also after FIB processing. At 4.2 K a critical current, Ic , of 17 mA was obtained, which corresponded to a critical current density of 5.67 MAcm−2 . It was, furthermore, noticed that the nanobridge suffered from degradation during a few months. In a different study on ultrathin FeSe films a depairing current density of 5.2 × 107 Acm−2 was estimated [54]. Reference [55] reports on the current-induced depairing in a 7 nm thin FeTe/Bi2 Te3 heterointerface. Transport bridges with w = 11.5 and 12 μm and l = 285 μm were patterned by photolithography and Ar+ ion milling. In [49] current-induced switching from the superconducting to the resistive state was analyzed for FeSe0.5 Te0.5 nanobridges (w = 500, 800 nm; l = 3 μm; t = 100 nm) on CaF2 substrates. At

6.1 Vortex Matter in Thin Films

263

4.2 K the critical current densities were 3.2 × 104 and 8.1 × 105 Acm−2 . The pinning potential range was estimated to be 6–25 nm, depending on the bridge width (500–800 nm). Pinning Forces and Defects In magnetization measurements, the critical current density is proportional to the hysteretic magnetization (loop width), Jc ∝ ΔM, and can be evaluated by applying the Bean model. The pinning force is derived from the critical current densities through (6.7) Fp (B, T ) ∝ |Jc (B, T )B| , for a configuration where Jc ⊥B. Information about the defect microstructure and the vortex pinning mechanism can be extracted from the magnetic field dependence of Fp . For a detailed analysis, the normalized pinning force, f p = Fp /Fp,max , is plot against the reduced field, b = B/Birr , with Birr = μ0 Hirr being the irreversibility field. f p (b) vanishes at the boundaries b = 0 and b = 1 and shows a maximum between, as shown by Fietz and Webb [57] and discussed empirically by Kramer [58]. f p (b) scales with temperature describing a universal curve C(T )b0.5 (1 − b)2 , where C(T ) is a temperature (and strain) dependent constant. From this, Kramer proposed the estimation of the irreversibility line from the linear extrapolation of (Jc )0.5 (b)0.25 ∝ (1 − b) to zero (‘Kramer plot’). Dew-Hughes [59] introduced a generalized scaling approach (6.8) f p = C(T )b p (1 − b)q , b = B/Birr with at least three important scaling parameters: Birr and the two exponents for the magnetic field dependence, p and q. The scaling parameters contain technologically important information for applications like superconducting magnets and cables. Within this approach, the type of the pinning mechanism (magnetic or core pinning) and the dimensionality of the pinning centers (point, surface, volume) are derived from the exponents. For example, vortex core pinning at point-defects results in p = 1 and q = 2 with a pinning force maximum at b = 0.33, whereas p = 0.5 and q = 2 with a pinning force maximum at b = 0.2 results from core pinning at planar defects. Core pinning at volume defects results in p = 0 and q = 2 and shows a monotonic decrease with magnetic field (Fig. 6.3). Fe-chalcogenide thin films are characterized by almost isotropic critical current densities and a predominant core pinning by point-defects. Point defects could be generated by Te substitution. Several studies have mentioned an enhancement in vortex pinning with higher Te content. Examples can be found in [60], where also a vortex liquid – vortex glass transition was proposed for FeSe1−x Tex films with high Te content, or in [61] with similar observations for FeSe0.1 Te0.9 films. FeSe1−x Tex films with different Te contents showed a maximum impurity scattering for x = 0.43, and significant changes in Hall coefficient in the range of x = 0.43–0.85 pointed towards modifications in the band structure with a stronger sensitivity of the hole band to Te substitution [62]. TEM investigations found small defect clusters with a cross section

264

6 Thin Film Studies Under Focus

Fig. 6.3 Reduced pinning force, f p , versus b = B/Birr for selected pinning mechanisms and defects according to Dew-Hughes (see text and Table 6.3)

smaller than 5 × 20 nm2 in FeSe1−x Tex films deposited on CaF2 substrates [63] and a subsequent pinning analysis proposed also core pinning on point defects [64]. Compared to the almost isotropic Jc in films grown on CaF2 , films on SrTiO3 exhibit a weak Jc -anisotropy with Jcc > Jcab , indicating c-axis-oriented pinning. Threading dislocations were proposed to be active pinning sites in PLD-grown FeSe0.5 Te0.5 films on SrTiO3 substrates [65]. The films were deposited with a thickness of 100 nm and revealed strong pinning with a single vortex pinning regime up to μ0 H = 9 T. The films showed larger Jc values for μ0 H  c than for μ0 H  ab. At 4 K Jc,sf = 4 × 105 Acm−2 and remains above 105 Acm−2 at 9 T. STM topographic images revealed a homogeneous distribution of darker spots with a nearest c neighbor distance of 10 nm (corresponding to a matching field of Bφ ≈ 20 T). These defects were 2 nm in diameter and Since they were only found in films grown on SrTiO3 , it was speculated that the outgassing O2 in UHV before deposition facilitated the defect formation. The pinning force analysis for films deposited on CaF2 suggested a δl-pinning mechanism (due to fluctuations of the mean free path, l) with a mixed interactions between vortices and point- as well as surface defects [66]. For the sake of completeness it is to note that FeSe0.5 Te0.5 films deposited on LaAlO3 substrates exhibit a Jc -anisotropy with Jcab > Jcc as expected from the electronic mass anisotropy [67]. Scaling of the pinning force was found for sputtered FeSe films on SrTiO3 (110) substrates [68]. Exponents p = 0.5 and q = 2 indicated core pinning on surfaces. Grain boundaries and a small number of voids were mentioned as possible pinning active defects. Vortex pinning was also analyzed in (Li,Fe)OHFeSe films without and with Mn-addition [69]. The critical current densities determined at 1 μVcm−1 showed an increase from ∼0.3 × 105 (pure) to 3.2 × 105 Acm−2 (with Mn) in the high magnetic field region at 33 T. Jc at ∼10 T increases from ∼1.2 × 105 (pure) to Jcc . The measurements were performed in high magnetic fields (μ0 H = 35 T) on a microbridge (w = 40 μm,

6.1 Vortex Matter in Thin Films

267

Table 6.4 Self-field critical current densities in BaFe2 (As1−x Px )2 thin films Method

Substrate

x

t

Tc,on

w

E-crit.

(nm)

(K)

(μm)

(μVcm−1 ) (MAcm−2 @ K)

50

Jc,sf @ T

Refs.

PLD

MgO

0.34

90

26.5

10

3.5 @ 4.2

PLD

(La,Sr)(Al,Ta)O3

0.26

130

28.5

1

5@4

[80] [81]

PLD

MgO

0.22

130

26.5

1

6.7 @ 4

[81]

PLD

MgO

0.22

150–200

26.5

MBE

MgO

0.22

107

30.7

MBE

MgO

0.32

100

1

7@4

[84]

40

1

6.3 @ 4.2

[83]

30

1

7.3 @ 4

[82]

l = 1 mm) that was prepared by laser cutting. Except the self-field value, Jc (B) in the MBE-grown film is slightly lower than in the PLD-grown films [81, 84]. No conclusion was provided from the evaluation of the pinning forces at 4.2 K, but the inspection of Fp (b) suggests p ≈ 0.5 and q ≈ 2, that is indicative of core pinning at planar defects. Vortex Pinning in Films Grown on CaF2 Substrates Reference [85] pointed out first that FeSe1−x Tex (xnom = 0.5) thin films on CaF2 substrates potentially show high critical current densities of Jc (10 T, 4.2 K) = 5.9 × 104 Acm−2 (at 1 μVcm−1 ), however the reported data was limited at that time. During the last years the improvement of critical current densities in FeSe1−x Tex films deposited on CaF2 substrates progressed from Jc,sf (4 K) ≈ 3 × 104 Acm−2 in [86] to 1 MAcm−2 [87] and Jc,sf (4.2 K) = 1.36 MAcm−2 , in [64]. In [86], films with Tc = 20.6 K were directly deposited on small strips (w = 1 mm) and were neither processed by photolithography, nor underwent Ar+ ion etching. In [87] the transport critical current densities were measured on microbridges (w = 10, 20 and 50 μm, l = 65 μm), that were fabricated by photolithography and Ar+ ion etching (500 eV, 0.1 mAcm−2 ), and in [64] the microbridges of FeSe0.5 Te0.5 films on CaF2 had dimensions of w = 20 μm, l = 100 μm and were also fabricated by photolithography and Ar+ ion etching. The magnetic field dependence of Jc is shown in Fig. 6.5a. Jc (θ ) does not show a strong anisotropy with small variation between μ0 H  c and  ab [64, 87]. The recent developments suggest that films grown on CaF2 substrates are able to carry higher critical current densities than films grown on other substrates (LaAlO3 , SrTiO3 , YSZ) deposited at comparable conditions. Benchmarks of 1 MAcm−2 at 4 K were obtained in self-field in films with [87] and without [64] reaction layer between film and substrate. Less attention has been paid on the processing conditions (Ar+ ion etching) in the fabrication of the microbridges (Table 6.5). A δl-pinning mechanism was suggested for FeSe1−x Tex films on CaF2 in [66]. There, the result of a pinning force analysis was interpreted as a mixture of core pinning on point-defects as well as on surface defects. A similar discussion is provided by [12], where vortex pinning was described as a mixture of δl-pinning on point-like defects (∼66%) and on surface defects (∼34%) based on weighted contributions for vortex pinning by two types of defects. It was pointed out that the actual composition of the PLD-grown films at TS = 550 ◦ C is Fe1.02 Se0.68 Te0.32 or Fe0.98 Se0.67 Te0.33

268

6 Thin Film Studies Under Focus

Fig. 6.5 Critical current densities in a FeSe1−x Tex and b Ba(Fe0.92 Co0.08 )2 As2 films on CaF2 substrates. Data taken from Fig. 4a in [64] and Fig. 2a in [70]. Both compounds exhibit a modest decrease of Jc with magnetic field at liquid He temperatures Table 6.5 Self-field critical current densities, Jc,sf (4 K), in FeSe0.5 Te0.5 films on CaF2 (1 μVcm−1 ). The films were prepared by PLD under similar conditions (see text) Bridge w (μm) Tc (K) Jc,sf (Acm−2 ) Refs. fabrication Deposition on 1000 thin strip Photolithography, 10–50 Ar+ ions

20.6

3 × 104

[86]

20.6

1 × 106

[87]

and thus deviates strongly from the nominal one [12, 73]. Alternatively, the nature of vortex pinning in FeSe0.5 Te0.5 on CaF2 was described as δTc -pinning at 3D-like defects [73]. Transport critical current densities in Ba(Fe0.92 Co0.08 )2 As2 films grown by PLD under HV conditions were measured in [88]. Transport bridges (w = 40 μm, l = 1 mm) were fabricated from films with Tc,0 = 25.4 K by laser cutting. TEM investigations revealed a reaction layer between film and substrate, stacking faults and threading dislocations through the whole film cross section. The dislocation denc sity corresponds to a matching field Bφ < 3 T. The angular dependence of Jc (θ ) below and above the matching field indicates different pinning regimes for different temperatures. Concurrent weak pinning at dislocations and strong pinning at pointdefects was proposed. Jc,sf (4.2 K) = ∼3 MAcm−2 and Jc falls below 1 MAcm−2 in magnetic fields above 2.6 T and below 105 Acm−2 above 25 T (at 1 μVcm−1 ). A multilayer deposition was efficient in further increasing the pinning force to Fp = 70 and 84 GNm−3 for μ0 H  c and  ab at 4.2 K. The pinning force increased by ∼60% compared to films grown from a single target. In 150 nm thin Ba(Fe0.92 Co0.08 )2 As2 films deposited on CaF2 substrates the transport critical current densities reached self-field values of above 1 MAcm−2 in a

6.1 Vortex Matter in Thin Films

269

wide temperature range from 4.2–20 K [70]. The films had a Tc,0 = 24.5 K. Jc measurements were performed on microbridges (w = 20 μm, l = 100 μm) fabricated by photolithography and Ar+ ion etching and an evaluation criterion of 1 μVcm−1 was used. Jc (B) is shown for various temperatures in Fig. 6.5b. The inspection of the film cross section by TEM revealed stacking faults parallel to the ab-planes with a spacing of 5–10 nm. In addition, defects are visible parallel to the c-axis of the film. A pinning analysis pointed towards core pinning at surface defects for μ0 H  ab and a core pinning mechanism at point defects for μ0 H  c. A similar study [7] investigated the transport critical current densities in 100 nm thin Ba(Fe0.95 Ni0.05 )2 As2.05 films on CaF2 . Transport bridges with w = 16 μm and l = 100 μm were prepared by photolithography and Ar+ ion etching. A criterion of 1 μVcm−1 was used. Jc,sf (4.2 K) = 1.14 MAcm−2 , but Jc decreases by one order of magnitude in magnetic fields up to 9 T. Based on the temperature dependence of Jc /Jc (0), δl-pinning was described as dominant mechanism for magnetic fields up to 2 T. A vortex glass phase was proposed. In [89] Jc,sf (4.2 K) determined by magnetization measurements is 2.8 MAcm−2 and Jc = 8 × 104 Acm−2 at 12 T and 4.2 K for a Ba(Fe0.95 Ni0.05 )2 As2.1 film on CaF2 . Pinning Enhancement by Secondary Phases Vortex pinning can be enhanced by secondary (impurity) phases, by introducing nanoparticles of a secondary phase into the Fe-pnictide or Fe-chalcogenide matrix, or by engineering heterostructures (using buffer, cap or interlayers). Two types of nanoparticles can be found in Fe-based superconductors: (i) naturally occurring, nano-sized secondary (or impurity) phases that are result of the growth process and (ii) artificially included secondary phases and nanoparticles (see also Sects. 5.1 and 5.4): • naturally occurring BaFeO3−x nanoparticles/-rods in Ba(Fe1−x Cox )2 As2 films; • heterostructures/superlattices in FeSe1−x Tex films with artificially grown CeO2 buffer, cap and interlayers or with magnetic (CoFe2 O4 )0.1 (CeO2 )0.9 nanocomposites; • artificially included BaZrO3 (BZO) nanoparticles in Fe-pnictide films. Among the naturally occurring impurity phases, there are typically Fe-containing phases, such as Fe nanoparticles, Fe3 O4 nanoparticles, and perovskite-like BaFeO3−x . BaFeO3−x is a naturally occurring secondary phase in the PLD growth of Ba(Fe1−x Cox )2 As2 films on SrTiO3 -buffered substrates under HV conditions [90– 92]. It turned out, that it grows in the shape of nanorods and nanoparticles (see Sect. 5.4) that may have favorable flux line pinning properties. Due to the orientation of the nanorods parallel to the c-axis lattice constant to the Fe-pnictide film, enhanced pinning in magnetic fields μ0 H  c can be expected. A first assessment of the critical current densities in films containing BaFeO3−x nanorods revealed Jc,sf between 5.5 × 104 –105 Acm−2 at 12 K [77]. The films with a thickness of 350 nm were deposited on SrTiO3 -buffered (La,Sr)(Al,Ta)O3 substrates with buffer layer thicknesses of 50, c (12 K) ≈ 100 and 150 uc. Best values, Tc,0 = 20.5 K, Jc,sf (12 K) = 105 Acm−2 , Fp,max

270

6 Thin Film Studies Under Focus

Fig. 6.6 Critical current densities in Co-substituted BaFe2 As2 films without and with secondary BaFeO3−x phases. Data taken from Fig. 4 in [93], Fig. 5 in [94], Fig. 2 in [95]

5 GNm−3 were obtained for a buffer layer thickness of 100 uc. The angular dependence of the transport critical current densities showed a pronounced maximum for μ0 H  c, that is in accordance with the defect structure. For μ0 H  c the pinning force analysis revealed p = 1 and q = 1 with a maximum at B/Birr = 0.5. According to the classification by Dew-Hughes [59] the exponents indicate core volume pinning with a pinning mechanism due to variations in the Ginzburg-Landau parameter, Δκ. In a subsequent study [95], 400–420 nm thin films were grown from pure and Oenriched targets in order to increase the fraction of nanoscale O-rich impurity phases in Ba(Fe0.92 Co0.08 )2 As2 films. Transport critical current densities (at 1 μVcm−1 ) increased to Jc,sf (12 K) = 5.5 × 105 Acm−2 in the O-enriched films, and up to Jc,sf (12 K) = 106 Acm−2 in films grown from a phase-pure target and for multilayers deposited from pure and O-enriched targets. Self-field critical current densities at 4.2 K are 6–8 × 105 Acm−2 in O-enriched films and >1 MAcm−2 in films using a pure target. Nevertheless, at 4.2 K the pinning force increased for μ0 H  c to Fp,max = 52 GNm−3 when the O-enriched target was used compared to 38 GNm−3 for the phase pure target. The pinning force maximum also shifted from 7 T to 10–15 T. The analysis of the defect structure by TEM has found thin columnar defects (nanorods) of 4 –5 nm in diameter as well as nanoparticle arrays along the ab-planes for the multilayer film. From the average spacing of 12.5 nm a matching c field of Bφ = 13.2 T was determined, that is in agreement with the experimentally determined maximum pinning force. Thicker nanorods of 20 nm in diameter were also found in the films, but these could be less effective for vortex pinning. The fraction of defects was estimated to be 12–16 vol.%. A comparison of Jc (B) in Co-substituted BaFe2 As2 films is shown in Fig. 6.6. A promising route in the improvement of vortex pinning in Fe-chalcogenide films employs heterointerfaces with CeO2 nanolayers. The structural properties of these kind of heterointerfaces were already discussed in Sect. 5.1. The development of CeO2 /FeSe1−x Tex heterostructures adapts an idea from YBa2 Cu3 O7−δ coated conductor technology and was introduced in [100, 101]. It has constantly advanced

6.1 Vortex Matter in Thin Films

271

Fig. 6.7 Critical current densities in FeSe1−x Tex films with CeO2 and CoFe2 O4 -CeO2 (CFOCeO2 ) composite intra-, buffer and cap layers: a 60 nm thin FeSe0.1 Te0.9 films with CeO2 buffer or cap layer; taken from Fig. 4a in [96]. b Effect of O2 annealing in 130 nm thin FeSe0.5 Te0.5 /CeO2 films; taken from Figs. 2,4 in [97]. c 20 nm thin FeSe0.1 Te0.9 films with nanocomposite cap; taken from Fig. 5 in [98]. d (2 pulses) CeO2 /FeSe1−x Tex multilayers compared to the pure films; taken from Fig. 6a in [99]

during the last decade and increased the self-field Jc beyond 1 MAcm−2 at liquid He temperature [76]. An increased Jc was reported for a 7 nm thin CeO2 interlayer in FeSe1−x Tex films deposited on SrTiO3 substrates [100]. The values were derived from magnetization loops at constant temperatures by applying the Bean model. The 150 nm thin films with Tc,on ≈ 12 K showed Jc (2 K,7 T) = 5 × 103 Acm−2 without and 3.8 × 104 Acm−2 with CeO2 interlayer. The self-field critical current densities increased from 3.2 × 104 to 9 × 104 Acm−2 at 2 K. The mentioned films were grown under HV (1.3 × 10−6 mbar). The increase in Jc in films with a CeO2 interlayer was explained by additional interfacial defects (dislocations) leading to additional strain fields. Furthermore, Se-rich/Te-deficient nanoclusters of 20 nm in diameter were found in films with CeO2 interlayer. Smaller nanoclusters of 10 nm in diameter were also observed in single layer FeSe0.5 Te0.5 films (without CeO2 interlayer) grown under O2 atmosphere with a pressure of 1.3 × 10−4 mbar. The enhancement of Jc was also found in FeSe0.1 Te0.9 thin films on SrTiO3 when either a CeO2 buffer or a CeO2 cap layer was introduced [96]. Films on a CeO2 buffer showed Tc,on ≈ 12.5 K and

272

6 Thin Film Studies Under Focus

a self-field Jc of 8.9 × 105 Acm−2 at 4 K and slightly above 106 Acm−2 at 2 K (Fig. 6.7a). Increased transport critical current densities were also found after O2 annealing of FeSe0.5 Te0.5 films on CeO2 buffered single crystal substrates [97]. Figure 6.7b shows the enhancement of Jc of Fe-chalcogenide films deposited on a CeO2 buffer layer and annealed in O2 atmosphere. Critical currents were evaluated at a voltage drop of 1 μV measured on a laser-patterned bridge. The inclusion of ferromagnetic precipitates in CeO2 layers, so-called (CoFe2 O4 )0.1 (CeO2 )0.9 nanocomposite, as artificial pinning centers in FeSe0.1 Te0.9 films was proposed in [98]. The study showed enhanced critical current densities, Jc , derived from magnetization measurements compared to as-grown FeSe0.1 Te0.9 films when the nanocomposite was used either as a buffer or as a cap layer. A self-field value Jc = 1.2 × 106 Acm−2 was reached at 4 K. It was argued that introduced defects as well as magnetic pinning mechanisms are responsible for the improved pinning capabilities. Figure 6.7c shows Jc (B) at 2, 4 and 8 K for a capped FeSe0.1 Te0.9 film. In [99] CeO2 /FeSe1−x Tex multilayers and quasi-multilayers were grown by PLD with the aim of tuning the pinning force. The amount of CeO2 additions was varied from 2–20 pulses between 20 nm thin FeSe1−x Tex layers. In the limit of 2 pulses, CeO2 nanoinclusions are formed rather than continuous layers with the idea of introducing strain fields within the FeSe1−x Tex film that are able to pin the vortices. In this limit, the critical current densities (self-field and up to μ0 H = 13 T) were enhanced compared to the pure FeSe1−x Tex film. Jc,sf (4.2 K) reached values above 3 MAcm−2 . Interlayers with thicknesses of 5, 10, and 20 pulses on the CeO2 target deteriorated Jc . Figure 6.7d shows Jc (B) derived from magnetization loops at 4.2–12 K with a comparison to the pure film (at 4.2 and 12 K). Finally, nanoparticles of a perovskite phase, such as BaZrO3 (BZO), can be found added in PLD-grown Ba(Fe1−x Cox )2 As2 and BaFe2 (As1−x Px )2 films. The addition of BZO and related secondary phases is a conceptual adaption of well-known engineering paths in YBa2 Cu3 O7−δ coated conductor technology. Reference [102] showed that higher and more isotropic critical current densities were achieved in 72–80 nm thin BaFe2 (As0.66 P0.33 )2 films with BZO addition. At 5 K the self-field critical current densities, Jc,sf , increased from 3 × 106 (pure film) to 3.7 × 106 (1 mol% BZO) and 5.2 × 106 Acm−2 (3 mol% BZO). At 15 K, Jc,sf increased from 1.4 × 106 (pure film) to 2.2 × 106 (1 mol% BZO) and 3.0 × 106 (3 mol% BZO). At the same temperature and at a magnetic field of 1 T the critical current densities were 1.5 × 106 Acm−2 . The 3 mol% BZO addition to BaFe2 (As0.67 P0.33 )2 films was forming nanoparticles with a diameter of 8 nm and a density of 6.8 × 1022 m−3 (average particle spacing 24 nm). In [22] the enhancement of Jc,sf (4.5 K) from 4 × 106 to ∼4.5 × 106 Acm−2 was given. The critical current densities were obtained from magnetization loops. Tc decreases by 1.3 K when 3 mol.% BZO is added. More recently, the critical currents were further increased in 80 nm thin, PLDgrown BaFe2 (As0.66 P0.33 )2 films on MgO substrates with up to 3 mol% BZO addition [103]. The BZO nanoparticles had a size of 9 ± 5 nm. The self-field critical current densities at 4 K reached 7.2 MAcm−2 . This is comparable to values found in other thin films grown on MgO without secondary phase additions (Table 6.4). Similarly,

6.1 Vortex Matter in Thin Films

273

2 mol% BZO addition in 460 nm thin Ba(Fe1−x Cox )2 As2 films resulted in Jc = 1.3 × 106 Acm−2 at 13 T and 4.2 K [104]. The enhancement of the critical currents was 14 times higher compared to pure films. Coated Conductor Development Biaxial grain alignment (texture) has been the most important issue in the growth of YBa2 Cu3 O7−δ superconductors on the flexible metal tapes, because grain misalignment with small-angle grain boundaries with a mismatch angle larger than 4◦ suppress critical current densities strongly [105–107]. In order to control the film texture in high-temperature superconductors, pre-textured IBAD-MgO-based templates on Hastelloy [108] as well as buffer layer architectures on rolled Ni-W tapes (RABiTS) were developed and optimized. For Fe-based superconductors the biaxial grain alignment is less stringent, because critical currents do not significantly decrease below a mismatch angle of 9◦ [109]. (See also the following topic in this section.) Around 2011 application-oriented research started with testing the coated conductor technology for Fe-based superconductors (Table 6.6). PLD of Fe-chalcogenide and Fe-pnictide compounds on flexible metal tapes and templates can be found for • FeSe1−x Tex films [75, 76, 110–114]; • Ba(Fe1−x Cox )2 As2 films [71, 72, 115, 116]; • BaFe2 (As1−x Px )2 films [117, 118]. Details of film growth on metal tapes are described in Chap. 2. The metal tapes are made of Hastelloy, Ni-W or stainless steel. Hastelloy C-276 is a Ni-Mo-Cr-containing corrosion-resistant alloy with W and Fe additions, that is widely used for industrial applications. The flexible tapes have a high mechanical tensile strength of 0.8 GPa [75] and can be coated in a reel-to-reel setup and wound to superconducting high field magnets. Alternatively, Ni-5 at.% W tapes with good oxidation resistance and 310 stainless steel tapes can be found in the processing of coated conductors. Recently, the commercially available Fe-Ni alloy with 36 at.% Ni (Invar 36) was also tested for Fe-chalcogenide film growth. Present research activities favor the development of FeSe1−x Tex coated conductors (Fig. 6.8a) because of their promising performance at high magnetic fields. Starting in 2011, a 100 nm thin FeSe0.5 Te0.5 film on MgO/IBAD-MgO/Y2 O3 -buffered Hastelloy tapes was presented in [75], however its critical current densities on the metal template were yet smaller than of a comparable film on a single crystalline LaAlO3 substrate. At 4.2 K Jc,sf of the coated conductor was only ∼105 Acm−2 , while for the film on LaAlO3 Jc,sf exceeded already 3 × 105 Acm−2 . In a subsequent work, the critical currents could be slightly increased in FeSe1−x Tex films on CeO2 buffered RABiTS [76]. Jc,sf (4.2 K) reached the benchmark of 1 MAcm−2 and Jc remained above 105 Acm−2 in magnetic fields of 30 T at 4.2 K. A maximum pinning force, Fp (4.2 K) ≈ 70 GNm−3 was obtained. The growth of FeSe0.1 Te0.9 films on amorphous Al2 O3 buffer layers on stainless steel tapes abandons the idea of a pre-texture and epitaxial growth of the film and was proposed as an option for cost reduction [110]. The critical current densities were

274

6 Thin Film Studies Under Focus

Fig. 6.8 Magnetic field dependence of critical current densities in different Fe-chalcogenide and Fepnictide coated conductors: a FeSe1−x Tex ; Data taken from [76, 111, 114]. b Ba(Fe1−x Cox )2 As2 ; Data taken from [71, 116]. c BaFe2 (As1−x Px )2 ; Data taken from [78, 118]. Closed symbols refer to Jc (B) for μ0 H  ab, open symbols for μ0 H  c

yet low with Jc,sf (4 K) = 2.1 × 104 Acm−2 . A direct deposition of Fe-chalcogenide films on an Invar 36 tape was tested in [112], where a 200 nm FeSe0.5 Te0.5 seed layer was first grown at 400 ◦ C with a repetition rate of 10 Hz, before the 250 nm thin, functional FeSe0.5 Te0.5 layer was grown at 200 ◦ C with a repetition rate of 3 Hz. Both examples largely simplify the coated conductor architecture, but are not competitive in their superconducting parameters at present. Further attempts in growing FeSe0.5 Te0.5 coated conductors were carried out in [111, 113], where 100 nm thin Fe-chalcogenide films were deposited on CeO2 buffered Ni-5 at.% W tapes (RABiTS) as well as on a randomly oriented native oxide layer on top of a Hastelloy C-276 tape. The highest self-field critical current densities at 4.2 K reached 1.7 × 105 Acm−2 . Chemical solution deposited (CSD) Zr-doped CeO2 (ZCO) buffer layers with a thickness of 30 nm are currently explored, but the superconducting properties of the FeSe1−x Tex films subsequently deposited on these buffer layers still need to be optimized [119]. To date, the superconducting characteristics of films grown on metal tapes are still inferior compared to those of films deposited on single crystal substrates. The present status for Fe-pnictide coated conductors requires similar attention: although high self-field current densities of 1 MAcm−2 were reached at 4 K, vortex

6.1 Vortex Matter in Thin Films

275

pinning (in particular, in high magnetic fields) must be improved. Ba(Fe1−x Cox )2 As2 films were deposited on buffered Hastelloy C-276 tapes. From top-to-bottom, the complete template is composed of a 150–160 nm thin homoepitaxial MgO layer, a 10–50 nm thin, textured IBAD-MgO layer, an amorphous Y2 O3 layer (10 nm–1 μm) and finally, the polycrystalline and electropolished metal tape. It was shown that the shape of the resistive transition is influenced by the buffer layer thickness that either avoids shunting with the Hastelloy metal tape (in case of a thick a-Y2 O3 layer) or not (for thin a-Y2 O3 layers) [120]. In [116], 130–220 nm thin Ba(Fe1−x Cox )2 As2 films were deposited on three different IBAD-MgO templates showing a FWHM, Δφ, of the MgO 202 reflection of 5.5, 6.1 and 7.3◦ . The in-plane alignment of the Fe-pnictide layer, given by Δφ of the Ba(Fe1−x Cox )2 As2 103 reflection, varied between 3.2–3.5◦ . Transport bridges with w = 10 μm and l = 300 μm and a criterion of 1 μVcm−1 were employed for the measurements of the critical currents. Jc,sf exceeded 1 MAcm−2 at temperatures below 10 K and reached values of 1.2–3.6 MAcm−2 at 2 K. The results indicated that a less well texture (of the IBAD-MgO) could be beneficial for flux line pinning. A drawback of the study is, that the film thicknesses were not kept constant as they varied between 130 and 220 nm. It should be pointed out further, that Jc,sf (2 K) = 2.2 MAcm−2 was obtained for films deposited on single crystalline MgO substrates [121] and Jc,sf (4 K) ≈ 4 MAcm−2 on (La,Sr)(Al,Ta)O3 substrates [93]. At intermediate temperatures (12 and 16 K) the transport critical current densities, Jc , exhibited a change in anisotropy from Jcc > Jcab below μ0 H ≈ 5 and 3 T, respectively, to Jcab > Jcc . At lower temperatures (4 K), Jcab > Jcc (Fig. 6.8b). In [71, 115] Ba(Fe1−x Cox )2 As2 /Fe bilayers were grown on IBAD-MgO buffered Hastelloy C-276 tapes with a buffer layer sequence as described above. The thicknesses of the homoepitaxial MgO and the IBAD-MgO layers were 40 and 5 nm [115]. In [71] the homoepitaxial MgO layer had a thickness of 160 nm. The pretreatment of the metal substrate before the deposition of the Fe buffer layer at room temperature included annealing at 800 ◦ C for 20 minutes in UHV. In [115] the critical current densities evaluated at 8 K were slightly larger than 105 Acm−2 in self-field, but dropped to 3 × 103 Acm−2 at 9 T. These values were one magnitude lower than those of a comparable bilayer on an MgO single crystalline substrate. Higher critical current densities were accomplished in [71] with Jc,sf = 2 MAcm−2 at 4 K (Fig. 6.8b). TEM micrographs revealed defects parallel to ab that could be responsible for Jcab > Jcc at constant temperature. The comparison of the critical current densities in Fe-chalcogenide and Fe-pnictide films on metal substrates (Fig. 6.8a, b) suggests that a thickness dependence cannot be excluded: it is possible that the pinning capabilities deteriorate for thicker films. Pinning properties of P-substituted BaFe2 As2 films on metal tapes with an MgO/IBAD-MgO/Y2 O3 buffer layer architecture were investigated in [78, 117, 118]. A comparison of the results shows a sample-to-sample variation and an increase for Jc for μ0 H  ab (as indicated by red arrows in Fig. 6.8c). The variation could result from different substrate temperatures (1050–1250 ◦ C) used in the deposition of the films: [117] indicates that higher substrate temperatures lead to an increase in Jc,sf from 1 to 2 MAcm−2 . At substrate temperatures higher than 1200 ◦ C, epitaxial film

276

6 Thin Film Studies Under Focus

Table 6.6 Critical current densities in thin films on flexible metallic tapes Compound

t

Tc,0 –Tc,on

Jc,sf @ T

Jc @ μ0 H ; T Refs.

(nm)

(K)

(Acm−2 @ K)

(Acm−2 @ T; K)

100

16–18.1

1.7 × 105 @ 4.2

3 × 104 @ 18; 4.2

[111]

18–20

1 × 106 @ 4.2

1 × 105 @ 31; 4.2

[76]

5–10

1.34 × 104 @ 2.5 × 103 @ 4 6; 4

CeO2 /Ni-W RABiTS FeSe0.5 Te0.5 FeSe0.5 Te0.5 a-Al2 O3 /stainless steel FeSe0.1 Te0.9

150

[110]

FeSe0.5 Te0.5 (seed)/Invar-36 FeSe0.5 Te0.5

250

[112]

LMO/MgO/IBAD-MgO/Y2 O3 /Al2 O3 /Hastelloy C-276 FeSe0.5 Te0.5

200

14–

4.3 × 105 @ 4.2

3.9 × 105 @ 9; 4.2

Ba(Fe0.92 Co0.08 )2 As2 /SrTiO3

110

19.0–20.2

1.14 × 106 @ 9.8 × 105 @ 4.2 9; 4.2

11–

2 × 105 @ 4

20.5–22

1.8 × 106 @

[114] [72]

MgO/IBAD-MgO/Y2 O3 /Hastelloy C-276 FeSe0.5 Te0.5 Ba(Fe1−x Cox )2 As2

100 220

104 @ 25; 4.2 [75] [116]

4 Ba(Fe0.9 Co0.1 )2 As2 /Fe

50/25

17.5–21

105 @ 8

3 × 103 ; 9; 8

[115]

Ba(Fe1−x Cox )2 As2 /Fe

70/25

22–24

2 × 106 @ 4

BaFe2 (As1−x Px )2

150–200

23–26

1.2 × 106 @ 4

1.6 × 105 ; 9; 4

[118]

BaFe2 (As1−x Px )2

185

–28.3

4 × 106 @ 4.2

>105 @ 15; 4.2

[78]

BaFe2 (As0.72 P0.28 )2

150–200

22.4–26.6

106 @ 4

>7 × 104 @ 9; 4

[117]

11.1–13.5

1.2 × 104 @ 5

[71]

FeSe0.5 Te0.5 (seed)/native oxide/Hastelloy C-276 FeSe0.5 Te0.5

130

[113]

growth is perturbed and 110-aligned Fe-pnictide grains occur. A similar observation was made already in [118]: higher Jc was found in films on less well aligned templates. In addition, the critical current densities decrease for P-contents, x > 0.30. The evaluated pinning force in [78] proposes core pinning on surface-like defects. STEM investigations of the defect structure revealed dislocations along the c-axis of the films [118]. However, the pinning forces only scale up to magnetic fields that correspond to the maximum of the pinning force. All transport critical currents were determined at a criterion of 1 μVcm−1 on microbridges (w = 10, 20 μm; l = 300 μm [117, 118] and w = 15 μm; l = 500 μm [78]), that were prepared by photolithography and Ar+ ion milling.

6.1 Vortex Matter in Thin Films

277

6.1.4 The Role of Grain Boundaries The influence of grain boundaries (GBs) on the superconducting characteristics (order parameter, critical currents) of Fe-based superconducting thin films is an important criterion for applications. GBs are surface defects and typically described by the misorientation between two adjoining grains. Besides a geometrical description, physical properties (electric and magnetic) can be assigned to GBs, that strongly depend on the segregation of impurities. Impurity segregation does not only alter the superconducting properties close to the GB but also increases its effective width. In Fe-based superconductors the spatial extension of a Cooper pair (measured by the coherence length) is small. GBs can thus easily lead to a suppression of the superfluid density. On the microscopic level (bond contraction model) the weak link behavior of GBs in high-temperature superconductors was qualitatively described by Guy Deutscher [122]. He argued that the tensile strain field at the dislocations diminishes the overlap of Fe 3d orbitals in the Fe2 X2 (X = chalcogen, pnictogen) planes and, in turn, weakens Cooper pairing. GBs naturally appear in polycrystalline or granular films and in films that lack in-plane alignment. In granular films, the fraction of grain volume to GBs determines regimes of either percolation or tunneling of the electronic current (see Sect. 6.2.1). For instance, studies on films grown by a two-stage process based on an ex-situ heat treatment can be insightful, for example (Ba1−x Kx )Fe2 As2 [123] and LaO1−x Fx FeAs [124]. In addition, comparison of critical current densities in epitaxial and polycrystalline LaO1−x Fx FeAs films demonstrated their enhancement by at least one order of magnitude when superconducting grains were biaxially aligned [44]: in the polycrystalline film, Jc,sf (4 K) is ∼2 × 103 Acm−2 for μ0 H perpendicular to the film plane, whereas Jc,sf (4 K) increased to ∼8 × 104 Acm−2 for μ0 H  c. The influence of GBs in granular FeSe films was investigated in [68]. The sputtered FeSe films on SrTiO3 (110) were patterned with two microbridges (w = 150 μm; l = 750 μm) ¯ S . The elongated, platelike FeSe grains are uniaxially aligned.  [001]S and  [110] The anisotropy of the critical currents was investigated by comparing the results of different orientations of the microbridges across the grains. Critical current densities of ∼104 Acm−2 are comparable to values obtained in FeSe crystals. Based on a proximity model, the power law dependence of Jc ∝ (1 − T /Tc )β with β = 2 indicates the presence of superconducting-normal-superconducting (SNS) GB-junctions. GBs with a defined misorientation angle θ are usually obtained by using bicrystalline substrates, which applies to the majority of examples discussed for Fe-based superconducting thin films. Another sophisticated method for the formation of GBs in thin films includes a specific pretreatment of the substrate. An example can be found in [125], where the in-plane alignment of FeSe0.3 Te0.7 films on MgO was controlled by Ar+ ion milling of selected areas on the substrate surface prior to deposition. As discussed before (Table 6.3), GBs also can act as pinning centers for vortices. Such a behavior is evidenced in sputtered FeSe films [68], although the pinning forces

278

6 Thin Film Studies Under Focus

Fig. 6.9 a Suppression of Jcinter (B) compared to Jcintra (B) in Ba(Fe1−x Cox )2 As2 on SrTiO3 . Data taken from [126]. b Comparison of Jc (θ) for various Fe-based superconductors compared with YBa2 Cu3 O7−δ (gray line and area). Some data sets suggest a critical misorientation angle of 9◦ and constant Jc (θ) for θ above 30◦

are weak. Claims for GB-pinning were also made for epitaxially grown, P-substituted BaFe2 As2 films [78]. Bicrystal Grain Boundaries Transport critical currents in epitaxial films on bicrystals are usually distinguished between intergrain critical currents (across the GB) and intragrain critical currents (within a grain). An important result for YBa2 Cu3 O7−δ high-temperature superconductors turned out to be the exponential decrease of the intergrain critical current densities from 108 to 104 Acm−2 with increasing misorientation angle of the bicrystal GB along a transition between strongly coupled grains to weak link behavior at misorientations of θ = 5 – 10◦ [105–107]. The fact that GBs in Fe-pnictides also act as weak links was first reported for Ba(Fe1−x Cox )2 As2 films on SrTiO3 bicrystals [127] and for polycrystalline LaO1−x Fx FeAs thin films on LaAlO3 substrates [124]. Ba(Fe1−x Cox )2 As2 films on bicrystals were studied in [109, 127–130]. Reference [127] reported first, that [001]-tilt GBs exponentially suppress the critical current densities with increasing misorientation angle θ from 6◦ to 24◦ and, therefore, act as weak links. The studied films had a thickness of 350 nm and were investigated at T = 12, 14 and 16 K. It was shown as well, that Jcinter (B) is progressively reduced compared to Jcintra (B) with increasing temperature (Fig. 6.9a). A larger study of Ba(Fe1−x Cox )2 As2 films on [001]-tilt MgO and (La,Sr)(Al,Ta)O3 bicrystal substrates has noticed that the critical current densities do not deteriorate up to a critical misorientation angle of θc ≈ 9◦ [109]. This was confirmed for Jc (θ ) at T = 4 and 12 K. For large-angle GBs with θc < θ < 30◦ , critical currents were significantly suppressed (Fig. 6.9b). In YBa2 Cu3 O7−δ superconductors on bicrystals, the minimum value for a critical angle is 4–5◦ . MO imaging proved flux penetration into the GB with larger misorientation angles [106, 131]. In the fabrication of Ba(Fe1−x Cox )2 As2 coated conductors, the advantage of θc ≈ 9◦ could lead to a cost reduction because the requirement of a well-textured template drops. The supercurrent through highangle GBs (θ ≥ 16◦ ) is predominantly governed by the Josephson current and can

6.1 Vortex Matter in Thin Films

279

be described by Jcinter ∝ exp(−θ/θc ). The GBs in the films form superconductingnormal-superconducting (SNS) junctions with Rn A = 5 × 10−11 cm2 (θ = 16◦ ) and 5×10−10 cm2 (θ = 45◦ ). The bicrystal GB junctions are metallic and do not show a hysteretic current-voltage characteristics. Analysis of the Burgers vector b in HR-TEM plan view images revealed dislocation spacings d = (|b| /2) sin(θ/2) of 5 nm (θ = 4◦ ), 1.2 nm (θ = 24◦ ), and 0.5 nm (θ = 45◦ ). Further characterization of the GBs in the mentioned films can be found in [128]. For the determination of critical currents, microbridges (w = 8 μm, l = 300 μm) were prepared by photolithography and Ar+ ion milling. Transport current densities were evaluated at a criterion of 1 μVcm−1 . The temperature dependence of Ic Rn of a 30◦ bicrystal GB junction of a Ba(Fe0.92 Co0.08 )2 As2 film on (La,Sr)(Al,Ta)O3 (microbridges with w = 10 μm) reveals clear devations from the Ambegaokar-Baratoff relation with at least three kinks [130]. A Josephson penetration depth of λJ = 1.8 μm was evaluated. Reference [129] reported the growth of Ba(Fe0.92 Co0.08 )2 As2 films on Fe-buffered MgO and Fe/MgAl2 O4 -buffered SrTiO3 bicrystals with [001]-tilt and θ = 36.8◦ and 30◦ , respectively. The Fe-pnictide films had a thickness of 100 nm, the Fe-buffer layer was ∼20 nm thin. Films were covered by a Au protection layer before transport bridges (w = 0.5 mm, l = 1 mm) were prepared by Ar+ ion beam etching. A criterion of 1 μVcm−1 was used in the evaluation of the critical currents. A weak-link behavior of GBs was confirmed. In total, no secondary phase segregation was found in or around the GBs. Reference [82] investigated a 100 nm thin MBE-grown BaFe2 (As1−x Px )2 (x = 0.24) film on a MgO bicrystal with [001]-tilt boundary and a misorientation of θ = 24◦ . For transport-Jc measurements, microbridges (w = 30 μm) were fabricated on the bicrystal by photolithography using Ar+ ion milling. The almost unchanged onset of the superconducting transition, Tc,on = 29.5 K with ΔTc = 1 K was taken as indication that the photolithographic process had little impact on the superconducting transition. (A protection layer was not mentioned.) The resulting GB-junction was metallic and showed Joule heating for high current densities. The junction was described by Rn = 4.4 m, Rn A = 1.3 × 10−10 cm2 , Ic = 8.5 mA and a fraction of 0.8 of the Josephson current. The product, Ic Rn = 37.4 μV. Jcinter = 1 MAcm−2 was measured at 4 K, whereas Jcintra was extrapolated to 7.3 MAcm−2 . This value is comparable to films grown on MgO single crystalline substrates, for which Jc was obtained from magnetization measurements. In general, it was found that the critical current densities depend on the Fe-content in the films. A variation of the Fe/Ba ratio in the films from 1.83 to 2.57 resulted in films with Tc between 28 and 30.5 K. Films with Fe/Ba ≈ 2 have the highest Tc = 30.5 K. However, Jc,sf at 4.2 K increases in Fe-rich films (Fe/Ba = 2.4), having a maximum value exceeding 10 MAcm−2 . The need of a NdOF cap layer in the MBE-growth of NdO1−x Fx FeAs films turns out to be disadvantageous in the engineering of coated conductors, as a recent work suggests [132]. NdOF/NdOFeAs bilayer films were grown on [001]-tilt MgO bicrystal substrates with misorientation angles of 6◦ , 12◦ , 24◦ and 45◦ . The GBs were analyzed by TEM-EDS and described as ‘damaged’, due to preferred F-diffusion from NdOF into the GB that assist flux flow. It was also found that, the superconducting transition of the films decreased with increasing GB misorientation angle, Tc ≈ 46 K

280

6 Thin Film Studies Under Focus

for 0◦ and 6◦ ; ∼44 K for 12◦ and 24◦ and ∼42 K at 45◦ . Critical current measurements were performed on microbridges (w = 20–40 μm, l = 1 mm) that were prepared by photolithography and Ar+ -ion etching. Jcintra was evaluated at a criterion 1 μVcm−1 for a power-law behavior U ∝ I n , and because the U (I )-characteristics across the GBs are strongly linear, Jc,inter were evaluated by the intersection with U = 0. While intra is above 1 MAcm−2 at 4.2 K, a strong reduction of the critical current densities Jc,sf with increasing misorientation angle could be noticed without indication for a critical inter ◦ inter (6 ) ≈ 4.2 × 105 Acm−2 , Jc,sf (12◦ ) ≈ 4.2 × 105 Acm−2 . For angle, θc > 0: Jc,sf larger misorientations the critical currents disappeared. It is pointed out here, that an inspection of the temperature dependence of the critical current densities through a 6◦ GB, indicates Jc (T ) ∝ (1 − T /Tc )1.5 , similar to the findings in LaO1−x Fx FeAs polycrystalline films [124]. A few studies also dealt with GBs in Fe-chalcogenide films. Recently, 1 uc, 10 uc, 20 uc and 30 uc FeSe films were grown by MBE on specially developed [001]tilt SrTiO3 bicrystals with θ = 10◦ and 30◦ [133]. Single-facet GBs were mapped by STM in the as-grown FeSe films. FeSe1−x Tex films on CeO2 -buffered [001]-tilt SrTiO3 bicrystals with misorientation angles of 4◦ , 7◦ , 15◦ and 24◦ were characterized in [134]. There, microbridges (w = 20–25 μm, l = 300 μm) were fabricated across the GBs by laser cutting and critical currents were evaluated at 1 μVcm−1 . At T = inter (θ ) decreases for misorientation angles larger than θc ≈ 9◦ , similar to 4.2 K, Jc,sf the observations made for Ba(Fe1−x Cox )2 As2 thin films discussed above. A 24◦ GB showed a resistivity of Rn A = 7 × 10−10 and Ic Rn = 22 μV. Comparable values, Ic Rn = 17.7–32.8 μV and Rn A = 1.05–1.13 × 10−9 cm2 were obtained in 150 nm thin FeSe0.5 Te0.5 films on [001]-tilt SrTiO3 bicrystals with high-angle GBs (θ = 45◦ ) [67, 135]. A summary of GB studies is given in Table 6.7. Grain Boundaries as Weak Links in SQUIDs After early explorations on junction fabrication using Fe-pnictide thin film superconductors [137], attempts to exploit GBs in the realization of Josephson junctions and Superconducting Quantum Interference Devices (SQUIDs) were made with FeSe0.5 Te0.5 [136, 138] (Fig. 6.10), (Ba0.6 K0.4 )Fe2 As2 [123] and Ba(Fe1−x Cox )2 As2 thin films [139]. A relevant quantity for Josephson junctions is a large Ic Rn product, which is fulfilled in superconducting-insulating-superconducting (SIS) GBjunctions. For Fe-based superconductors on bicrystals, a superconducting-normalsuperconducting (SNS) GB-junction behavior is manifest since the experimentally determined Ic Rn products are in the range of 20–60 μV, which are only 0.2–6% of the value obtained in YBa2 Cu3 O7−δ bicrystal GB-junctions (with 1–10 mV [107]). GB resistivities in the Fe-based superconductors are in the range of 5 × 10−11 – 10−9 cm2 and, therefore, at least two orders of magnitude smaller than those in YBa2 Cu3 O7−δ bicrystals [107]. At present, GBs are not yet more advantageous than other methods in producing weak links in Fe-based superconductors. Geometrical constrictions in nanobridges patterned by FIB have been tested as well. FeSe0.5 Te0.5 nanobridge junctions (w = 564 nm, Fig. 6.2b) exhibited a Ic Rn product of 6 mV at liquid He temperature and Shapiro steps upon microwave irradiation [50]. It was found that Ic Rn (T ) followed

6.1 Vortex Matter in Thin Films

281

Table 6.7 Selected grain boundary studies in thin films of Fe-based superconductors: GB type, critical angle (θc ), normal state interface resistivity (Rn A), the Ic Rn product at liquid He temperatures and film thickness (t) are indicated Substrate

GB type; θ

θc

Rn A

Ic Rn

Tc,on

t

(◦ )

(◦ )

(cm2 )

(μV)

(K)

(nm)

11

520

[68]

20

100

[134]

150

[135]

Refs.

FeSe SrTiO3 (110)

polycrystalline

FeSe1−x Te x CeO2 /SrTiO3

[001]-tilt; 4–24

≤9

7× 10−10

22

SrTiO3

[001]-tilt; 45

n.a.

1.05 × 10−9

32.8

SrTiO3

[001]-tilt; 10–45

≤10

13

100

[136]

Fe/MgO

[001]-tilt; 36.8

n.a.

20

100

[129]

Fe/MgAl2 O4 /SrTiO3

[001]-tilt; 30

n.a.

(La,Sr)(Al,Ta)O3

[001]-tilt; 30

n.a.

(La,Sr)(Al,Ta)O3

[001]-tilt; 3–45

≤9

MgO

[001]-tilt; 3–45

≤9

SrTiO3

[001]-tilt; 3–24

≤3

[001]-tilt; 24

n.a.

Ba(Fe1−x Cox )2 As2 100

[129]

22.6

250

[130]

5× 10−11

21.6

250–350

[109]

5× 10−10

20.7

250–350

[109]

20.7

350

[127]

29.36

100

[82]

28

700

[124]

47

160

[132]

56

BaFe2 (As1−x Px )2 MgO

1.3 × 10−10

37.4

LaO1−x Fx FeAs LaAlO3

polycrystalline

NdO1−x Fx FeAs MgO

[001]-tilt; 6–45

Fig. 6.10 Example of a GB-SQUID (SEM image) as shown in Fig. 1 in [138]: 70 nm thin FeSe1−x Tex films on SrTiO3 [001]-tilt bicrystal with θ = 24◦ . Hole area = 10 × 10 μm2 ; loop inductance, L = 25.8 pH; Ic Rn (4.2 K) = 4.4 μV. (© IOP Publishing. Reproduced with permission. All rights reserved)

n.a.

282

6 Thin Film Studies Under Focus

the Ambegaokar-Baratoff relation [140] Δ(T ) πΔ tanh . Ic Rn (T ) = 2e 2kB T

(6.9)

The above equation is derived for single band BCS superconductors. Generalizations to multiple gaps are derived in [141]. An even larger Ic Rn value of 180 mV was recently reported for a nanobridge (w = 860 nm) in a 160 nm thin FeSe0.5 Te0.5 film on SrTiO3 . A confirmation of this result could rise the application potential of Fe-chalcogenide films for high-frequency applications. For comparison, Ic Rn products in heterojunctions typically range from 10 μV (Sr(Fe1.74 Co0.26 )2 As2 / (Ba0.23 K0.77 )Fe2 As2 single crystal) [142] to 0.3 mV (Pb/(Ba1−x Kx )Fe2 As2 single crystal 4.2 K) [143]. Fe-pnictide thin film heterojunctions such as Ba(Fe1−x Cox )2 As2 / Au/PbIn [144] or Ba(Fe1−x Cox )2 As2 /TiOx /Pb [145] define SNS-junctions with Ic Rn ≈ 8 and 90 μV at 4.2 K, respectively.

6.2 Superconductor-to-Insulator (SIT) Transitions The dimensional confinement of electrons and Cooper pairs into the Fe-planes of the layered Fe-based superconductors is origin of quantum effects close to zero temperature which manifest themselves in drastic changes in the electronic properties, such as superconductor-to-insulator (SIT) transitions. SITs were experimentally found in sputtered FeSe films, in ultrathin crystalline FeSe films and in gate voltage driven electric double layer transistor (EDLT) devices using FeSe films, exfoliated flakes [146] and (Li,Fe)OHFeSe flakes covered by ionic liquids [147]. According to [148] a disorder induced SIT occurs in Ba(Fe1−x Cox )2 As2 after irradiation with 3 He+ (see also Sect. 6.8.3).

6.2.1 Granular and Crystalline FeSe Films A thickness-induced SIT was found and discussed in granular FeSe films [149]. The films with thicknesses between 1 and 1622 nm were grown on MgO substrates at 480 ◦ C by RF magnetron sputtering [150] and showed a dominant c-axis texture and a small fraction of misoriented grains. The film microstructure was described as ‘FeSe crystallites embedded in a matrix’ [151]. Thick films (t ≥ 300 nm) exhibited a full superconducting transition (bulk-like regime) with Tc = 8.6 K. (The slightly increased Tc values for films with thicknesses around 1 μm and above were explained by annealing effects due to longer deposition times at 480 ◦ C.) For thinner films (t < 300 nm) the temperature dependence of the resistance indicated a SIT that was explained in the frame of continuous quantum phase transitions [149, 151]. In contrast to thermodynamic phase transitions, quantum phase transitions occur at the absolute zero and are driven by quantum fluctuations, that are tuned by a control parameter (e.g. the film thickness, magnetic field, etc.). At the critical value of the control parameter, the ground state of the physical system changes. This is

6.2 Superconductor-to-Insulator (SIT) Transitions

283

Fig. 6.11 SIT in the temperature dependence of the sheet resistance, R (T ). The respective film thicknesses are 1, 2, 10, 19, 20, 29, 64, 80, 95, 263, 800 and 1300 nm. The critical thickness was determined to be 19.5 nm. The separation between insulating and superconducting regime (separatrix) is indicated by a dashed line. The levels of quantum resistances for unpaired electrons, h/e2 , and for paired electrons, h/(2e)2 , are indicated at the right margin. (Adapted with permission from [149]; © (2012) by the American Physical Society)

reflected by R(T )-curves that change from a complete to an incomplete transition with decreasing film thickness (Fig. 6.11). The incomplete transitions show a tendency towards saturation when the temperature approaches 0 K. Such a residual resistance was explained as a signature of gradual loss of global phase coherence within a superconducting state that is confined in two dimensions. Phenomenologically, the transition into an insulating state is characterized by a so-called separatrix (a temperature-independent resistance) that is found for film thicknesses of 19–20 nm. In the FeSe films, the critical sheet resistance at the separatrix (Rc = 19.8 k) is higher than the expected quantum resistance of Cooper pairs, Rq = h/(2e)2 , in a two-dimensional system in the presence of a disorder-driven SIT [152]. A thickness dependence of Rc was found and the magnetic field scaling of the resistance indicated a reduced value of the critical resistance at Rc = 10.4 k (at Bc = 8.92 T and with a scaling variable of zν = 2.33). It is noteworthy, that the experimentally found separatrix, Rc , is in fact much closer to the quantum resistance of individual electrons, h/e2 . The residual resistance for films of intermediate thickness points towards an intermediate metallic state and a superconductor-metal-insulator transition. Transport measurements alone could not clarify, whether the localized charges in the insulating phase are unpaired or paired electrons [151]. In the insulating regime (t < 19 nm) the sheet resistance per FeSe layer increases exponentially with decreasing thickness, R = ρ/c ∝ exp(−t) (where a c-axis lattice constant of 5.5 Å was used). For T ≤ 4 K, the Coulomb interaction between localized charge carriers becomes dominant and the sheet resistance could be explained by the Efros-Shklovskii variable-range-hopping model [153]. A subsequent analysis has identified two additional temperature regimes for the electrical conductivity in the insulating phase of the granular films: a Mott variable-range-hopping (4–50 K) and an activated regime (T ≥ 50 K) [151]. Reference [154] claimed a SIT in ultrathin crystalline FeSe films grown by MBE that was induced upon variation of the post-growth annealing time (0–55 hours). The as-grown film (without post-growth annealing) displayed an increasing resistance

284

6 Thin Film Studies Under Focus

with decreasing temperature, whereas annealed films (10, 36 and 55 hours at an annealing temperature of T = 500 ◦ C) exhibited strong variations in the temperature dependence of the resistance with increasing Tc (25, 39, 30 K). The post-annealing strongly affects the electronic band structure and the Fermi surface, as demonstrated by the change in the Hall coefficient RH from hole to electron conduction.

6.2.2 Electrostatic Doping in EDLT/FeSe Films and SIT The electrostatic modification of charge carrier concentrations by engineering fieldeffect transistor (FET) structures on superconductors has opened the path for a new type of doping experiment (electrostatic doping) for tuning superconducting properties in a reversible way. In contrast to charge carrier doping by chemical substitution the electrostatic method neither changes compound stoichiometry nor introduces an additional disorder potential into the material. Electrostatic gating is, in turn, mainly confined to a ‘channel layer’ close to the gate insulator/superconductor interface. The ideas for a modulation of the charge density in superconductors date back at least to 1960 [155]. The electric field effect enhances in superconductors with a small density of mobile charge carriers and, consequently, a weak shielding. The extension of the channel layer is only a few unit cells. Since the late 1980s and 1990s FET structures have been applied to cuprate superconductors which opened exciting new paths into the field of superconducting electronic devices [156, 157]. In a FET the number of injected charge carriers depends on the capacitance of the gate insulator, C = ε0 εr A/d, that increases with decreasing thickness of the insulator, d, or by the choice of a high-dielectric material (large εr ). A newer development, the electric double-layer transistor (EDLT), uses an electrolyte as dielectric medium. The electric charge is accumulated not only along the electrolyte/channel interface but also along the gate/electrolyte interface. The doubling of the surface area at which charge accumulation takes place leads to an increase in capacitance while the dielectric distance (‘Helmholtz layer’) is in the range of 1 nm. A first electric field-effect device based on an Fe-chalcogenide was published in [160] where a 20 nm thin Tl1−x Fe1.6 Se2 film was employed as channel layer. The ionic liquid N,N-diethyl-N-methyl-N-(2-methoxyethyl)ammonium bis(trifluoromethanesulphonyl)imide (DEME-TFSI) was used as electrolytic medium that consists of the polyatomic cations [C8 H20 ON]+ and anions [(CF3 SO2 ) 2 N]− (Table 6.8). With a gate voltage up to 4 V the sheet resistance could be reduced, however no superconducting state could be induced. The Tl1−x Fe1.6 Se2 film in this study was grown by PLD on CaF2 at 600 ◦ C with a fluence of 10 Jcm−2 and a repetition rate of 10 Hz. A silica glass tube was used to hold the ionic liquid above the film. Table 6.9 summarizes the specifications for various EDLT/Fe-chalcogenide experiments. A clear effect on the superconducting state was achieved for FeSe films that were integrated in an EDLT device. In [161] the residual sheet resistance of PLD-grown FeSe thin films could be tuned with the application of a gate voltage, VG , between 0 V (discharged) and 5 V (charged), where a maximal onset transition Tc,on = 40 K

6.2 Superconductor-to-Insulator (SIT) Transitions

285

Table 6.8 Ionic liquids used in EDLT/Fe-chalcogenide experiments Ionic liquid

Valence

Refs.

Monovalent

[158]

IL2-TFSI

Divalent

[159]

IL4-TFSI

Tetravalent

[159]

DEME-TFSI

Formula     C8 H20 ON + - (CF3 SO2 )2 N −

Table 6.9 Selected EDLT/Fe-chalcogenide experiments Refs. [160] [54, 161] Source Drain Gate Gate insulator

In/Au In/Au Pt coil DEME-TFSI

In In Pt plate DEME-TFSI

Channel layer Channel geometry Substrate

Tl1−x Fe1.4 Se2 500 × 200 μm2

FeSe 2 × 8 mm2

CaF2

MgO

[162]

IL2-TFSI, IL4-TFSI FeSe

MgO

[163] In/Au In/Au Pt coil DEME-TFSI FeSe 500 × 200 μm2 SrTiO3

was evaluated (Fig. 6.12). The films in this study were fabricated by PLD from a stoichiometric FeSe target. Films were deposited on MgO at 300 ◦ C and annealed insitu at 450 ◦ C. Pt was used as electrode material. The ionic liquid (DEME-TFSI) had two functions: (i) It acted as electrolyte layer, where the thickness of the accumulated charge layer in the liquid is usually in the range of 1 nm, which guarantees a high capacitance together with the doubling of the area. (ii) The ionic liquid was used for electrochemical etching of the as-grown film. The originally 13 and 18 nm thick films were etched at T = 245 K to a thickness of 3.7 nm and ∼0.6 nm. Similar to the superconductor-insulator transition in granular FeSe films discussed above the separatrix between metallic and insulating-like sheet resistances of the FeSe/MgO film with a thickness of 0.6 nm (∼1 uc) matches very well with the quantum resistance of single electrons, h/e2 , indicating the possibility of an intermediate metallic regime. More experimentation with EDLT/FeSe devices on MgO substrates can be found in [162], where the effect of three different ionic liquids were compared: DEMETFSI (as mentioned above), and the oligomeric ionic liquids, IL2-TFSI and IL4TFSI (Table 6.8). The EDLT/FeSe with the divalent IL2-TFSI showed the largest Tc -enhancement after application of VG = +5 V. The measured Hall coefficients, RH , at a constant temperature (T = 50 K) and a gate voltage of +5 V have a nonlinear dependence on the FeSe film thickness. Superconductivity was induced by an electrostatic field effect into an insulating FeSe film [163]. The onset of the superconducting transition could be enhanced up

286

6 Thin Film Studies Under Focus

Fig. 6.12 a EDLT device. The effective thickness of the gate electrolyte corresponds to a Helmholtz layer of ∼1 nm. b Electrostatic tuning of the superconducting transition in FeSe films of different thickness. The separatrix (indicated by a dashed line) was added to the data and differentiates between a positive and a negative temperature coefficient, dR/dT . (Adapted with permission from Nature Publishing Group: Fig. 3d in [161]; © (2016))

to 35 K at an estimated sheet carrier density of ΔNe = 1.4 × 1015 cm−2 (average carrier density of 1.7 × 1021 cm−3 ) under a maximum gate voltage of VG = 5.5 V. The superconducting state with zero resistance was obtained below Tc,0 = 10.8 K. The 10 nm thin FeSe film with a channel geometry of 200 × 500 μm2 was grown by MBE using a shadow mask. The SrTiO3 substrate was pretreated with buffered HF solution in a wet-etching process and annealed at 1050 ◦ C. Fe and Se fluxes were provided from effusion cells with having cell temperatures at 1100 ◦ C and 140 ◦ C. The optimal substrate temperature was found to be 500 ◦ C. Au contacts were deposited using a shadow mask. The ionic liquid (DEME-TFSI) on top of the channel was hold by a silica-glass cup that was fixed by an epoxy adhesive. A Pt coil served as gate electrode. Reference [164] proposed the appearance of two proximity coupled superconducting layers in EDLT/FeSe devices fabricated on SrTiO3 substrates, since charge accumulation does not only appear on top of the film due to ionic liquid gating but also due to an expected electron-injection from the SrTiO3 substrate at the bottom of the FeSe film. As a result, the superconducting order parameter Δ(z) varies along the film thickness. With decreasing film thickness the two thin superconducting layers become proximity coupled. A thickness and angle dependent nucleation of superconductivity was found. A maximum Tc,on ≈ 40 K was found at a gate voltage of VG = 5 V in FeSe films thinner than 10 nm. This value exceeds the highest pressure-tuned Tc,on of 36.7 K at 8.9 GPa (quasihydrostatic pressure in a diamond anvil cell) measured in Fe1.01 Se single crystals [165] and of Tc,on = 38.3 K at ∼6 GPa (hydrostatic pressure in a cubic anvil cell) in FeSe [166]. Recently, electrochemical etching of FeSe0.8 Te0.2 thin films by the ionic liquid DEME-TFSI was demonstrated in [167]. In a series of films grown on SrTiO3 , LaAlO3 and CaF2 the top surface layer became superconducting up to a maximum of Tc,on ≈ 38 K due to an electrochemical reaction between the Fe-chalcogenide and the ionic liquid, independent from the initial Tc of the untreated film. Reference [168]

6.2 Superconductor-to-Insulator (SIT) Transitions

287

reports the enhancement of the Seebeck coefficient in a DEME-TFSI/FeSe device gated by a Pt electrode.

6.3 Electronic Phase Diagrams 6.3.1 FeSe1−x Te x and FeSe1−x S x Several thin film research activities were devoted to FeSe1−x Tex , in particular to the study of its electronic phase diagram. There are subtle differences between FeSe and FeTe as pointed out by single crystal and bulk studies. Both crystallize at room temperature in the space group P4/nmm (no. 129). FeSe adopts the tetragonal antiPbO structure-type, whereas FeTe crystallizes in a tetragonal Cu2 Sb-type structure with unoccupied Fe sites (and is not ‘isostructural’ to the anti-PbO structure) [169, 170]. Both compounds undergo structural instabilities at low temperatures: FeSe changes from tetragonal to orthorhombic (space group: Cmma) below 90–100 K. The structural transition of Fe1+x Te depends on the Fe-content. For small Fe excess the structure changes from tetragonal to monoclinic (space group: P112/n) below 65–70 K. FeSe and FeTe differ in their electronic ground states: FeSe becomes superconducting below 8 K, whereas FeTe has an antiferromagnetic ground state below an ordering temperature at 65 – 70 K and with a propagation vector of the spin density wave (SDW) of Q = (1/2, 0, 1/2). For this reason, FeTe (instead of FeSe) was proposed as parent compound for the 11 Fe-chalcogenides. The effect of chemical substitution on the electronic ground states is of great interest. The larger ionic radius of Te causes a lattice expansion when it is substituted for Se in FeSe. This is confirmed by the increase of the c-axis lattice parameter with increasing Te-content. In addition, the critical temperature enhances up to a maximum value at a Te-content of x ≈ 0.5 – 0.6. For higher Te-contents, Tc decreases again. In total, the superconducting ground state spans from x = 0 to ∼0.94. In FeSe1−x Tex crystals and bulk specimens structural and chemical phase separations at the nanoscale were found [171, 172]. Bulk specimens with a Te-content between 0.1 and 0.3 do show phase separations between a hexagonal and a tetragonal or of two tetragonal phases [173, 174]. The lack of single-phase FeSe1−x Tex with low Te-content has been attracting attention until today. A description of the FeSe1−x Tex solid solution derived from bulk data is given in [175]. A first report on the evolution of structural and superconducting parameters with tuned Se/Te ratio can be found for PLD-grown FeSe1−x Tex films in [176]. The films were deposited on MgO substrates at temperatures between 250–500 ◦ C under HV conditions ( p = 10−5 mbar) using a KrF excimer laser with a repetition rate of 2 Hz and an energy density on the target surface of 5–6 Jcm−2 for ablation. The resulting FeSe1−x Tex films have two (001)-oriented domains that differ by an in-plane rotation of 45◦ (see Sect. 2.1.2). The violation of the stoichiometric transfer during PLD and Te losses were assumed. Therefore, the Te-contents were corrected based on the c-axis

288

6 Thin Film Studies Under Focus

Fig. 6.13 Evolution of the FeSex Te1−x 001 reflection (XRD) for Te-contents x = 0.0–0.9. (Adapted from Fig. II-1 in [176]; © (2009), with permission from Elsevier)

lattice parameters and were smaller than the nominal values. It was also found that the electrical resistivities and the critical temperatures of the films depend sensitively on the film thickness. The smaller Tc of the films compared to the bulk values were attributed to strain effects induced by the MgO substrate. Although no clear phase separation was claimed for FeSe1−x Tex (x ≤ 0.3) films grown on MgO, the (001)reflections of the films showed a large broadening for x = 0.1 and 0.3 [176], which is an indication of peak splitting (Fig. 6.13). Inhomogeneous Se and Te distributions in the film lattice were proposed. An important parameter in the comparison of the electronic properties is the film thickness. According to [176] films thicker than 140 nm are less affected by the substrate strain. Thinner films could show a suppression of the structural transition upon cooling. Neutron diffraction on a 90 nm thin Fe1+x Te film deposited on MgO has substantiated a film lattice accommodation to the substrate lattice close to the film/substrate interface [177]. However, the tensile strain of the substrate affects the film lattice only in its first few unit cells and relaxation occurs along the in-plane and out-of-plane directions. An interesting experiment was reported in [178], where solid solutions of FeSe0.92 and FeSe0.5 Te0.5 were grown on LaAlO3 substrates in the fashion of multilayers by an alternating ablation from two Fe-chalcogenide targets with compositions FeSe0.92 and FeSe0.5 Te0.5 and laser pulse ratios of 1:1 and 2:1. The resulting epitaxial thin films were single-phase with a c-axis that increased with nominal Te-content (x = 0, 25, 33, 50). Unfortunately, the resulting chemical composition of the films was not examined. In [179] FeSe1−x Tex thin films of variable Te-content (0 ≤ x ≤ 1) were grown on CaF2 substrates at 450 ◦ C by PLD using a Nd:YAG(3ω) laser and under HV (∼10−6 mbar). FeSe1−x Tex targets with nominal compositions of x = i/10 (i = 0, 1, 2, .., 10) were used. A drawback of the study is the assumption of stoichiometric transfer during deposition and the neglected determination of the chemical composition of the films. As pointed out already in earlier (Fig. 2.7b), the film stoichiometry depends on the substrate choice and the growth parameters. The work focused on the Se-rich side (nominal composition) of the electronic phase diagram (Fig. 6.14): For 0.2 ≤ x ≤ 0.4, single-phase films were grown with a c-axis that lin-

6.3 Electronic Phase Diagrams

289

Fig. 6.14 a c-axis lattice parameter variation with Te-content in FeSe1−x Tex thin films (open symbols) and bulk specimens (closed symbols). The region with an apparent FeSe/FeTe phase separation and two c-axis values is indicated by a yellow background. b Electronic phase diagram for FeSe1−x Tex thin films on oxide substrates (open symbols) and bulk specimens (closed symbols) and c for films on CaF2 . Data shown for films on MgO (black) [176], films on CaF2 (red) [179], films on CaF2 (orange) and on LaAlO3 (blue) [181] as well as for films on SrTiO3 (green) [61]. Te-contents were corrected in [176]. All other reports are based on the nominal Te contents

early varied with Te-content (Vegard’s law), which is in contrast to two structurally distinct phases found in bulk compounds [173]. An independent study [180] has grown FeSe1−x Tex films with 0.1 ≤ x ≤ 0.4 on CaF2 substrates under different conditions (at TS = 280 ◦ C, p = 10−7 mbar and using a KrF laser). The resulting films were of a single tetragonal phase. Again, stoichiometric transfer was assumed when the electronic phase diagram was plotted. The same investigation was performed for films on LaAlO3 (100) substrates deposited at 300 ◦ C [181]. Figure 6.14 displays thin film and bulk data of Tc (x). Large deviations from the bulk behavior were noted for FeTe films and in films with a Te-content of 0.2 ≤ x ≤ 0.4. The electronic phase diagram depends on the substrate choice and attention must be paid to the film growth conditions. Both affects film composition and strain. Enhanced superconductivity was found in films with a nominal Te-content of 0.2 ≤ x ≤ 0.4 deposited on CaF2 . It is not clarified, why the Tc enhancement appears exactly in the doping range, for which bulk specimens can hardly be grown

290

6 Thin Film Studies Under Focus

as single-phase compounds. Final conclusions cannot be drawn as long as the phase diagrams were constructed from nominal film compositions. In the characterization of Fe-chalcogenide thin films, the chemical homogeneity plays an important role. In RF-sputtered Fe1+y Se1−x Tex thin films local inhomogeneities in the chemical composition were detected by SEM-EDS mapping [182]. The average Te-content in the sputtered films depends on the substrate temperature, TS . Besides the phenomenon of re-evaporation, a strongly temperature dependent sticking coefficient of Te and preferential re-sputtering were mentioned as main reasons for a reduced Te yield in the films when TS > 300 ◦ C. For a better control of the Te sputter transfer efficiency, sputter targets with enriched Se and Te content or the use of multiple targets were proposed [183]. It is interesting to note that ex-situ annealing in Ar atmosphere ( pAr = 2 · 10−2 mbar; 400 ◦ C) of room temperature sputtered Fe1.18 Se0.83 Te0.17 films resulted in the coexistence of two structurally similar phases with slightly different lattice parameters [184]. Chemical homogeneity was also studied in PLD-grown Fe1+y Se1−x Tex films on SrTiO3 substrates by means of EDS-TEM and STEM [185]. An almost uniform chemical composition and a random distribution of Se and Te ions was found in a Fe1.10 Se0.55 Te0.45 thin film grown under HV conditions ( p ≈ 10−6 mbar) at 400 ◦ C. A change in the deposition conditions to p = 10−4 mbar O2 atmosphere resulted in Fe-deficiency and a stronger variation of the film composition with Te-rich clusters. Similar results were reported for a Te-rich film FeSe0.1 Te0.9 deposited on SrTiO3 where Se-rich and Te-poor clusters of nanometer size were found [61]. In the latter study all films with a nominal composition between FeTe and FeSe0.1 Te0.9 displayed higher superconducting transition temperatures compared to bulk specimens. The observation of superconductivity in the FeTe films was not commented in detail, but O incorporation could be responsible as it was previously shown in [186]. The idea that the O incorporation could suppress the antiferromagnetic order due to lattice shrinkage was picked up in experiments on polycrystalline FeSe1−x Tex samples [187]. An alternative explanation can be found in a very early study [188], where misfit strain between film and substrate lattice was proposed to be responsible for the superconducting transition in FeTe films. The importance of valence states was discussed as third possibility and was investigated in [189, 190]. Superconductivity in some FeTe films has not been fully clarified until today (see Sect. 2.1.2). Appearance and absence of superconductivity in FeTe films indicates that investigations of the electronic properties and the FeSe1−x Tex phase diagram sensitively depends on the film growth conditions and the film thickness. An extension to the above discussion is provided by [191], where the evolution of the superconducting phase with S-substitution in FeSe was studied (Fig. 6.15). In the evolution of the isoelectronically substituted series from FeS over FeSe to FeTe the ionic radii, rS < rSe < rTe , cause a continuous expansion in a- and c-axis lattice parameters. Consequently, the electronic properties of FeSe1−x Sx and FeSe1−x Tex are modified due to chemical pressure. For the series FeTe – FeSe – FeS, the bond lengths decrease and orbitals overlap more strongly. The increased bandwidths result in a monotonic decrease of electronic correlations from FeTe to FeSe and finally to FeS [192]. Due to the yet difficult synthesis of FeSe1−x Sx single crystals, success-

6.3 Electronic Phase Diagrams

291

Fig. 6.15 Electronic phase diagram of FeSe1−x Sx thin films (open symbols) adapted from [191] and bulk specimens (closed symbols) adapted from [193]. Red symbols indicate the superconducting (SC) transition, blue symbols indicate the structural transition between a nematic (N) state with orbital ordering and a tetragonal state

ful thin film growth could contribute to elucidate the interplay between the orbital ordering and superconductivity.

6.3.2 FeSe and K-Coated FeSe Surface A STM/STS study of the electronic phase diagram of K-coated FeSe films revealed two disconnected superconducting phases upon variation of surface K dose [194]. Here, the dose reflects the number of evaporated K ions on the FeSe surface in units of monolayers (MLs). For calibration, the density of Se ions (∼7 × 1014 ions cm−2 ) of the top-most layer was defined as 1 ML. The corresponding electron doping levels of the Fe plane, x, were estimated from the K dose. The FeSe films were grown by MBE with thicknesses of 4–7 uc on SiC substrates (see Sect. 2.2.4). The pure FeSe film showed a gap of Δ = 2.2 meV in the dI /dV spectrum. After a small, initial K coating (x ≈ 0.009) the gap decreases with further doping and vanishes at a K dose of x = 0.016. The gap recovers at higher K doses (x ≈ 0.052) and is one order of magnitude larger than for the undoped film. A two-gap signature in dI /dV with Δ1,2 = 8.5 and 14 meV was found for x ≈ 0.103. The final electronic phase diagram was constructed from the dependence of spectral weight loss (after normalization of dI /dV ) on the electron doping level x (Fig. 6.16). Note that there is a qualitative difference in the surface topographies: for a low K dose the individual K adatoms at the surface can be resolved well, which is not the case for the higher K doses. It was mentioned in [195] that high K coverages result in cluster formation on the film surface. A similar work investigated K-coated FeSe films up to an electron-doping level of x = 0.228 by ARPES [196]. The resulting phase diagram (Fig. 6.16b) shows a broad nematic phase at low doping levels, followed by a superconducting dome

292

6 Thin Film Studies Under Focus

Fig. 6.16 a Electronic phase diagram of K-coated FeSe thin films showing two disconnected superconducting phases (gray). The spectral weight loss (yellow area) is sketched on the left. The right panels show the non-normalized dI /dV spectra as well as surface topographies for increasing K coverage. (Adapted with permission from Figs. 2 and 3b in [194]; © (2016) by the American Physical Society.) b Electronic phase diagram for FeSe/SrTiO3 based on nematic band splitting and superconducting gap and Tc . Adapted from Fig. 4b in [196]

with a maximum Tc = 46 K. The appearance of superconductivity in undoped and underdoped films could not be measured due to experimental constraints (T > 25 K). With increasing electron doping an insulating phase appears at x = 0.19 ± 0.02. Metallicity is recovered beyond x = 0.21. 1 uc FeSe/SrTiO3 films show a qualitative difference, pointed out in [195], where the evolution of the superconducting gap size of 1 uc and 2 uc FeSe films as function of K coverage was compared. In superconducting 1 uc FeSe films the superconducting gap is monotonously decreasing from Δ = 14 meV to 11.5 meV with increasing K dose up to 0.15 ML. In addition, K adsorption did not induce superconductivity

6.3 Electronic Phase Diagrams

293

in initially non-superconducting monolayers. In initially non-superconducting 2 uc FeSe/SrTiO3 , K adsorption induces superconductivity with Δ ≈ 8 meV at a K coverage of 0.05 ML. With increasing K coverage (up to 0.2 ML) the gap is enhanced to Δ = 14.5 meV.

6.3.3 Ba(Fe1−x Co x )2 As2 Electronic phase diagrams for PLD-grown Ba(Fe1−x Cox )2 As2 thin films in dependence of their Co-content (Fig. 6.17) can be found in [197, 198]. While a domeshaped, superconducting phase in Ba(Fe1−x Cox )2 As2 thin films on (La,Sr)(Al,Ta)O3 substrates reproduced the Tc (x) obtained from bulk and single crystal specimens [197], deviations were found in films grown on an Fe buffer layer [198]. The modifications of the electronic phase diagram and Tc (x) in Co-substituted BaFe2 As2 /Fe bilayer films included higher Tc,on compared to bulk specimens for the underdoped as well as for the overdoped regime. Analysis of the film composition revealed As deficiency and local inhomogeneities of the Co content, that were discussed as possible candidates for being responsible for the variations in Tc (x): In Ba(Fe1−x Cox )2 As2 /Fe bilayers with large Co content (overdoped regime), AES and APT depth profiles confirmed that Co diffuses into the Fe buffer layer [44]. Consequently, a gradient in the Co content along the film thickness is observed with a Co concentration close to the optimal one near the Ba(Fe1−x Cox )2 As2 /Fe interface. In Ba(Fe1−x Cox )2 As2 /Fe bilayers with small Co-content (underdoped regime)

Fig. 6.17 Electronic phase diagram of Co-substituted BaFe2 As2 . Comparison between films on different substrates and single crystal data. (Reprinted from Fig. 11 in [44], © IOP Publishing. Reproduced with permission. All rights reserved)

294

6 Thin Film Studies Under Focus

it was suggested, that additional disorder scattering at As vacancies could result in an increased Tc following the argumentation in [199], that impurity scattering in underdoped films can suppress the antiferromagnetic order. The density of states, that gradually recovers with impurity scattering, becomes available for the competing superconducting pairing mechanism. A discussion of the electronic phase diagram can also be found in [200], where it was shown that the slopes of the upper critical fields, |μ0 d Hc2 /dT 1−x Cox )2 As2 /Fe bilayers, vary linearly with |T c in the Ba(Fe −1 2.5 to 2 TK for the actual Co-content. While μ0 d Hc2c /dT T c decreases from Co content in the range of 0.015 ≤ x ≤ 0.107, μ0 d Hc2ab /dT T c increases from ∼3.6 to 4.9 TK−1 for 0.015 ≤ x ≤ 0.075.

6.3.4 BaFe2 As2 /SrTiO3 Superlattices An interesting electronic phase diagram was obtained for BaFe2 As2 /SrTiO3 superlattices [201]. The superlattices deposited by PLD revealed atomically sharp interfaces with reduced interdiffusion between the Fe-pnictide and the perovskite oxide layers (Sect. 5.3). Structural investigations confirmed that the tetrahedral bond angle in BaFe2 As2 can be tuned in superlattices by a variation of the modulation wavelengths, Λ = dSTO + d122 , (dSTO = 14 nm and d122 = 3.5, 7, 10, 20 nm). With increasing d122

Fig. 6.18 Electronic phase diagram for BaFe2 As2 /SrTiO3 superlattices grown on CaF2 substrates: structural transition (TS ), Neél transition (TN ), superconducting onset (Tc,on ) and superconducting offset (Tc,0 ). Data taken from Figs. 3c,5 in [201]. In contrast to the publication the phase diagram here is plotted against the As-Fe-As bond angle in the direction of decreasing orthorhombic distortion. (Reproduced and adapted with permission from PNAS)

6.3 Electronic Phase Diagrams

295

the orthorhombic distortion, δ = (a − b)/(a + b) increased and the bond angles in the FeAs4 tetrahedron deviated linearly from the optimal bond angle of ∼109.5◦ . A thickness-dependent electronic phase diagram was drawn with Tc,0 , Tc,on , a Neél transition TN obtained from resistivity measurements and a structural transition TS obtained from synchrotron XRD investigations (Fig. 6.18). The total change of the As-Fe-As bond angle within the sample series is less than 1◦ . In superlattices, where the thickness of the BaFe2 As2 layer, d122 , is only 3.5 nm the orthorhombic distortion is smallest and the As-Fe-As bond angle is almost matching the value for a perfect tetrahedron (109.47◦ ). The superconducting transition in this superlattice is, however, not complete. With increasing layer thickness, a complete superconducting transition develops showing a maximum when d122 = 7 nm. With increasing orthorhombic distortion, Tc decreases again, which is in qualitative agreement with the bulk state. An interesting property of the superlattice is the coexistence between superconductivity and orthorhombic lattice distortion and a possible spin density wave state (below TN ).

6.4 Metastable Compounds Pulsed laser deposition has been advantageously used in the past for the synthesis of metastable compounds that cannot be grown by bulk solid state reactions. One example is bulk (Ba1−x Lax )Fe2 As2 that has not yet been synthesized successfully. In this case, thin film growth enabled access to the study of La-substituted BaFe2 As2 . The substitution of the divalent Ba2+ with the smaller trivalent La3+ ion is expected to result in electron doping of the Fe2 As2 layers. La is directly succeeding Ba in the periodic table of elements, has no 4 f electrons and allows a direct comparison with electron-doping by Co-substitution. It is established that Co-substitution results in a doping amount of one electron per Fe-site (xCo = n e /Fe). With La-substitution only half amount of electrons are doped per Fe-site (xLa /2 = n e /Fe) [202]. The reasons for the failed synthesis of bulk (Ba1−x Lax )Fe2 As2 are not explicitly stated so far. It was speculated that an increased density of states at the Fermi level, N (E F ), that cannot be explained by a simple rigid band shift, could be responsible for the difficulties in the synthesis of the bulk compound [203, 204]. The theoretical investigation of different electron doping effects in SrFe2 As2 , in particular in [204], has also shown that the Fe magnetic moment increases with La-substitution. These disparities between Co-substitution of the Fe-site (‘direct doping’ or doping within the [Fe2 As2 ] layers or chemical substitution at the Fe-site) and the substitution of the alkaline earth site (‘indirect doping’ or doping from outside the [Fe2 As2 layers]) with a different orbital occupancy related to the As z position was pointed out in [205]. In 2012 the growth of (Ba1−x Lax )Fe2 As2 thin films was realized by PLD on MgO(100) substrates [202]. The c-axis parameter of the thin films decreases approximately linearly with increasing La-content, whereas there is a less clear change in the a-axis parameter and its value scatters largely. Nevertheless, the linear variation of the c-axis lattice parameter indicates a substitution of the La3+ ion on the alkaline

296

6 Thin Film Studies Under Focus

earth site in the thin film samples, in contrast to the bulk target where the additional La is not incorporated in the BaFe2 As2 phase and no change in the c-axis parameter is found. Similarly, rare-earth-substituted (Ba1−x RE x )Fe2 As2 (RE = Ce, Pr, Nd) films were grown by PLD on MgO(100) substrates under similar conditions and a substrate temperature of 850 ◦ C [208]. Again, the c-axis of the (Ba1−x RE x )Fe2 As2 thin films decreases linearly with RE-substitution, whereas the trend of the a-axis with substitution was less clear and the values scattered largely. Epitaxial strain effects do not play a role because the thickness of the films is exceeding 100 nm. (Ba1−x Lax )Fe2 As2 thin films show a negative Hall coefficient down to 25 K indicating that electrons are responsible for the electronic transport properties. The maximum resistive transition temperature in the films was found at Tc,on = 22.4 K for x = 0.13. As a first result, the electronic phase diagram (TN and Tc ) of La-substituted BaFe2 As2 thin films matched that of Co-substituted BaFe2 As2 thin films in terms of the number of doped electrons, n e . The authors have therefore concluded identical effects of indirect and direct electron doping on the superconducting transition. In a more recent publication [206] the subtle effects of La-substitution on the geometry of the FeAs4 tetrahedron were investigated by synchrotron X-ray diffraction. As a main result it was found that the structural trends of the FeAs tetrahedron in La-substituted BaFe2 As2 are opposite to those in Co-substituted BaFe2 As2 . The linearized evolution of the c-axis, the height of the As-site from the Fe plane, h X , the angle between two As sites, αX-M-X , and the bonding distance between Fe and As, M¯X , with increasing doping content per Fe-site, n e , are graphically displayed in Fig. 6.19a–d. The following relationships exist (see also Fig. 1.2): h X = (z X − 0.25)c

(6.10)

α = 2 arctan(a/2h X )

(6.11)

h X = M¯X cos(α/2)

(6.12)

Despite the fact that in both cases of substitution the c-axis is shrinking with increasing doping, the geometry of the FeAs tetrahedron is affected differently. Whereas Co-substitution pulls the As closer to the Fe plane (dh As /dn e < 0), La-substitution causes the opposite behavior (dh As /dn e > 0). Furthermore, the As z position in the unit cell is increasing with La-content and decreasing with Co-content. Both is marked by differently colored arrows on the As ions (Fig. 6.19f). It was argued [206] that different As z positions lead to comparable maximum critical temperatures in Ba(Fe1−x Cox )2 As2 and (Ba1−x Lax )Fe2 As2 upon electron doping. As conclusion, the electronic density would be the significant parameter for Tc , not the height of the As ion (see also Fig. 1.8). It has to be added that changes of the Fe magnetic moment (that could be reflected by the Fe-As bond length) or the band dispersion were not taken into account in this study. The comparison between La- and Co-substitution confirms again that chemical pressure is strongly site-dependent and there are obviously distinct ways of structural modifications of the FeAs tetrahedron. It can be also recognized that the unit cell

6.4 Metastable Compounds

297

Fig. 6.19 Comparison between La- (blue) and Co- (red) substitution in BaFe2 As2 . Linearized evolution of a c-axis b height of the As ion from the Fe plane, h As c tetrahedral angle, αAs-Fe-As d bonding distance between Fe and As, dFe-As . e Schematic unit cell of BaFe2 As2 with different doping sites and their effect on the As ions (arrows) indicated. f Superconducting transition temperature versus electron doping. g Plot of the maximum superconducting transition temperatures versus h As for different Fe-based superconductors (dark symbols) and Tc values for Co- and La-substituted BaFe2 As2 . Enlarged view in the inset: The direction of increasing doping is marked by arrows. (Adapted from [206, 207])

lattice parameters (sometimes summarized as c/a-ratio) do not reflect the complete structural information. A comparison between Sr and P substitution (both called isoelectronic doping) in BaFe2 As2 single crystals revealed, for example, that SDW suppression followed by superconductivity appears only for BaFe2 (As1−x Px )2 despite the same unit cell shrinkage [209]. In this study the authors argued that the shrinkage of the Fe-As bond length may be responsible for a reduction in the Fe magnetic moment and the suppression of the SDW accordingly. It would be thus certainly interesting to compare Sr- and La-substituted BaFe2 As2 because both have similar structural development. Considering the empirical plot of the maximum Tc versus the As height above the Fe plane for various Fe-based superconductors [207] the reported values for the maximum Tc of Co- and La-substituted BaFe2 As2 are found on opposite sides of the cusp-shaped maximum at an optimal h As,opt (Fig. 6.19g). The Tc (h As ) plot offers a qualitative explanation to pressure experiments. The total change of dTc,max /d p is given by dTc,max /dh As · dh As /d p. Since an externally applied hydrostatic pressure decreases h As , the sign of dTc,max /dp depends finally on the slopes left (positive) or right (negative) from the cusp at h As,opt . There is thus the ability to increase Tc for under- and overdoped (Ba1−x Lax )Fe2 As2 , whereas in Ba(Fe1−x Cox )2 As2 Tc can be increased for underdoped compounds but is limited for overdoped ones. The increase

298

6 Thin Film Studies Under Focus

in Tc for under- and overdoped (Ba1−x Lax )Fe2 As2 (x = 0.08–0.21) by hydrostatic pressure [210] fits well into this empirical scenario. As a final remark, a series of La-substituted SrFe2 As2 thin films was grown by PLD [211]. The resulting electronic phase diagram was compared to the superconducting phase of Co-substituted SrFe2 As2 thin films. Both, maximum Tc and the extension of the superconducting dome from 0.05 to 0.25 electrons/Fe are comparable.

6.5 The Tc Boost in FeSe Monolayers The structural simplicity of binary FeSe – it is solely composed of the elementary motif, the [Fe2 Se2 ] layers – is often emphasized. It is tremendously attractive and called a ‘unique’ solid state system. Similar to the Fe-pnictides, it allows for a wide tunability of its properties upon chemical substitution, pressure, strain, or ionic liquid gating. However, it differs from the Fe-pnictides due to its 2D character, its classification as a van der Waals compound, the absence of a magnetic long range order (SDW) close to the structural transition, and its strongly correlated character with a high degree of orbital-dependency. In particular, ‘monolayer’ or 1 uc FeSe/SrTiO3 films have raised enormous attention since 2012 [212], certainly with favorable support from certain media and journals, despite of the fact that the majority of experimental works on monolayer FeSe films originates only from very few research laboratories yet. The 1 uc FeSe/SrTiO3 system has to be differentiated from bulk FeSe, other thin films with a thickness of more than 1 uc and even monolayers on other substrates, due to a very distinct Fermi surface (FS) topology, high superconducting transition temperatures and the absence of a nematic phase. Insofar, the often attributed ‘model character’ of (post-growth annealed) 1 uc FeSe/SrTiO3 for all Fe-based superconductors must be questioned. From the actual experimental evidence, 1 uc FeSe films are rather found at the extreme limit in comparison with other Fe-based superconductors with properties that arise from the proximity of the substrate. SrTiO3 itself is an incipient ferroelectric material with a structural phase transition at ∼105 K. Most of the experimental data on 1 uc FeSe films confirmed that the substrate plays a decisive role for the superconducting pairing mechanism. Two of the debated interfacial effects will be discussed in the preceding sections: (1) charge transfer from the substrate to the monolayer (Sect. 6.5.2), and (2) interfacial electron-phonon coupling (Sect. 6.5.3). An accepted conclusive statement cannot be given. One should not wonder that attempts in creating clarity often ended up in new obscurities, as pointed out by Igor Mazin, who called superconductivity in FeSe a ‘riddle’ [213]. A surprising difference between 1 uc FeSe/SrTiO3 and other Febased superconductors was revealed in ARPES experiments and in electronic band structure calculations [214–217]. The FS topology of the FeSe monolayer consists only of electron pockets around the M-point. Their bottom lies ∼50–60 meV below the Fermi level, E F . The hole-like band at the Γ -point is shifted downwards and lies 60–80 meV below E F . Consequently, 1 uc FeSe/SrTiO3 lacks the typical FS nesting

6.5 The Tc Boost in FeSe Monolayers

299

properties and the superconducting order parameter symmetry does not fit into the proposed s± -scenario. It became clear, that the explanation for the high critical temperatures (typically up to 40–65 K and a maximum gap closing temperature of 75 K measured in [218]) and the much larger superconducting gap values (up to 15–20 meV) compared to bulk FeSe will be a highly challenging task and will have to incorporate the substrate in some manner. Several candidate mechanisms were proposed to be responsible for the high Tc in 1 uc FeSe on SrTiO3 : a polaronic effect caused by the high dielectric constant of the SrTiO3 substrate [212], the interface enhancement of an effective antiferromagnetic interaction, J [218], and most prominently charge transfer and an interfacial (or ‘cooperative’) electron-phonon interaction [217, 219], including composite Cooper pairing mechanisms where a primary interaction is enhanced by a secondary (‘helper fluctutations’) one [220]. Indeed, many publications find an interfacial electron-phonon interaction substantiated by the appearance of replica bands, which are detected in ARPES measurements ∼100 meV below the Fermi level at M. They could be a direct consequence of the high polarizability of surface ions of the SrTiO3 substrate. As pointed out in [221], the relative displacement between Ti and O ions results in a ferroelectric phonon mode (Fig. 6.20) and is reflected by a large dielectric constant at low temperatures. As a first consequence, the occurring symmetry-breaking leads to a mixing of electronic states. As a second consequence, the electron-electron repulsion is screened. This scenario is, however, full of controversies. Although the (‘cooperative’) electronphonon interaction in 1 uc FeSe/SrTiO3 based on the ferroelectric phonons from the TiO2 interface is larger compared to conventional electron-phonon coupling in bulk FeSe, the high superconducting transition temperatures in the monolayers are still not explained [222]. Other proposals include an increased electron-phonon interaction (however with FeSe phonon modes) due to the proximity of the substrate [223] or an excitonic mechanism, which was, however, highly questioned in [217]. Detailed ideas about interface enhanced superconductivity are given in [220, 224,

Fig. 6.20 Left: Distortion of the TiO2 lattice plane. Right: Schematic frozen ferroelectric phonon with atomic displacement along [001]. (Reprinted with permission from Fig. 1 in [221]. © (2012) by the American Physical Society)

300

6 Thin Film Studies Under Focus

225]. The role of spin fluctuations was recently rediscussed on the basis of spin spiral states in [226]. Their incoherent superposition could also explain the observed paramagnetic state in 1 uc FeSe/SrTiO3 . A conceptual problem arose in 2012–2014, when the interpretation of the large energy gaps seen in ARPES or STS measurements as mean field superconducting temperature, Tc , was doubted. It was argued that the gaps seen in ARPES or STM were hastily interpreted as superconducting gaps, and the temperature, at which the gap vanished, was prematurely called Tc . After first critical remarks, the temperatures were more carefully denoted as a ‘gap closing temperature’. A key problem for the research on 1 uc FeSe films is their restriction to in-situ methods. Handling of the monolayers outside of an UHV environment is still unsatisfactorily solved by capping the monolayer by additional overlayers. Nevertheless, capping allowed to perform ex-situ electrical transport measurements in order to be more conclusive on the origin of the energy gap. The monolayer films were protected with layers of either amorphous Si, amorphous Se or several unit cells of crystalline FeTe. The large discrepancies of 20–40 K between the ‘gap closing temperature’ determined from in-situ ARPES or STM experiments and Tc evaluated from the resistance drop in ex-situ performed transport measurements were explained by a degradation effect of the overlayer. Another problem was triggered by the expectation that the nucleation temperature of superconductivity in 1 uc FeSe/SrTiO3 films could be raised above the temperature of liquid nitrogen (77.4 K). The first hype culminated finally in a publication entitled ‘Superconductivity above 100 K’ [227], where critical temperatures of 99 and 109 K were claimed for 1 uc FeSe/SrTiO3 in an in-situ transport measurement based on a specially developed probe using pressed contacts [228]. Importantly, several critical questions were raised in [229]. The simultanoeusly published response unfortunately lacks convincing power. The results have never been repeated or confirmed by another method so far. Considering, that (i) the experimental setup suffers from an undefined current path (conductive SrTiO3 versus FeSe), (ii) a spectroscopic measurement was not performed on the same sample, (iii) the presentation of the results had several weaknesses (such as using a linear representation of the resistance curves), while simultaneously, (iv) serious doubts still exist (due to the vicinity of a structural transition in SrTiO3 , or due to the sharpness of the transition), such unvalidated claims must be handled with extreme care.

6.5.1 Fermi Surface, Topology and Energy Gap As mentioned above, the FS of a post-growth annealed 1 uc FeSe/SrTiO3 film differs topologically from the FSs found in bulk FeSe, films with larger thickness or unannealed monolayers (Fig. 6.21a). The purely electron-like FS of 1 uc FeSe/SrTiO3 (compare Fig. 1.5e, f) was first noticed in [230] and described as two almost circular surfaces around the M-point with an electron count of 0.10–0.12 e− per Fe (i.e. a Luttinger count of n ≈ 6.12). The maximum of the hole-pocket at the Γ point

6.5 The Tc Boost in FeSe Monolayers

301

Fig. 6.21 a Schematic Fermi surface topology for bulk FeSe, 1 uc FeSe/SrTiO3 before and after annealing. b The evolution of the Fermi surface of 1 uc FeSe on SrTiO3 with annealing. The annealing conditions and electron doping level are indicated. (Adapted with permission from Nature Publishing group Fig. 1 in [231]; © (2013).) c The evolution of the Fermi surface of 1 uc FeSe on SrTiO3 with FeSe thickness. (Adapted with permission from Nature Publishing group: Fig. 1a in [232]; © (2013))

lies 80 meV below E F . This distinctive FS develops during post-growth annealing. Before the annealing process, the 1 uc FeSe film has (similar to the bulk) an additional hole-like FS around the Γ -point [231]. With increasing annealing time and temperature, the band structure is lowered and the hole-pocket shrinks, whereas the electron-like Fermi sheets gradually grow (Fig. 6.21b). Finally, the hole-pocket disappears completely and the hole-like bands are shifted below the Fermi level. An analogous evolution of FS topology has also been observed with changing the FeSe thickness [232] as shown in Fig. 6.21c. Several origins for the electron doping or a charge transfer were proposed (Se loss, O vacancies in SrTiO3 , Fe and Se atom rearrangement), however, it remained speculative why and how the monolayer films become electron doped during the post-growth annealing process [231, 232]. For example, the growth of 1 uc FeSe on TiO2 with tunable O vacancies did not produce an effect on Tc and apparently contradicts an electron doping mechanism by O vacancies [233]. Furthermore, bulk Li1−x Fex OHFeSe shares similar features in

302

6 Thin Film Studies Under Focus

the Fermi surface topology with the monolayer [234]. More systematic experiments were, therefore, demanded in [229]. Distinct energy dispersions are revealed by band structure calculations for bulk FeSe, a freestanding FeSe monolayer, a 1 uc FeSe/SrTiO3 , or a 1 uc FeSe/SrTiO3 with O vacancies in the substrate. Here, simple LDA calculations failed to reproduce the band structure for an isolated FeSe monolayer as it is experimentally known by ARPES [214]. This demonstrates that the substrate has to be included in the theoretical calculations. In contrast, LDA calculations that included the substrate also found O 2 p surface states around M, similar to some ARPES results. The introduction of O vacancies leads formally to electron doping and a FS topology similar to the experimentally observed one [235]. Electronic correlation effects in Fe-chalcogenides are generally strong, regardless of the distinct FS topologies that exist for 1 uc FeSe/SrTiO3 , bulk FeSe or other Fechalcogenides [236]. In particular, electronic bands with dx y orbital character are strongly renormalized. Reference [235] emphasized that the electronic correlations in 1 uc FeSe/SrTiO3 are originating much stronger from Hund’s (rule) coupling than in bulk FeSe and are controlled by the Se-Fe-Se bonding angle. Electron doping enhances these electronic correlations in 1 uc FeSe/SrTiO3 , but diminuishes them in bulk FeSe. In 2014 it was proposed that monolayer FeSe exhibits topological properties induced by the lattice mismatch between FeSe and the SrTiO3 substrate [237]. In addition, the electronic band structure changes from trivial to nontrivial with increasing spin orbit coupling. New experimental investigations continued the discussion about the nontrivial band structure and the possibility of band inversion. 1 uc FeSe/SrTiO3 has also empty states in an electron pocket at the Γ -point 75 meV above E F [238]. The dispersion of this electron pocket can be tuned by the anion height, h Se . Other calculations in [239, 240] predicted a topological phase transition in FeSe1−x Tex (not only in monolayers) which is tunable with Te-content. Band crossings and band inversion at the Γ -point can lead to a nontrivial Z2 topological invariance that is modulated with film thickness. In addition, topological (1D) edge states are discussed for FeSe as well as for FeSe1−x Tex which could give rise to a quantum spin Hall state [241, 242]. FeSe films in the nematic state (either when films are thicker than 1 uc or unannealed and thus without electron doping) reveal also two spots with Dirac cone band dispersions close to the M-point at 10 meV below E F (Sect. 6.7.4) [243, 244]. A pure 2D Dirac semimetal was achieved in an undoped FeSe monolayer by a low-temperature annealing procedure [244]. A recent summary of this growing research area can be found in [245]. Within the actual paradigm, superconductivity in 1 uc FeSe/SrTiO3 arises with a nodeless and slightly anisotropic energy gap [246]. The gap has an U-shape in STM tunneling spectra and appears robust in size up to temperatures of at least ∼40 K. This allows either s-wave or nodeless d-wave pairing symmetries (Fig. 1.9). Latter scenario was supported by a recent STM-experiment based on the measurement of the de Gennes extrapolation length b ∝ (∂Δ/∂ x)/Δ, which becomes orientation dependent in the presence of sign changes in the complex order parameter Δ [247].

6.5 The Tc Boost in FeSe Monolayers

303

Table 6.10 Selected measured gap values Δ(T ) at temperature T and gap closing temperatures TΔ=0 for 1 uc FeSe films on SrTiO3 Δ (meV) T (K) TΔ=0 (K) Method Remark Refs. 13 13 ± 2, 15 ± 2 14.5 ± 0.3 18 ± 0.4 19

16 20 4 4 20

20.1

4.2

58 ± 7 55 ± 5 17–19 17–19 65

ARPES ARPES STM STM ARPES STM

 [010]Fe  [110]Fe Optimal annealing

[248] [230] [247] [247] [231] [212]

Fig. 6.22 a STM (dI /dV ) tunneling spectra of 1 uc FeSe on SrTiO3 between 4.2 and 42.9 K. (Adapted with permission from Fig. 2 in [212]; © Chinese Physics Letters). b Anisotropy of the superconducting gap, Δ(φ), values at 20 K (open circles) and at 16 K (closed circles). Data taken from Fig. 4b in [250] and from Fig. 2f in [248]. c Temperature dependence of the gap, Δ(T ), at the M point in a 1 uc FeSe/SrTiO3 film evaluated from ARPES. Closed circles taken from Fig. 3d in [230]; open circles taken from Fig. 2d in [248]

Gap closing temperatures between 45–75 K were reported, corresponding gap values, Δ(T ), range between 13 meV (16 K) [248] and 20.1 meV (4.2 K) [212] (Table 6.10). These values are much larger than the gap size in bulk FeSe at ∼2 meV. Although [212] has originally mentioned four superconducting coherence peaks at ±9 and ±20.1 meV in the STM tunneling spectrum at 4.2 K (Fig. 6.22a) a two-gap interpretation was never confirmed by ARPES measurements [230]. Interestingly, similar dI /dV curves recorded on 1 uc FeSe grown on insulating SrTiO3 were neither commented, nor underpinned claims of a second gap [249]. Calculations have associated the specific double-peak features in the dI /dV spectra to Fe phonon modes [223]. In general, gap values around each FS pocket are almost identical. The gap anisotropy was investigated in [230, 248, 250]. The distribution of gap maxima and minima was attributed to the multiorbital character of the Fermi surface. The gap minima appear due to a possible sign change on the electron pockets or a competition between intra- und interorbital pairing, but seem to disagree with a d-wave, an extended s-wave and an s ± -symmetry of the order parameter.

304

6 Thin Film Studies Under Focus

Fig. 6.23 a Δ1 b Δ2 as a function of η = I1 /I0 with I1 (I0 ) being the intensities of the γ’ replica (γ main) band at M. (Reprinted with permission from Fig. 4 in [251]; Creative Commons CC BY license)

In [251] attempts were made to tune the anticipated interfacial electron-phonon coupling by an isotope effect. In the relevant experiment the O isotope (16 O, 18 O) was controlled in a 60 uc thin SrTiO3 buffer layer grown on a SrTiO3 substrate. In an ARPES investigation, the intensity ratio of the replica (γ’) and the main (γ) band were used for the determination of the electron-phonon coupling constant. In comparison with other data on 1 uc FeSe/SrTiO3 , a linear dependence of the superconducting gaps Δ1 and Δ2 around the elliptical FSs at M was found (Fig. 6.23).

6.5.2 Charge Transfer Several works have examined the charge transfer from the substrate to the FeSe monolayer film as a result of band bending effects that occur at the interface of FeSe and SrTiO3 . Density functional calculations based on an ideal SrTiO3 cell were first performed in [252] and do not support a charge transfer because the Fermi level in the FeSe monolayer was found on top of the valence band of the SrTiO3 but below the conduction band. Experimentally, the SrTiO3 substrates are electron-doped and its band structure shows impurity bands within the gap, mainly close to the conduction band. However, discussion based on a Schottky model found that charge transfer can be driven by the work function difference between FeSe and SrTiO3 , which was assumed to be in the range of Δφ = 2–3 eV. A band bending scheme was proposed in [256] and is shown in Fig. 6.24a–c. The work functions were determined to be φ = 4.5 eV for SrTiO3 , φ = 5.1 eV for a 20uc FeSe film on SrTiO3 , and φ = 4.8–5.2 eV for 1 uc FeSe/SrTiO3 . It was,

6.5 The Tc Boost in FeSe Monolayers

305

Fig. 6.24 a Band gap and work function for SrTiO3 and work function for a 20 uc FeSe film on SrTiO3 . b, c Band bending effects at the interface of 1 uc FeSe/SrTiO3 . (Reprinted with permission from Fig. 4 in [253]. © The authors. (2017) Creative Commons CC BY license.) d EELS high loss mapping at 10 K for a 1 uc FeSe/SrTiO3 capped with FeTe and Te layers. Blue shift (ΔE > 0) of the Fe L 3 state at the interface (indicated by a dashed line). e Fermi level adjustment between SrTiO3 and FeSe and f schematic explanation of the band bending effect. (Reprinted with permission of AAAS from Figs. 2d,h,i in [254]. © The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. Distributed under a Creative Commons Attribution NonCommercial License 4.0 (CC BY-NC).http://creativecommons.org/licenses/by-nc/ 4.0/.) g Schematics of the photo-induced charge transfer. h Polar distortion of the TiO2 layer. i Resistance R(T ) and increase in Tc with illumination and van der Pauw geometry for resistance measurement (inset). (Reprinted with permission from Figs. 1a, b and 4a in [255]. © The authors. (2017) Creative Commons CC BY license)

therefore, argued that an upward band bending occurs in SrTiO3 which leads to a charge transfer from SrTiO3 to FeSe. In [254] the interface between SrTiO3 and FeSe was investigated by core-loss EELS mapping which has resolved a blue-shift of the Fe L3 state at the film/substrate interface (Fig. 6.24d). It was assumed that the Fermi level (work function) difference is similar to the band gap in SrTiO3 (≈ 3.3 eV) as shown in Fig. 6.24e. In contrast to the scheme discussed above, the band bending occurs also in FeSe. The total charge transfer results in an electric potential at the interface. Due to the metallic

306

6 Thin Film Studies Under Focus

nature of FeSe, the electrical potential is screened along a distance of 2 uc. Band bending leads to an increased energy of Fe L 3 (2 p3/2 ) and Fe L 2 (2 p1/2 ) states, which explains finally the blue shift (∼0.5 eV) of the transferred electrons (Fig. 6.24f). exsitu electrical transport measurements confirmed Ton ≈ 30 K and Tc,0 ≈ 15 K in 1 uc FeSe/SrTiO3 . In addition, backgating increased Tc,0 ≈ 21 K. It was proposed that a positive backgating pulls the electrons closer to the film/substrate interface and thus enhances the interaction between electrons and interfacial phonons which, in turn, leads to an increase in Tc . The effect of band bending at the FeSe/SrTiO3 interface was theoretically examined in [257] and is believed to be responsible for a charge transfer effect. It was pointed out that the 2 × 1 reconstructed, Ti-rich SrTiO3 surface favors hightemperature superconductivity. Another interesting experiment is reported in [255], where Tc in 1 uc FeSe was raised upon illumination by a continuous UV-light source (Fig. 6.24g–i). The photovoltage was obtained upon illumination of the film from a 3.5 eV UV light emitting diode with a power density of 10 μWcm−2 . For the ex-situ experiment, 1 uc FeSe/SrTiO3 was capped by a 10 uc thin FeTe layer. No effect on Tc was found when the film was illuminated with light of 1.5, 2.3 and 3.1 eV, which is below the band gap of SrTiO3 . The light-induced switching to higher Tc is assumed to occur in the kHzrange. The exact mechanism of photoexcitation that leads to an increase in Tc was controversially discussed. Transfer of photoexcited electrons from the SrTiO3 to the FeSe are possible. At high temperatures (T > 100 K) they recombine fast, whereas at lower temperatures, the generated holes lead to doping of FeSe while simultaneously SrTiO3 becomes photoconductive. The spatial cahrge separation (electronholes) prevents a recombination. However, it remained unclear how hole doping of 1 uc FeSe could lead to an enhancement in Tc . Alternatively, a strong photon-phonon coupling in SrTiO3 was suggested to result in a metastable polar lattice distortion at the film/substrate interface and the additional TiO2 layer (Fig. 6.24h).

6.5.3 Interfacial Electron-Phonon Coupling Interfacial (or ‘cooperative’) electron-phonon coupling is dealt as hot candidate for Cooper pairing in 1 uc FeSe/SrTiO3 , although it could not yet determine the origin of the high-temperature superconductivity satisfactorily. It was suggested after the discovery of so-called ‘replica bands’ at the M point well below the electron pocket by ARPES [248]. The bottom of the electron pocket is located ∼60 meV below E F , whereas the replica bands (‘shake-off bands’) were found 100 meV further below. They almost ‘copy’ the electron bands in size and shape. The apparent energy shift without large momentum transfer (small q) was attributed to an electron-phonon interaction between Fe 3d states and a bosonic mode, for example, optical phonons from O2− ion displacements on the SrTiO3 surface. An electron-phonon coupling constant of λ = 0.5 and an effective phonon-mediated attraction strength for Cooper pairing of νeff ≈ 10 meV were estimated.

6.5 The Tc Boost in FeSe Monolayers

307

Replica bands turned out to be a generic feature of monolayers on SrTiO3 substrates. They were also observed in lattice-expanded 1 uc FeSe on SrTiO3 /KTaO3 or on Nb:BaTiO3 -buffered KTaO3 [218]. Replica bands furthermore occur in the electronic spectra of 1 uc FeSe on SrTiO3 (110) substrates. The (110) substrate surface leads to a C2 lattice distortion in FeSe but leaves high-temperature superconductivity intact [256]. Therefore, it is assumed that all these substrates give rise to a similar effective electron-phonon interaction. Another ARPES study compared 1 uc FeSe/SrTiO3 with 1 uc FeSe films on TiO2 and again explained the high Tc by an interfacial electron-phonon coupling and an additional charge transfer effect [258]. In contrast, [259] found replica bands in superconducting 1 uc FeSe as well as in non-superconducting 1 uc FeS films. Although the replica bands were assumed to originate from an electron-phonon interaction, it was concluded that the effective electron-phonon interaction is too weak for explaining high-temperature superconductivity in 1 uc FeSe. The origin of the replica bands has been controversially discussed until today. LDA calculations and LDA combined with DMFT in [215] did not find evidence for a strong influence of the substrate on the band structure except a lifting of the degenerated dx z /d yz -orbitals. ARPES results from [248] could be reproduced theoretically upon consideration of band renormalization due to electron correlations. Replica bands were described as renormalized bands of the monolayer FeSe and they were located in the outer electron pockets. In contrast, [260] has attributed the replica bands to extrinsic photoelectrons that experience an energy loss due to their strong coupling to Fuchs-Kliewer surface phonons. Consequently, the replica bands would not originate from an electron-phonon interaction between Fe 3d electrons in FeSe and substrate phonons. This interpretation was supported in [261], pointing out that the replica bands only appear for the occupied unshifted electronic bands and are absent in STM experiments. Recent isotope experiments [251] also disagreed with the renormalization interpretation given in [215]. Quantum Monte Carlo simulations reproduced replica bands by including a small-momentum electron-phonon interaction to the electrons of FeSe [262]. The role of Fuchs-Kliewer surface phonon modes was discussed first in [263, 264] by applying high-resolution electron energy loss spectroscopy (HREELS), a surface sensitive technique for mapping energy losses (below E loss = 100 meV) due to phonons. Besides one acoustic phonon (≤7 meV) and two optical phonons (at 20 and 32 meV) from the film, two Fuchs-Kliewer surface phonon modes (β at 0 = 60 and α at 0 = 92 meV) were detected. Latter create a long-range electric dipole field, that penetrates into the 1 uc FeSe layer and interacts with the Fe 3d electrons. It was proposed that Fuchs-Kliewer surface phonons (Fig. 6.25) and the interfacial coupling between the substrate and the monolayer FeSe are responsible for the strongly enhanced Tc . A coupling constant λ ≈ 0.25 meV was evaluated for the 92 meV phonon mode. The estimated penetration depth of the phonon modes is 2.5 uc. The exponential decay of the superconducting gap size Δ(t) with increasing thickness has a comparable decay length of 2.4 uc [265]. It was, therefore, argued that these surface phonons give rise to the pairing interaction at the interface. Furthermore,

308

6 Thin Film Studies Under Focus

Fig. 6.25 α and β Fuchs-Kliewer surface phonon modes in SrTiO3

highly ionic oxides with high-energy Fuchs-Kliewer surface phonon modes were proposed as preferable substrates for an increased interface superconductivity. Although strain may affect a nematic state in non-superconducting 1 uc FeSe/ SrTiO3 , it seems not to alter significantly superconductivity in superconducting monolayers. It was noted that the substrate lattice (a = 3.78–3.99 Å) has neither influence on the lateral atomic registry nor the superconducting gap [229]. The observation of replica bands together with interfacial electron-phonon coupling in 1 uc FeSe films grown on different oxide substrates (SrTiO3 (100), SrTiO3 (110), or TiO2 ) suggested, that there is only a limited effect of lattice strain or the high dielectric constant of the substrate on the superconducting transition temperature, Tc [258]. Forward Electron-Phonon Scattering The appearance of replica bands supports the theory of an electron-phonon interaction with strong forward scattering peak, i.e. an electron-phonon coupling constant that peaks for small q-vectors [266–268]. It was argued that such a mechanism does not require spin fluctuations enhanced by FS nesting. It is mainly an intraband interaction, which makes the difference to other Fe-based superconductors evident. This very promising proposal for Cooper pairing in 1 uc FeSe/SrTiO3 has produced a broader theoretical discussion [262, 269–271]. Recent theories propose that Cooper pairing is additionally enhanced by the small-momentum electron-phonon interaction, while the initial pairing interaction is of different origin [262]. The theoretical description is based on a single-band model Hamiltonian with electron, phonon and electronphonon terms, H = He + Hph + He-ph , like H=



  1 + q bq† bq + 2 q  

† † g(k, q)ck+q,σ ck,σ b−q + bq ,

† ck,σ + (εk − μ) ck,σ

k,σ

1 +√ N



(6.13)

k,q,σ

† where g(k,q) is a momentum-dependent electron-phonon coupling, ck,σ , ck,σ are the electron creation and annihilation operators for an electron of wave vector k and spin σ , and bq† , bq are phonon creation and annihilation operators for a phonon of wave

6.5 The Tc Boost in FeSe Monolayers

309

vector q. εk is the electronic band dispersion, μ is the chemical potential and q is the phonon frequency.

6.5.4 Vortices and Andreev Bound States Reference [233] reports the mapping of vortices by STM in 1 uc FeSe grown on a TiO2 (100). The vortex lattice undergoes a transition from a 4-fold to a 6-fold symmetry between μ0 H = 6 and 9 T (Fig. 6.26). An Andreev bound state was found in the vortex core at an energy bias E 0 = 0.6 meV.

6.6 High Magnetic Field Studies Magnetic Fields The Fe-based superconductors are extreme type-II superconductors with upper critical fields, μ0 Hc2 (0), reaching several tens of teslas. In the Fe-oxyarsenides μ0 Hc2 (0) can exceed values of 100 T which is beyond the experimental accessibility even in highly specialized laboratories with pulsed magnetic field facilities. High magnetic fields can be considered as extreme condition for the investigated material as well as for the magnetic field producing solenoids. Standard laboratory cryostat systems equipped with superconducting solenoids are often limited to magnetic fields in the range of μ0 H = 5–17 T. Higher static magnetic fields can be produced up to 30 T. Pulsed magnetic fields of 50–80 T with pulse durations from 5–350 ns are routinely available. The world record for pulsed magnetic fields without destroying the solenoid is 100 T. Magnetic field generation beyond 100 T can only be achieved by destructive methods (Table 6.11). Upper Critical Fields The upper critical field belongs to the fundamental properties of a type-II superconductor. Its description of the orbital upper critical field is based on the GinzburgLandau (GL) theory and its extensions. It is directly linked to the GL coherorb = φ0 /(2π ξ 2 ), that gives the length scale over which ence length, ξ , via μ0 Hc2 the superconducting order parameter varies. The flux quantum is given by φ0 = 2.07 × 10−15 Tm2 . The GL coherence lengths at zero temperature in Fe-based superconductors are typically in the range of ξ(0) = 0.5–5 nm. (BCS coherence lengths are comparable, ξBCS = vF /2π kB Tc ≈ 1–3 nm with Fermi velocities vF ≈ 106 – 107 cm·s−1 [278].) The GL theory was originally developed for isotropic single-band superconductors, therefore some caution is needed in the treatment of anisotropic multiband Fe-based superconductors. Due to their layered structure in tetragonal unit cells, the electronic properties (i.e. the effective electronic mass) are anisotropic and

310

6 Thin Film Studies Under Focus

Fig. 6.26 Vortex lattice in 1 uc FeSe/TiO2 at different magnetic fields at T = 4.2 K. Left: Zero-bias conductance (ZBC) maps (100 nm × 50 nm). Right: Corresponding Fast Fourier Transformation (FFT) power spectra of the ZBC maps. Reprinted with permission from Figs. 2d,e in [233]; © (2016) by the American Physical Society

should be captured by the Anisotropic Ginzburg Landau (AGL) theory. For uniaxial superconductors the main orientations of the applied magnetic field are defined by the c-axis (i.e. perpendicular to the [Fe2 X2 ] layers) and are written in the frame of the AGL as:

6.6 High Magnetic Field Studies

311

Table 6.11 Selected high magnetic field studies of thin films of Fe-based superconductors Compound

Laboratory

Bmax (T)

Method

1 uc FeSe

WHMFC Wuhan

52

pulsed

[34]

FeTe

NHMFL Tallahassee

35

static

[272]

FeSe0.5 Te0.5

HFML Nijmegen, NHMFL Tallahassee

30, 35

static

[66]

FeSe0.5 Te0.5

NHMFL Los Alamos

45

static

[273]

NHMFL Tallahassee

60

pulsed

FeTe0.55 S0.095

NHMFL Los Alamos

35

pulsed

Sr(Fe1−x Cox )2 As2

NHMFL Los Alamos

50

pulsed

[275]

BaFe2 (As1−x Px )2

NHMFL Tallahassee

35

static

[78, 83]

LaO1−x Fx FeAs NdO1−x Fx FeAs

Refs.

[274]

IFW Dresden

72

pulsed

[79, 124]

HLD Rossendorf

72

pulsed

[79, 124]

HLD Rossendorf

72

pulsed

a

SmO1−x Fx FeAs

HLD Rossendorf

62

pulsed

[276]

SmO1−x Fx Fe1−y Co y As

HLD Rossendorf

62

pulsed

[277]

a Shown

in this monograph

φ0 , 2 2π ξab φ0 = . 2π ξab ξc

c

μ0 Hc2 = ab

μ0 Hc2

ab

c

The anisotropy of the upper critical field is defined as γ Hc2 = Hc2 /Hc2 and the angular dependence of the upper critical field describes an ellipse equation with 

Hc2 (θ ) sin θ c

Hc2



2 +

Hc2 (θ ) cos θ ab

Hc2

2 = 1.

For thin films having a thickness comparable to the coherence length, the above formula modifies to   2 H (θ ) sin θ Hc2 (θ ) cos θ c2 = 1, + c ab Hc2 Hc2 a result, that was found by Michael Tinkham [279] and is called ‘Tinkham formula’. Following the GL theory, signatures of a 2D superconductivity can be found for thin films (with tsc denoting the thickness of the superconducting layer) in the temperature dependence of the upper critical field when measured parallel to the film surface

312

6 Thin Film Studies Under Focus

 μ0 Hc2

√   T 1/2 3φ0 1− = . π ξ tsc Tc

The upper critical field perpendicular to the film plane varies linearly with temperature like for a 3D superconductor:   T φ0 ⊥ 1− . μ0 Hc2 = 2π ξ 2 Tc In the above equations, Tc is the critical temperature in zero magnetic field and ξ is the in-plane coherence length. The square-root signature with its steep slopes, −dHc2 /dT |Tc , indicates that the superconducting film behaves like a stack of individual superconducting layers. A similar behavior is found in Fe-chalcogenide thin films. An important issue for strong type-II superconductors like the Fe-based superconductors is the pair breaking mechanism due to spin alignment. The breaking of (singlet) Cooper pairs due to the parallel alignment of the electron spins is not orb . Here, the so-called paramagnetic described by the orbital upper critical field, μ0 Hc2 limit (‘Pauli limit’), first stated by Albert M. Clogston and Bellur Sivaramiah Chandrasekhar [280], can lead to a flattening of μ0 Hc2 (T ) for T → 0 and an apparent isotropic μ0 Hc2 . The Pauli limiting field is estimated by √ 2Δ , HP = gμB where Δ is the superconducting gap, g ∼2 denotes the Landé factor, and μB is the Bohr magneton. For a single band BCS superconductor (weak interactions) the Pauli limiting field is expressed as μ0 HP = 1.84Tc (in Tesla). HP can be enhanced, for example, due to strong coupling, which is considered via a correction term leading to 1.84(1 + λ)Tc with λ the electron-boson coupling constant. In the multiband case, the electron-boson coupling constants define the matrix λi j = Vi j N j with interaction matrix elements Vi j , the density of states N j , and the band indices i, j. For i = j they are called ‘interband coupling constants’, for i = j they are called ‘intraband coupling constants’. Their value is of importance in Fe-based superconductors. In the presence of spin fluctuations, larger interband coupling constants are assumed. Fundamental theoretical descriptions of the upper critical field were obtained in the works of Lev Petrovich Gor’kov, Pierre-Gilles de Gennes and Kazumi Maki, that provided a temperature dependence of μ0 Hc2 (T ), that is valid for all temperatures below Tc . In three seminal publications Nathan Richard Werthamer, Eugene Helfand and Pierre Claude Hohenberg (WHH) have outlined a theory (‘WHH theory’) for the temperature dependence of μ0 Hc2 for any impurity level and including the effects of Pauli spin paramagnetism [281–283]. It is often the first choice in fitting Hc2 (T )-data and deviations are attributed to multiband effects. The multiband nature manifests itself in the temperature dependence of μ0 Hc2 (T ) with curvatures different from the WHH theory. It also results in a temperature dependent γ Hc2 . The upper critical field

6.6 High Magnetic Field Studies

313

in multiband superconductors is often treated in the frame of the GL theory [284] or based on a self-consistent BCS approach [285]. Since the experimental access to the high upper critical fields at low temperatures orb (0) is extrapolated from the slopes of dHc2 /dT at the critical is often constrained, Hc2 temperature dHc2 orb . Hc2 (0) = −0.69Tc dT Tc The extremely large slopes in Fe-based superconductors result in very large orbital upper critical field values and small coherence lengths. Actual μ0 Hc2 values, however, are much lower, due to a Pauli limiting effect. References [79, 286] showed that in LaO1−x Fx FeAs films with low and almost isotropic pinning, the anisotropies γ Hc2 ≈ γm are equal and could be obtained in an alternative way from the anisotropy c of the critical currents. It was verified that the multiplication of the smaller μ0 Hc2 c ab with the anisotropy yielded γ Hc2 · μ0 Hc2 = μ0 Hc2 .

6.6.1 Fe-Chalcogenide Thin Films in High Magnetic Fields The temperature dependence of the upper critical fields, μ0 Hc2 (T ), of different Fechalcogenide thin films is summarized in Fig. 6.27 and relevant parameters are given in Table 6.12. The upper critical fields found for FeSe0.5 Te0.5 films are characterized by steep slopes at Tc , -dHc2 /dT |Tc and small anisotropies γ Hc2 > 1 close to Tc . Similar trends are found for FeTe0.9 S0.1 and oxygenated FeTe films which are also pseudoisotropic. At low temperatures, T → 0, the Fe-chalcogenides show almost isotropic μ0 Hc2 (γ Hc2 ≈ 1 − 2), which can be seen as a result of Pauli limitation. For a series of FeSe1−x Tex films, the variation of γ Hc2 with x is between 1.4 (x = 0.8) and 3.2 (x = 0.3). However, the upper critical fields and their anisotropy were extrapolated from -dHc2 /dT |Tc (0–9 T). An inversion of the upper critical field anisotropy (γ Hc2 < 1) was observed with decreasing temperatures in a FeTe0.9 Se0.1 film [274]. A Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state was proposed to be responsible for the appearance of the crossover from γ Hc2 > 1 to γ Hc2 < 1. In comparison, a reversal of the anisotropy was also found in a FeSe0.4 Te0.6 crystal [287]; the observation of an isotropic Hc2 in FeSe0.33 Te0.67 single crystals was attributed to a dominant Pauli limiting behavior [288]. In [289] Hc2 of a RF-sputtered FeSe film was determined in transport measurements in magnetic fields up to 14 T. The obtained coherence lengths are ξab = 4.0 nm ab and ξc = 1.7 nm, the extrapolated upper critical fields are Pauli limited μ0 Hc2 (0) c = 28.3 T (smaller than the orbital upper critical field) and μ0 Hc2 (0) = 22.4 T. The upper critical field anisotropy decreases with decreasing temperature from 3.5 at Tc to 1 < γ Hc2 < 2. The difference between upper critical field and mass anisotropy, γ Hc2 = γm , is not only a result of multiband superconductivity, as argued by the authors, but may also be the result of a non-isotropic GB pinning.

314

6 Thin Film Studies Under Focus

c

Fig. 6.27 Upper critical fields of different Fe-chalcogenide thin films. Open symbols denote μ0 Hc2 , ab closed symbols denote μ0 Hc2 . Lines are guide to the eyes. a PLD-grown films; b MBE-grown films showing a temperature dependence typical for 2D superconductivity. The inset explains the different temperature dependence for 3D and 2D superconductivity in the frame of GL theory. Data taken from [37, 66, 272–274, 290, 291]

c

In [34, 291] μ0 Hc2 of a 1 uc FeSe films with Tc = 31.6 K was investigated (Fig. 6.27b). A linear temperature dependence was found down to 4 K (corresponding to a reduced temperature of t = T /Tc ∼ 0.13) and up to magnetic fields of 52 T [291]. (It has to be pointed out that an ill-posed argument for 2D superconductivity was linked to the linear temperature dependence of the upper critical field parallel to the c c-axis direction only.) The upper critical field, μ0 Hc2 (0) = 56.8 T and the in-plane Table 6.12 Critical temperature (Tc,90 ), estimated upper critical fields (μ0 Hc2 (0)), slopes (−dHc2 /dT |Tc ), and calculated GL coherence lengths (ξ ) for different Fe-chalcogenide thin films shown in Fig. 6.27 c

ab

c

dHc2 dT |Tc (TK−1 )

ab

dHc2 dT |Tc (TK−1 )

Tc

μ0 Hc2 (0)

μ0 Hc2 (0) −

(K)

(T)

(T)

31.6

56.8

1.8

2.4

28.9

30.2

∼1.0

3.3

FeSe

7.4

12

FeTe/Bi2 Te3

10.2

17

FeTe0.55 S0.095

7.5

26

FeTe:Ox

7.0

40

FeSe0.5 Te0.5

18.5

55

FeSe0.5 Te0.5

20.5

Compound 1 uc FeSe

−

ξab

ξc or tsc

(nm)

(nm)

1.6

∞

4.5

1.6

∞

5.2

27

>15

>15

∼45

6.0

9.2

2.9

8

≥100

1.5

30

100

17

Refs. [291]

5.0

[290]

3.5

[274]

0.1, 2.4

[273]

[37] [272] [66]

6.6 High Magnetic Field Studies

315

coherence length, ξab = 2.4 nm, were extrapolated. The 1 uc FeSe film was grown on SrTiO3 (001) and contained a 10 uc thin FeTe cap layer and 30 nm amorphous c Si. A linear temperature dependence of the upper critical field, μ0 Hc2 , was also observed in a similar film grown on SrTiO3 (110), that had a slightly reduced Tc = 28.9 K (μ0 Hc2 was measured down to t = T /Tc ≈ 0.7). The linearly extrapolated value of the upper critical field at zero temperature was 30.2 T, which resulted in an in-plane coherence length of ξab = 3.3 nm. The corresponding electrical transport ab measurements in pulsed magnetic fields were, however, published in [34]. μ0 Hc2 was not determined. 2D superconductivity was also found in a FeTe/Bi2 Te3 heterostructure based on the temperature dependence of its upper critical field [37]. The evaluation resulted in an averaged coherence length of ξ = 5.2 nm and a superconducting layer thickness of tsc ≈ 7 nm. Interestingly, a 500 nm thick FeSe film grown by MBE follows a similar ab temperature dependence [290]. There, the temperature dependence of μ0 Hc2 can be   fitted well by 1 − T /Tc with a slightly reduced value for the critical temperature Tc = 7.0 K indicating a possible 3D/2D crossover between 7.0–7.4 K (Fig. 6.27)b). The upper critical fields in FeSe and FeTe films show a larger anisotropy at temperatures close to Tc than FeSe1−x Tex or FeTe0.9 S0.1 films. The same trend was found in single crystals [288].

6.6.2 Fe-Pnictide Thin Films in High Magnetic Fields Upper critical fields of Fe-pnictide thin films and their temperature dependence are compared in Fig. 6.28 and relevant parameters are given in Table 6.13. A Sr(Fe1−x Cox )2 As2 thin film shows μ0 Hc2 ≈ 45 T for both major directions [275]. Analysis by a two-band fit [285] assumed anisotropic electronic bands, electronboson coupling constants with λ22 /λ11 ≈ 0.42 and λ12 = λ21 = 0.23λ11 and similar diffusivity parameters for both electronic bands. The upper critical field was called ‘pseudo-isotropic’ because it does not reflect the anisotropic electronic structure of the compound. Large, isotropic upper critical fields are favorable for high magnetic field applications. The electronic phase diagram of BaFe2 (As1−x Px )2 is possibly governed by a quantum critical point (QCP) at x ≈ 0.3. It is, therefore, of fundamental interest if signatures of the QCP are also reflected in the upper critical field, due to the enhancement of the electronic mass. In addition, critical current densities in BaFe2 (As1−x Px )2 films reach values of 1 MAcm−2 and are, therefore, considered as candidates for practical high-field applications. High-field Hc2 data for a MBE-grown P-substituted ab BaFe2 As2 film with Tc,on = 30.7 K can be found in [83]. μ0 Hc2 (0) ≈ 62 T and c μ0 Hc2 (0) = 48 T were extrapolated and a (single band) WHH fit was proposed for Hc2 (T ). A Pauli-limiting behavior was assumed. A 185 nm thin P-substituted BaFe2 As2 film deposited by PLD on a metal template with Tc = 28.3 K was investigated in [78]. μ0 Hc2 was measured down to ∼0.4Tc and up to 35 T. Its temperature

316

6 Thin Film Studies Under Focus

c

Fig. 6.28 Upper critical fields of different Fe-pnictide thin films. Open symbols denote μ0 Hc2 , ab closed symbols denote μ0 Hc2 . Lines are guide to the eyes if not indicated otherwise. a Comparison of PLD-grown Sr(Fe1−x Cox )2 As2 film (with two-band fit) and BaFe2 (As1−x Px )2 film. b Comparison of Fe-oxyarsenide thin films: LaO1−x Fx FeAs film (2-stage process); PLD-grown SmO1−x Fx FeAs and SmO1−x Fx Fe1−y Co y As films, and MBE-grown NdO1−x Fx FeAs film. Data taken from [78, 83, 200, 275–277]

dependence suggest comparable values to the MBE-grown film in [83]. The slopes of μ0 Hc2 close to Tc were investigated in [292] in magnetic fields up to 9 T for PLD-grown BaFe2 (As1−x Px )2 films with x = 0.28, 0.35, 0.45. It was found that Tc decreased from 28.9 K to 26.7 K and 24.2 K. The slopes, −μ0 dHc2 /dT |Tc , were Table 6.13 Critical temperature (Tc,90 ), estimated upper critical fields (μ0 Hc2 (0)), slopes (−dHc2 /dT |Tc ), and calculated GL coherence lengths (ξ ) or the superconducting layer thickness (tsc ) for different Fe-pnictide thin films shown in Fig. 6.28 ab dHc2 dT |Tc ξab (TK−1 ) (nm)

ξc (tsc ) (nm)

Refs.

(T)

c dH − dTc2 |Tc (TK−1 )

45

45

2.5

2.86

2.71

2.71

[275]

∼48

∼62

2.62

2.03

[275]

28

41

62

25

42

77

1.37

4.4–5

2.8

1.5

[200]

31.3

>50

>90

1.1

5.25

3.2

Tc (K)

c μ0 Hc2 (0)

ab μ0 Hc2 (0)

(T)

Sr(Fe1−x Cox )2 As2

∼20

BaFe2 (As1−x Px )2 LaO0.9 F0.1 FeAsa LaO1−x Fx FeAs

30.7

(La1−y Sm y )O1−x Fx FeAs

Compound

a Polycrystalline

−

[124]

film (Reproduced and adapted with permission from PNAS)

[200]

6.6 High Magnetic Field Studies

317

2.96 TK−1 (for x = 0.28) and marginally smaller for larger P contents in the case of μ0 H  c. For μ0 H  ab, the slopes were 5.23 TK−1 (for x = 0.28) and marginally higher for larger P contents. The GL coherence lengths were ξab = 2.36 nm and ξc = 1.33 nm. Upper critical fields in Fe-oxyarsenide thin films are highest among the Febased superconductors and were determined for polycrystalline and epitaxial LaO1−x Fx FeAs films grown by a two-stage process [79, 124, 200] with a two-band model discussed in [286], for (La1−y Sm y )O1−x Fx FeAs films grown by a two-stage process [200], PLD-grown SmO1−x Fx FeAs films that have a hybrid structure due to the F-diffusion gradient [276], and co-doped SmO1−x Fx Fe1−y Co y As films grown by PLD [277]. Based on a two-band fit [285], decoupling of the electronic bands and a dominating intraband versus interband coupling, λ11 λ22 > λ12 λ21 was regarded to be responsible for the strong increase of μ0 Hc2 towards lowest temperatures [286]. Fe-pnictides are characterized by small and temperature dependent anisotropies γ Hc2 . While the temperature dependence is a typical signature of a multiband superconductor, the small absolute values of γ Hc2 are remarkable because of the anisotropic unit cells and electronic band structure of the Fe-pnictide superconductors. Almost isotropic upper critical fields were determined for Sr(Fe1−x Cox )2 As2 films with 1.0 ≤ γ Hc2 ≤ 1.5 in the whole temperature range up to Tc,90 ≈ 20 K [275]. γ Hc2 ≈ 1.3 for T → 0 in a P-substituted BaFe2 As2 film [83]. Close to Tc , upper critical field anisotropies of 1.5, 1.7 and 2.0 were found in BaFe2 (As1−x Px )2 thin films for x = 0.28, 0.35 and 0.45 [292]. The anisotropy in an underdoped film (x = 0.19) was 2.2. Although the upper critical field does not display an anomaly near the QCP, the anisotropy, γ Hc2 showed a minimum for x = 0.28. In [79, 200] γ Hc2 could be related to the electronic mass anisotropy γm = (m c /m ab )0.5 and determined via using an AGL scaling of critical currents, that reflect the electronic mass anisotropy in the absence of a directional vortex pinning sites (Fig. 6.29a, b). A detailed discussion can be found in [286]. Within the frame of a two-band GL theory [284] it could be argued, that in the limits of T → 0 and T → Tc , γ Hc2 ≈ 3 and 5, respectively, offers access to the electronic mass anisotropies of the decoupled bands. The discussion was restricted to two bands. The practical use is shown in Fig. 6.29c, d, where for an Fe-oxyarsenide film the upper critical fields, ab c μ0 Hc2 beyond 100 T can be estimated by multiplying the obtained γ Hc2 by μ0 Hc2 .

6.7 Electromagnetic Properties, Superconducting Gaps and Fermi Surfaces from Spectroscopy 6.7.1 DC Transport and Response to Low Frequency Fields DC Hall Effect The transverse (Hall) resistivity in the normal state results from the Lorentz force that acts on charge carriers in a magnetic field. A widely used experimental configuration

318

6 Thin Film Studies Under Focus

Fig. 6.29 In the absence of directional vortex pinning, γ = γm ≈ γ Hc2 . The anisotropy can be determined for low temperatures from the AGL scaling of the critical current densities. In [200] it was finally demonstrated for an epitaxial LaO1−x Fx FeAs film that a γm from AGL scaling of the critical current densities agrees with γ Hc2 from upper critical field measurements in the accessible temperature window. b Upper critical fields for a LaO1−x Fx FeAs film (2-stage process). c Application of this procedure and determination of γm ≈ γ Hc2 for an epitaxial, 10 nm thin NdO1−x Fx FeAs ab film (MBE). d The corresponding measured upper critical fields and the extrapolated μ0 Hc2

for epitaxial thin films is the application of the magnetic field perpendicular to the film plane (i.e. parallel to the c-axis in most epitaxial thin films), expressed as a component Hz , and having the current flow and voltage drop within the film ab-plane. The Hall resistivity is written then as ρx y = RH Bz . RH is called Hall coefficient and its sign is commonly used to determine the dominant charge carriers in the material, which is negative for electrons and positive for holes. Fe-chalcogenide thin films show in general a positive Hall coefficient at room temperature. However, upon cooling, the temperature-dependence of RH (T ) exhibits one or two sign changes and is not necessarily monotonic. At low temperatures (typically close to Tc ) the sign of the Hall coefficient varies from negative in FeTe films to positive in FeSe films. The temperature dependence of RH in other Fechalcogenide compounds, such as FeSe1−x Tex and FeSe1−x Sx , is found between those of FeSe and FeTe, but behaves more complex and depends on the doping level. For a discussion of the Hall resistivity a minimal two carrier model was introduced, that includes two independent (electron and hole) charge carriers of charge e, that

6.7 Electromagnetic Properties, Superconducting Gaps and Fermi Surfaces …

319

Fig. 6.30 a Temperature dependence of Hall coefficients, RH (T ) for different Fe-chalcogenide and Fe-pnictide thin films. The Hall bar geometry was produced by using a metal shadow mask during the deposition of the thin films. Data taken from Fig. 3 in [295], Fig. 2 in [299], Fig. 5 in [298] and Fig. 2b in [121]. b Tc,on in FeSe-EDLT devices on different substrates as a function of RH at 50 K. (Reprinted with permission from Fig. 4 in [296]; © (2017) by the American Physical Society)

differ in their mobilities, μe , μh , and their densities n e , n h . Since the conductivities of both carriers are additive, the resulting Hall resistivity in the frame of the Boltzmann transport theory is ρx y (B) =

1 (n h μ2h − n e μ2e ) B. e (n h μh + n e μe )2

(6.14)

Available mobilities and carrier densities must be treated with care, because the two carrier model neglects interband transitions and only approximates the multiband semimetals [293]. A pronounced temperature dependence of RH (T ) accompanied with sign changes across the structural (nematic) transition or the magnetic transition from paramagnetic into a SDW state were commonly ascribed to Fermi surface reconstructions. Selected results for RH (T ) in the normal state between Tc and 300 K are compared in Fig. 6.30a and are summarized below. Reference [294] offers data for the temperature evolution of RH (T ) in a 150 nm thin FeSe film deposited on CaF2 . A positive Hall coefficient of +0.7 × 10−9 m3 C−1 was measured at room temperature. A small negative RH appears between 115– 200 K which reflects an almost compensated semimetallic state with n e ≈ n h . Upon decreasing the temperature, RH is strongly increasing and positive with a value of +6.6 × 10−9 m3 C−1 closely above Tc = 11.4 K. In the limit of low temperatures, it appears convenient to reduce the description to a single hole band with RH = 1/n h e and a hole density of n h = 1021 cm−3 . Reference [295] discussed the influence of in-plane strain on RH (T ) for a series of 30–75 nm thin films grown from an Fe1.1 Se target on different substrates. Here, the in-plane strain was defined by ε = (af − abulk )/abulk , where af denotes the a-axis parameter of the film and abulk denotes the a-axis parameter of a comparable bulk (literature value) at room-temperature. A variable in-plane strain, −1.55% ≤ ε ≤ +1.5% was found in films deposited on CaF2 ,

320

6 Thin Film Studies Under Focus

LaAlO3 , LaAlO3 -buffered (La,Sr)(Al,Ta)O3 and (La,Sr)(Al,Ta)O3 substrates. Within the nematic state (T ≤ 70 K), the temperature dependence of RH (T ) became strongly influenced by the strain. At 20 K the Hall coefficient showed positive values ranging from +9 × 10−9 m3 C−1 for ε = −1.5% (Fe1.1 Se/CaF2 ) to +29 × 10−9 m3 C−1 for ε = +1.1% (Fe1.1 Se/(La,Sr)(Al,Ta)O3 ). The above results for thin films are in contrast to RH (T ) in bulk FeSe, where a negative Hall coefficient at 20 K was reported. Reference [296] addressed the influence of different oxide substrates (KTaO3 , MgO, SrTiO3 ) on the transport properties of FeSe films (with total thicknesses of 26.7, 10.4 and 14.0 nm, respectively) in EDLT devices, in which Tc,on was raised to a maximum value of 40 K upon application of a gate voltage (Sect. 6.2.2). Due to the electrostatic field the FeSe film is divided up into three layers, a ∼3 nm thin electronrich layer near the surface that is in contact with the ionic liquid, an intermediate layer with bulk-like properties and dominant hole conductivity, and an electron-rich bottom layer at the film/substrate interface. The thickness of the latter charge transfer layer was negligible in MgO, 4 nm (for the film on SrTiO3 ), and 13 nm (for the film on KTaO3 ). The measured Hall coefficient RH at 50 K depended sensitively on the majority charge carriers within each of the layers. When the whole film was governed by the electron-rich layers, RH became negative. It was found, that Tc,on correlated with RH at 50 K (Fig. 6.30b). Hall resistivities of FeTe films of varying thickness deposited on MgO or LaAlO3 substrates were investigated in [297, 298]. At 300 K, RH takes values of +1.6 − +1.75 × 10−6 m3 C−1 . The sign reversal in RH from positive to negative occurs at ∼70 K in films with thicknesses of 165 and 400 nm, whereas RH becomes negative at a reduced temperature of ∼40 K in the 40 nm thin film. It was concluded that the sign reversal of RH appears at the paramagnetic-antiferromagnetic transition. At T = 10 K the values for the Hall coefficient range from −2.9 × 10−6 to −2.4 × 10−6 m3 C−1 in films with thicknesses t ≥ 165 nm, whereas RH = −0.7 × 10−6 m3 C−1 in a 40 nm thin film. The Hall resistivity was experimentally determined also for various FeSe1−x Tex films [297, 299–302] and FeSe1−x Sx films [299, 301] with different Te and S contents. The mixed state Hall resistivity in FeSe1−x Tex films, addressed in [11], is mentioned in Sect. 6.1. Reference [121] studies the normal state Hall effect in Ba(Fe1−x Cox )2 As2 films grown on MgO. The Hall coefficient for the electron-doped Ba(Fe0.92 Co0.08 )2 As2 film is – as expected – negative and decreases from RH = −0.55 × 10−9 m3 C−1 at 300 K continuously to −1.74 × 10−9 m3 C−1 at temperatures close to Tc (Fig. 6.30a). A Hall coefficient of −1.7 × 10−9 m3 C−1 at 25 K was also evaluated for a Ba(Fe0.92 Co0.08 )2 As2 film grown on (La,Sr)(Al,Ta)O3 in [28], where both, the longitudinal, ρx x , and the transversal resistivity, ρx y , were mainly studied in the reversible mixed state below Tc,on as a probe for vortex motion (see Sect. 6.1). A short notice is finally made to the anomalous Hall effect, that was mentioned for films of Ba(Fe1−x Cox )2 As2 [121] and FeSe0.5 Te0.5 [302]. The anomalous Hall effect, that arises in magnetic materials with a magnetization component Mz , adds with RAHE Mz to the total transverse resistivity. RAHE is called anomalous Hall coefficient. An intrinsic origin of the anomalous contribution in Fe-chalcogenides or Fe-pnictides

6.7 Electromagnetic Properties, Superconducting Gaps and Fermi Surfaces …

321

is unknown at present. An extrinsic origin originating from Fe impurity-clusters, that are not uncommon in PLD-grown films, could be regarded as plausible explanation. Electric Noise Measurements Voltage noise and its dependency on temperature- and bias current is an important parameter for the development of electronic circuits used in applications. It was experimentally determined in FeSe0.5 Te0.5 films on LaAlO3 [303, 304], FeSe0.5 Te0.5 films on SrTiO3 [305], as well as in Ba(Fe1−x Cox )2 As2 films [306]. The results are summarized below. In [303] the voltage noise spectral density SV of 150 nm thin films with Tc,0 = 18 K was measured in the range of f = 10 Hz–1 GHz by employing a four-probe contact method on 5 × 10 mm2 large film pieces. The instrumental background noise was 1.3 × 10−17 V2 ·Hz−1 . The low frequency noise showed the characteristic 1/ f dependence, which is also known as flicker or excess noise. The voltage-dependence of SV (V ) at a constant frequency of 90 Hz and at different temperatures was discussed in the frame of two models: (i) A resistance fluctuation model, that accounts for a non-uniform Ohmic conductivity with SV (V ) = a2 (T )V 2 + a0 , failed to fit the experimental data at temperatures above 100 K; (ii) an excess 1/ f noise model with a power law SV (V ) = a(T )V b(T ) + c could fit the data for all measured temperatures (up to 300 K). Excess noise occurred above a threshold voltage of 0.22 ± 0.01 V. This threshold was associated with a change of the dominant charge carrier channel at higher temperatures (T ≥ 70 K), i.e. additional hole conductivity may give rise to nonequilibrium fluctuations. In the temperature-dependence, the noise abruptly increased at the normal-to-superconducting transition. A current percolation model with a resistance noise level f · S N ∝ R −1.54 was applied in accordance with a 2D behavior for film thicknesses smaller than the percolation length. The voltage noise spectral density was also measured in UV photo-lithographically patterned FeSe0.5 Te0.5 films in a signal range of 1 Hz–100 kHz [304]. The current paths for the four-probe contact method were 495 μm long and 2–16 μm wide, however, after photo-lithographic treatment and air exposure Tc reduced from 18 to 15.2 K. Similar to the the results on unpatterned films, a threshold electric field for the excess noise was observed. Reference [305] reports on the voltage noise effects in 150–200 nm thin FeSe0.5 Te0.5 films deposited on SrTiO3 substrates. Unpatterned and patterned films were investigated. In comparison to the previous reports above, the phenomenological description of the voltage noise was extended to a two carrier model that accounts for electrons and holes. The spectral density of the voltage fluctuations at low temperatures (T ≤ 70 K) was ascribed to resistance fluctuations with a 1/ f dependence based on the empirical formula SV = αH · V 2 /(N f ), where N is the number of free charge carriers in the system, f is the frequency and the Hooge parameter, αH , which is a proportionality factor with a value of ∼10−3 . In order to include nonlinear field dependencies of SV , the authors proposed a modification of the empirical formula. Finally, the same research group also applied voltage noise spectroscopy to 100 nm thin Ba(Fe1−x Cox )2 As2 films in the range of 10 Hz–60 kHz [306]. The films were deposited by PLD on Fe/MgAl2 O4 -buffered roof-type bicrystal SrTiO3 substrates (misorientation angle = 45◦ ) and patterned using photolithography by a complex

322

6 Thin Film Studies Under Focus

arrangement of current paths along and across the GB. Tc,50 of the film was reduced to ∼15 K. SV ( f ) ∝ 1/ f was detected for Ba(Fe1−x Cox )2 As2 at all temperatures, and the normal-to-superconducting transition was modeled by a 3D percolation network. Across the GB, the spectral density changed to SV ( f ) = K / f γ + c, where K is a temperature- and current-dependent noise amplitude, and c a temperature-dependent constant. The exponent γ increased with decreasing temperature from 1.2 to 1.5 at Tc and jumped to a value of 2 in the superconducting state. The current path across the GB can be viewed as multiple parallel point contacts or weak links with fluctuating critical current, which leads to a Lorentzian-type spectrum with SV ( f ) = K / f 2 + c.

6.7.2 Radio Frequency and Microwave Techniques The radio-frequency (RF) spectral range of ac electromagnetic fields is defined between 3 kHz and 300 GHz and includes microwaves at 300 MHz–300 GHz. The electromagnetic response of superconductors in RF fields is of vital importance in the technology of particle accelerators, where resonant cavities are made of or coated with superconducting materials. In addition, superconducting thin films are also implemented in a variety of microwave devices. In contrast to dc superconductivity, superconductors are not free from dissipation in ac fields which results in a residual surface resistance. It originates from unpaired electrons in the superconductor and is frequency- and temperature-dependent. At cryogenic temperatures (and well below Tc ), the surface resistance becomes much smaller compared to that in a normal conductor. Due to the contribution of vortices (and their normal conducting cores) to the losses in type II superconductors, RF or microwave studies also provide fundamental insight into vortex dynamics. The electrodynamics of superconductors is conveniently studied by the microwave surface impedance. The surface impedance, Z s , can be determined by resonance methods, which are restricted to distinct frequencies and thus cannot be exploited for spectroscopy. Furthermore, resonance methods are sensitive to an average value of Z s . In contrast, the so-called Corbino disk setup works in a dynamic frequency range. In this geometry, the current is injected by the inner core of a coaxial cable and flows radially in the film to the outer shield of the coaxial cable. Local measurements of Z s are possible by imaging/scanning methods, where the sample surface is only locally excited. Limited application of both methods can be found in the investigation of Fe-based superconducting thin films. The surface impedance of a bulk superconductor, Z s,∞ , is given as ratio between the tangential electric field to the tangential magnetic field on the film surface and is a complex valued quantity, Z s = Rs + i X s with surface resistance Rs and surface reactance X s . For a thin film with a thickness t comparable to the penetration depth λ or smaller, a non-negligible part of the incoming electromagnetic wave propagates through the film and is reflected again partially at the film/substrate interface. The thin film surface impedance is then expressed in terms of the reduced thickness x = t/λ as Z s = Z s,∞ coth (x). In addition, when a thin metallic cap layer is deposited onto the

6.7 Electromagnetic Properties, Superconducting Gaps and Fermi Surfaces …

323

superconducting film, the final effective surface impedance, Z s,e f f , is approximated by the sum of Z s and the contribution of the cap layer, tc /δc Rc , where tc , δc and Rc are the thickness, the skin depth and the surface resistance of the cap layer. The principle of the resonator method is based on the detection of changes in the resonant frequency, f 0 and the quality factor Q. The effective microwave surface resistance is given by the change in Q −1 multiplied by a geometry factor, As : Rs,eff =

−1 Q −1 f − Q0 . As

(6.15)

The effective surface reactance is X s,eff = X s,eff (0) + ΔX s,eff (T ) 2Δf (T ) ΔX s,eff (T ) = , As f 0

(6.16) (6.17)

determined by the frequency shift Δf . Surface resistance and reactance are measures for the power dissipation caused by the electromagnetic wave and the electromagnetic energy, that can be stored inside the superconductor. The surface reactance is directly linked to fundamental quantities such as the skin depth (normal state) or the penetration depth (superconducting state). Surface Impedance of Fe-Chalcogenide Thin Films The surface impedance of a FeSe0.3 Te0.7 film was investigated in a series of publications [307–310]. The experimental setup based on a sapphire dielectric cavity resonator at a resonance frequency of 9.375 GHz and with a quality factor of Q 0 = 45000 (at room temperature). The cavity was specially designed for small sample sizes (1–2 cm) and the measurement of the TE011 -mode, and a coefficient of inclusion, As = 2.9 × 10−4 −1 was determined for the film. The film under investigation was grown by PLD on LaAlO3 with a thickness t = 100 nm and a superconducting transition at Tc,on = 14.8 K (ΔTc = 1.6 K). The obtained surface impedance at low temperatures (T ∈ [0, 0.5Tc ]) for the used field configuration was evaluated using   i kt Z s,eff = − Z s cot 2 2

    t t t λ + cosec2 ≈ 2Rs Rs,eff (T ) = 0.5Rs coth λ 2λ 2λ t   λ t ≈ 2X s X s,eff (T ) = 0.5X s coth 2λ t Results are shown in Fig. 6.31. The peak in Rs,eff below Tc was explained by the authors as a result of a change in the direction of the microwave magnetic field above the film surface from parallel to the film surface towards a direction perpendicular to the film surface. From the temperature dependence of the effective surface reactance

324

6 Thin Film Studies Under Focus

Fig. 6.31 Microwave surface impedance of FeSe0.3 Te0.7 film. Temperature dependence of the a resonator frequency, f , b quality factor, Q, c effective surface resistance, R, d effective surface reactance, X , e penetration depth, λ and the skin depth, and f Δλ. The superconducting state is indicated by a gray background. Taken from Figs. 1,2,4 in [308]

and a penetration depth value of λ(0) = 560 nm the temperature dependence of λ could be analysed. In addition, a power law Δλ ∝ T n with n = 2.4 [308] or 2.95 [310] in a temperature interval of 1.7–7 K was found. The power law was not interpreted in terms of gap nodes. For a further analysis of the superfluid density ∝ λ2 a two-gap model with 2Δ1 /kB Tc = 0.86 and 2Δ2 /kB Tc = 2.44. It significantly deviates from a single band BCS fit. The quasiparticle scattering rate with τ −1 (0) ≈ 2 × 1011 s−1 increases with temperature. Subsequent studies [309, 311] used FeSe0.5 Te0.5 films grown on CaF2 with Tc = 18.8 K (ΔTc = 0.8 K) and focused on two different film orientations with c-axis parallel and perpendicular to the microwave magnetic field. The film thickness was 100 nm, the lateral film size was 1 × 1 mm2 and 2 × 2 mm2 , respectively. A sapphire ring in a cylindrical copper case was used as resonator, where the H011 -mode was excited. The resonant frequency is 9.38 GHz and  not influenced by the CaF2 substrate. The penetration depth was modeled by λ(0)( 1 − (T /Tc )2.7 )−1 [309]. A recent microwave surface impedance study on 240 nm thin FeSe1−x Tex thin films with Tc = 18 K can be found in [312]. The skin depth was determined from the normal state resistivity to be 6.8 μm (5.4 μm) for the TE011 (TE021 ) mode. The films were in the single vortex pinning regime up to μH0 = 1.2 T. Microwave Spectroscopy for FeSe0.5 Te0.5 Reference [313] provides microwave spectroscopy applied to FeSe0.5 Te0.5 films in the superconducting transition up to the normal state. The films were grown by PLD on CaF2 substrates with thicknesses of 30, 60, 116 and 150 nm, which are much

6.7 Electromagnetic Properties, Superconducting Gaps and Fermi Surfaces …

325

smaller than the skin depth δ = 20 μm at 1 GHz. Tc,0 of the films varied from 15.9 – 16.9 K. Gold electrodes in Corbino disk geometry were sputtered on the films. The complex-valued reflection coefficient, S11 , was determined for frequencies in the range of 45 MHz – 10 GHz using a vector network analyzer. The fluctuation conductivity was analyzed according to the theory by Fisher, Fisher and Huse [314]. A description of the superconducting transition within a 3D-XY model was suggested for the Fe-chalcogenide. A dimensional crossover between 3D and 2D conductivity fluctuations in dependence of the film thickness was observed, which is expected when the out-of-plane coherence length, ξ⊥ (T ) = ξ⊥ (0) (T /Tc − 1)−ν , exceeds the film thickness. With ν = 0.67 and ξ⊥ (0) = 1 nm, the criterion resulted in ξ⊥ (T ) ≈ 100 nm for temperatures at T /Tc − 1 ≈ 10−3 . Due to the fluctuations, the onset of the superconducting transition overestimates the critical temperature of the superconductor, Tc,on by ≈ 1.1Tc . Local Surface Impedance of Fe-Pnictide Thin Films Two additional publications are mentioned in this section: In [315] a two-coil mutual inductance apparatus operated at 50 kHz was applied to Ba(Fe0.92 Co0.08 )2 As2 films that were deposited by PLD under HV condition. Film thicknesses were 100 nm. Here, the penetration depth was evaluated via the complex-valued sheet conductivity. A value of λ(0) = 350–430 nm was evaluated, the temperature dependence for λ(T)−2 is in accordance with a small s-wave gap 2Δ/kB Tc = 2.2 ± 0.1. In addition, a power law Δλ/λ(0) = 0.60·(T /Tc )2.5±0.1 was found. Compared to results in single crystals, the superfluid density in the films is reduced by 33%. The reduction could be explained only partially (∼10%) by additional BaFeO3−x impurities in the films. A similar film of 200 nm thickness was investigated by near field magnetic field microwave microscopy in [316]. The film was capped additionally by a 20 nm thin Pt layer. The resulting capped film had a superconducting transition of 18.1 K. Within the setup an RF magnetic field at GHz frequencies with an amplitude of 200 mT and in a vertical distance of 0.2–1.0 μm above the film interacted with the thin film. The reflected linear (S11 ) as well as the non-linear (3r d harmonic power, P3f ) response signals were recorded for different temperatures. A maximum surface current density of 8 × 105 Am−2 is locally generated in the film. According to the authors, the nonlinear response originated from a current-induced modulation of the order parameter suppression near Tc and from a vortex motion at low temperatures. A contribution to the nonlinear response from normal-superconducting junctions below 6 K due to the capping layer could not be excluded.

6.7.3 Optical (IR/THz) Spectroscopy Optical spectroscopy probes the frequency-dependent response of matter to electromagnetic radiation. In particular, it allows the study of the optical conductivity, charge carrier dynamics and low-energy excitations in thin films. The spectroscopic methods are generally classified by the spectral range of the electromagnetic radia-

326

6 Thin Film Studies Under Focus

tion (expressed in wave-numbers or frequencies), although most commercial spectrometers already cover a large spectral range from the ultraviolet (UV) to the terahertz region. In the investigation of superconductors the infrared (IR) and terahertz (THz) regions are of primary interest, because the frequency matches with the energies of superconducting gaps and those excitations that mediate Cooper pairing. IR spectroscopy is typically carried out for ν ∼ 33–13000 cm−1 (1–390 THz), THz spectroscopy uses ν ∼ 3.3–330 cm−1 (0.1–10 THz). Latter is sometimes synonymously called far infrared (FIR) spectroscopy because of the spectral range overlap. Spectroscopic methods are further divided into steady-state or time-dependent and the techniques are specified into Fourier-transform (FT), backward-wave oscillator based (BWO), pump-probe or time-domain spectroscopy (TDS), that differ in frequency range, resolution and dynamical range. The experimentally accessible quantities, the frequency- and temperaturedependent reflectance, R(), and transmittance, T (), are related to the complexvalued index of refraction, n˜ = n + iκ (with n the (real) index of refraction and κ the attenuation coefficient). Sample inhomogeneities and multiple layers (including substrates, buffer layers, capping layers) must be taken into account during the numerical analysis done in a set of Fresnel equations. The optical response of the bare substrate and additional layers must be either known from literature or measured separately (see, for example, data for Al2 O3 [317] or DyScO3 [318]). The optical response of metals and superconductors is traditionally discussed in terms of the complex-valued dielectric function ε˜ () = ε1 () + iε2 () or the complex-valued optical conductivity σ˜ () = σ1 () + iσ2 () with ε1 (σ1 ) the real part and ε2 (σ2 ) the imaginary part. The parameters are derived from n˜ by ε˜ = n˜ 2 , ε1 = n 2 − κ 2 , ε2 = 2nκ and σ˜ = iε0 ε˜ , where ε0 is the vacuum permittivity. In the general (non-isotropic case) they are tensors. The real part of the optical conductivity describes the dissipation of the electromagnetic radiation, whereas the imaginary part accounts for the screening of the radiation field. In simple metals σ˜ is well described by the Drude-Lorentz model that includes the response of free charge carriers or plasmons (Drude term) as well as the response of bound charges or lattice vibrations (Lorentz term). The expression for the Drude term is σ˜ D () =

2p 1 + iτD 1 1 + iτD ne2 τD = = σdc 2 2 m 1 − iτ 4π 1 +  τD 1 + 2 τD2

(6.18)

with the electron density (n), a frequency independent relaxation rate (τD−1 ) and a frequency independent effective electronic mass defined from the curvature of the electronic band structure:  2 −1 2 ∂ E . (6.19) m= ∂k 2 The relation for the plasma frequency 2p = 4π ne2 /m and the dc conductivity σdc = σ1 ( = 0) are filled in above (6.18). The Lorentz term takes the vibration of bound

6.7 Electromagnetic Properties, Superconducting Gaps and Fermi Surfaces …

327

charges into account and is given as sum over multiple oscillators (optical phonons) with resonant frequency 0 and damping constant Γ = 1/τ σ˜ L () =



20, j 

j

i(0 , j 2 − 2 ) + Γ j 

.

(6.20)

The classical Drude term is often sufficient for a first description of the optical response of conducting systems. Multiple electronic bands can be treated by multiple Drude terms analogous to a parallel resistor configuration. The Drude model, however, fails in an accurate description of finite frequency absorptions, non-Fermi liquids, materials with band gaps or Dirac cones. For systems with strong electronphonon interaction or strong electron correlations, an extended Drude model with a frequency-dependent damping term was developed. In experiments performed on thin films, the precise knowledge of the film thickness is important for reducing the uncertainties in the Drude parameters p and τ −1 . An advantage of thin film samples is their use in transmission experiments. Typically, thin films are then deposited on transparent substrates of reduced thicknesses (∼0.15–0.5 mm), which are double-sided polished. The significance of FIR transmission studies on superconducting films is probably recalled best by the determination of the superconducting energy gap by Michael Tinkham and Rolfe Eldridge Glover in 1956. In the London-limit the real part of the conductivity can be expressed as a δ-function at  = 0 and the imaginary part diverges according to σ2 ∝ −1 : σ˜ sc (, T ) = σ1 (T ) + i

n s e2 m

(6.21)

Latter is connected to the superfluid density (ρs ) or the penetration depth (λ) via lim→0 μ0 σ2 (, T ) = ρs (T ) = λ(T )−2 . For a BCS superconductor, the real part of the optical conductivity is suppressed for all frequencies  < Δ. Although the BCS theory already includes the electromagnetic properties of conventional (weak-coupling and single band) superconductors, the theory of Mattis and Bardeen [319] has introduced a frequency-dependence of the optical response and σ1 ∝ 1 − (/kB Tc )1.65 . The theory of Mattis and Bardeen can be extended to include anisotropy and strong coupling effects. Zimmermann et al. [320] provided a formalism for BCS superconductors that is applicable in the clean as well as in the dirty limit. Important microscopic parameters of superconductors such as the electronelectron relaxation, the electron-phonon coupling constant or the different nature of superconducting and pseudogap phases can be investigated by ultrafast timeresolved (pump-probe) spectroscopy. The method employs femtosecond lasers that photo-excite (pump) quasiparticles. The complex-valued optical conductivity of Fe-based superconductors has been studied from reflectance measurements on crystals and reflectance and transmittance measurements on thin films. An informative review article is found in [321]. The liter-

328

6 Thin Film Studies Under Focus

ature on Fe-based superconducting thin films analyzes the normal state conductivity either by a single Drude (Drude-Lorentz) term or by two Drude components that reflect contributions from hole- and electron-like charge carriers. In contrast to studies carried out on crystals, the observation of a residual conductivity in the superconducting state has been commonly found in thin film studies. As a result, the gap-induced suppression of the in-plane optical conductivity is less pronounced, leading to different explanations: a strong anisotropic superconducting energy gap, a gap with nodes, pair breaking due to impurities and a generally unstable superfluid density [322–324]. A possible contribution from impurity phases, in particular Fe-containing precipitations or interfacial layers that are present in PLDgrown films, was indicated in [321]. A consequence of the residual conductivity in the superconducting state is that the proportionality between superfluid density, ρs and σ2 () is not longer valid and a correction term must be included in the evaluation of the London penetration depth, λL , that accounts for additional screening effects from non-superconducting charge carriers [325]. At present, the values of the penetration depth resulting from optical spectroscopy on thin films are uncorrected. Superconducting gap energies obtained from FeSe0.5 Te0.5 thin films scatter largely: Δ(0) = 0.45 ± 0.15 meV [323], 2.1 meV [294], Δ = 4.6 ± 0.4 meV [326]. Two gap values of Δ1 (0) = 1.5 meV and Δ2 (0) = 3 meV are given in [324]. For Co-substituted BaFe2 As2 the number of superconducting gaps detected by optical spectroscopy mainly depends on the used fits and models. A single small gap of 2Δ = 2.1 kB Tc ≈ 3.7 meV was found at 5 K in the frame of the Matthis-Bardeen model [322], two gaps of 2Δ1 = 2.9 kB Tc ≈ 6 meV and 2Δ2 = 16 meV were identified at 2–5 K using a 2-gap model in [327] and three gaps of 2Δ1 ≈ 3.8 meV, 2Δ1 ≈ 5.6 meV and 2Δ3 ≈ 8.1 cm−1 were extracted from a 3-gap model [328]. In all cases Ba(Fe1−x Cox )2 As2 on (La,Sr)(Al,Ta)O3 with thicknesses of 20–100 nm were investigated. In the next paragraphs, details of optical, IR and THz spectroscopy studies on Fe-chalcogenide and Fe-pnictide thin films are summarized. In the described experiments thin films were prepared by PLD (except in [317, 329]) and were of sufficient crystalline quality (either epitaxial or grown with a preferred orientation). The film composition must be taken as nominal when not explicitly stated otherwise, which is a drawback in most of the thin film studies. In particular, deviations in the Seand Te-content in FeSe0.5 Te0.5 films can be expected. A solid analysis of the optical response as a function of charge carrier doping is currently missing. IR/THz Spectroscopy Studies for Fe-Chalcogenide Thin Films Optical spectroscopy on Fe-chalcogenide thin films can be divided into (Table 6.14) • optical, near- and far-infrared (NIR/FIR) spectroscopy studies that probe steady state and time-dependent reflectance (reflectivity) in the normal state of FeSe films [330–334]; • reflectance measurements of FeSe0.5 Te0.5 films in the normal and superconducting state [326]; • THz spectroscopy for FeSe [294, 335] and FeSe0.5 Te0.5 [294, 323, 324];

6.7 Electromagnetic Properties, Superconducting Gaps and Fermi Surfaces …

329

Table 6.14 Overview of IR/THz spectroscopy studies and their spectral range (ν) on different Fe-chalcogenide thin films with thickness t, and superconducting transition temperature Tc Substrate t (nm) Tc (K) ν (cm−1 ) Method Refs. FeSe MgO

450, 460

10

4800–52000

CaF2 CaF2 SrTiO3 CaF2 CaF2

160 950 205 60

6; 11 11.53 7 11 12

12500–33333 5260–9090a 20–25000b 40–10000c 17 –58

LaAlO3

46

3

8–64.5

FeSe0.5 Te0.5 LaAlO3 LaAlO3 CaF2

150 200 50

16.2 13.7 18

12–900d 17–58

LaAlO3

100

12.1

3.3–4.3

MgO

100

14

5–35

a iHR320

Ellipsometry, pump probe Ellipsometry NIR R() R() R() THz-TDS T () THz-TDS T () pump probe IR/THz R() THz-TDS T () THz-TDS T () THz-BWO T ()

[330] [331] [332] [333] [334] [294] [335]

[336] [326] [294] [323] [324]

HORIBA Jobin Yvon; b Bruker IFS 80v/s and 113v, c Bruker Vertex 80v, d Bruker 70v

• a femtosecond pump probe spectroscopy study of FeSe0.5 Te0.5 [336]. In [330] two different FeSe films grown on MgO substrates were studied by ellipsometry and time-resolved pump probe spectroscopy: a 460 nm thick film with a preferred FeSe(101) out-of-plane orientation and a 450 nm thick film with FeSe(001) out-ofplane orientation. The preparation conditions, that result in different growth orientations can be found in [337]. The complex-valued optical conductivity obtained from the reflectivity in the visible and near-infrared (NIR) range is dominated by intraband and interband transitions between Fe 3d to hybridized Fe 3d – Se 4 p orbitals. Redistribution of optical spectral weight with decreasing temperature was noticed from the resonantly probed (hν = 1.55 eV) interband transition. The pump-probe spectroscopy (Ti:sapphire laser, repetition rate 76 MHz) with a pulse duration of 170 fs and a pump fluence of 5.3 μJcm−2 revealed two decay components in the picosecond response of ΔR/R: a fast with Afast exp(−t/τfast ), and a slow one with Aslow exp(−t/τslow ). The fast decay component emerged below T ≈ 130 K and was related to a temperature independent ‘pseudogap’ with Δ = 36 ± 4 meV. The slow decay component occurred up to room temperature, was anisotropic and was attributed to quasiparticle 100 001 = 2.7 ps−1 , τslow ≈ 0.2 ps−1 . thermalization via scattering by slow phonons: τslow A gap associated with the slow decay component was estimated to be Δ = 9.2 ±

330

6 Thin Film Studies Under Focus

1.5 meV. The authors concluded that a short-range nematic order developed already at ∼130 K and was responsible for the gap opening, before the film turned into a long-range nematic order at the structural transition Tstruct . A recent spectroscopic ellipsometry study compared two FeSe films deposited on CaF2 [331]. Data was gathered for UV and optical wavelengths (300–800 nm) with a spectral resolution of 5 nm at incident an angle of 75◦ . Within a simple Drude model, the two films with Tc,0 = 6 and 11 K distinguish in their scattering rates τ −1 ≈ 152 × 103 and 45 × 103 cm−1 and their plasma frequencies p = 126 × 103 and 75 × 103 cm−1 . Normal state properties were also investigated for two 160 nm thin FeSe films on CaF2 substrates with Tc,0 (Tc,on ) = 9.55 K (11.25 K) and 9.26 K (11.53 K), respectively [332]. The complex-valued conductivity was described using a Drude-Lorentz model (for T < 100 K) and the Drude-Smith formula (for T ≥ 100 K). As a qualitative result, the relaxation time τ decreases with increasing temperature up to 100 K (which could be related to the structural transition temperature, Tstruct ) and remains nearly constant above 100 K. The dc conductivity decreases with increasing temperature which was primarily explained by the decreasing relaxation time, τ , due to electronphonon scattering. Other studies refer to two Drude components in the description of the optical conductivity, as for example [333]. Here, optical reflectance spectroscopy was carried out on a 950 nm thick FeSe film on SrTiO3 with Tc ≈ 7 K. SEM-EDS confirmed a Fe:Se ratio of 1:1. The normal state spectra were described by two Drude components: a broad and a narrow one with  p1 = 1300 cm−1 ,  p2 = 10900 cm−1 and τ1−1 = 20 cm−1 , τ2−1 = 840 cm−1 (at 300 K) and  p1 = 2700 cm−1 ,  p2 = 10600 cm−1 and τ1−1 = 16 cm−1 , τ2−1 = 830 cm−1 (at 8 K). The overall plasma frequency was p = (2p1 + 2p2 )0.5 = 11000 cm−1 (1.36 eV). In comparison with the theoretical plasma frequency obtained from DFT (∼3 eV), a band renormalization of 2p,DFT /2p,exp ≈ 5 was suggested. A similar study can be found for a 205 nm thin FeSe film grown on CaF2 [334]. Although the substrate exerts compressive strain along the a-axes, the structural phase transition is not suppressed, which occurs at Tstruct = 90 K. The transition to superconductivity is found at Tc = 11 K. In the normal state the optical conductivity consists of two Drude components: a narrow one (with small spectral weight) and a broad one (with large spectral weight) which correspond to coherent and incoherent charge dynamics and reflect the multiband nature of FeSe. Above Tstruct the temperature dependence of the narrow Drude component, which is dominated by the hole-like charge carriers, is mainly governed by the temperature dependence of the scattering rate. Below Tstruct the spectral weight of the narrow Drude component decreased and the charge carrier density was suppressed. The spectra revealed also two interband transitions at 2000 and 5000 cm−1 . The optical conductivity was gradually suppressed across Tc and the superfluid density increased only slowly with decreasing temperature. It was noted, that transverse and longitudinal phonon modes of CaF2 at 265 cm−1 and 500 cm−1 appeared in the spectra, but this substrate contribution could be removed. An important result is related to the optical phonon mode (E u ) in FeSe, that increases with decreasing temperature from 249 cm−1 (at room temperature) to ∼248 cm−1 (at 100 K). Below the structural transition the frequency

6.7 Electromagnetic Properties, Superconducting Gaps and Fermi Surfaces …

331

remains almost ∼248 cm−1 (down to 4 K), which indicates a change in the bonding between Fe and Se ions due to the coupling between lattice and electronic orbitals when FeSe undergoes a structural transition. Reflectance measurements on FeSe0.5 Te0.5 films in the normal and superconducting state are found in [326]. The experimental data was described by a twocomponent Drude model having a broad and a narrow component with parameters:  p1 = 7050 cm−1 ,  p2 = 1600 cm−1 and τ1−1 = 1050 cm−1 , τ2−1 = 200 cm−1 . The overall plasma frequency is ∼0.9 eV. The dc conductivity, given by σ0,1 + σ0,2 , is 790 + 220 −1 cm−1 . In the superconducting state (at 6 K) a gap opening was only observed on the narrow Drude component with a value of Δ = 4.6 ± 0.4 meV. Among the THz spectroscopy studies, reference [335] has accessed charge carrier dynamics in a 46 nm thin FeSe thin film on LaAlO3 with Tc,0 = 3 K and Tstruct = 80 K using THz time-domain spectroscopy (THz-TDS). A two-band Drude model with electron-like and hole-like charge carriers was applied to describe the diagonal (or longitudinal) σ˜ x x as well as the off-diagonal (or Hall) σ˜ x y contributions in the normal state at 7 K. For T → 0 the electron density n e = 5.4 × 1019 cm−3 is approximately half the value of the hole density n h = 1.7 × 1020 cm−3 . The temperature dependence of both charge carrier densities develops with opposing trends: while the density of holes increases, the density of electrons decreases with temperature. The model yields effective electron and hole masses of m e = 0.96 m e , and m h = 2.90 m e , respectively. At low temperatures (T < 100 K) the electron and hole scattering times start to deviate from each other when T → 0: the electron scattering rate increases only marginally and approaches τe = 0.11 ps, the hole scattering rate increases up to τh = 0.45 ps. Latter explains the increase of the Hall coefficient, RH , below 150 K for T → 0 up to 1.5 × 10−8 m3 C−1 . THZ-TDS was also carried out in [294] on a 60 nm thin FeSe on a CaF2 substrate. Based on a discussion of the normal state optical conductivity in the limit of a single-band metal, FeSe was characterized as system with weak electron correlations, which is in contrast to the established view of stronger electron correlations in FeSe. The complex-valued conductivity, σ (), was described by a Drude term with a real part σ1 ∼ 5000 −1 cm−1 and an imaginary part σ2 ∼ 1000 −1 cm−1 (at 1 THz and between 90 and 120 K). The dc conductivity was found to decrease moderately with increasing temperature from σ0 ∼6100 −1 cm−1 at 20 K down to 4500 −1 cm−1 at 125 K showing a weak suppression at Ts . The temperature dependence of the relaxation time, τ = τh , shows a sharp change around Ts = 90 K. Low temperature (T < 90 K) values for the relaxation time are ∼0.026 ps, for T > 90 K, τ decreases to ∼0.05 ps. The dominant charge carriers at low temperatures are holes, and additional transport measurements on a 150 nm thin FeSe film revealed an increasing (positive) Hall coefficient, RH > 0, below Tstruct . A hole density of n h = 1021 cm−3 and a hole mass enhancement of m h /m = 1.3 were evaluated. THz-TDS was also performed on a 50 nm thin FeSe0.5 Te0.5 film grown on CaF2 [294]. The optical conductivity of the superconducting state below Tc = 18 K was discussed in the frame of a two-fluid model consisting of contributions from a superfluid and Drude quasiparticles by introducing the superfluid fraction f s = n s /n n as a parameter, which is the ratio of the density of paired charge carriers in the superconducting state and the density of unpaired charge carriers (measured in

332

6 Thin Film Studies Under Focus

the normal state). The superfluid density increases gradually below Tc and is found to be only 30% at 0.6T /Tc . A gap value of 2.1 meV was evaluated, resulting in 2Δ/kB Tc = 2.7 ± 0.5. An early transmission THz spectroscopy study [323] investigated a 100 nm thin FeSe0.5 Te0.5 film on LaAlO3 with Tc,on = 12.1 K and Tc,0 = 9.8 K. No strong frequency dependence was observed for the real part of the complex-valued conductivity, σ1 , whereas the imaginary part increased with frequency above Tc like in a Drude metal, σ2 ∝ /(1 + (τ )2 ). The plasma frequency p = 0.3–0.5 eV and the relaxation time τ = 10−2 ps were estimated. Below Tc the frequency dependence of σ2 changed to σ2 ∝ 2.5 . A superconducting gap of Δ(0) = 0.3–0.6 meV was evaluated. In [324] THz backward-wave-oscillator (BWO) transmission spectroscopy using a Mach-Zehnder interferometer setup was performed on a 100 nm thin FeSe0.5 Te0.5 film. The film grown on MgO showed a Tc of 14 K. The optical properties of the 0.5 mm thick MgO substrate with refractive index n ≈ 3.13 neither depend strongly on temperature nor on frequency, however, Fabry-Pérot-type interferences occur within the substrate. For low frequencies, the normal state optical conductivity was described as a Drude metal with a large effective mass of m  = 11 m e (determined from the Faraday rotation), a plasma frequency p = 0.79 eV, a Drude scattering rate of (2π τ )−1 = 200 cm−1 and a quasiparticle scattering rate in −1 = 63 cm−1 . The superconducting state was described with the normal state of τqp a two-band model assuming s± order parameter symmetry. A residual conductivity (in σ1 ) measured down to 2 K was explained as signature of a strongly anisotropic gap. Experimentally, only the smaller gap value was determined at Δ1 (0) = 12 cm−1 (1.5 meV), whereas the larger gap, Δ2 (0) = 24 cm−1 (3 meV), was obtained from a fit procedure. The penetration depth at low temperatures was estimated as λ = 550 ± 10 nm. The photoinduced reflectivity change, ΔR/R versus delay time, of a 150 nm thin FeSe0.5 Te0.5 film was obtained in a pump probe experiment (Ti:sapphire laser: λ = 810 nm, repetition rate 82 MHz) with a pulse duration of 100 fs [336]. The pump fluence was 3–9.5 μJcm−2 . The film was grown on LaAlO3 and showed a superconducting transition at Tc = 19.1 ± 0.9 K. Restricted by experimental resolution, it was not possible to probe the fast electron-electron scattering, but only the electronphonon interaction. ΔR/R curves at various temperatures were described by a single exponential decay ∝ exp(−t/τe-ph ). From the temperature evolution of the electronphonon relaxation time below Tc , τe-ph (T ), the authors extracted a superconducting gap of Δ(0) = 4.1 ± 0.4 meV (resulting in a value of 2Δ/kB Tc = 4.9 ± 0.5, indicative for strong electron coupling). From a two-temperature model the electron-phonon coupling constant was estimated to be λe-ph = 0.6 ± 0.1. IR/THz Spectroscopy Studies for Fe-Pnictide Thin Films In the following, IR and THz spectroscopy studies of Fe-pnictide thin films are summarized as (Table 6.15) • optical, IR and THz spectroscopies applied to Co-substituted BaFe2 As2 ; • IR/THz spectroscopy of other Fe-pnictides: BaFe2 As2 , BaFe1.84 Co0.16 As2 -based superlattices, Ba(Fe1−x Nix )2 As2 , (Ba1−x Kx )Fe2 As2 , and LaO1−x Fx FeAs.

6.7 Electromagnetic Properties, Superconducting Gaps and Fermi Surfaces …

333

Table 6.15 Overview of IR/THz spectroscopy studies and their spectral range (ν) on different Fe-pnictide thin films with thickness t, and superconducting transition temperature Tc Substrate

t (nm)

Tc (K)

ν (cm−1 )

Method

Refs.

63

–

6.7–67

THz-TDS

[338]

BaFe2 As2 MgO

Ba(Fe0.92 Co0.08 )2 As2 /SrTiO3 buffer DyScO3

350

22.5

20–220

THz R()a

[339]

(La,Sr)(Al,Ta)O3

40

17.5

12–140

THz R(), T()a,b

[340]

20.6

6.7–67

THZ-TDS

[341]

THZ T (), IR R(),

[322, 328]

(La,Sr)(Al,Ta)O3 Ba(Fe0.9 Co0.1 )2 As2 (La,Sr)(Al,Ta)O3

90

20

4–35000

ellipsometry

[342]

(La,Sr)(Al,Ta)O3

20, 100

25

4–47

THz-BWOc

[327]

(La,Sr)(Al,Ta)O3

25, 30, 50

22, 23, 21

4–45

THz-FT

[343]

Ba(Fe1−x Cox )2 As2 MgO

110

∼20

3.3–43.4

THz-TDS

[323]

(La,Sr)(Al,Ta)O3

69.5

19.9

3.3–43.4

THz-TDS

[323]

BaFe1.84 Co0.16 As2 / superlattices ( = SrTiO3 or O-enriched BaFe2 As2 ) on SrTiO3 buffer (La,Sr)(Al,Ta)O3

343

20–8000

IR R()a,e

[344]

(La,Sr)(Al,Ta)O3

384

20–8000

IR R()a,e

[344]

22.5

50–7000

IR R()f

[89]

400

40

50–7000

IR R()f

[317]

300

30

20–120

IR R(), T (), pump probeb,d

[329]

Ba(Fe1−x Nix )2 As2 CaF2 Ba0.6 K0.4 Fe2 As2 Al2 O3 LaO1−x Fx FeAs LaAlO3 a Synchrotron

radiation (IR beamline at SISSI, Elettra Trieste); b Bruker IFS66v; c Mach-Zehnder interferometer; d Beamline U4IR of the National Synchrotron Light Source (NSLS, Brookhaven National Laboratory); e Bruker 70v; f Bruker Vertex 80v

The electrodynamics of Co-substituted BaFe2 As2 films was frequently investigated. Three interrelated studies [322, 328, 342] provide a combined optical spectroscopy analysis (THz T (), IR R(), optical ellipsometry) of a 90 nm thin Ba(Fe0.9 Co0.1 )2 As2 film deposited on a (La0.7 Sr0.3 )(Al0.65 Ta0.35 )O3 substrate in a wide range from THz to UV. In the normal state the conductivity can be described by a Drude-Lorentz model containing two Drude terms (corresponding to two charge carriers) and two Lorentz terms (that describe interband transitions at 4400 and 20800 cm−1 ). The normal state conductivity is dominated by the electron-like charge carriers. An estimated value for the interband electron-boson coupling constant was given in [342] with λeb ≈ 0.45. Description of σ () in the superconducting state requires two additional Drude terms. From the suppression of the conductivity a superconducting gap value of 2Δ(0) = 3.7 ± 0.3 meV could be extracted (2Δ/kB Tc = 2.1), which opens around one electron-like FS sheet. A second gap with 2Δ(0) =

334

6 Thin Film Studies Under Focus

7.9 meV around one hole-like FS sheet was introduced as a fit parameter [342]. In a large temperature range (30–300 K) the the THz conductivity did not show a strong frequency dependence. The coherence peak was found to be more pronounced and shifted stronger below Tc . The experimentally obtained penetration depth was λ(0) = 360 ± 50 nm, which is in agreement with estimations from a BCS-like model [320] extended to two bands. The used model provides the individual contributions of hole- and electron-bands to the penetration depth with λh = 753 nm and λe = −2 −0.5 = 330 nm. In a subsequent work [328] 370 nm, that result in λtot = (λ−2 h + λe ) a three-band model was applied to the temperature dependence of the superfluid density ρs (T ), revealing three superconducting gap values: Δ1 ≈ 15 cm−1 (1.86 meV), Δ2 ≈ 21 cm−1 (2.60 meV) and Δ3 ≈ 30–35 cm−1 (3.72–4.34 meV). In [339] THz reflectance of a Ba(Fe0.92 Co0.08 )2 As2 film grown on a SrTiO3 buffered DyScO3 (110) substrate was studied. Film thickness and superconducting transition temperature were 350 ± 25 nm and Tc = 22.5 K, respectively. The electromagnetic response of the bare DyScO3 substrate was published separately in [318]. No parasitic contribution to the spectra was expected from the very thin SrTiO3 buffer layer. The complex-valued conductivity in the normal state could be described by a Drude model and the superconducting state was analyzed using the model of Zimmermann et al. for BCS superconductors [320]. A one-band fit (with three parameters: , γ , Δ) significantly failed in the description of the spectra, whereas a two-band fit with six parameters was more successful. The obtained Drude plasma frequencies, Drude scattering rates and superconducting gaps were p,1 = 1 eV, p,2 = 2 eV, γ1 = 200 cm−1 , γ2 = 2500 cm−1 , and Δ1 ≈ 15.5 cm−1 (1.86 meV), Δ2 ≈ 55 cm−1 (6.82 meV). These gap values correspond to 2Δ/kB Tc = 2 and 7. The total plasma frequency, given by (2p,1 + 2p,2 )0.5 , is 2.2 ± 0.3 eV and the dc conductivity of σ0−1 = ρ0 = 0.140 ± 0.015 mcm agreed with the residual resistivity at 25 K obtained from electrical transport measurements. It is interesting to note that the temperature dependence of the superconducting gaps is BCS-like within the error bars. It was noted that deviations from the BCS behavior could be due to the presence of a third gap or due to nodes in one of the gaps. A follow-up study on similarly fabricated films is given in [340], for which THz transmittance (T /Tn ) and reflectance ratios (R/Rn ) of a 40 nm thin Ba(Fe0.92 Co0.08 )2 As2 film were recorded. Here, the film was grown on a 20 nm thin SrTiO3 buffer on a LaAlO3 substrate and additionally capped by a 10 nm thin Pt layer. The optical response of the SrTiO3 buffer layer was again neglected, whereas the Pt capping layer exerted a screening effect and it possibly contributes to the finite conductivity below the superconducting gap. For a comparable film Tc = 17.5 K was determined by electrical transport measurements. Two gaps were found at Δ1 = 17 cm−1 (2.11 meV) – with a temperature dependence of a weak-coupling BCS-like superconductor and corresponding to 2Δ/kB Tc ≈ 3.52 – and at Δ2 = 8 cm−1 (∼1.0 meV), which corresponds to 2Δ/kB Tc ≈ 2.0. The results support a description of slightly overdoped Ba(Fe1−x Cox )2 As2 within a weak-coupling BCS theory. The dynamical optical conductivity was investigated for Ba(Fe0.9 Co0.1 )2 As2 films on a (La,Sr)(Al,Ta)O3 substrate using THz-BWO transmission spectroscopy [327]. The investigation included two films with thicknesses of 20 nm and 100 nm. The

6.7 Electromagnetic Properties, Superconducting Gaps and Fermi Surfaces …

335

thinner film showed a better signal-to-noise ratio. A simple Drude model applied to the normal state conductivity resulted in σdc = 6000 −1 cm−1 , τ −1 = 200 cm−1 and p = 8500 cm−1 (1.05 eV). The superconducting transition started at Tc,on = 25 K and coherence peaks in σ1 appeared at ∼21 K for measurements performed at 10.6 and 14.6 cm−1 . The penetration depth was estimated to be λ(2 K) = 450 ± 20 nm. From the latter the superfluid plasma frequency was evaluated to be p,s ≈ 0.45 eV. A power law behavior for the temperature dependence of the penetration depth with an exponent close to 2 was found: Δλ ∝ (T /Tc )2 and a superconducting gap of Δ(0) ≥ 2.9 meV could be obtained. The theoretical analysis employed a twoband model for σ (, T ) based on the assumption of an s-wave gap around the hole pocket and an s + d-wave gap around the electron pocket. It was proposed that the highly anisotropic gap due to the s + d-symmetry has a dominant s-wave contribution in order that the nodes could be lifted at low temperatures, which would explain apparently contradicting results in the temperature dependence of the penetration depth. THz-TDS was carried out for a Ba(Fe0.92 Co0.08 )2 As2 film grown on a SrTiO3 buffered (La,Sr)(Al,Ta)O3 substrate [341]. The midpoint of the superconducting transition in the electrical resistivity was Tc = 20.6 K. The real part of the complexvalued conductivity is not completely suppressed in the superconducting state even down to 2 K, which was explained by impurity induced pair-breaking. The imaginary part of the complex-valued conductivity is smaller than expected from BCS theory but it is proportional to 1/. A coherence peak in the temperature dependence of the real part, σ1 () near Tc was well observed for 220 GHz and was found to be gradually suppressed for higher frequencies. Application of the Mattis-Bardeen theory with a single gap yields Δ = 6.0 meV. The penetration depth displayed a power law behavior with λ(T ) − λ(0) ∝ (T /Tc )3.1 . The large exponent of 3.1 and the reduced superfluid density were explained to be a consequence of pair breaking rather than seen as a fingerprint of nodes in the superconducting order parameter. Reference [323] offers an independent THz-TDS investigation for a 69.5 nm thin, optimally doped Ba(Fe1−x Cox )2 As2 film on (La,Sr)(Al,Ta)O3 with Tc,on = 19.9 K and a 110 nm thin, underdoped Ba(Fe1−x Cox )2 As2 film on MgO with Tc,on ∼ 20 K. For the underdoped film on MgO the complex-valued conductivity in the normal state agrees with a Drude response. The plasma frequency is p = 0.5 eV at 50 K ≤ T ≤ 200 K. Below 70 K the charge carriers localize. The strong residual conductivity in σ1 could be also due to an unstable superfluid density in the film that gradually decreased during the experiment. For the thinner, optimally doped film on (La,Sr)(Al,Ta)O3 the plasma frequency of the Drude response is p = 0.56 eV at 200 K. For the residual conductivity below 0.5 THz impurity scattering in the film and an anisotropic or even nodal gap were proposed. In the superconducting state, the penetration depth λ = 710 ± 70 nm and a superconducting gap of 2Δ(0) = 5.6 ± 1.0 meV were extracted from the spectra. The gap value corresponds to 2Δ(0)/kB Tc = 3.6 ± 0.6. The authors suggested that Ba(Fe1−x Cox )2 As2 is a strong-coupling superconductor in the dirty limit. In [343] a Fabry-Pérot resonance technique was applied to a set of three Ba(Fe0.9 Co0.1 )2 As2 thin films on (La,Sr)(Al,Ta)O3 substrates with thicknesses of 25, 30 and 50 nm. The respective transition temperatures of the films were Tc = 22,

336

6 Thin Film Studies Under Focus

23 and 21 K. The resonator consisted of two identical films on a substrate placed face-to-face to each other separated by a spacer. Such a setup promises enhanced accuracy in the determination of σ1 (). For the thinnest film the largest penetration depth (λ(5K) ≈ 1460 nm) was found and the overall film quality was rated to be lower than that of the other two films. Thicker films of 50 nm were of better quality, however, their transmissivity became too low. Additional limitations arose from non-plane-parallel substrates, where deviations in the μm-range already broadened the resonance peaks in the spectra and severely complicated further evaluation of the superconducting gaps. Optical spectroscopy carried out for other Fe-pnictide thin films include the undoped parent compound BaFe2 As2 [338], BaFe2 As2 /SrTiO3 superlattices [344], Ba(Fe1−x Nix )2 As2 [89], Ba0.6 K0.4 Fe2 As2 [317] and LaO1−x Fx FeAs [329]. The optical conductivity of a 63 nm thin BaFe2 As2 film on MgO was investigated by means of THz-TDS [338]. Main focus of the study was to probe the dynamics of the massless fermions that appear in the band structure of the undoped compound and which were proposed to be of Dirac-type [345, 346]. A simple Drude term analysis applied to spectra down to TN ≈ 140 K, worked well for real and imaginary part of the conductivity. Below 140 K the imaginary part, σ2 (), became smaller than the expected values from the Drude model. The deviation was proposed to be a result from interband excitations within the Dirac cone. It was proposed to better describe the optical conductivity by the combination of a Drude and a Dirac term, where the Drude term accounts for the contribution of electron- and hole-like charge carriers in the parabolic bands, and the Dirac term includes the interband transitions of Dirac quasiparticles. In [344] the IR reflectance of BaFe1.84 Co0.16 As2 -based superlattices was investigated (Sect. 5.3). The first superlattice consisted of a stack of 24 × 13 nm thin BaFe1.84 Co0.16 As2 and 1.3 nm SrTiO3 layers. Due to diffusion, the actual composition of the perovskite layers was finally (Ba0.5 Sr0.5 )(Fe0.5 Ti0.5 )O3 . The second investigated superlattice was a stack of 24 × 13 nm thin BaFe1.84 Co0.16 As2 and 3 nm thin O-rich BaFe2 As2 layers. The superlattices were deposited on a 40 nm thin SrTiO3 buffer layer on a (La,Sr)(Al,Ta)O3 substrate. The reflectance was determined at 300 and 25 K and compared to a pure BaFe1.84 Co0.16 As2 film of 400 nm in thickness. The complex-valued conductivity was analyzed by using a Drude-Lorentz model with two Drude terms that account for two electronic bands. The Drude parameters for the pure film were p,1 = 7170 cm−1 (0.89 eV), p,2 = 17150 cm−1 (2.13 eV) and γ1 = 100 cm−1 , γ2 = 4000 cm−1 . The analysis of the superlattices required the inclusion of multiple reflections from all 48 interfaces and additional assumptions on the refractive index of the interlayers. Based on this approach, the Drude parameters in the Fe-pnictide/perovskite superlattice were p,1 = 8165 cm−1 (1.01 eV), p,2 = 11580 cm−1 (1.44 eV) and γ1 = 200 cm−1 , γ2 = 4000 cm−1 . In the Fe-pnictide superlattice with doping modulation the parameters were p,1 = 17360 cm−1 (2.15 eV), p,2 = 30160 cm−1 (3.74 eV) and γ1 = 1565 cm−1 , γ2 = 4000 cm−1 . The superconducting state was discussed based on a generalized Mattis-Bardeen theory [320] with two gap values Δ1 = 18 cm−1 (2.23 meV) and Δ2 = 60 cm−1 (7.44 meV) for

6.7 Electromagnetic Properties, Superconducting Gaps and Fermi Surfaces …

337

the pure film. In both superlattices, the smaller gap decreased to 7 cm−1 (0.87 meV), whereas the large gap remained stable. IR reflectance was used to determine the optical conductivity of a Ba(Fe1−x Nix )2 As2 film deposited on CaF2 [89]. In the normal state the conductivity was described using a two-component Drude-Lorentz model: A narrow Drude component was modeled with a temperature independent plasma frequency p1 ≈ 0.98 eV, a broad Drude component had a temperature independent plasma frequency, p2 ≈ 1.51 eV. The scattering rate τ1−1 increased to ≈ 0.084 eV between 50 and 300 K, whereas τ2−1 was nearly temperature independent at ≈ 0.17 eV. The superfluid plasma frequency p,s = 7033 cm−1 (0.87 eV) was obtained from the Ferrel-GloverTinkham sum rule. The corresponding value for the London penetration depth was λL (8 K) = c/p,s = 226 ± 20 nm. In [317] IR reflectance experiments were carried out on a 100 nm thin Ba0.6 K0.4 Fe2 As2 film grown in a two-stage process on Al2 O3 . The evaluated skin depth for Ba0.6 K0.4 Fe2 As2 was δ = 300 nm (40 K) and 650 nm (300 K). The separable substrate contribution in the reflectance spectra originated predominantly from phonon modes of Al2 O3 . The optical conductivity was described by a Drude-Lorentz model with two Drude components that account for the multiband character of the Fe-pnictide film: A narrow Drude component (coherent mode) with p1 ≈ 0.49 eV and a broad Drude component (incoherent mode) with p2 ≈ 1.04 eV. Both plasma frequencies do not show a strong temperature dependence between 40 and 300 K. The relaxation rate τ1−1 varies linearly from 100 cm−1 (at 40 K) to 400 cm−1 (at 300 K), whereas τ2−1 is constantly at 1700 cm−1 over the whole temperature range. The superfluid plasma frequency, p,s (30 K), obtained from the Ferrell-Glover-Tinkham sum rule, was 3860 cm−1 (0.48 eV) leading to a London penetration depth of λL (30 K) = 412 nm. For Fe-oxyarsenides, steady state and time-resolved (pump-probe) IR spectroscopy were carried out on a 300 nm thin LaO1−x Fx FeAs film with Tc = 30 K, that was fabricated in a two-stage process [329]. The film was grown on a LaAlO3 substrate, for which no temperature dependence of the transmittance and reflectance was found in the range of 4–35 K and for 20–120 cm−1 . The transmittance of the film in the normal state (at 33 K) was modeled using a Drude-Lorentz model with a plasma frequency P = 4595 cm−1 (0.57 eV) and a scattering rate τ −1 ≥ 800 cm−1 for the Drude term. The Lorentzian term described a low-frequency lattice oscillation involving vibrations of La, Fe and As ions, that could be fit with a resonance frequency 0 = 99 cm−1 , a phonon plasma frequency ph = 200 cm−1 and a linewidth γph = 5 cm−1 . The superconducting state was modeled by a two-fluid model with a Drude and a Mattis-Bardeen term for the normal (p,n = 3844 cm−1 ) and superconducting charge carriers (p,s = 2517 cm−1 ) combined with an analysis based on the model of Zimmermann et al. [320]. Residual absorption resulted in a nonvanishing real part of the conductivity. A gap value of 2Δ(0) ≈ 6.20–6.45 meV was determined. The pump-probe experiment used a Ti-sapphire laser for photoexcitation with a pulse fluence of 1.6 nJcm−2 (to avoid heating of the sample) and the synchrotron radiation pulse as probe beam. An increased quasiparticle lifetime of 1.8 ± 0.2 ns (T = 3.5 K) was determined, which is in accordance with the phonon bottleneck effect

338

6 Thin Film Studies Under Focus

explained by the Rothwarf-Taylor model. The results implied at least one nodeless superconducting gap in the Fe-oxyarsenide.

6.7.4 Photoelectron Spectroscopies Photoelectron spectroscopy (PES) methods are surface sensitive, analytical techniques based on the photoelectric effect. Variants include the excitement of photoelectrons by UV radiation (UPS) or X-rays (XPS), which is typically used for extracting information about the chemical composition and bonding. Angle-resolved photoelectron spectroscopy (ARPES) provides scans of the electronic band dispersion and maps of the Fermi surface (FS). It can also be performed in a time-resolved manner (trARPES) in a pump-probe experiment. With the exception of MBE-grown FeSe monolayers and ultrathin films (see Sect. 6.5), PES and ARPES studies performed on thin films of Fe-based superconductors are yet rare. The main reason for this is found in the lack of UHV transfer systems and the technological difficulty to maintain film surfaces clean enough. Combined Ar+ sputtering and annealing of film surfaces that were once exposed to air is most times not efficient enough for removing contaminants or oxidized layers and can lead to film damage in the worst case. Therefore, direct UHV transfer systems from the growth chamber ( pbase ≈ 10−9 – 10−8 mbar) to the analytic PES/ARPES chamber ( pbase ≈ 10−10 –10−9 mbar) turned out to be a technological prerequisite for PES and ARPES investigation on film surfaces. For example, the characterization of a KFe2 Se2 film by UPS/XPS was performed in-situ, i.e. inside UHV [347]. However, even if the transfer of the film from the growth to the analysis chamber is fully carried out in-situ, the film surface can deteriorate. A well known procedure is capping of the film surface directly after growth by a removable protection layer. The selection of the protection layer material is crucial as well. In [348] the surface of a PLD-grown FeSe0.5 Te0.5 film was protected by a Se layer that was deposited for 10 min at 100 ◦ C. After transferring the film to the ARPES system (into a preparatory chamber), the cap layer was removed by annealing the film at 450 ◦ C for 7 hours. In the subsequent ARPES study of a 100 nm thin FeSe0.5 Te0.5 film on MgO, FS and the band structure were recorded at 30 K. The authors concluded that the quality of the thin film is comparable to that of single crystals. A 25 nm thin Se cap layer was also chosen in [349] for protecting a thin FeSe film grown on SrTiO3 . It was removed in the ARPES chamber after heating the film to 400◦ . In an ARPES study of FeSe films on CaF2 substrates [350], the 160 nm thin film was cleaved in-situ in UHV ( p = 8 × 10−11 mbar) at T = 20 K. The surface quality after cleaving was indicated to be good enough for ARPES. Reference [349] studied the band structure of a 35 ML thin FeSe thin film grown by MBE on SrTiO3 by ARPES (Scienta R4000, Stanford Synchrotron Radiation Lightsource). The nematic transition in the film occurred at T = 125 K, no trace of superconductivity appeared (down to 20 K). The lack of a long-range magnetic order raised doubts that spin fluctuations are the driving force for nematicity. A strong

6.7 Electromagnetic Properties, Superconducting Gaps and Fermi Surfaces …

339

momentum dependence of the energy splitting of 3dx z and 3d yz orbitals and a hopping anisotropy (between Γ − M X and Γ − MY ) also implied constraints on orbital ordering models. It was suggested that nematicity competes with superconductivity. In [243], ARPES (Scienta R4000, He discharge lamp) revealed the electronic band structure in the nematic state of FeSe films (with thicknesses larger than 1 uc). Close to the M-point two spots with Dirac cone band dispersions were found at −10 meV leading to small electron pockets. The FS topology of the FeSe films in the nematic state resembles that of BaFe2 As2 . Increasing Co addition suppressed nematicity and the Dirac cone band dispersion simultaneously. A related study on Cs-coated FeSe films (20 uc) can be found in [392]. ARPES investigations (Scienta R4000, rare gas discharge lamp emitting HeI resonance line with hν = 21.218 eV) were also carried out on in-situ cleaved FeSe films deposited on CaF2 again with a focus on the nematic state [350]. Films with a thickness of 160 nm and a Tc of 4, 9 and 14 K were prepared by varying the Secontent of the FeSe1±x PLD targets in the range of −0.03 ≤ x ≤ +0.10 [351]. The band structure of all films was comparable to the band structure of bulk FeSe: At the Γ -point (BZ center) three hole-like bands (α, β, γ) contribute to a hole-like FS. The band structure around the Γ -point did neither change strongly within the sample series nor with temperature. Around the M-points (BZ corner) the FS was described by one small electron-like pocket and four spot-like parts. In the band dispersion one electron-like band (ε) was observed together with two hole-like bands (δ, η) that arise from splitting of the dx z /d yz -orbitals in the nematic state at low temperatures. The band splitting of the δ and η bands was taken as definition for the nematic temperature, which appeared at 150 ± 10 K, which is ∼50 K higher than in bulk FeSe. The nematic temperatures decreased from 160 to 140 K with increasing Tc , however, an uncertainty of ±10 K in the determination of the nematic temperature is high. The band-splitting reaches values between 43 meV (film with Tc = 4 K) and 53 meV (film with Tc = 14 K) at 30 K. Additional outer electron bands were not resolved. An upward-shift of the electron-like band, ε, was identified as the main trend within the sample series, that causes a shrinking of the electron-like FS with increasing Tc . The electronic bands around the M-point changed with temperature (30–170 K) and seemed to be mostly affected by the nematic phase transition. In the same study [350] surface electron doping by K evaporation resulted in a shrinking of the hole-like FS around Γ , whereas the band structure around M changed qualitatively from three to two bands. A circular electron-like pocket developed, which enlarged upon increasing electron doping. In [352] comparative ARPES investigations (Scienta-Omicron SES2002, rare gas discharge lamp emitting HeI resonance line with hν = 21.218 eV) offered an insight into the strain-dependence of the FS in FeSe. The study compared an FeSe film under compressive strain (deposited on CaF2 with a thickness t = 300 uc) having a critical temperature of Tc = 12 K with a non-superconducting FeSe film under tensile strain (deposited on SrTiO3 with a thickness of t = 20 uc) and an FeSe crystal. The films grown on different substrates show remarkable differences in the electronic band structure (Fig. 6.32): At temperatures of 120–180 K and compared to the bulk state, the two hole-like bands (denoted here as α, α’) around the Γ -point shift upward

340

6 Thin Film Studies Under Focus

(downward) in energy while the electron-like bands (γ, ε) shift downward (upward) in the film on CaF2 (SrTiO3 ). At T = 30 K a nematic transition was characterized by the lifting of the degeneracy of the dx z /d yz -orbitals, which results in a splitting of the εband into ε1 and ε2 . This result was found in both FeSe films (as well as in the crystal). Consequently, neither in FeSe/SrTiO3 nor in FeSe/CaF2 , the interaction between film and substrate is strong enough to pin the tetragonal FeSe unit cell. Specific features of the band structure, such as the electron-hole band overlap ΔE h-e and the splitting between ε1 and ε2 at 30 K were discussed as function of in-plane strain expressed by the room-temperature in-plane lattice parameter a with aFeSe/SrTiO3 > aFeSe-bulk > aFeSe/CaF2 .The splitting of the ε-band at 30 K varies from ∼70 meV (in FeSe/SrTiO3 ) to 45 meV (in FeSe/CaF2 ), which is comparable to the value given in [350], whereas the electron-hole band overlap increases from 20 meV (in FeSe/SrTiO3 ) to 70 meV (in FeSe/CaF2 ). The variation of Tc is proportional to ΔE h-e . The size of the Fermi surface (and, therefore, the charge carrier concentration) increases in FeSe upon compressive strain (on CaF2 ) compared to FeSe upon tensile strain (on SrTiO3 ). Phonon frequencies (Se A1g phonon mode) in FeSe films of varying thicknesses (1, 3, and 60 uc) grown on SrTiO3 were revealed in femtosecond time- and angleresolved photoelectron spectroscopy (trARPES) [353]. The experiment was performed with a Coherent RegA Ti:sapphire laser (at 312 kHz repetition rate). In the pump-probe experiment the phonon mode of the Se ion in the films was photoexcited by an ultrafast (∼50 fs) 1.5 eV (IR) pump pulse (incident pump fluence = 0.54 mJcm−2 ) and probed at a delayed time (∼100 fs) by a 6 eV (UV) pulse with an energy resolution of 22 meV. During relaxation of the non-equilibrium state, the induced lattice oscillations lead to a periodic change in Se height, z Se , and, therefore, a change in bonding lengths and bonding angles. The two hole-like electronic bands around Γ at 80 and 200 meV below the Fermi level (1 uc FeSe/SrTiO3 ) perform intensity oscillations and energy oscillations. From the measured intensity oscillations at 20 K a softening of the A1g mode from 5.25 to 5.00 THz with decreasing film thickness from 60 to 1 uc was concluded. (Lattice strain softens the phonon mode by 4–5%.) In a subsequent experiment [354], the electron-phonon coupling and electron correlations were studied in a 60 uc thin FeSe film grown on SrTiO3 . In addition to trARPES as described above, a 8.7 keV X-ray pulse probed the lattice dynamics by using time-resolved X-ray diffraction (trXRD). From the oscillations of the Se-ion with height (A1g optical phonon) induced by the pump pulse, the electron-phonon deformation potentials, expressed as band shift divided by the Se displacement, were determined as ΔE x z/yz /Δz Se = −13.0 ± 2.5 and E z 2 /Δz Se = −16.5 ± 3.2 meV/pm. Earlier predictions made by DFT-DMFT calculations [355] match with the experimental result. The failure of DFT calculations in reproducing the electron-phonon deformation potentials indicated the importance of electronic correlations in FeSe, that are responsible for an enhancement of the electron-phonon coupling.

6.7 Electromagnetic Properties, Superconducting Gaps and Fermi Surfaces …

341

Fig. 6.32 Band dispersions around the Γ - and the M-point (for two different temperature ranges) measured by ARPES: Scienta-Omicron SES2002, rare gas discharge lamp emitting HeI resonance line with hν = 21.218 eV. (Reprinted with permission from Fig. 2 in [352]; © (2017) by the American Physical Society)

342

6 Thin Film Studies Under Focus

6.7.5 Point-Contact Spectroscopy So far, only a limited number of point-contact and point-contact Andreev reflection spectroscopies (PCS/PCARS) for Fe-chalcogenides and Fe-pnictides were performed on thin film samples. Although thin films can be easily incorporated into point-contact fabrication through lithography (see [356, 357]), they do not necessarily have a specific advantage over single crystals. Point-contacts between two metals are realized when the size of their mutual contact d, becomes comparable to the elastic and inelastic mean free paths, le,i . The conditions d 1) favors tunneling effects when the bias voltage increases the energies of the injected quasiparticles. The mentioned dimensionless parameter Z (also called barrier strength) is related to the transmissivity of the pointcontact according to T = (1 + Z )−1 . Typical Z -parameters in the discussed studies below are 0.16–0.38 for Ag/Ba(Fe1−x Cox )2 As2 [363], 0.2 for Ag/BaFe2 (As1−x Px )2 [364], 0.3 [365] for Ag/FeSe1−x Tex , and 0.41 [359] for Cu/SmO1−x Fx FeAs. For a Bi2 Te3 /FeTe heterostructure, a two-gap BTK model with Z 1 ≥ 0.35 and Z 2 ≈ 1000 was employed [366]. dI /dV -curves of N/S-contacts are usually described by means of the BlonderTinkham-Klapwijk (BTK) theory [367], where the superconducting gap, Δ, the quality of the interface, Z , and the quasiparticle scattering rate expressed as broadening of the density of states, Γ , are the usual fit parameters. The BTK theory can be extended to the case of two bands (or gaps). The typical signature for Andreev reflection, the zero-bias anomaly in the dI /dV -curves, results in a plateau-like maximum at low temperatures. A schematic representation of dI /dV with tuned Z is given in Fig. 6.33d. For an introduction to the method the valuable textbook by Jurij G. Naidyuk and Igor K. Yanson is recommended [368]. Early reviews on PCS and PCARS with results for Fe-based superconductors are provided by [369, 370]. In the following, selected studies on different Fe-based thin films are summarized. In all experiments the current is predominantly injected along the c-axis of the films, which coincides with the surface normal. A single gap BTK fit turned out to describe the dI /dV -curves sufficiently well in individual cases. A BTK analysis with two gaps was, however, chosen by the majority. Symmetric and nodeless gaps with a temperature evolution close to the BCS trend were typically discussed. Point-contact fabrication based on junction design of Au/AlOx /FeTe:Ox and Au/AlOx /Al/FeSe1−x Tex by using photolithography is presented in [356, 357]. The point-contacts arise as nanometer-sized conductive channels (shorts) inside the AlOx barrier. Typical film thicknesses are 20–60 nm, the amorphous AlOx layer is ∼2 nm in the one case, in the other case, Al and AlOx layers are 14 nm in total. The Au counter-electrode has a thickness of 16 nm. Au/AlOx /FeTe:Ox junctions were characterized as point-contacts in the thermal limit. Point contacts were also generated along the cross section of a Bi2 Te3 /FeTe heterostructure [366]. The heterostructure was mechanically attached with its cross section to a Si substrate. An Au contact with an area of 100 × 149 nm2 was fabricated by Au deposition and subsequent FIB patterning. Directional PCS was possible

6.7 Electromagnetic Properties, Superconducting Gaps and Fermi Surfaces …

345

with a current injected parallel as well as perpendicular to the interface. Contacts with resistances in the k-range were prepared by Ag paint at the top edge of the Bi2 Te3 layer. The heterostructures display interface superconductivity with Tc = 12 K. dI /dV curves were analyzed by a two-gap BTK and by a Dynes model respectively. In case of the BTK model, a smaller anisotropic gap, Δ1 = 6 meV, and a large, isotropic gap, Δ2 = 12 meV. were found. The non-monotonous temperature variation of the larger gap was explained as a result of a superposition of a superconducting gap (below Tc ) and a pseudogap (above Tc up to 40 K). PCARS performed on Fe-chalcogenide films are found in [365]. Fe(Se1−x Tex ) films with x = 0.5, 0.6, 0.7 were investigated using a soft point contact method. The films were deposited by PLD on CaF2 substrates and had a thickness of 86 or 100 nm. Interdiffusion near the film/substrate interface was regarded to be negligible, because PCARS is surface sensitive. The symmetric maxima in the differential conductance curves, dI /dV , are clear signatures of a superconducting gap with a size Δ ≈ 2.75 kB Tc . The authors linked this gap to the electron-like Fermi sheet. In the film with x = 0.5, evidence for a second, smaller gap with 1.75 kB Tc was seen. Both gaps are isotropic without the presence of nodes. In addition, Δ∗ ≈ 6kB Tc was interpreted as a signature of a strong coupling of the electrons with a bosonic mode. Empirically, the mode peaks at the spin-resonance energy 0 = 4.65 kB Tc . In a more recent study [15], PCARS was carried out on a thin FeSe0.45 Te0.55 film that was prepared by mechanical exfoliation of a single crystal down to a thickness below ∼10 nm. The superconducting transition of the film was Tc,on = 14.2 K with a width of ΔTc = 0.4 K. According to the authors many parallel point contacts form when the film is pressed onto micro-sized Au electrodes. Due to the granular nature and the surface roughness of the sputtered Au electrodes, many parallel contacts a generated with a size comparable of the Au grain size. dI /dV spectra for a 15 nm thin crystal film are shown in Fig. 6.35a for different temperatures. In the superconducting state Andreev reflection sets in and is responsible for the symmetric peak around zero bias voltage. At low temperatures a broad plateau formed. The coherence peaks are indicated by black arrows at ±4 mV. Additional nonlinearities appear at ±10 mV and were attributed to electron-boson coupling. A single band BTK analysis was applied to dI /dV , which resulted in a superconducting gap Δ = 4.0 ± 0.3 meV at lowest temperatures (3.5 K). Its temperature dependence was compared to the BCS solution (Fig. 6.35b). A Ba(Fe0.92 Co0.08 )2 As2 film with Tc = 23.7 K was investigated in [360, 361]. Hard point-contacts using a Ag tip in the ballistic regime were employed for PCARS. The size of the point-contacts was estimated to be 2.5 nm using Wexler’s formula (6.22), which is smaller than the mean free path l = 3.5 nm. As already mentioned above, the size of the point-contact seems to be underestimated because films have typically a residual resistivity of ρ = ∼500 μcm. A more realistic value for the contact size would be, therefore, ∼50 nm. In this case, the point-contacts are indeed inhomogeneous and contain regions of Ba(Fe0.92 Co0.08 )2 As2 as well as of columnar Ba-Fe-O impurity phases, because films were grown by PLD under HV. The Ba-FeO columns have a diameter of ∼5 nm and are found densely distributed within the Fe-pnictide matrix (see Fig. 1 in Ref [91]). The inhomogeneous point-contacts were

346

6 Thin Film Studies Under Focus

Fig. 6.34 Gap amplitudes Δ1,2 (0) versus transition temperatures Tc for Ba(Fe1−x Cox )As2 (x = 0.04 – 0.15) (left) and Au3+ ion irradiated (Φmax = 7.3 × 1011 ions·cm−2 ) BaFe2 (As0.81 P0.19 )2 films (right). (Reprinted with permission from Fig. 5 in [363]; © (2013) by the American Physical Society. Adapted from Fig. 7 in [364]; © IOP Publishing. Reproduced with permission. All rights reserved)

unfortunately not considered. A thermal regime of the point contact cannot be ruled out completely: The asymmetry in the differential conductance dI /dV between −V and +V bias, studied between 10 and 33 K [360], could be of thermoelectric origin (i.e. temperature gradient in the point-contact), which was too hastily ruled out. From the observation of Andreev reflection in the normal state up to a temperature of 1.3Tc the authors concluded the formation of phase-incoherent quasiparticle pairs, that results in a pseudogap [361]. The analysis of the spectra using BTK provided the temperature dependence of two gaps with Δ1 (5 K) = 10 meV, Δ2 (5 K) = 15 meV and a pseudogap with Δpg (5 K) = 60 meV. A series of Ba(Fe1−x Cox )2 As2 films with 0.04 ≤ x ≤ 0.15. was studied in [363] using a soft point-contact method. The films were grown with a thickness of ∼50 nm on CaF2 substrates by PLD. A two-band 2D BTK analysis was applied to the dI /dV spectra, although in the underdoped film (x = 0.04) a one-band fit would have been possible as well. For the smaller gap a BCS ratio 2Δ1 /kB Tc = 3.53 was found, whereas for the larger gap, the larger ratio 2Δ2 /kB Tc = 8.5 was evaluated (linear fits shown in Fig. 6.34). The linear correlation proposed by the authors is not properly supported within the film sample series as shown by a diverging fit (dashed line) with increasing slopes (red tangent) when Tc approaches Tcmax of the compound. The authors argued that only the gap amplitudes in the overdoped film (x = 0.15) deviate significantly from the linear correlation between Δ(0) and Tc . Based on an Eliashberg model (with s± -symmetry of the superconducting order parameter) the result could be explained by a decreasing interband coupling with proceeding loss of FS nesting and spin fluctuations in the overdoped region of the electronic phase diagram. In [364] a two-gap analysis was applied to unirradiated and 250 MeV Au3+ ion irradiated BaFe2 (As1−x Px )2 (x = 0.19, 0.20) films (see Sect. 6.8.3). The films inves-

6.7 Electromagnetic Properties, Superconducting Gaps and Fermi Surfaces …

347

Fig. 6.35 Selected results of PCARS: Temperature dependence of dI /dV -curves (or dV /dI -curves) and superconducting gaps extracted from BTK theory for a and b (four different films shown) FeSe0.45 Te0.55 (Reprinted from Figs. 5b,d in [15]; © IOP Publishing. Reproduced with permission. All rights reserved.) c and d heavy ion irradiated BaFe2 (As1−x Px )2 film (Reprinted from Figs. 5a,b in [364]; © IOP Publishing. Reproduced with permission. All rights reserved.) e and f SmO1−x Fx FeAs (Reprinted from Fig. 2 in [359]; © IOP Publishing. Reproduced with permission. All rights reserved.) The gap values are compared with the BCS temperature dependence (line) in b), d and f

tigated in this study were grown by MBE on MgO substrates with a thickness of 50 nm. Differential conductance spectra of a film after irradiation with the highest fluence of 7.3 × 1011 ions·cm−2 measured at different temperatures between 4 and 30 K are displayed in Fig. 6.35c. The symmetric maxima in dI /dV were found to be in agreement with an s-wave symmetry of the superconducting gap. Corresponding fits based on a two-band 2D BTK analysis (with the assumption of spherical Fermi surfaces) are indicated in the figure. A BCS-like evolution of both gap values with temperature is shown in Fig. 6.35d and results in Δ1 (0) ≈ 2.6 meV and Δ2 (0) ≈ 6.6 meV. It was noted that point-contacts were in the ballistic limit at low temperatures, however, at higher temperatures (close to Tc ) point-contacts suffered from current-induced pair breaking. Furthermore, the gap amplitudes decreased linearly with increasing fluence (for Δ1 (0) from 8.5 to ∼5 meV and for Δ2 (0) from ∼4 to 2.5–3 meV) while Tc was reduced from 31.5 to 30.72 K. The much stronger decrease in the superconducting gap amplitudes (by 20–40%) compared to the accompanied suppression of Tc (by 2.5–3%) due to irradiation induced disorder was called ‘decoupling’ between Tc and Δ (Fig. 6.34). The authors proposed that irradiation induced defects lead to a temperature dependent localization at low temperatures, that results

348

6 Thin Film Studies Under Focus

in a temperature dependent density of states. It has to be pointed out, however, that the observed strong decrease of superconducting gap amplitude is very close to Tcmax and can also be observed in the unirradiated Ba(Fe1−x Cox )2 As2 films with variable Co-content [363] (compare slopes in Fig. 6.34). Fe-oxyarsenide thin films of LnO1−x Fx FeAs (Ln = La, Sm) grown by a two-stage process were characterized by PCARS in [359]. The point-contacts were prepared by the needle-anvil method using a Cu wire with a sharpened end. dV /dI -curves showed pronounced asymmetries between +V and −V , that originate from thermoelectric voltage due to heat generation upon increasing bias voltage. Fe-oxyarsenides exhibit large thermoelectric properties and the Seebeck coefficient may account for the additional thermovoltage. In addition, the point-contact is in a nonequilibrium electronic state, producing nonequilibrium phonons. In electrical transport measurements the SmO1−x Fx FeAs film showed a superconducting transition at Tc,on = 34 K. Application of a single-band BTK analysis and under the assumption of a BCS ratio 2Δ/kB Tc∗ = 3.6, the temperature dependence of the gap revealed by PCARS indicates a Tc∗ at 21.6 K already, although the zero-bias minimum in dV /dI , which is attributed to Andreev reflection, is visible up to 30 K before it disappears. At low temperatures, dV /dI shows minima at ±3 mV. Deviations from the theoretically expected shape in dV /dI between 20 and 30 K could be a result of larger inhomogeneities within the point-contact and the fact that the point-contact is in the thermal limit. Results for SmO1−x Fx FeAs are shown in Fig. 6.35e, f. A gap value of Δ(0) = 3.55 meV was obtained. Similarly, for LaO1−x Fx FeAs the superconducting gap extracted from the BTK analysis with Δ(0) ≈ 2.73 meV disappears already at Tc∗ = 18.1 K while superconductivity is still observed up to 25 K.

6.8 Irradiation and Implantation Irradiation effects in superconductors are of specific fundamental and technological interest. Typical irradiation studies focus on the relation between the artificially generated disorder and the critical parameters of the superconductor, newly induced vortex pinning sites, or threshold doses for radiation damage and device breakdown. The defects in superconductors created by particle irradiation are classified according to their dimensionality as point defects, amorphous ion tracks, or agglomerated defect clusters (Fig. 6.36a). The particular defect microstructure, individual defect size and shape depend on the microscopic details of the interaction between the incident particles and the material as well as on the corresponding energy transfer. The microscopic processes leading to material damage are governed by the energy loss of the incident particle inside the target medium due to either (i) elastic collisions with atoms or, (ii) inelastic collisions with electrons inside the target. Other mechanisms of energy loss (for example, radiative) do exist, but are less relevant here. The energy loss per unit length is called stopping power, S = −dE/dx. According to the above classification, nuclear (Sn ) and electronic (Se ) stopping powers are distinguished. Energy loss due to elastic collisions with atoms is, for example, dominant in irradiation experiments using protons, high-energetic neutrons or low-energetic

6.8 Irradiation and Implantation

349

Fig. 6.36 a Schematic representation of irradiation-induced defects classified as point defects (typically after electron irradiation), defect clusters (after neutron and proton irradiation), and ion tracks (after heavy ion irradiation). b Radiation damage measured in displacements per atom (dpa) along a μm long penetration path. The different regimes for irradiation and implantation (near the so-called Bragg peak) are indicated. c TRIM simulation for the irradiation of a Ba(Fe1−x Cox )2 As2 film with 30 keV 3 He+ ions. (Reprinted from Fig. 1a in [377]; © IOP Publishing. Reproduced with permission. All rights reserved)

ions, where defect generation is understood and described in terms of displacement cascades. A so-called primary knock-on atom is removed from its lattice site and induces a series of further atom displacements before it comes to rest by creating an interstitial-vacancy pair (Frenkel defect). This happens on extremely short time scales of below 0.1 ps. A large fraction of created displacements anneals out already within 1 ns, whereas the final stable defect microstructure develops within 1 ms. In contrast, in the irradiation with heavy ions of high kinetic energy or the bombardment of insulating material, inelastic collisions with electrons become the dominant mechanism. The time scales for the electronic excitations are even below 1 fs. The energy in the electronic system is transferred to the lattice due to electron-phonon coupling initiating lattice processes responsible for defect generation within 1 ns. The formation of continuous or discontinuous ion tracks has often been reported and different models were proposed in order to explain the macroscopic tracks that generate columnar defects. Additional radioactivation appears after irradiation with nucleons (neutrons, protons). When taking the different interaction mechanisms into account, it is evident that the resulting defect landscape can develop complexities with a variety of defect types. Electron and proton irradiation, for example, produce interstitial-vacancy pairs (Frenkel defects), which have been already studied in a number of Fe-pnictide crystals [372–374]. From irradiation experiments on FeSe1−x Tex crystals it is known that highly energetic Au-ions produce amorphous defect tracks with a metallic core of 3 nm in diameter, but also displaced Fe atoms. Both become effective vortex pinning sites in different magnetic field ranges [375]. Another irradiation study has shown that the irradiation of NdO0.85 FeAs crystals with 2 GeV Ta-ions results in collinear columnar tracks [376]. Most irradiation studies were carried out on Fe-

350

6 Thin Film Studies Under Focus

Fig. 6.37 Irradiation-induced defects in FeSe0.5 Te0.5 thin films: a HR-TEM image of a defect cluster in the size of 10–15 nm generated by 6 MeV Au3+ ion irradiation. (Reprinted from Fig. 4b in [378]; © IOP Publishing. Reproduced with permission. All rights reserved.) b HR-TEM image of a defect cascade after proton irradiation. (Reprinted with permission from Fig. 2b in [74]; © The Authors. Creative Commons CC BY license)

pnictide and Fe-chalcogenide crystals, and there are less examples that study and image irradiation-induced defects in thin films. Figure 6.37 shows two kind of defects in irradiated FeSe0.5 Te0.5 thin films: defect clusters developed after an irradiation with Au3+ ions, whereas defect cascades appeared after proton irradiation. With the controlled modification of the microstructure by irradiation, the study of irradiation-induced defects in superconductors has thus been extremely helpful in the understanding of Cooper pair-breaking mechanisms. The defect scattering of the electrons is tuned by the particle type and flux, while simultaneously parasitic effects, that usually appear in substitutional chemistry (for example, additional charge carrier doping or chemical pressure), are largely avoided. The primary irradiation effect on superconductors is usually noted by a change of the critical temperature, ΔTc = Tcunirr − Tcirr , where Tcunirr denotes the critical temperature of the unirradiated (pristine) sample. A suppression of the critical temperature is measured after sequential irradiation with cumulative fluence, Φ. Conventionally, the simultaneous change in normal state resistivity, Δρ, is recorded with increasing fluence and ΔTc (Φ) is given as a function of Δρ(Φ). Occasionally, the maximum fluence, at which superconductivity disappears, is also determined, for example, for 3 He+ ion irradiation on a Ba(Fe1−x Cox )2 As2 thin film [148]. The variation of other superconducting parameters, such as ΔHc2 and ΔJc are dealt as useful indicators for the potential of superconducting applications for radioactive environments. Furthermore, a radiation-caused damage is rated as ben-

6.8 Irradiation and Implantation

351

eficial when it helps raising the ability of a superconductor to carry larger critical currents. Defects, with a size that matches the size of the normal vortex core, are considered as extremely useful in the increase of flux pinning. The study of irradiationinduced flux pinning centers became a prominent research topic in applied superconductivity. Reference [379] reviews the effects of irradiation on Fe-based superconductors and points out general trends, such as the suppression of Tc after neutron irradiation and an unaffected Hc2 close to Tc (0). Critical current densities in clean crystal samples show the potential to enhance up to an order of magnitude by irradiation. A difference between single crystals and thin films is that the latter are attached to a substrate, that is also affected by the irradiation process. In single crystals with thicknesses below 100 μm the energy release and the defect concentration are approximately constant over the crystal dimensions. The energy release is also constant in much thinner films (typically 100 nm), however, the substrates have thicknesses of 250–1000 μm and the radiation also modifies the substrate properties. In addition, ions are implanted inside the substrate material. In most cases, the irradiation damage of the substrate has no influence on the superconducting properties of the thin film, but attention should be paid to this issue as pointed out in [364]. In comparing different types of radiation, it is recommended to measure the radiation damage given in displacements per atom (dpa) rather than fluences. For example, the defect generation rate differs significantly between different types of radiation and is 10−7 –10−6 dpa·s−1 for neutrons whereas 10−4 dpa·s−1 for ions. Important experimental conditions cover, therefore, the source and type of radiation (photons, electrons, nucleons and ions), the kinetic energy (in the range of keV–GeV), the incident fluence (particles per area), the irradiation angle of an ion beam with respect to the crystallographic lattice of the irradiated material, and the description of the sample conditions during irradiation, such as the sample temperature or masks. Experiments with pure irradiation-induced defects differ from those where the thin film sample is masked by a thick foil in order that ions are implanted in the thin film rather than in the substrate (Fig. 6.36b). The effects of ion implantation can include doping, change in chemical composition, destruction of crystallographic long-range order, or increased amorphization. The Stopping and Range of Ions in Matter (SRIM) code as well as the Transport of Ions in Matter (TRIM) are frequently used simulation tools for the calculation of the damage and penetration depth of ions in a material (Fig. 6.36c).

6.8.1 Laser Light Irradiation of and Ion Implantation in FeTe Films Although the following examples of irradiation and implantation experiments focused on the optical properties of FeTe films and their application potential as phase change material, they should be shortly mentioned here. Phase change materials like some

352

6 Thin Film Studies Under Focus

Fig. 6.38 Optical micrographs of a Fe1+x Te film showing color and reflectivity changes after laser light irradiation (KrF excimer laser, λ = 248 nm, τ = 30 ns): a change from amorphous to crystalline (2 pulses at ε = 42.5 mJcm−2 ); b change from crystalline to amorphous (5 pulses at ε = 52.5 mJcm−2 ). (Reproduced from Fig. 5 in [380] with the permission of AIP Publishing.) Reversible (amorphization/crystallization) phase changes when switching the laser fluence between 47.5 and 35.0 mJcm−2 were demonstrated in [381]

chalcogenide glasses are used for data recording and memory devices and make use of the different optical reflectivities in their amorphous and crystalline phases. The effect of laser irradiation on amorphous and crystalline FeTe and Fe1.19 Te films was first studied in [380]. Films of 50 nm in thickness were prepared by PLD under high vacuum conditions ( p ≈ 2 × 10−8 mbar) on Si substrates held at room temperature and at TS = 220 ◦ C. For film irradiation a diode laser with wavelength λ = 635 nm and a power of 1 mW was employed. Changes in the reflectivity upon heating were recorded by a photodiode detector. The crystallization temperature was determined to be 180 ◦ C and 214 ◦ C for the Fe1.19 Te and the FeTe film. Crystallization (amorphization) could be achieved by only 2 (5) pulses of laser irradiation. The corresponding color changes of the film surface were visible in optical micrographs (Fig. 6.38). For wavelengths in the range of λ = 200 − −800 nm the reflectivity of the amorphous phase (Ra ) was higher than that of the crystalline phase (Rc ). Based on this ratio, Ra /Rc > 1, FeTe was considered to be an unconventional or anomalous phase change material. A follow-up study [381] attempted to explain the higher electrical conductivities and optical reflectivities due to delocalized Te p-states that hybridize with Fe d-states in amorphous FeTe, whereas crystalline FeTe was characterized by localized lone-pairs. The role of O2− ions in FeTe thin films is controversially discussed and was additionally studied by O ion implantation in [382]. The Fe1+x Te films in this study were prepared by PLD on SrTiO3 substrates and showed a (001)-oriented and a (101)-oriented domain in XRD (Bragg Brentano scans). The ion implantation was performed by using the 150 kV gaseous ion implanter at the Indira Gandhi Centre for Atomic Research with O2− ion doses of 2 × 1016 , 5 × 1016 and 10 × 1016 ions·cm−2 at room temperature. Ion implantation at low doses resulted in a gradual loss of texture and the formation of a Fe3 O4 secondary phase. A dose of 10 × 1016 ions·cm−2

6.8 Irradiation and Implantation

353

resulted in the complete amorphization of the crystal structure with an absence of reflections in the XRD pattern. Simultaneously, a gradual increase in film resistance was observed. Based on Mott’s variable hopping model the electrical transport shows disorder-induced localization. Compared to the crystalline film, a smaller optical reflectivity for the amorphous film was reported (Ra /Rc < 1), which is opposed to the reflectivity change after laser light irradiation found in [380]. It was proposed that different amorphization routes could result in different local electronic structures.

6.8.2 Irradiation and Implantation Effects in FeSe1−x Te x Films Irradiation experiments on Fe-chalcogenide superconductors are yet sporadic and early studies have interestingly reported an initial increase of Tc at low fluences [383] or no change in Tc [375]. Irradiation experiments on PLD-grown FeSe0.5 Te0.5 films were carried out using high-energetic neutrons [384], protons [74, 385–387], and Au3+ ions [378]. An overview is given in Table 6.17. The mentioned experiments have predominantly demonstrated a reduction of Tc with irradiation, except the implantation experiment in [74]. Neutron irradiation was performed on PLD-grown FeSe0.5 Te0.5 films deposited on LaAlO3 substrates [384]. A batch of four samples was investigated with film thicknesses of 105 and 200 nm, respectively. A neutron fluence of 2 × 1021 m−2 was achieved after irradiation for 7 hours and 19 minutes. The high-energetic neutrons (E > 0.1 MeV) produced uncorrelated and randomly distributed defects. The reduction in Tc for the given fluence was 0.3 K for a film with initial Tcunirr = 19.3 K. Furthermore, it was concluded, that the neutron irradiation-induced disorder had only a small effect on the upper critical field, the irreversibility field and the critical currents when the sample-to-sample variation was taken into account. A comparison with neutron irradiation experiments on Fe-chalcogenide crystals [383] suggests, that the critical temperature should be reduced severely with fluences beyond 1023 m−2 . An atypical increase of critical temperature, Tc , from 18.0 to 18.5 K was reported after proton irradiation of FeSe0.5 Te0.5 films, that were grown by PLD on CeO2 buffered SrTiO3 substrates [74]. The irradiation was performed using 190 keV protons with a fluence of 1015 protons cm−2 (and a flux of 6 × 1012 protons cm−2 ·s−1 ). The thin film (with a thickness of 130 nm) was covered by a 1.5 μm thick Al foil, which shifts the stopping range of the protons into the film close to the FeSe0.5 Te0.5 /CeO2 interface. In contrast to the conventional irradiation experiments, where the ions are stopped far from the thin film inside the substrate, one must conclude that in this particular experiment also proton implantation takes place and thus affects the properties of the Fe-chalcogenide thin film (e.g. by doping). However, in [74] only a strain-analysis of the irradiation-induced defects and a possibly proximity effect were proposed to explain the unusual Tc -enhancement after irradiation. A possible doping effect due to ion implantation was neglected, as well as a more

354

6 Thin Film Studies Under Focus

detailed analysis of the implantation region. The experiment was carried out on a single sample and the result was not yet reproduced. HR-TEM analysis identified splayed cascade defects in the upper part of the FeSe0.5 Te0.5 film (Fig. 6.37b). The self-field critical current densities show an enhancement from 0.9–1.4 MAcm−2 at 4.2 K for μ0 H  c, that could be attributed to the irradiation-induced defect structure. A pinning force analysis found a maximum pinning force of ∼38 GNm−3 at 4.2 K and μ0 H c = 12 T as well as ∼120 GNm−3 at 4.2 K and μ0 H ab = 28 T. A clear change is seen for the exponents p and q in 6.8 (see Sect. 6.1.3 and Table 6.3). The pinning force anisotropy does not reduce after irradiation in an intermediate magnetic field region (15–30 T). Reference [388] suggested that the anisotropy of the critical current densities decreases after irradiation from JcH ab /JcH c = 3.8 to 1.9 at T = 4.2 K and μ0 H = 15 T. It has to be pointed out again, that this experiment is in contrast to the other irradiation experiments carried out on Fe-based superconductor thin films, for which solely irradiation effects occur (that usually record a decrease in Tc and an enhancement in Jc ). Proton irradiation effects on FeSe1−x Tex films (x = 0.4, 0.55) were investigated in [385]. Only limited information on the irradiation experiment itself is available: films were irradiated with a total fluence of 5 × 1015 cm−2 and proton currents in the samples of 10 and 100 nA. The films were deposited on CaF2 substrates using PLD. After irradiation the c-axis lattice parameter decreased in both films (by 0.08 and 0.65%). No clear conclusion could be drawn from the (residual) lattice strain that was evaluated by the Williamson-Hall method. The anisotropy of the upper critical ab c field, γ = μ0 Hc2 /μ0 Hc2 decreased from 3.1 to 2.2. A pure proton irradiation experiment on a FeSe0.5 Te0.5 film can be found in [387], where a batch of five 100 nm thin films deposited on CaF2 substrates by PLD was studied. 3.5 MeV and 1.43 MeV protons (decelerated by a 80 μm thick Al foil) were used. The protons were implanted in the substrate with an implantation depth of 21 μm (with Al foil) and 86 μm (without Al foil). The proton flux was kept below 1012 cm−2 ·s−1 in order to avoid sample heating during irradiation. Fluences in the range of 0.70–7.30×1016 protons·cm−2 resulted in a damage of 2.5 × 10−4 – 2.59 × 10−3 dpa. Random point defects and defect clusters of nanometer size were expected to occur with irradiation. After irradiation, the largest measurable suppression of Tc was 0.6 K. Furthermore, a modest Jc -enhancement was found. The overall low sensitivity of superconducting and normal-state properties to the proton irradiation indicated that FeSe0.5 Te0.5 has a certain robustness against irradiation-induced defects, which makes it a suitable candidate for particle accelerator applications. More results of the same study can be found in [386, 389]. An Au3+ ion irradiation experiment was carried out on a 100–130 nm thin FeSe0.5 Te0.5 film that was deposited by PLD on CeO2 -buffered SrTiO3 [378]. For the heavy-ion irradiation the samples were sealed in vacuum. The irradiation was performed at room temperature. The 6 MeV Au3+ ions produced cluster-like defects with a size of 10–15 nm that were identified by HR-TEM imaging. A fluence of 1012 ions·cm−2 resulted in a damage of 6.42 × 10−3 dpa. The corresponding ion flux was 2 × 1010 ions·cm−2 s−1 with an ion beam current density of ∼34 nAcm−2 . unirr The superconducting transition of the Fe-chalcogenide film decreased from Tc,0 =

6.8 Irradiation and Implantation

355

Table 6.17 Summary of irradiation experiments on FeSe1−x Tex thin films Particle Source E (MeV) Φmax (m−2 ) Refs. Neutrons Protons Protons Protons Au3+

TRIGA MARK II reactor, TU Vienna BNLb MC-50 Cyclotron, KIRAMSa CN Van de Graaf Acc., INFN-LNLb 15 MV tandem Van de Graaff Acc., BNLc

>0.1

2 × 1021

[384]

0.19 3.5

1019 5 × 1019

[74, 388] [385]

1.43; 3.5

7.3 × 1020

[386, 387, 389]

6

1016

[378]

a Korea

Institute of Radiological and Medical Sciences; b Istituto Nazionale die Fisica Nucleare – Laboratori Nazionali di Legnaro, Italy; c Brookhaven National Laboratory, USA

irr 17.9 K to Tc,0 = 17.4 K. No broadening of the resistive transition was seen after irradiation. An increase of the critical current densities by 70% was found at 10 K in a magnetic field of μ0 H = 9 T.

6.8.3 Irradiation of Fe-Pnictide Thin Films Irradiation studies on Fe-pnictide thin films were performed using protons, He+ , He2+ and Au3+ ions (Table 6.18). The effects of proton irradiation (3 MeV) on two Ba(Fe1−x Cox )2 As2 films were investigated in [94]. The films were prepared on a (La,Sr)(Al,Ta)O3 substrates using PLD. Irradiation doses of 1 × 1016 cm−2 and 2 × 1016 cm−2 were employed, which produced random point defects and defect clusters with an average spacing of 3.6 nm and 2.8 nm, respectively. The critical temperature of the film decreased from 21.5 K successively to 21 K and 20.5 K. The evaluated linear suppression of Tc,on and Tc,90 was averaged to ∂ Tc /∂Φ = −(0.53 ± 0.01) × 10−16 K·cm2 per proton. The irradiation study focused primarily on the variation of critical current density with increasing fluence. It was found that proton irradiation did not have a qualitative effect on the Jc (H ) variation, that was described as Jc (H ) ∝ H −α with α = 0.27–0.30 in a temperature range of 2.5–1 K. While a decrease of Jc was found in low magnetic fields around 1 T, Jc increased mildly at high magnetic fields and at low temperatures. Predominantly, the angular dependence of the critical current densities, Jc (θ ), was modified due to the irradiation process and became more isotropic. Non-magnetic, point atomic displacement defects are expected to occur after irradiation of 50 nm thin PLD-grown Ba(Fe1−x Cox )2 As2 thin films on CaF2 substrates with 200 keV 3 He+ -ions [148]. The ion current density during irradiation was kept

356

6 Thin Film Studies Under Focus

below 10 nAcm−2 in order to avoid sample heating. The sample temperature during irradiation was held at 300 K. A sequential irradiation with cumulative fluences up to 3.5 × 1015 ions·cm−2 was performed. The critical temperature of the unirradiated thin film was Tcunirr = 24.5 K. A linear decrease in Tc with increasing fluence down to a complete suppression of superconductivity was observed, which could be described as ∂ Tc /∂Φ ≈ −0.7 × 10−14 K·cm2 per ion. Simultaneously, the resistivity of the thin films increased and a superconductor-to-insulator-transition was induced by increasing disorder. Another 3 He+ -ion irradiation experiment can be found in [377]. The motivation for this study was not the creation of irradiation-induced pinning centers but the fabrication of Josephson-junctions by using a focused 3 He+ -ion beam for the patterning of sub-nanometer-sized barriers. In the described experiment a focused beam of 30 keV ions with a small spot size of 0.5 nm using a He ion microscope (Zeiss Orion Plus) was employed. The 50 nm thin Ba(Fe1−x Cox )2 As2 (xnom = 0.08) films were deposited on (La,Sr)(Al,Ta)O3 (100) substrates at 730 ◦ C by PLD. In addition, the films were covered by a 20 nm thin Au layer that was deposited at 200 ◦ C and a 7 nm SiO2 passivation layer was deposited by RF magnetron sputtering. The irradiation was carried out along a centered line on a 4 × 10 μm2 bridge. The ions penetrated the thin film sample and were almost completely implanted within the substrate (Fig. 6.36c). Ion irradiation at low doses of 2 × 1010 m−2 modified the initial superconducting transition at 17.9 K and induced an additional lower transition Tc ’ at 7.7 K across the bridge. Doses of 1011 m−2 and larger resulted in the complete loss of superconductivity in the irradiated area, leading to a residual resistivity ρ0 below the global superconducting transition, Tc . The evolution of Tc ’/Tc and ρ0 with increasing irradiation dose is shown in Fig. 6.39. A total vacancy concentration in the order of 1015 m−3 was evaluated for an ion irradiation dose of 5 × 1010 m−2 . The same study also investigated the hillock formation by AFM due to the swelling of the substrate material after irradiation. The height of the hillock grows according to a power law with increasing dose (in the range of 5 × 1010 –1014 m−2 . A height of 28 nm was determined across a single ion irradiation track after the irradiation with a dose of 3 × 1012 m−2 . For doses of 1013 m−2 the height of the hillock exceeded the film thickness. Recent irradiation experiments using 600 keV He+ ions were performed on 150 nm thin Ba(Fe1−x Cox )2 As2 films on CaF2 substrates [390]. Tc was reduced from 25 K to 20 K after irradiation with a dose of 1020 m−2 . The critical current densities were enhanced only after the lowest irradiation dose of 5 × 1017 m−2 from 0.5 MAcm−2 to 2.4 MAcm−2 (at T = 4.5 K, μ0 H = 1 T). A further increase of the irradiation dose (≥5 × 1014 cm−2 ) deteriorated the critical current densities again. A pinning force analysis suggested that the pinning mechanism does not change with irradiation, i.e. the exponents p and q from the normalized pinning force f (b) ∝ b p · (1 − b)q do not alter strongly. An irradiation experiment with 2 MeV 4 He2+ -ion (α-particle) was performed on a 90 nm thin NdO1−x Fx FeAs film, that was grown by MBE on a MgO substrate [391]. The film was uniformly irradiated because the calculated mean free path of the ions was 4.2 μm. A sequential irradiation with accumulated fluences of 4 × 1014 , 2 × 1015 ,

6.8 Irradiation and Implantation

357

Fig. 6.39 Critical temperature normalized to the initial value of 17.9 K (Tc ’/Tc ) and residual resistivity (ρ0 ) of a Ba(Fe1−x Cox )2 As2 thin film (4 × 10 μm2 transport bridge) versus the 3 He+ ion dose. (Reprinted from Fig. 4b in [377]; © IOP Publishing. Reproduced with permission. All rights reserved) Table 6.18 Summary of irradiation experiments on Fe-pnictide thin films Particle Source E (MeV) Φmax (m−2 ) Ba(Fe1−x Cox )2 As2 Protons LANLa 3 He+ DANFYSIK type 911A ion source 3 He+ Zeiss Orion Plus HIMb 3 He+ HVEE Surrey Ion Beam Centre NdO1−x Fx FeAs 4 He2+ Tandem Acc., Arizona State University BaFe2 (As1−x P x )2 Au3+ Tandem XTU Acc., INFN-LNLc

Refs.

3 0.2

2 × 1020 3.5 × 1019

[94] [148]

0.03

1016 –1021

[377]

0.6

5 × 1017 –1020

[390]

2

5 × 1019

[391]

250

7.3 × 1015

[364]

a Los Alamos National Laboratory, USA; b He-ion microscope; c Istituto Nazionale die Fisica Nucle-

are – Laboratori Nazionali di Legnaro, Italy

and finally 5 × 1015 ions·cm−2 was carried out. The critical temperature of the unirunirr = 49.0 K, which was suppressed to 45.8 K after the third irraradiated film was Tc,90 diation step (highest fluence level). The linear decrease of Tc,90 with fluence extracted from the provided data is ∂ Tc /∂Φ ≈ −0.64 × 10−15 K·cm2 per ion, the suppression of the offset superconducting transition, Tc,0 , was slightly stronger. Upon irradiation the slopes of the upper critical fields, |dHc2 /dT |Tc , increased monotonously for μ0 H  c and, after the second irradiation step, also for μ0 H  ab. The critical current densities, Jc , decreased upon irradiation, except for larger magnetic fields,

358

6 Thin Film Studies Under Focus

μ0 H  c (≥8 T) and low temperatures (∼10 K), i.e. after the maximum in pinning force was reached. 250 MeV Au3+ -ion irradiation of BaFe2 (As1−x Px )2 films with x = 0.19 and 0.20 were performed with fluences of 2.4 × 1011 , 4.8 × 1011 , and 7.3 × 1011 ions·cm−2 [364]. The batch of three films with thicknesses of ∼50 nm were grown by MBE on MgO substrates. During irradiation the flux was kept below 2 × 108 cm−2 ·s−1 and the ion beam was directed normal to the film surface (i.e.  c). The calculated ion implantation depth was 14 μm. The ionization energy released in the film, E i = 2.9 × 1011 eV·Φ cm−3 , corresponded to a dpa of 3.3 × 10−16 × Φ. In this study the superconducting gaps were determined by point-contact Andreev reflection spectroscopy. A monotonous suppression of Tc,90 upon irradiation was found in electrical transport measurements with ∂ Tc /∂Φ ≈ −0.25×10−11 K·cm2 per ion. In addition, a monotonous suppression of the superconducting gap sizes (two-band model) was found from Δ1 = 8.45 to 5.95 meV and from Δ2 = 3.95 to 2.9 meV (see Sect. 6.7.5). In comparison, the reported values of linear suppression of the critical temperatures with fluence, ∂ Tc /∂Φ, are in the range of 10−18 –10−11 K·cm2 per particle. They increase with particle size (neutrons, protons, ions) and damage (given in dpa), respectively (Fig. 6.40). Fe-pnictide thin films seem to be more sensitive to particle irradiation than Fe-chalcogenides.

Fig. 6.40 Comparison of reported ∂ Tc /∂Φ values for Fe-chalcogenide (yellow) and Fe-pnictide (blue) superconductor thin films irradiated by different particles

References

359

References 1. Lin, H.T., Wu, S.L., Wang, J.W., Chen, T.J., Wang, M.J., Chen, J.C., Wu, M.K., Chi, C.C.: Determination of the London penetration depth of FeSe0.3 Te0.5 thin films by scanning SQUID microscope. Supercond. Sci. Technol. 28, 085006 (2015) 2. Blatter, G., Feigel’man, M.V., Geshkenbein, V.B., Larkin, A.I., Vinokur, V.M.: Vortices in high-temperature superconductors. Rev. Mod. Phys. 66, 1125 (1994) 3. Huebener, R.P.: Magnetic Flux Structures in Superconductors, 2nd edn. Springer, Berlin, Heidelberg (2001) 4. Kumar, R., Mitra, A., Varma, G.D.: Study of vortex glass-liquid transition in superconducting Fe(Se, Te) thin films on LaAlO3 substrates. J. Appl. Phys. 125, 193902 (2019) 5. Oh, M.J., Lim, H.J., Seo, M.S., Park, S.Y., Kang, W.N., Jo, Y.: Strong flux pinning caused by phase distribution characteristics in (Ba, K)Fe2 As2 films. IEEE Trans. Appl. Supercond. 28, 7300405 (2018) 6. Oh, M.J., Lee, J., Seo, S., Yoon, S., Seo, M.S., Park, S.Y., Kim, H.-S., Ha, D.-W., Lee, S., Jo, Y.J.: Vortex pinning in artificially layered Ba(Fe, Co)2 As2 film. Cryogenics 92, 1 (2018) 7. Xu, Z., Dong, C., Fan, F., Vlasko-Vlasov, V., Welp, U., Kwok, W.-K., Ma, Y.: Transport characterization and pinning analysis of BaFe1.9 Ni0.1 As2.05 thin films. Supercond. Sci. Technol. 33, 044002 (2020) 8. Anderson, P.W.: Theory of flux creep in hard superconductors. Phys. Rev. Lett. 9, 309 (1962) 9. Kumar, R., Mitra, A., Varma, G.D.: Vortex state study of superconducting Fe(Te, Se) thin films deposited on SrTiO3 substrate by pulsed laser deposition. AIP Adv. 9, 125128 (2019) 10. Ahmad, D., Choi, W.J., Seo, Y.I., Seo, S., Lee, S., Kwon, Y.S.: Thermally activated flux flow in superconducting epitaxial FeSe0.6 Te0.4 thin film. Results Phys. 7, 16 (2017) 11. Ogawa, R., Ishikawa, T., Kawai, M., Nabeshima, F., Maeda, A.: Direct current measurement of Hall effect in the mixed state for the iron-chalcogenide superconductors. IOP Conf. Ser.: J. Phys.: Conf. Ser. 1054, 012021 (2018) 12. Leo, A., Grimaldi, G., Guarino, A., Avitabile, F., Nigro, A., Galluzzi, A., Mancusi, D., Polichetti, M., Pace, S., Buchkov, K., Nazarova, E., Kawale, S., Bellingeri, E., Ferdeghini, C.: Vortex pinning properties in Fe-chalcogenides. Supercond. Sci. Technol. 28, 125001 (2015) 13. Sun, Y., Zhang, W., Xing, Y., Li, F., Zhao, Y., Xia, Z., Wang, L., Ma, X., Xue, Q.-K., Wang, J.: High temperature superconducting FeSe films on SrTiO3 substrates. Sci. Rep. 4, 6040 (2014) 14. Zhao, W., Chang, C.-Z., Xi, X., Mak, K.F., Moodera, J.S.: Vortex phase transitions in monolayer FeSe film on SrTiO3 . 2D Mater. 3, 024006 (2016) 15. Tang, F., Wang, P., Wang, P., Gan, Y., Gu, G.D., Zhang, W., He, M., Zhang, L.: Quasi-2D superconductivity in FeTe0.55 Se0.45 ultrathin film. J. Phys.: Condens. Matter 31, 265702 (2019) 16. Liu, H.-C., Li, H., He, Q.L., Sou, I.K., Goh, S.K., Wang, J.: Robust two-dimensional superconductivity and vortex system in Bi2 Te3 /FeTe heterostructures. Sci. Rep. 6, 26168 (2016) 17. White, W.R., Kapitulnik, A., Beasley, M.R.: Collective vortex motion in a-MoGe superconducting thin films. Phys. Rev. Lett. 70, 670 (1993) 18. Triscone, J.-M., Fischer, Ø.: Superlattices of high-temperature superconductors: synthetically modulated structures, critical temperatures and vortex dynamics. Rep. Prog. Phys. 60, 1673 (1997) 19. Kidszun, M.: Herstellung und Charakterisierung von oxidischen Eisen-Pniktid-Supraleitern. PhD thesis Dresden: Technische Universität (2012) 20. Iida, K., Hänisch, J., Tarantini, C., Kurth, F., Jaroszynski, J., Ueda, S., Naito, M., Ichinose, A., Tsukuda, I., Reich, E., Grinenko, V., Schultz, L., Holzapfel, B.: Oxypnictide SmFeAs(O, F) superconductor: a candidate for high-field magnet applications. Sci Rep. 3, 2139 (2013) 21. Brandt, E.H.: Dynamics of flux-line lattice in high-Tc oxides. Physica C 185–189, 270 (1991) 22. Eley, S., Miura, M., Maiorov, B., Civale, L.: Universal lower limit on vortex creep in superconductors. Nat. Mater. 16, 409 (2017)

360

6 Thin Film Studies Under Focus

23. Yeshurun, Y., Malozemoff, A.P., Shaulov, A.: Magnetic relaxation in high-temperature superconductors. Rev. Mod. Phys. 68, 911 (1996) 24. Anderson, P.W., Kim, Y.B.: Hard superconductivity: theory of the motion of Abrikosov flux lines. Rev. Mod. Phys. 36, 39 (1964) 25. Luo, J., Orlando, T.P., Graybeal, J.M., Wu, X.D., Muenchausen, R.: Scaling of longitudinal and Hall resistivities from vortex motion in YBa2 Cu3 O7 . Phys. Rev. Lett. 68, 690 (1992) 26. Vinokur, V.M., Geshkenbein, V.B., Feigel’man, M.V., Blatter, G.: Scaling of Hall resistivity in high-Tc superconductors. Phys. Rev. Lett. 71, 1242 (1993) 27. Wang, Z.D., Dong, J., Ting, C.S.: Unified theory of mixed state Hall effect in type-II superconductors: scaling behavior and sign reversal. Phys. Rev. Lett. 72, 3875 (1994) 28. Sato, H., Katase, T., Kang, W.N., Hiramatsu, H., Kamiya, T., Hosono, H.: Anomalous scaling behavior in a mixed-state Hall effect of a cobalt-doped BaFe2 As2 epitaxial film with a high critical current density over 1 MA/cm2 . Phys. Rev. B 87, 064504 (2013) 29. Wang, L.M., Sou, U.-C., Yang, H.C., Chang, L.J., Cheng, C.-M., Tsuei, K.-D., Su, Y., Wolf, Th., Adelmann, P.: Mixed-state Hall effect and flux pinning in Ba(Fe1−x Cox )2 As2 single crystals (x = 0.08 and 0.10). Phys. Rev. B 83, 134506 (2011) 30. Berezinskii, V.L.: Destruction of long-range order in one-dimensional and two-dimensional systems having a continuous symmetry group I. Classical systems. Soviet Phys. JETP 32, 493 (1971) [Zh. Eksp. Teor. Fiz. 59, 907 (1970)] 31. Berezinskii, V.L.: Destruction of long-range order in one-dimensional and two-dimensional systems having a continuous symmetry group II. Quantum systems. Soviet Phys. JETP 34, 610 (1972) [Zh. Eksp. Teor. Fiz. 61, 1144 (1971)] 32. Kosterlitz, J.M., Thouless, D.J.: Ordering, metastability and phase transitions in twodimensional systems. J. Phys. C: Solid State Phys. 6, 1181 (1973) 33. Schneider, R., Zaitsev, A. G., Fuchs, D., Löhneysen, H.v.: Excess conductivity and Berezinskii-Kosterlitz-Thouless transition in superconducting FeSe thin films. J. Phys.: Condens. Matter. 26, 455701 (2014) 34. Zhang, W.-H., Sun, Y., Zhang, J.-S., Li, F.-S., Guo, M.-H., Zhao, Y.-F., Zhang, H,-M., Peng, J.-P., Xing, Y., Wang, H.-C., Fujita, T., Hirata, A., Li, Z., Ding, H., Tang, C.-J., Wang, M., Wang, Q.-Y., He, K., Ji, S.-H., Chen, X., Wang, J.-F., Xia, Z.-C., Li, L., Wang, Y.-Y., Wang, J., Wang, L.-L., Chen, M.-W., Xue, Q.-K., Ma, X.-C.: Direct observation of high-temperature superconductivity in one-unit-cell FeSe films. Chin. Phys. Lett. 31, 017401 (2014) 35. Zhao, W.-L., Zhu, X., He, Z.-H., Gao, K.-H., Li, Z.Q.: The vortex state in FeSe superconducting thin film. Supercond. Sci. Technol. 33, 105010 (2020) 36. Mei, C., Lin, Z., Zhang, R., Xu, C., Huang, H., Dong, Y., Meng, M., Gao, Y., Zhang, X., Zhang, Q., Gu, L., Yang, H., Tian, H., Li, J., Lu, Y., Zhang, G., Zhao, Y.: Growth of highquality superconducting FeSe0.5 Te0.5 films on Pb(Mg1/3 Nb2/3 )0.7 Ti0.3 O3 and electric-field modulation of superconductivity. ACS Appl. Mater. Interfaces 12, 12238 (2020) 37. He, Q.L., Liu, H., He, M., Lai, Y.H., He, H., Wang, G., Law, K.T., Lortz, R., Wang, J., Sou, I.K.: Two-dimensional superconductivity at the interface of a Bi2 Te3 /FeTe heterostructure. Nat. Commun. 5, 4247 (2014) 38. Lin, Z., Mei, C., Wei, L., Sun, Z., Wu, S., Huang, H., Zhang, S., Liu, C., Feng, Y., Tian, H., Yang, H., Li, J., Wang, Y., Zhang, G., Lu, Y., Zhao, Y.: Quasi-two-dimensional superconductivity in FeSe0.3 Te0.7 thin films and electric-field modulation of superconducting transition. Sci. Rep. 5, 14133 (2015) 39. Dean, C.L., Kunchur, M.N., He, Q.L., Liu, H., Wang, J., Lortz, R., Sou, I.K.: Current driven vortex-antivortex pair breaking and vortex explosion in the Bi2 Te3 /FeTe interfacial superconductor. Physica C 527, 46 (2016) 40. Liangby PLD , J., Zhang, Y.J., Yao, X., Li, Z.-X., Wang, J., Chen, Y., Seo, I.K.: Studies on the origin of the interfacial superconductivity of Sb2 Te3 /Fe1+y Te heterostructures. PNAS 117, 221 (2020) 41. Dean, C.L., Kunchur, M.N., Shahesteh-Mogaddam, N., Varner, S.D., Knight, J.M., Ivlev, B.I., He, Q.L., Liu, H., Wang, J., Lortz, R., Sou, I.K.: Superconductivity and oscillatory magnetoresistance at a topological-insulator/chalcogenide interface. AIP Conf. Proc. 1832, 020001 (2017)

References

361

42. Likharev, K.K.: Superconducting weak links. Rev. Mod. Phys. 51, 101 (1979) 43. Gurevich, A.: Challenges and opportunities for applications of unconventional superconductors. Annu. Rev. Condens. Matter Phys. 5, 35 (2014) 44. Haindl, S., Kidszun, M., Oswald, S., Hess, C., Büchner, B., Kölling, S., Wilde, L., Thersleff, T., Yurchenko, V.V., Jourdan, M., Hiramatsu, H., Hosono, H.: Thin film growth of Fe-based superconductors: from fundamental properties to functional devices. A comparative review. Rep. Prog. Phys. 77, 046502 (2014) 45. Pallecchi, I., Eisterer, M., Malagoli, A., Putti, M.: Application potential of Fe-based superconductors. Supercond. Sci. Technol. 28, 114005 (2015) 46. Shimoyama, J.: Potentials of iron-based superconductors for practical future applications. Supercond. Sci. Technol. 27, 044002 (2014) 47. Zhang, W., Miao, W., Wang, Z., Zhou, K.M., Zhong, J.Q., Li, J., Guo, X.H., Shi, S.C., Yan, L., Ding, H.: Characterization of superconducting FeSe0.5 Te0.5 hot electron bolometer. AsiaPacific Microwave Conference (APMC). IEEE (2015) 48. Rehm, L., Henrich, D., Hofherr, M., Wuensch, S., Thoma, P., Scheuring, A., Il’in, K., Siegel, M., Haindl, S., Iida, K., Kurth, F., Holzapfel, B., Schultz, L.: Infrared photo-response of Fe-shunted Ba-122 thin film microstructures. IEEE Trans. Appl. Supercond. 23, 7501105 (2013) 49. Nappi, C., Camerlingo, C., Enrico, E., Bellingeri, E., Braccini, V., Ferdeghini, C., Sarnelli, E.: Current induced resistive state in Fe(Se, Te) superconducting nanostrips. Sci. Rep. 7, 4115 (2017) 50. Wu, C.H., Chang, W.C., Jeng, J.T., Wang, M.J., Li, Y.S., Chang, H.H., Wu, M.K.: Transport properties in FeSe0.5 Te0.5 nanobridges. Appl. Phys. Lett. 102, 222602 (2013) 51. Hong, S.-H., Lee, S.-G., Jung, S.-G., Kang, W.N.: Properties of FeSe nanobridges prepared by using a focused ion beam. J. Kor. Phys. Soc. 61, 1430 (2012) 52. Rall, D., Il’in, K., Iida, K., Haindl, S., Kurth, F., Thersleff, T., Schultz, L., Holzapfel, B., Siegel, M.: Critical current densities in ultrathin Ba(Fe, Co)2 As2 microbridges. Phys. Rev. B 83, 134514 (2011) 53. Li, J., Yuan, J., Yuan, Y.-H., Ge, J.-Y., Li, M.-Y., Feng, H.-L., Pereira, P.J., Ishii, A., Hatano, T., Silhanek, A.V., Chibotaru, L.F., Vanacken, J., Yamaura, K., Wang, H.-B., TakayamaMuromachi, E., Moshchalkov, V.V.: Direct observation of the depairing current density in single-crystalline Ba0.5 K0.5 Fe2 As2 microbridge with nanoscale thickness. Appl. Phys. Lett. 103, 062603 (2013) 54. Harada, T., Shiogai, J., Miyakawa, T., Nojima, T., Tsukazaki, A.: Critical current enhancement driven by suppression of superconducting fluctuation in ion-gated ultrathin FeSe. Supercond. Sci. Technol. 31, 055003 (2018) 55. Kunchur, M.N., Dean, C.L., Shayesteh, M., Knight, J.M., He, Q.L., Liu, H., Wang, J., Lortz, R., Sou, I.K., Gurevich, A.: Current-induced depairing in the Bi2 Te3 /FeTe interfacial superconductor. Phys. Rev. B 92, 094502 (2015) 56. Wang, G., Raine, M.J., Hampshire, D.P.: How resistive must grain boundaries in polycrystalline superconductors be, to limit Jc ? Supercond. Sci. Technol. 30, 104001 (2017) 57. Fietz, W.A., Webb, W.W.: Hysteresis in superconducting alloys - temperature and field dependence of dislocation pinning in niobium alloys. Phys. Rev. 178, 657 (1969) 58. Kramer, E.J.: Scaling laws for flux pinning in hard superconductors. J. Appl. Phys. 44, 1360 (1970) 59. Dew-Hughes, D.: Flux pinning mechanisms in type II superconductors. Phil. Mag. 30, 293 (1974) 60. Chang, H.H., Luo, J.Y., Wu, C.T., Hsu, F.C., Huang, T.W., Wu, P.M., Wu, M.K., Wang, M.J.: The vortex state of FeSe1−x Tex superconducting thin films. Supercond. Sci. Technol. 24, 105011 (2011) 61. Chen, L., Huang, J., Tsai, C.-F., Zhu, Y., Jian, J., Chen, A., Bi, Z., Khatkhatay, F., Cornell, N., Zakhidov, A., Wang, H.: Superconducting properties of Fex Te1−x thin film with a composition close to antiferromagnetic ordering. Supercond. Sci. Technol. 26, 112001 (2013)

362

6 Thin Film Studies Under Focus

62. Chang, H.H., Luo, J.Y., Wu, C.T., Hsu, F.C., Chen, T.K., Wu, P.M., Wu, M.K., Wang, M.J.: Te substitution effect on electronic properties of β-FeSe thin films. Physica C 470, S480 (2010) 63. Yuan, P., Xu, Z., Zhang, H., Wang, D., Ma, Y., Zhang, M., Li, J.: High performance FeSe0.5 Te0.5 thin films grown at low temperature by pulsed laser deposition. Supercond. Sci. Technol. 28, 065009 (2005) 64. Yuan, P., Xu, Z., Ma, Y., Sun, Y., Tamegai, T.: Angular-dependent vortex pinning mechanism and magneto-optical characterizations of FeSe0.5 Te0.5 thin films grown on CaF2 substrates. Supercond. Sci. Technol. 29, 035013 (2016) 65. Bellingeri, E., Kawale, S., Pallecchi, I., Gerbi, A., Buzio, R., Braccini, V., Palenzona, A., Putti, M., Adamo, M., Sarnelli, E., Ferdeghini, C.: Strong vortex pinning in FeSe0.5 Te0.5 epitaxial thin film. Appl. Phys. Lett. 100, 082601 (2012) 66. Bellingeri, E., Kawale, S., Caglieris, F., Braccini, V., Lamura, G., Pellegrino, L., Sala, A., Putti, M., Ferdeghini, C., Jost, A., Zeitler, U., Tarantini, C., Jaroszynski, J.: High field vortex phase diagram of Fe(Se, Te) thin films. Supercond. Sci. Technol. 27, 044007 (2014) 67. Kawale, S., Bellingeri, E., Braccini, V., Buzio, R., Gerbi, A., Sala, A., Reich, E., Holzapfel, B., Adamo, M., Sarnelli, E., Tarantini, C., Putti, M., Ferdeghini, C.: Potentiality for low temperature-high field application of iron chalcogenide thin films. IEEE Trans. Appl. Supercond. 25, 7300305 (2015) 68. Schneider, R., Zaitsev, A.G., Fuchs, D., Hott, R.: Anisotropic grain-boundary effect on electronic transport in superconducting FeSe thin films. Supercond. Sci. Technol. 32, 025001 (2019) 69. Li, D., Yuan, J., Shen, P., Xi, C., Tian, J., Ni, S., Zhang, J., Wei, Z., Hu, W., Li, Z., Yu, L., Miao, J., Zhou, F., Pi, L., Jin, K., Dong, X., Zhao, Z.: Giant enhancement of critical current density at high field in superconducting (Li,Fe)OHFeSe films by Mn doping. Supercond. Sci. Technol. 32, 12LT01 (2019) 70. Yuan, P., Xu, Z., Wang, D., Zhang, M., Li, J., Ma, Y.: Vortex pinning properties in Co-doped BaFe2 As2 thin films with a high critical current density over 2 MAcm−2 at 9T. Supercond. Sci. Technol. 30, 025001 (2017) 71. Trommler, S., Hänisch, J., Matias, V., Hühne, R., Reich, E., Iida, K., Haindl, S., Schultz, L., Holzapfel, B.: Architecture, microstructure, and Jc anisotropy of highly oriented biaxially textured Co-doped BaFe2 As2 on Fe/IBAD-MgO-buffered metal tapes. Supercond. Sci. Technol. 25, 084019 (2012) 72. Xu, Z., Yuan, P., Fan, F., Chen, Y., Ma, Y.: Transport properties and pinning analysis for Co-doped BaFe2 As2 thin films on metal tapes. Supercond. Sci. Technol. 31, 055001 (2018) 73. Leo, A., Guarino, A., Grimaldi, G., Nigro, A., Pace, S., Bellingeri, E., Kawale, S., Ferdeghini, C., Giannini, E.: Comparison of the pinning energy in Fe(Se1−x Tex ) compound between single crystals and thin films. J. Phys.: Conf. Ser. 507, 010209 (2014) 74. Ozaki, T., Wu, L., Zhang, C., Jaroszynski, J., Si, W., Zhou, J., Zhu, Y., Li, Q.: A route for a strong increase of critical current in nanostrained iron-based superconductors. Nat. Commun. 7, 13036 (2016) 75. Si. W., Zhou, J., Jie, Q., Dimitrov, I., Solovyov, V., Johnson, P.D., Jaroszynski, J., Matias, V., Sheehan, C., Li, Q.: Iron-chalcogenide FeSe0.5 Te0.5 coated superconducting tapes for high field applications. Appl. Phys. Lett. 98, 262509 (2011) 76. Si, W., Han, S.J., Shi, X., Ehrlich, S.N., Jaroszynski. J., Goyal, A., Li, Q.: High current superconductivity in FeSe0.5 Te0.5 -coated conductors at 30 Tesla. Nat. Commun. 4, 1347 (2013) 77. Tarantini, C., Lee, S., Zhang, Y., Jiang, J., Bark, C.W., Weiss, J.D., Polyanskii, A., Nelson, C.T., Jang, H.W., Folkman, C.M., Baek, S.H., Pan, X.Q., Gurevich, A., Hellstrom, E.E., Eom, C.B., Larbalestier, D.C.: Strong vortex pinning in Co-doped BaFe2 As2 single crystal thin films. Appl. Phys. Lett. 96, 142510 (2010) 78. Iida, K., Sato, H., Tarantini, C., Hänisch, J., Jaroszynski, J., Hiramatsu, H., Holzapfel, B., Hosono, H.: High-field transport properties of a P-doped BaFe2 As2 film on technical substrate. Sci. Rep. 7, 39951 (2017)

References

363

79. Kidszun, M., Haindl, S., Thersleff, T., Hänisch, J., Kauffmann, A., Iida, K., Freudenberger, J., Schultz, L., Holzapfel, B.: Critical current scaling and anisotropy in oxypnictide superconductors. Phys. Rev. Lett. 106, 137001 (2011) 80. Adachi, S., Shimode, T., Miura, M., Chikumoto, N., Takemori, A., Nakao, K., Oshikubo, Y., Tanabe, K.: Pulsed laser deposition of BaFe2 (As, P)2 superconducting thin films with high critical current density. Supercond. Sci. Technol. 25, 105015 (2012) 81. Sato, H., Hiramatsu, H., Kamiya, T., Hosono, H.: Vortex pinning properties of phosphorousdoped BaFe2 As2 epitaxial films: comparison between (La, Sr)(Al, Ta)O3 and MgO substrates. IEEE Trans. Appl. Supercond. 25, 7500305 (2015) 82. Sakagami, A., Kawaguchi, T., Tabuchi, M., Ujihara, T., Takeda, Y., Ikuta, H.: Critical current density and grain boundary property of BaFe2 (As, P)2 thin films. Physica C 494, 181 (2013) 83. Kurth, F., Tarantini, C., Grinenko, V., Hänisch, J., Reich, E., Mori, Y., Sakagami, A., Kawaguchi, T., Engelmann, J., Schultz, L., Holzapfel, B., Ikuta, H., Hühne, R., Iida, K.: Unusually high critical current of clean P-doped BaFe2 As2 single crystalline thin film. Appl. Phys. Lett. 106, 072602 (2015) 84. Sato, H., Hiramatsu, H., Kamiya, T., Hosono, H.: High critical-current density with less anisotropy in BaFe2 (As, P)2 epitaxial thin films: effect of intentionally grown c-axis vortexpinning centers. Appl. Phys. Lett. 104, 182603 (2014) 85. Tsukada, I., Hanawa, M., Akiike, T., Nabeshima, F., Imai, Y., Ichinose, A., Komiya, S., Hikage, T., Kawaguchi, T., Ikuta, H., Maeda, A.: Epitaxial growth of FeSe0.5 Te0.5 thin films on CaF2 substrates with high critical current density. Appl. Phys. Express 4, 053101 (2011) 86. Kawale, S., Bellingeri, E., Braccini, V., Pallecchi, I., Putti, M., Grimaldi, G., Leo, A., Guarino, A., Nigro, A., Ferdeghini, C.: Comparison of superconducting properties of FeSe0.5 Te0.5 thin films grown of different substrates. IEEE Trans. Appl. Supercond. 23, 7500704 (2013) 87. Braccini, V., Kawale, S., Reich, E., Bellingeri, E., Pellegrino, L., Sala, A., Putti, M., Higashikawa, K., Kiss, T., Holzapfel, B., Ferdeghini, C.: Highly effective and isotropic pinning in epitaxial Fe(Se, Te) thin films grown on CaF2 substrates. Appl. Phys. Lett. 103, 172601 (2013) 88. Tarantini, C., Kametani, F., Lee, S., Weiss, J.D., Jaroszynski, J., Hellstrom, E.E., Eom, C.B., Larbalestier, D.C.: Development of very high Jc in Ba(Fe1−x Cox )2 As2 thin films grown on CaF2 . Sci. Rep. 4, 7305 (2014) 89. Yoon, S., Seo, Y.-S., Lee, S., Weiss, J.D., Jiang, J., Oh, M.J., Lee, J., Seo, S., Jo, Y.J., Hellstrom, E.E., Hwang, J., Lee, S.: Structural, electro-magnetic, and optical properties of Ba(Fe, Ni)2 As2 single-crystal thin film. Supercond. Sci. Technol. 30, 035001 (2017) 90. Lee, S., Jiang, J., Zhang, Y., Bark, C.W., Weiss, J.D., Tarantini, C., Nelson, C.T., Jang, H.W., Folkman, C.M., Baek, S.H., Polyanskii, A., Abraimov, A., Park, J.W., Pan, X.Q., Hellstrom, E.E., Larbalestier, D.C., Eom, C.B.: Template-engineering of Co-doped BaFe2 As2 singlecrystal thin films. Nat. Mater. 9, 397 (2010) 91. Zhang, Y., Nelson, C.T., Lee, S., Jiang, J., Bark, C.W., Weiss, J.D., Tarantini, C., Folkman, C.M., Baek, S.-H., Hellstrom, E.E., Larbalestier, D., Eom, C.-B., Pan, X.: Self-assembled oxide nanopillars in epitaxial BaFe2 As2 thin films for vortex pinning. Appl. Phys. Lett. 98, 042509 (2011) 92. Zhang, Y., Nelson, C.T., Lee, S., Jiang, J., Hellstrom, E.E., Larbalestier, D.C., Eom, C.B., Pan, X.Q.: TEM study of oxide nanopillars in superconducting BaFe2 As2 films for vortex pinning. Microsc. Microanal. 17(Suppl. 2), 1454 (2011) 93. Katase, T., Hiramatsu, H., Kamiya, T., Hosono, H.: High critical current density 4 MA/cm2 in Co-doped BaFe2 As2 epitaxial films grown on (La, Sr)(Al, Ta)O3 substrates without buffer layers. APEX 3, 063101 (2010) 94. Maiorov, B., Katase, T., Usov, I.O., Weigand, M., Civale, L., Hiramatsu, H., Hosono, H.: Competition and cooperation of pinning by extrinsic point-like defects and intrinsic strong columnar defects in BFe2 As2 thin films. Phys. Rev. B 86, 094513 (2012) 95. Tarantini, C., Lee, S., Kametani, F., Jiang, J., Weiss, J.D., Jaroszynski, J., Folkman, C.M., Hellstrom, E.E., Eom, C.B., Larbalestier, D.C.: Artificial and self-assembled vortex-pinning centers in superconducting Ba(Fe1−x Cox )2 As2 thin films as a route to obtaining very high critical-current densities. Phys. Rev. B 86, 214504 (2012)

364

6 Thin Film Studies Under Focus

96. Huang, J., Chen, L., Jian, J., Khatkhatay, F., Wang, H.: Nanostructured pinning centers in FeSe0.1 Te0.9 thin films for enhanced superconducting properties. Supercond. Sci. Technol. 27, 105006 (2014) 97. Zhang, C., Si, W., Li, Q.: Doubling the critical current density in superconducting FeSe0.5 Te0.5 thin films by low temperature oxygen annealing. Appl. Phys. Lett. 109, 202601 (2016) 98. Huang, J., Chen, L., Jian, J., Tyler, K., Li, L., Wang, H., Wang, H.: Magnetic (CoFe2 O44 )0.1 (CeO2 )0.9 nanocomposite as effective pinning centers in FeSe0.1 Te0.9 thin films. J. Phys.: Condens. Matter 28, 025702 (2016) 99. Seo, S., Noh, H., Li, N., Jiang, J., Tarantini, C., Shi, R., Jung, S.-G., Oh, M.J., Liu, M., Lee, J., Gu, G., Jo, Y.J., Park, T., Hellstrom, E.E., Gao, P., Lee, S.: Artificially engineered nanostrain in FeSex Te1−x superconductor thin films for supercurrent enhancement. NPG Asia Mater. 12, 7 (2020) 100. Chen, L., Tsai, C.-F., Zhu, Y., Chen, A., Bi, Z., Lee, J., Wang, H.: Enhanced flux pinning properties in superconducting FeSe0.5 Te0.5 thin films with secondary phases. Supercond. Sci. Technol. 25, 025020 (2012) 101. Chen, L., Tsai, C.-F., Chen, A., Su, Q., Wang, H.: Growth and pinning properties of superconducting nanostructured FeSe0.5 Te0.5 thin films on amorphous substrates. IEEE Trans. Appl. Supercond. 23, 7500904 (2013) 102. Miura, M, Maiorov, B., Kato, T., Schimode, T., Wada, K., Adachi, S., Tanabe, K.: Strongly enhanced flux pinning in one-step deposition of BaFe2 (As0.66 P0.33 )2 superconductor films with uniformly dispersed BaZrO3 nanoparticles. Nat. Commun. 4, 2499 (2013) 103. Miura, M., Tsuchiya, G., Harada, T., Tanabe, K., Kiuchi, M., Matsushita, T.: Enhanced critical current density in BaFe2 (As0.66 P0.33 )2 nanocomposite superconducting films. Supercond. Sci. Technol. 32, 064005 (2019) 104. Lee, J., Jiang, J., Kametani, F., Oh, M.J., Weiss, J.D., Collantes, Y., Seo, S., Yoon, S., Tarantini, C., Jo, Y.J., Hellstrom, E.E., Lee, S.: High critical current density over 1 MAcm−2 at 13 T in BaZrO3 incorporated Ba(Fe, Co)2 As2 thin film. Supercond. Sci. Technol. 30, 085006 (2017) 105. Dimos, D., Chaudhari, P., Mannhart, J., LeGoues, F.K.: Orientation dependence of grainboundary critical currents in YBa2 Cu3 O7−δ bicrystals. Phys. Rev. Lett. 61, 219 (1988) 106. Dimos, D., Chaudhari, P., Mannhart, J.: Superconducting transport properties of grain boundaries in YBa2 Cu3 O7 bicrystals. Phys. Rev. B 41, 4038 (1989) 107. Hilgenkamp, H., Mannhart, J.: Grain boundaries in high-Tc superconductors. Rev. Mod. Phys. 74, 485 (2002) 108. Sheehan, C., Jung, Y., Holesinger, T., Feldmann, D.M., Edney, C., Ihlefeld, J.F., Clem, P.G., Matias, V.: Solution deposition planarization of long-length flexible substrates. Appl. Phys. Lett. 98, 071907 (2011) 109. Katase, T., Ishimaru, Y., Tsukamoto, A., Hiramatsu, H., Kamiya, T., Tanabe, K., Hosono, H.: Advantageous grain boundaries in iron pnictide superconductors. Nat. Commun. 2, 409 (2011) 110. Huang, J., Chen, L., Jian, J., Khatkhatay, F., Jacob, C., Wang, H.: A simplified superconducting coated conductor design with Fe-based superconductors on glass and flexible metallic substrates. J. Alloys. Compd. 647, 380 (2015) 111. Sylva, G., Augieri, A., Mancini, A., Rufoloni, A., Vannozzi, A., Celentano, G., Bellingeri, E., Ferdeghini, C., Putti, M., Braccini, V.: Fe(Se, Te) coated conductors deposited on simple rolling-assisted biaxially textured substrate templates. Supercond. Sci. Technol. 32, 084006 (2019) 112. Sylva, G., Malagoli, A., Bellingeri, E., Putti, M., Ferdeghini, C., Vannozzi, A., Celentano, G., Hopkins, S.C., Lunt, A., Ballarino, A., Braccini, V.: Analysis of Fe(Se, Te) films deposited on unbuffered invar 36. IEEE Trans. Appl. Supercond. 29, 7300105 (2019) 113. Sylva, G., Bellingeri, E., Bernini, C., Celentano, G., Ferdeghini, C., Leveratto, A., Lisitskiy, M., Malagoli, A., Manca, N., Mancini, A., Manfrinetti, P., Pallecchi, I., Provino, A., Putti, M., Vannozzi, A., Braccini, V.: The role of texturing and thickness of oxide buffer layers in the superconducting properties of Fe(Se, Te) coated conductors. Supercond. Sci. Technol. 33, 114002 (2020)

References

365

114. Xu, Z., Yuan., P., Ma, Y., Cai, C.: High-performance FeSe0.5 Te0.5 thin films fabricated on less-well-textured flexible coated conductor templates. Supercond. Sci. Technol. 30, 035003 (2017) 115. Iida, K., Hänisch, J., Trommler, S., Matias, V., Haindl, S., Kurth, F., Lucas del Pozo, I., Hühne, R., Kidszun, M., Engelmann, J., Schultz, L., Holzapfel, B.: Epitaxial growth of superconducting Ba(Fe1−x Cox )2 As2 thin films on technical ion beam assisted deposition MgO substrates. Appl. Phys. Express 4, 013103 (2011) 116. Katase, T., Hiramatsu, H., Matias, V., Sheehan, C., Ishimaru, Y., Kamiya, T., Tanabe, K., Hosono, H.: Biaxially textured cobalt-doped BaFe2 As2 films with high critical current density over 1 MA/cm2 on MgO-buffered metal-tape flexible substrates. Appl. Phys. Lett. 98, 242510 (2011) 117. Hiramatsu, H., Sato, H., Kamiya, T., Hosono, H.: BaFe2 (As1−x Px )2 (x = 0.22 – 0.42) thin films grown on practical metal-tape substrates and their critical current densities. Supercond. Sci. Technol. 30, 044003 (2017) 118. Sato, H., Hiramatsu, H., Kamiya, T., Hosono, H.: Enhanced critical-current in P-doped BaFe2 As2 thin films on metal substrates arising from poorly aligned grain boundaries. Sci. Rep. 6, 36828 (2016) 119. Vannozzi, A., Prili, S., Sylva, G., Masi, A., Angrisani Armenio, A., Mancini, A., Pinto, V., Rufoloni, A., Piperno, L., Augieri, A., Rizzo, F., Manfrinetti, P., Braccini, V., Putti, M., Silva, E., Celentano, G.: Epitaxial Zr-doped CeO2 films by chemical solution deposition as buffer layers for Fe(Se, Te) film growth. Supercond. Sci. Technol. 33, 084004 (2020) 120. Trommler, S., Hühne, R., Hänisch, J., Reich, E., Iida, K., Haindl, S., Matias, V., Schultz, L., Holzapfel, B.: The influence of the buffer layer architecture on transport properties for BaFe1.8 Co0.2 As2 films on technical substrates. Appl. Phys. Lett. 100, 122602 (2012) 121. Mohan, S., Taen, T., Yagyuda, Y., Nakajima, Y., Tamegai, T., Katase, T., Hiramatsu, H., Hosono, H.: Transport and magnetic properties of Co-doped BaFe2 As2 epitaxial thin films grown on MgO substrate. Supercond. Sci. Technol. 23, 105016 (2010) 122. Deutscher, G.: Origin of weak-link behavior of grain boundaries in superconducting cuprates and pnictides. Appl. Phys. Lett. 96, 122592 (2010) 123. Hong, S.-H., Lee, N.H., Kang, W.N., Lee, S.-G.: Observation of weak coupling effects in Ba0.6 K0.4 Fe2 As2 junctions patterned across a naturally formed grain boundary. Supercond. Sci. Technol. 27, 055007 (2014) 124. Haindl, S., Kidszun, M., Kauffmann, A., Nenkov, K., Kozlova, N., Freudenberger, J., Thersleff, T., Hänisch, J., Werner, J., Reich, E., Schultz, L., Holzapfel, B.: High upper critical fields and evidence of weak-link behavior in superconducting LaFeAsO1−x Fx thin films. Phys. Rev. Lett. 104, 077001 (2010) 125. Lin, K.C., Li, Y.S., Shen, Y.T., Wu, M.K., Chi, C.C.: Tunneling spectra and superconducting gaps observed by scanning tunneling microscopy near the grain boundaries of FeSe0.3 Te0.7 films. Physica C 495, 74 (2013) 126. Lee, N.H., Jung, S.-G., Kim, D.H., Kang, W.N.: Potassium-doped BaFe2 As2 superconducting thin films with a transition temperature of 40 K. Appl. Phys. Lett. 96, 2020505 (2010) 127. Lee, S., Jiang, J., Weiss, J.D., Folkman, C.M., Bark, C.W., Tarantini, C., Xu, A., Abraimov, D., Polyanskii, A., Nelson, C.T., Zhang, Y., Baek, S.H., Jang, H.W., Yamamoto, A., Kametani, F., Pan, X.Q., Hellstrom, E.E., Gurevich, A., Eom, C.B., Larbalestier, D.C.: Weak-link behavior of grain boundaries in superconducting Ba(Fe1−x Cox )2 As2 bicrystals. Appl. Phys. Lett. 95, 212505 (2009) 128. Hiramatsu, H., Katase, T., Ishimaru, Y., Tsukamoto, A., Kamiya, T., Tanabe, K., Hosono, H.: Microstructure and transport properties of [001]-tilt bicrystal grain boundaries in iron pnictide superconductor, cobalt-doped BaFe2 As2 . Mat. Sci. Eng. B 177, 515 (2012) 129. Iida, K., Haindl, S., Kurth, F., Hänisch, J., Schultz, L., Holzapfel, B.: BaFe2 As2 /Fe bilayers with [001]-tilt grain boundary on MgO and SrTiO3 bicrystal substrates. Phys. Procedia 45, 189 (2013) 130. Katase, T., Ishimaru, Y., Tsukamoto, A., Hiramatsu, H., Kamiya, T., Tanabe, K., Hideo, H.: Josephson junction in cobalt-doped BaFe2 As2 epitaxial thin films on (La, Sr)(Al, Ta)O3 bicrystal substrates. Appl. Phys. Lett. 96, 142507 (2010)

366

6 Thin Film Studies Under Focus

131. Polyanskii, A.A., Gurevich, A., Pashitski, A.E., Heinig, N.F., Redwing, R.D., Nordman, J.E., Larbalestier, D.C.: Magneto-optical study of flux penetration and critical current densities in [001] tilt YBa2 Cu3 O7−δ thin-film bicrystals. Phys. Rev. B 53, 8687 (1996) 132. Omura, T., Matsumoto, T., Hatano, T., Iida, K., Ikuta, H.: Fabrication of grain boundary junctions using NdFeAs(O,F) superconducting thin films. J. Phys.: Conf. Series 1054, 012024 (2018) 133. Ding, C., Gong, G., Liu, C., Yang, H., Dong, W., Zhang, Z., Li, Y., Wang, L., Xue, Q.K.: Preparation of SrTiO3 bicrystal substrates with atomic-level controlled boundaries for Josephson junction fabrication. Phys. Rev. Mat. 4, 050401(R) (2020) 134. Si, W., Zhang, C., Shi, X., Ozaki, T., Jaroszynski, J., Li, Q.: Grain boundary junctions of FeSe0.5 Te0.5 thin films on SrTiO3 bi-crystal substrates. Appl. Phys. Lett. 106, 032602 (2015) 135. Sarnelli, E., Adamo, M., Nappi, C., Braccini, V., Kawale, S., Bellingeri, E., Ferdeghini, C.: Properties of high-angle Fe(Se, Te) bicrystal grain boundary junctions. Appl. Phys. Lett. 104, 162601 (2014) 136. Sarnelli, E., Nappi, C., Camerlingo, C., Enrico, E., Bellingeri, E., Kawale, S., Braccini, V., Leveratto, A., Ferdeghini, C.: Properties of Fe(Se, Te) bicrystal grain boundary junctions, SQUIDs, and nanostrips. IEEE Trans. Appl. Supercond. 27, 7776776 (2017) 137. Seidel, P.: Josephson effects in iron based superconductors. Supercond. Sci. Technol. 24, 043001 (2011) 138. Sarnelli, E., Nappi, C., Leveratto, A., Bellingeri, E., Braccini, V., Ferdeghini, C.: Fe(Se, Te) superconducting quantum interference devices. Supercond. Sci. Technol. 30, 065003 (2017) 139. Katase, T., Ishimaru, Y., Tsukamoto, A., Hiramatsu, H., Kamiya, T., Tanabe, K., Hosono, H.: DC superconducting quantum interference devices fabricated using bicrystal grain boundary junctions in Co-doped BaFe2 As2 epitaxial films. Supercond. Sci. Technol. 23, 082001 (2010) 140. Ambegaokar, V., Baratoff, A.: Tunneling between superconductors. Phys. Rev. Lett. 10, 486 (1963) 141. Ota, Y., Nakai, N., Nakamura, H., Machida, M., Inotani, D., Ohashi, Y., Koyama, T., Matsumoto, H.: Ambegaokar-Baratoff relations for Josephson critical current in heterojunctions with multigap superconductors. Phys. Rev. B 81, 214511 (2010) 142. Zhang, X., Saha, S.R., Butch, N.P., Kirshenbaum, K., Paglione, J., Greene, R.L., Liu, Y., Yan, L., Oh, Y.S., Kim, K.H., Takeuchi, I.: Josephson effect between electron-doped and hole-doped iron pnictide single crystals. Appl. Phys. Lett. 95, 062510 (2009) 143. Zhang, X., Oh, Y.S., Liu, Y., Yan, L., Kim, K.H., Greene, R.L., Takeuchi, I.: Observation of the Josephson effect in Pb/Ba1−x Kx Fe2 As2 single crystal junctions. Phys. Rev. Lett. 102, 147002 (2009) 144. Schmidt, S., Döring, S., Schmidl, F., Grosse, V., Seidel, P., Iida, K., Kurth, F., Haindl, S., Mönch, I., Holzapfel, B.: BaFe1.8 Co0.2 As2 thin film hybrid Josephson junctions. Appl. Phys. Lett. 97, 172504 (2010) 145. Döring, S., Monecke, M., Schmidt, S., Schmidl, F., Tympel, V., Engelmann, J., Kurth, F., Iida, K., Haindl, S., Mönch, I., Holzapfel, B., Seidel, P.: Investigation of TiOx barriers for their use in hybrid Josephson and tunneling junctions based on pnictide thin films. J. Appl. Phys. 115, 083901 (2014) 146. Lei, B., Cui, J.H., Xiang, Z.J., Shang, C., Wang, N.Z., Ye, G.Y., Luo, X.G., Wu, T., Sun, Z., Chen, X.H.: Evolution of high-temperature superconductivity from a low-Tc phase tuned by carrier concentration in FeSe thin flakes. Phys. Rev. Lett. 116, 077002 (2016) 147. Lei, B., Xiang, Z.J., Lu, X.F., Wang, N.Z., Chang, J.R., Shang, C., Zhang, A.M., Zhang, Q.M., Luo, X.G., Wu, T., Sun, Z., Chen, X.H.: Gate-tuned superconductor-insulator transition in (Li, Fe)OHFeSe. Phys. Rev. B 93, 060501(R) (2016) 148. Blokhin, I.S., Gavrilkin, S.Yu., Gorshunov, B.P., Dravin, V.A., Zhukova, E.S., Ivanenko, O.M., Iida, K., Krasnosvobodtsev, S.I., Kurth, F., Mitsen, K.V., Tsvetkov, A.Yu.: Effect of radiation defects on the magnetotransport properties of Ba(Fe1−x Cox As)2 high-temperature superconductor. JETP Lett. 101, 247 (2015) 149. Schneider, R., Zaitsev, A.G., Fuchs, D., Löhneysen, H.v.: Superconductor-insulator quantum phase transition in disordered FeSe thin films. Phys. Rev. Lett. 108, 257003 (2012)

References

367

150. Schneider, R., Zaitsev, A.G., Fuchs, D., Fromknecht, R.: Analysis of superconducting FeSe thin films deposited by a sputtering technique. Supercond. Sci. Technol. 26, 055014 (2013) 151. Schneider, R., Zaitsev, A.G., Fuchs, D., Löhneysen, H.v.: Superconducting and insulating phases of disordered FeSe thin films. Eur. Phys. J. B 88, 14 (2015) 152. Fisher, M.P.A., Grinstein, G., Girvin, S.M.: Presence of quantum diffusion in two dimensions: universal resistance at the superconductor-insulator-transition. Phys. Rev. Lett. 64, 587 (1990) 153. Efros, A.L., Shklovskii, B.I.: Coulomb gap and low temperature conductivity of disordered systems. J. Phys. C: Solid State Phys. 8, L49 (1975) 154. Wang, Q., Zhang, W., Zhang, Z., Sun, Y., Xing, Y., Wang, Y., Wang, L., Ma, X., Xue, Q.-K., Wang, J.: Thickness dependence of superconductivity and superconductor-insulator transition in ultrathin FeSe films on SrTiO3 (001) substrate. 2D Mater. 2, 044012 (2015) 155. Glover, III., R.E., Sherril, M.D.: Changes in superconducting critical temperature produced by electrostatic charging. Phys. Rev. Lett. 5, 248 (1960) 156. Kleinsasser, A.W., Gallagher, W.J.: Three terminal devices. In: Ruggerio, S.T., Rudman, D.A. (eds.) Superconducting Devices, pp. 325–372. Academic Press, Boston (1990) 157. Mannhart, J., Bednorz, J.G., Müller, K.A., Schlom, D.G.: Electric field effect on superconducting YBa2 Cu3 O7−δ . Z. Physik B - Condens. Matter 83, 307 (1991) 158. Sato, T., Masuda, G., Takagi, K.: Electrochemical properties of novel ionic liquids for electric double layer capacitor applications. Electrochimica Acta 49, 3603 (2004) 159. Matsumoto, M., Shimizu, S., Sotoike, R., Watanabe, M., Iwasa, Y., Itoh, Y., Aida, T.: Exceptionally high electric double layer capacitances of oligomeric ionic liquids. J. Am. Chem. Soc. 139, 16072 (2017) 160. Katase, T., Hiramatsu, H., Kamiya, T., Hosono, H.: Electric double-layer transistor using layered iron selenide Mott insulator TlFe1.6 Se2 . Proc. Nat. Acad. Sci. 111, 3979 (2014) 161. Shiogai, J., Ito, Y., Mitsuhashi, T., Nojima, T., Tsukazaki, A.: Electric-field-induced superconductivity in electrochemically etched ultrathin FeSe films on SrTiO3 and MgO. Nat. Phys. 12, 42 (2016) 162. Miyakawa, T., Shiogai, J., Shimizu, S., Matsumoto, M., Ito, Y., Harada, T., Fujiwara, K., Nojima, T., Itoh, Y., Aida, T., Iwasa, Y., Tsukazaki, A.: Enhancement of superconducting transition temperature in FeSe electric-double-layer transistor with multivalent ionic liquids. Phys. Rev. Mat. 2, 031801 (2018) 163. Hanzawa, K., Sato, H., Hiramatsu, H., Kamiya, T., Hosono, H.: Electric field-induced superconducting transition of insulating FeSe thin film at 35 K. PNAS 113, 3986 (2016) 164. Shiogai, J., Kimura, S., Awaji, S., Nojima, T., Tsukazaki, A.: Anisotropy of the upper critical field and its thickness dependence in superconducting FeSe electric-double-layer transistors. Phys. Rev. B 97, 174520 (2018) 165. Medvedev, S., McQueen, T.M., Troyan, I.A., Palasyuk, T., Eremets, M.I., Cava, R.J., Naghavi, S., Casper, F., Ksenofontov, V., Wortmann, G., Felser, C.: Electronic and magnetic phase diagram of β-Fe1.01 Se with superconductivity at 36.7 K under pressure. Nat. Mater. 8, 630 (2008) 166. Sun, J.P., Matsuura, J., Ye, G.Z., Mizukami, Y., Shimozawa, M., Matsubayashi, K., Yamashita, M., Watashige, T., Kasahara, S., Matsuda, Y., Yan, J.-Q., Sales, B.C., Uwatoko, Y., Cheng, J.-G., Shibauchi, T.: Dome-shaped magnetic order competing with high-temperature superconductivity at high pressures in FeSe. Nat. Commun. 7, 12146 (2016) 167. Kuono, S., Sato, Y., Katayama, Y., Ichinose, A., Asami, D., Nabeshima, F., Imai, Y., Maeda, A., Ueno, K.: Superconductivity at 38 K at an electrochemical interface between an ionic liquid and FeSe0.8 Te0.2 on various substrates. Sci. Rep. 8, 14731 (2018) 168. Shimizu, S., Shiogai, J., Takemori, N., Sakai, S., Ikeda, H., Arita, R., Nojima, T., Tsukazaki, A., Iwasa, Y.: Giant thermoelectric power factor in ultrathin FeSe superconductor. Nat. Commun. 10, 825 (2019) 169. Grønvold, F., Haraldsen, H., Vihovde, J.: Phase and structural relations in the system iron telluride. Acta Chem. Scand. 8, 1927 (1954) 170. Okamoto, H., Tanner, L.E.: The Fe-Te (iron-tellurium) system. Bull. Alloy Phase Diagr. 11, 371 (1990)

368

6 Thin Film Studies Under Focus

171. He, X., Li, G., Zhang, J., Karki, A.B., Jin, R., Sales, B.C., Sefat, A.S., McGuire, M.A., Mandrus, D., Plummer, E.W.: Nanoscale chemical phase separation in FeTe0.55 Se0.45 as seen via scanning tunneling spectroscopy. Phys. Rev. B 83, 220502(R) (2011) 172. Hu, H., Zuo, J.-M., Wen, J., Xu, Z., Lin, Z., Li, Q., Gu, G., Park, W.K., Greene, L.H.: Phase separation in the iron chalcogenide superconductor Fe1+y Tex Se1−x . New J. Phys. 13, 053031 (2011) 173. Fang, M.H., Pham, H.M., Qian, B., Liu, T.J., Vehstedt, E.K., Liu, Y., Spinu, L., Mao, Z.Q.: Superconductivity close to magnetic instability in Fe(Se1−x Tex )0.82 . Phys. Rev. B 78, 224503 (2008) 174. Yeh, K.-W., Huang, T.-W., Huang, Y.-L., Chen, T.-K., Hsu, F.-C., Wu, P.M., Lee, Y.-C., Chiu, Y.-Y., Chen, C.-L., Luo, J.-Y., Yan, D.-C., Wu, M.-K.: Tellurium substitution effect on superconductivity of the α-phase iron selenide. Europhys. Lett. 84, 37002 (2008) 175. Martinelli, A., Bernardini, F., Massidda, S.: The phase diagrams of iron-based superconductors. Theory and experiments. C. R. Physique 17, 5 (2016) 176. Wu, M.K., Hsu, F.C., Yeh, K.W., Huang, T.W., Luo, J.Y., Wang, M.J., Chang, H.H., Chen, T.K., Rao, S.M., Mok, B.H., Chen, C.L., Huang, Y.L., Ke, C.T., Wu, P.M., Chang, A.M., Wu, C.T., Perng, T.P.: The development of the superconducting PbO-type β-FeSe and related compounds. Physica C 469, 340 (2008) 177. Demirdi¸s, S., Su, Y., Nemkowski, K., Wang, R., Huang, Z.X., Cao, L.X.: Neutron scattering study of magnetic Fe1+d Te thin films grown under tensile stress. Physica B 474, 53 (2015) 178. Stepantsov, E.A., Kazakov, S.M., Belikov, V.V., Makarova, I.P., Arpaia, R., Gunnarsson, R., Lombardi, F.: Investigation into the growth and structure of thin-film solid solutions of Febased superconductors in the FeSe0.92 –FeSe0.5 Te0.5 system. Crystallogr. Rep. 58, 735 (2013) 179. Zhuang, J., Yeoh, W.K., Cui, X., Xu, X., Du, Y., Shi, Z., Ringer, S.P., Wang, X., Dou, S.X.: Unabridged phase diagram for single-phased FeSex Te1−x thin films. Sci. Rep. 4, 7273 (2014) 180. Imai, Y., Sawada, Y., Nabeshima, F., Maeda, A.: Suppression of phase separation and giant enhancement of superconducting transition temperature in FeSe1−x Tex thin films. PNAS 112, 1937 (2015) 181. Imai, Y., Sawada, Y., Nabeshima, F., Asami, D., Kawai, M., Maeda, A.: Control of structural transition in FeSe1−x Tex thin films by changing substrate material. Sci. Rep. 7, 46653 (2017) 182. Speller, S., Aksoy, C., Saydam, M., Taylor, H., Burnell, G., Boothroyd, A.T., Grovenor, C.R.M.: Analysis of Fe y Se1−x Tex thin films grown by radio frequency sputtering. Supercond. Sci. Technol. 24, 075023 (2011) 183. Mousavi, T., Grovenor, C., Speller, S.: Characterization of superconducting Fe y (Se1−x Tex ) thin films deposited on MgO substrates by sputtering. J. Mater. Sci. 50, 6970 (2015) 184. Mousavi, T., Grovenor, C., Speller, S.: Effects of processing condition on the properties of Fe(Se, Te) thin films grown by sputtering. IEEE Trans. Appl. Supercond. 25, 7500604 (2015) 185. Zhu, Y., Chen, L., Ciston, J., Wang, H.: Atomic-scale investigation of intrinsic chemical inhomogeneity in superconducting Fe1+y Se1−x Tex epitaxial films. J. Phys. Chem. C 117, 7170 (2013) 186. Nie, Y.F., Telesca, D., Budnick, J.I., Sinkovic, B., Wells, B.O.: Superconductivity induced in iron telluride films by low-temperature oxygen incorporation. Phys. Rev. B 82, 020508 (2010) 187. Zhao, P.H., Zhu, H.F., Tian, Y.J., Li, D.L., Ma, L., Suo, H.L., Nie, J.C.: O2 annealing induced superconductivity in FeTe1−x Sex : on the origin of superconductivity in FeTe films. J. Supercond. Nov. Magn. 30, 871 (2017) 188. Han, Y., Li, W.Y., Cao, L.X., Wang, X.Y., Xu, B., Zhao, B.R., Guo, Y.Q., Yang, J.L.: Superconductivity in iron telluride thin films under tensile stress. Phys. Rev. Lett. 104, 017003 (2010) 189. Telesca, D., Nie, Y., Budnick, J.I., Wells, B.O., Sinkovic, B.: Surface valence states and stoichiometry of non-superconducting and superconducting FeTe films. Surf. Sci. 606, 1056 (2012) 190. Telesca, D., Nie, Y., Budnick, J.I., Wells, B.O., Sinkovic, B.: Impact of valence states on the superconductivity in iron telluride and iron selenide films with incorporated oxygen. Phys. Rev. B 85, 214517 (2012)

References

369

191. Nabeshima, F., Ishikawa, T., Oyanagi, K., Kawai, M., Maeda, A.: Growth of superconducting epitaxial films of sulfur substituted FeSe via pulsed laser deposition. J. Phys. Soc. Jpn. 87, 073704 (2018) 192. Miao, H., Niu, X.H., Xu, D.F., Yao, Q., Chen, Q.Y., Ying, T.P., Li, S.Y., Fang, Y.F., Zhang, J.C., Ideta, S., Tanaka, K., Xie, B.P., Feng, D.L., Chen, F.: Electronic structure of FeS. Phys. Rev. B 95, 205127 (2017) 193. Watson, M.D., Kim, T.K., Haghighirad, A.A., Blake, S.F., Davies, N.R., Hoesch, M., Wolf, T., Coldea, A.I.: Suppression of orbital ordering by chemical pressure in FeSe1−x Sx . Phys. Rev. B 92, 121108(R) (2015) 194. Song, C.-L., Zhang, H.-M., Zhong, Y., Hu, X.-P., Ji, S.-H., Wang, L., He, K., Ma, X.-C., Xue, Q.-K.: Observation of double-dome superconductivity in potassium-doped FeSe thin films. Phys. Rev. Lett. 116, 157001 (2016) 195. Tang, C., Zhang, D., Zang, Y., Liu, C., Zhou, G., Li, Z., Zheng, C., Hu, X., Song, C., Ji, S., He, K., Chen, X., Wang, L., Ma, X., Xue, Q.-K.: Superconductivity dichotomy in K-coated single and double unit cell FeSe films on SrTiO3 . Phys. Rev. B 92, 180507(R) (2015) 196. Wen, C.H.P., Xu, H.C., Chen, C., Huang, Z.C., Lou, X., Pu, Y.J., Song, Q., Xie, B.P., AbdelHafiez, M., Chaarev, D.A., Vasiliev, A.N., Peng, R., Feng, D.L.: Anomalous correlation effects and unique phase diagram of electron-doped FeSe revealed by photoemission spectroscopy. Nat. Commun. 7, 10840 (2016) 197. Katase, T., Hiramatsu, H., Kamiya, T., Hosono, H.: Thin film growth by pulsed laser deposition and properties of 122-type iron-based superconductor AE(Fe1−x Cox )2 As2 (AE = alkaline earth). Supercond. Sci. Technol. 25, 084015 (2012) 198. Kurth, F., Iida, K., Trommler, S., Hänisch, J., Nenkov, K., Engelmann, J., Oswald, S., Werner, J., Schultz, L., Holzapfel, B., Haindl, S.: Electronic phase diagram of disordered Co doped BaFe2 As2 . Supercond. Sci. Technol. 26, 025014 (2013) 199. Fernandes, R.M., Vavilov, M.G., Chubukov, A.V.: Enhancement of Tc by disorder in underdoped iron pnictide superconductors. Phys. Rev. B 85, 140512 (2012) 200. Haindl, S., Kidszun, M., Kampert, E.: Iron pnictide thin films: Synthesis and physics. Phys. Stat. Sol. B 254, 1600341 (2017) 201. Kang, J.H., Kim, J.-W., Ryan, P.J., Xie, L., Guo, L., Sundahl, C., Schad, J., Campbell, N., Collantes, Y.G., Hellstrom, E.E., Rzchowski, M.S., Eom, C.B.: Superconductivity in undoped BaFe2 As2 by tetrahedral geometry design. Proc. Nat. Acad. Sci. 117, 21170 (2020) 202. Katase, T., Iimura, S., Hiramatsu, H., Kamiya, T., Hosono, H.: Identical effects of indirect and direct electron doping of superconducting BaFe2 As2 thin films. Phys. Rev. B 85, 140515(R) (2012) 203. Kasinathan, D., Ormeci, A., Koch, K., Burkhardt, U., Schnelle, W., Leithe-Jasper, A., Rosner, H.: AFe2 As2 (A = Ca, Sr, Ba, Eu) and SrFe2−x TMx As2 (TM = Mn Co, Ni): crystal structure, charge doping, magnetism and superconductivity. New J. Phys. 11, 025023 (2009) 204. Leithe-Jasper, A., Schnelle, W., Geibel, C., Rosner, H.: Superconducting state in SrFe2−x Co2 As2 by internal doping of the iron arsenide layers. Phys. Rev. Lett. 101, 207004 (2008) 205. Krellner, C., Caroca-Canales, N., Leithe-Jasper, A., Rosner, H., Ormeci, A., Geibel, C.: Magnetic and structural transitions in layered iron arsenide systems: AFe2 As2 versus RFeAsO. Phys. Rev. B 78, 100504(R) (2008) 206. Kobayashi, K., Nakao, A., Maki, S., Yamamura, J., Katase, T., Sato, H., Sagayama, H., Kumai, R., Kuramoto, Y., Murakami, Y., Hiramatsu, H., Hosono, H.: Structure determination in thin film Ba1−x Lax Fe2 As2 : Relation between the FeAs4 geometry and superconductivity. Phys. Rev. B 96, 125116 (2017) 207. Mizuguchi, Y., Hara, Y., Deguchi, K., Tsuda, S., Yamaguchi, T., Takeda, K., Kotegawa, H., Tou, H., Takano, Y.: Anion height dependence of Tc for the Fe-based superconductor. Supercond. Sci. Technol. 23, 054013 (2010) 208. Katase, T., Hiramatsu, H., Kamiya, T., Hosono, H.: Magnetic scattering and electron pair breaking by rare-earth-ion substitution in BaFe2 As2 epitaxial films. New J. Phys. 15, 073019 (2013)

370

6 Thin Film Studies Under Focus

209. Rotter, M., Hieke, C., Johrendt, D.: Different response of the crystal structure to isoelectronic doping in BaFe2 (As1−x Px )2 . Phys. Rev. B 82, 014513 (2010) 210. Katase, T., Sato, H., Hiramatsu, H., Kamiya, T., Hosono, H.: Unusual pressure effects on the superconductivity of indirectly electron-doped (Ba1−x Lax )Fe2 As2 epitaxial films. Phys. Rev. B 88, 140503 (2013) 211. Hiramatsu, H., Katase, T., Kamiya, T., Hosono, H.: Superconducting properties and phase diagram of indirectly electron-doped (Sr1−x Lax )Fe2 As2 epitaxial films grown by pulsed laser deposition. IEEE Trans. Appl. Supercond. 23, 7300405 (2013) 212. Wang, Q.-Y., Li, Z., Zhang, W.-H., Zhang, Z.-C., Zhang, J.-S., Li, W., Ding, H., Ou, Y.-B., Deng, P., Chang, K., Wen, J., Song, C.-L., He, K., Jia, J.-F., Ji, S.-H., Wang, Y.-Y., Wang, L.L., Chen, X., Ma, X.-C., Xue, Q.-K.: Interface-induced high-temperature superconductivity in single unit-cell FeSe films on SrTiO3 . Chin. Phys. Lett. 29, 037402 (2012) 213. Mazin, I.I.: The FeSe riddle. Nat. Mater. 14, 755 (2015) 214. Nekrasov, I.A., Pavlov, N.S., Sadovskii, M.V., Slobodchikov, A.A.: Electronic structure of FeSe monolayer superconductors. Low Temp. Phys. 42, 891 (2016) 215. Nekrasov, I.A., Pavlov, N.S., Sadovskii, M.V.: On the origin of the shallow and “replica” bands in FeSe monolayer superconductors. JETP Lett. 105, 370 (2017) 216. Nekrasov, I.A., Pavlov, N.S., Sadovskii, M.V.: Electronic structure of FeSe monolayer superconductors: shallow bands and correlations. J. Exp. Theor. Phys. 126, 485 (2018) 217. Sadovskii, M.V.: High-temperature superconductivity in FeSe monolayers. Phys. Usp. 59, 947 (2016) 218. Peng, R., Xu, H.C., Tan, S.Y., Cao, H.Y., Xia, M., Shen, X.P., Huang, Z.C., Wen, C.H.P., Song, Q., Zhang, T., Xie, B.P., Gong, X.G., Feng, D.L.: Tuning the band structure and superconductivity in single-layer FeSe by interface engineering. Nat. Commun. 5, 5044 (2014) 219. Xu, X., Zhang, S., Zhu, X., Guo, J.: Superconductivity enhancement in FeSe/SrTiO3 : a review from the perspective of electron-phonon coupling. J. Phys.: Condens. Matter 32, 343003 (2020) 220. Li, Z.-X., Wang, F., Yao, H., Lee, D.-H.: What makes the Tc of monolayer FeSe on SrTiO3 so high: a sign-problem-free quantum Monte Carlo study. Sci. Bull. 61, 925 (2016) 221. Xiang, Y.-Y., Wang, F., Wang., D., Wang, Q.-H., Lee, D.-H.: High-temperature superconductivity at the FeSe/SrTiO3 interface. Phys. Rev. B 86, 134508 (2012) 222. Li, B., Xing, Z.W., Huang, G.Q., Xing, D.Y.: Electron-phonon coupling enhanced by the FeSe/SrTiO3 interface. J. Appl. Phys. 115, 193907 (2014) 223. Coh, S., Cohen, M.L., Louie, S.G.: Large electron-phonon interactions from FeSe phonons in a monolayer. New J. Phys. 17, 073027 (2015) 224. Lee, D.-H.: What makes Tc of FeSe/SrTiO3 so high? Chin. Phys. B 24, 117405 (2015) 225. Lee, D.-H.: Routes to high-temperature superconductivity: a lesson from FeSe/SrTiO3 . Annu. Rev. Condens. Matter Phys. 9, 261 (2018) 226. Shishidou, T., Agterberg, D.F., Weinert, M.: Magnetic fluctuations in single-layer FeSe. Commun. Phys. 1, 8 (2018) 227. Ge, J.-F., Liu, Z.-L., Liu, C., Gao, C.-L., Dong, Q., Xue, Q.-K., Liu, Y., Jia, J.-F.: Superconductivity above 100 K in single-layer FeSe films on doped SrTiO3 . Nat. Mater. 14, 285 (2014) 228. Ge, J.-F., Liu, Z.-L., Gao, C.-L., Qian, D., Liu, C., Jia, J.-F.: Development of micro-four-point probe in a scanning tunneling microscope for in situ electrical transport measurement. Rev. Sci. Inst. 86, 053903 (2015) 229. Huang, D., Hoffman, J.E.: Monolayer FeSe on SrTiO3 . Annu. Rev. Condens. Matter Phys. 8, 311 (2017) 230. Liu, D., Zhang, W., Mou, D., Je, J., Ou, Y.-B., Wang, Q.-Y., Li, Z., Wang, L., Zhao, L., He, S., Peng, Y., Liu, X., Chen, C., Yu, L., Liu, G., Dong, X., Zhang, J., Chen, C., Xu, Z., Hu, J., Chen, X., Ma, X., Xue, W., Zhou, X.J.: Electronic origin of high-temperature superconductivity in single-layer FeSe superconductor. Nat. Commun. 3, 931 (2012)

References

371

231. He, S., He, J., Zhang, W., Zhao, L., Liu, D., Liu, X., Mou, D., Ou, Y.-B., Wang, Q.-Y., Li, Z., Wang, L., Peng, Y., Liu, Y., Chen, C., Yu, L., Liu, G., Dong, X., Zhang, J., Chen, C., Xu, Z., Chen, X., Ma, X., Xue, Q., Zhou, X.J.: Phase diagram and electronic indication of high-temperature superconductivity at 65 K single-layer FeSe films. Nat. Mater. 12, 605 (2013) 232. Tan, S., Zhang, Y., Xia, M., Ye, Z., Chen, F., Xie, X., Peng, R., Xu, D., Fan, Q., Xu, H., Jiang, J., Zhang, T., Lai, X., Xiang, T., Hu, J., Xie, B., Feng, D.: Interface-induced superconductivity and strain-dependent spin density waves in FeSe/SrTiO3 thin films. Nat. Mater. 12, 643 (2013) 233. Ding, H., Lv, Y.-F., Zhao, K., Wang, W.-L., Wang, L., Song, C.-L., Chen, X., Ma, X.-C., Xue, X.-K.: High-temperature superconductivity in single-unit-cell FeSe films on anatase TiO2 (001). Phys. Rev. Lett. 117, 067011 (2016) 234. Zhao, L., Liang, A., Yuan, D., Hu, Y., Liu, D., Huang, J., He, S., Shen, B., Xu, Y., Liu, X., Yu, L., Liu, G., Zhou, H., Huang, Y., Dong, X., Zhou, F., Liu, K., Lu, Z., Zhao, Z., Chen, C., Xu, Z., Zhou, X.J.: Common electron origin of superconductivity in (Li, Fe)OHFeSe bulk superconductor and single-layer FeSe/SrTiO3 films. Nat. Commun. 7, 10608 (2016) 235. Mandal, S., Zhang, P., Ismail-Beigi, S., Haule, K.: How correlated is the FeSe/SrTiO3 system? Phys. Rev. Lett. 119, 067004 (2017) 236. Yi, M., Liu, Z.-K., Zhang, Y., Yu, R., Zhu, J.-X., Lee, J.J., Moore, R.G., Schmitt, F.T., Li, W., Riggs, S.C., Chu, J.-H., Lv, B., Hu, J., Hashimoto, M., Mo, S.-K., Hussain, Z., Mao, Z.Q., Chu, C.W., Fisher, I.R., Si, Q., Shen, Z.-X., Lu, D.H.: Observation of universal strong orbital-dependent correlation effects in iron-chalcogenides. Nat. Commun. 6, 7777 (2015) 237. Hao, N., Hu, J.: Topological phases in the single-layer FeSe. Phys. Rev. X 4, 031053 (2014) 238. Huang, D., Song, C.-L., Webb, T.A., Fang, S., Chang, C.-Z., Moodera, J.S., Kaxiras, E., Hoffman, J.E.: Revealing the empty-state electronic structure of single-unit-cell FeSe/SrTiO3 . Phys. Rev. Lett. 115, 017002 (2015) 239. Wang, Z., Zhang, P., Xu, G., Zeng, L.K., Miao, H., Xu, X., Qian, T., Weng, H., Richard, P., Fedorov, A.V., Ding, H., Dai, X., Fang, Z.: Topological nature of the FeSe0.5 Te0.5 superconductor. Phys. Rev. B 92, 115119 (2015) 240. Wu, X., Qin, S., Liang, Y., Fan, H., Hu, J.: Topological characters in Fe(Te1−x Sex ) thin films. Phys. Rev. B 93, 115129 (2016) 241. Chen, L., Liu, H., Jiang, C., Shi, C., Wang, D., Cui, G., Li, X., Zhuang, Q.: Topological edge states in high-temperature superconductiving FeSe/SrTiO3 films with Te substitution. Sci. Rep. 9, 4154 (2019) 242. Wang, Z.F., Zhang, H., Liu, D., Liu, C., Tang, C., Song, C., Zhong, Y., Peng, J., Li, F., Nie, C., Wang, L., Zhou, X.J., Ma, X., Xue, Q.K., Liu, F.: Topological edge states in a high-temperature superconductor FeSe/SrTiO3 (001) film. Nat. Mater. 15, 968–973 (2016) 243. Tan, S.Y., Fang, Y., Xie, D.H., Feng, W., Wen, C.H.P., Song, Q., Chen, Q.Y., Zhang, W., Zhang, Y., Luo, L.Z., Xie, B.P., Lai, X.C., Feng, D.L.: Observation of Dirac cone band dispersions in FeSe thin films by photoemission spectroscopy. Phys. Rev. B 93, 104513 (2016) 244. Kanayama, S., Nakayama, K., Phan, G.N., Kuno, M., Sugawara, K., Takahashi, T., Sato, T.: Two-dimensional Dirac semimetal phase in undoped one-monolayer FeSe film. Phys. Rev. B 96, 220509(R) (2017) 245. Liu, C., Wang, J.: Heterostructural one-unit-cell FeSe/SrTiO3 : from high-temperature superconductivity to topological states. 2D Mater. 7, 022006 (2020) 246. Fan, Q., Zhang, W.H., Liu, X., Yan, Y.J., Ren, M.Q., Peng, R., Xu, H.C., Xie, B.P., Hu, J.P., Zhang, T., Feng, D.L.: Plain s-wave superconductivity in single-layer FeSe on SrTiO3 probed by scanning tunnelling microscopy. Nat. Phys. 11, 946 (2015) 247. Ge, Z., Yan, C., Zhang, H., Agterberg, D., Weinert, M., Li, L.: Evidence for d-wave superconducting in single layer FeSe/SrTiO3 probed by quasiparticle scattering off step edges. Nano Lett. 19, 2497 (2019) 248. Lee, J.J., Schmitt, F.T., Moore, R.G., Johnston, S., Cui, Y.-T., Li, W., Yi, M., Liu, Z.K., Hashimoto, M., Zhang, Y., Lu, D.H., Devereaux, T.P., Lee, D.-H., Shen, Z.-X.: Interfacial mode coupling as the origin of the enhancement of Tc in FeSe films on SrTiO3 . Nature 515, 245 (2014)

372

6 Thin Film Studies Under Focus

249. Zhang, W., Li, Z., Li, F., Zhang, H., Peng, J., Tang, C., Wang, Q., He, K., Chen, X., Wang, L., Ma, X., Xue, Q.-K.: Interface charge doping effects on superconductivity of single-unit-cell FeSe films on SrTiO3 substrates. Phys. Rev. B 89, 060506(R) (2014) 250. Zhang, Y., Lee, J.J., Moore, R.G., Li, W., Yi, M., Hashimoto, M., Lu, D.H., Devereaux, T.P., Lee, D.-H., Shen, Z.-X.: Superconducting gap anisotropy in monolayer FeSe thin film. Phys. Rev. Lett. 117, 117011 (2016) 251. Song, Q., Lu, T.L., Lou, X., Xie, B.P., Xu, H.C., Wen, C.H.P., Yao, Q., Zhang, S.Y., Zhu, X.T., Guo, J.D., Peng, R., Feng, D.L.: Evidence of cooperative effect on the enhanced superconducting transition temperature at the FeSe/SrTiO3 interface. Nat. Commun. 10, 758 (2019) 252. Zhou, Y., Millis, A.J.: Charge transfer and electron-phonon coupling in monolayer FeSe on Nb-doped SrTiO3 . Phys. Rev. B 93, 224506 (2016) 253. Zhang, H., Zhang, D., Lu, X., Liu, C., Zhou, G., Ma, X., Wang, L., Jiang, P., Xue, Q.-K., Bao, X.: Origin of charge transfer and enhanced electron-phonon coupling in single unit-cell FeSe films on SrTiO3 . Nat. Commun. 8, 214 (2017) 254. Zhao, W., Li, M., Chang, C.-Z., Jiang, J., Wu, L., Liu, C., Moodera, J. S., Zhu, Y., Chang, M.H.W.: Direct imaging of electron transfer and its influence on superconducting pairing at FeSe/SrTiO3 interface. Sci. Adv. 4, eaao2682 (2018) 255. Yang, M., Yan, C., Ma, Y., Li, L., Cen, C.: Light induced non-volatile switching of superconductivity in single layer FeSe on SrTiO3 substrate. Nat. Commun. 10, 85 (2019) 256. Zhang, C., Zhongkai, L., Chen, Z., Xie, Y., He, R., Tang, S., He, J., Li, W., Jia, T., Rebec, S.N., Ma, E.Y., Yan, H., Hashimoto, M., Lu, D., Mo, S.-K., Hikita, Y., Moore, R.G., Hwang, H.Y., Lee, D., Shen, Z.: Ubiquitous strong electron-phonon coupling at the interface of FeSe/SrTiO3 . Nat. Commun. 8, 14468 (2017) 257. Xu, M., Song, X., Wang, H.: Substrate and bend bending effects on monolayer FeSe on SrTiO3 (001). Phys. Chem. Chem. Phys. 19, 7964 (2017) 258. Rebec, S.N., Jia, T., Zhang, C., Hashimoto, M., Lu, D.-H., Moore, R.G., Shen, Z.-X.: Coexistence of replica bands and superconductivity in FeSe monolayer films. Phys. Rev. Lett. 118, 067002 (2017) 259. Shigekawa, K., Nakayama, K., Kuno, M., Phan, G.N., Owada, K., Sugawara, K., Takahashi, T., Sato, T.: Dichotomy of superconductivity between monolayer FeS and FeSe. PNAS 116, 24470 (2019) 260. Li, F., Sawatzky, G.A.: Electron phonon coupling versus photoelectron energy loss at the origin of replica bands in photoemission of FeSe on SrTiO3 . Phys. Rev. Lett. 120, 237001 (2018) 261. Jandke, J., Yang, F., Hlobil, P., Engelhardt, T., Rau, D., Zakeri, K., Gao, C., Schmalian, J., Wulfhekel, W.: Unconventional pairing in single FeSe layers. Phys. Rev. B 100, 020503(R) (2019) 262. Li, Z.-X., Devereaux, T.P., Lee, D.-H.: Electronic and phononic properties of a twodimensional electron gas coupled to dipolar phonons via small-momentum-transfer scattering. Phys. Rev. B 100, 241101(R) (2019) 263. Zhang, S., Guan, J., Jia, X., Liu, B., Wang, W., Li, F., Wang, L., Ma, X., Xue, Q., Zhang, J., Plummer, E.W., Zhu, X., Guo, J.: Role of SrTiO3 phonon penetrating into thin FeSe films in the enhancement of superconductivity. Phys. Rev. B 94, 081116(R) (2016) 264. Zhang, S., Guan, J., Wang, Y., Berlijn, T., Johnston, S., Jia, X., Liu, B., Zhu, Q., An, Q., Xue, S., Cao, Y., Yang, F., Wang, W., Zhang, J., Plummer, E.W., Zhu, X., Guo, J.: Lattice dynamics of ultrathin FeSe films on SrTiO3 . Phys. Rev. B 97, 035408 (2018) 265. Zhang, W., Liu, X., Wen, C., Peng, R., Tan, S., Xie, B., Zhang, T., Feng, D.: Effects of surface electron doping and substrate on the superconductivity of epitaxial FeSe films. Nano Lett. 16, 1969 (2016) 266. Kuli´c, M.L., Dolgov, O.V.: The electron-phonon interaction with forward scattering peaks is dominant in high Tc superconductors of FeSe films on SrTiO3 (TiO2 ). New J. Phys. 19, 013020 (2017) 267. Rademaker, L., Wang, Y., Berlijn, T., Johnston, S.: Enhanced superconductivity due to forward scattering in FeSe films on SrTiO3 substrates. New J. Phys. 18, 022001 (2016)

References

373

268. Wang, Y., Nakatsukasa, K., Rademaker, L., Berlijn, T., Johnston, S.: Aspects of electronphonon interactions with strong forward scattering in FeSe thin films on SrTiO3 substrates. Supercond. Sci. Technol. 29, 054009 (2016) 269. Bang, Y.: Phonon boost effect on the s± -wave superconductor with incipient band. Sci. Rep. 9, 3907 (2019) 270. Chen, X., Linscheid, A., Maiti, S., Hirschfeld, P.J.: Electron pairing in the presence of incipient bands in iron-based superconductors. Phys. Rev. B 92, 224514 (2015) 271. Wang, Y., Rademaker, L., Dagotto, E., Johnston, S.: Phonon linewidth due to electron-phonon interactions with strong forward scattering in FeSe thin films on oxide substrates. Phys. Rev. B 96, 054515 (2017) 272. Dimitrov, I.K., Si, W.D., Ku, W., Han, S.J., Jaroszynski, J.: Unusual persistence of superconductivity against high magnetic fields in the strongly-correlated iron-chalcogenide film FeTe:Ox . Low Temp. Phys. 39, 680 (2013) 273. Tarantini, C., Gurevich, A., Jaroszynski, J., Balakirev, F., Bellingeri, E., Pallecchi, I., Ferdeghini, C., Shen, B., Wen, H.H., Larbalestier, D.C.: Significant enhancement of upper critical fields by doping and strain in iron-based superconductors. Phys. Rev. B 84, 184522 (2011) 274. Maiorov, B., Mele, P., Baily, S.A., Weigand, M., Lin, S.-Z., Balakirev, F.F., Matsumoto, K., Nagayoshi, H., Fujita, S., Yoshida, Y., Ichino, Y., Kiss, T., Ichinose, A., Mukaida, M., Civale, L.: Inversion of the upper critical field anisotropy in FeTeS films. Supercond. Sci. Technol. 27, 044005 (2014) 275. Baily, S.A., Kohama, Y., Hiramatsu, H., Maiorov, B., Balakirev, F.F., Hirano, M., Hosono, H.: Pseudoistropic upper critical field in cobalt-doped SrFe2 As2 epitaxial films. Phys. Rev. Lett. 102, 117004 (2009) 276. Haindl, S., Kampert, E., Sasase, M., Hiramatsu, H., Hosono, H.: Low anisotropic upper critical fields in SmO1−x Fx FeAs thin films with a layered hybrid structure. Supercond. Sci. Technol. 32, 044003 (2019) 277. Haindl, S., Wurmehl, S., Büchner, B., Kampert, E.: PLD growth of iron-oxypnictides: Coand F-substitution. Supercond. Sci. Technol. 33, 105004 (2020) 278. Gurevich, A.: Iron-based superconductors at high magnetic fields. Rep. Prog. Phys. 74, 124501 (2011) 279. Tinkham, M.: Effect of flux quantization on transitions of superconducting films. Phys. Rev. 129, 2413 (1963) 280. Chandrasekhar, B.S.: A note on the maximum critical field of high-field superconductors. Appl. Phys. Lett. 1, 7 (1962) 281. Helfand, E., Werthamer, N.R.: Temperature and purity dependence of the superconducting critical field, Hc2 . Phys. Rev. Lett. 13, 686 (1964) 282. Helfand, E., Werthamer, N.R.: Temperature and purity dependence of the superconducting critical field, Hc2 II. Phys. Rev. 147, 288 (1966) 283. Werthamer, N.R., Helfand, E., Hohenberg, P.C.: Temperature and purity dependence of the superconducting critical field, Hc2 III. Electron spin and spin-orbit effects. Phys. Rev. 147, 295 (1966) 284. Askerzade, I.N.: Ginzburg-Landau theory: the case of two-band superconductors. Phys.-Usp. 49, 1003 (2006) 285. Gurevich, A.: Enhancement of the upper critical field by nonmagnetic impurities in dirty two-gap superconductors. Phys. Rev. B 67, 184515 (2003) 286. Haindl, S., Kidszun, M., Onken, F., Mietke, A., Thersleff, F.: Lessons from oxypnictide thin films. Int. J. Mod. Phys. B 27, 1330001 (2013) 287. Khim, S., Kim, J.W., Choi, E.S., Bang, Y., Nohara, M., Takagi, H., Kim, K.H.: Evidence for dominant Pauli paramagnetic effect in the upper critical field of single-crystalline FeTe0.6 Se0.4 . Phys. Rev. B 81, 1845011 (2010) 288. Her, J.L., Kohama, Y., Matsuda, Y.H., Kindo, Y., Yang, W.-H., Chareev, D.A., Mitrofanova, E.S., Volkova, O.S., Vasiliev, A.N., Lin, J.-Y.: Anisotropy in the upper critical field of FeSe and FeSe0.33 Te0.67 single crystals. Supercond. Sci. Technol. 28, 045013 (2015)

374

6 Thin Film Studies Under Focus

289. Schneider, R., Zaitsev, A.G., Fuchs, D., Hott, R.: Anisotropic field dependence of the electronic transport in superconducting FeSe thin films. Supercond. Sci. Technol. 33, 075011 (2020) 290. Jourdan, M., ten Haaf, S.: Preparation, characterization, and upper critical field of epitaxial FeSe thin films. J. Appl. Phys. 108, 023913 (2010) 291. Zhou, G., Zhang, D., Liu, C., Tang, C., Wang, X., Li, Z., Song, C.-L., Ji, S., He, K., Wang, L., Ma, X., Xue, Q.-K.: Interface induced high temperature superconductivity in single unit-cell FeSe on SrTiO3 (110). Appl. Phys. Lett. 108, 202603 (2016) 292. Miura, M., Adachi, S., Shimode, T., Wada, K., Takemori, A., Chikumoto, N., Nakao, K., Tanabe, K.: Anisotropy and superconducting properties of BaFe2 (As1−x Px )2 films with various phoshorus contents. Appl. Phys. Express 6, 093101 (2013) 293. Fanfarillo, L., Cappelluti, E., Castellani, C., Benfatto, L.: Unconventional Hall effect in pnictides from interband interactions. Phys. Rev. Lett. 109, 096402 (2012) 294. Maeda, A., Nabeshima, F., Takahashi, H., Okada, T., Imai, Y., Tsukada, I., Hanawa, M., Komiya, S., Ichinose, A.: Synthesis, characterization, Hall effect and THz conductivity of epitaxial thin films of Fe chalcogenide superconductors. Appl. Surf. Sci. 312, 43 (2014) 295. Kawai, M., Nabeshima, F., Maeda, A.: Transport properties of FeSe epitaxial films under in-plane strain. IOP Conf. Ser.: J. Phys.: Conf. Ser. 1054, 012023 (2018) 296. Shiogai, J., Miyakawa, T., Ito, Y., Nojima, T., Tsukazaki, A.: Unified trend of superconducting transition temperature versus Hall coefficient of ultrathin FeSe films prepared on different oxide substrates. Phys. Rev. B 95, 115101 (2017) 297. Tsukada, I., Hanawa, M., Komiya, S., Ichiniose, A., Akiike, T., Imai, Y., Maeda, A.: Hall effect of FeTe and Fe(Se1−x Tex ) thin films. Physica C 471, 625 (2011) 298. Tsukada, I., Hanawa, M., Komiya, S., Ichinose, A., Akiike, T., Imai, Y., Maeda, A.: Mobility analysis of FeTe thin films. J. Phys. Soc. Jpn. 80, 023712 (2011) 299. Nabeshima, F., Ishikawa, T., Shikama, N., Maeda, A.: Correlation between superconducting transition temperatures and carrier densities in Te- and S-substituted FeSe thin films. Phys. Rev. B 101, 184517 (2020) 300. Sawada, Y., Nabeshima, F., Imai, Y., Maeda, A.: Investigation of transport properties for FeSe1−x Tex thin films under magnetic fields. J. Phys. Soc. Jpn. 85, 073703 (2016) 301. Shikama, N., Ishikawa, T., Nabeshima, F., Maeda, A.: Transport properties of FeSe1−x Sx and FeSe1−y Te y epitaxial thin films under magnetic fields. IOP Conf. Ser.: J. Phys.: Conf. Ser. 1293, 012015 (2019) 302. Tsukada, I., Hanawa, M., Komiya, S., Akiike, T., Tanaka, R., Imai, Y., Maeda, A.: Hall effect in superconducting Fe(Se0.5 Te0.5 ) thin films. Phys. Rev. B 81, 054515 (2010) 303. Barone, C., Pagano, S., Pallecchi, I., Bellingeri, E., Putti, M., Ferdeghini, C.: Thermal and voltage activated excess 1/f noise in FeSe0.5 Te0.5 epitaxial thin films. Phys. Rev. B 83, 134523 (2011) 304. Barone, C., Pagano, S., Adamo, M., Sarnelli, E., Bellingeri, E., Ferdeghini, C.: Nonlinear conductivity fluctuations in Fe-chalcogenide superconductors. IEEE Trans. Appl. Supercond. 23, 8600304 (2013) 305. Barone, C., Bellingeri, E., Adamo, M., Sarnelli, E., Ferdeghini, C., Pagano, S.: Electric field activated nonlinear 1/f fluctuations in Fe(Te, Se) superconductors. Supercond. Sci. Technol. 26, 075006 (2013) 306. Barone, C., Romeo, F., Pagano, S., Adamo, M., Nappi, C., Sarnelli, E., Kurth, F., Iida, K.: Probing transport mechanisms of BaFe2 As2 superconducting films and grain boundary junctions by noise spectroscopy. Sci. Rep. 4, 6163 (2014) 307. Barannik, A.A., Wu, Y., He, Y.-S., Luo, S., Cao, L., Kharchenko, M.S., Cherpak, N.T.: Microwave effective and bulk surface impedance of thin FeSe0.3 Te0.7 film. In: International Kharkov Symposium on Physics and Engineering of Microwaves, Millimeter and Submillimeter Waves. IEEE (2013) 308. Barannik, A.A., Cherpak, N.T., Kharchenko, M.S., Wu, Y., Luo, S., He, Y., Porch, A.: Unusual microwave response and bulk conductivity of very thin FeSe0.3 Te0.7 films as a function of temperature. Low Temp. Phys. 40, 492 (2014)

References

375

309. Cherpak, N.T., Barannik, A.A., He, Y., Sun, L., Zhang, X., Ma, Y., Bian, Y., Li, G.: On the nature of microwave response of the resonator with a thin FeSe1−x Tex film near critical temperature. IEEE Trans. Appl. Supercond. 28, 1501104 (2018) 310. Wu, X., Zhou, S.Y., Wang, X.Y., Cao, L.X., Zhang, X.Q. Luo, S., He, Y.S., Barannik, A.A., Cherpak, N.T., Skresanov, V.N.: Microwave study of FeSe0.3 Te0.7 thin film by TE011 -mode sapphire dielectric resonator. IEEE Trans. Appl. Supercond. 21, 599 (2011) 311. Barannik, A.A., Cherpak, N.T., He, Y., Sun, L., Zhang, X., Vovnyuk, M.V., Wu, Y.: Microwave response of a cavity resonator with thin superconductor film depending on film temperature and orientation. Low Temp. Phys. 44, 247 (2018) 312. Pompeo, N., Torokhtii, Alimenti, A., Sylva, G., Braccini, V., Silva, E.: Pinning properties of FeSeTe thin film through multifrequency measurements of the surface impedance. Supercond. Sci. Technol. 33, 114006 (2020) 313. Nabeshima, F., Nagasawa, K., Maeda, A., Imai, Y.: Superconducting fluctuations in FeSe0.5 Te0.5 thin films probed via microwave spectroscopy. Phys. Rev. B 97, 024504 (2018) 314. Fisher, D.S., Fisher, M.P.A., Huse, D.A.: Thermal fluctuations, quenched disorder, phase transitions, and transport in type-II superconductors. Phys. Rev. B 43, 130 (1991) 315. Yong, J., Lee, S., Jiang, J., Bark, C.W., Weiss, J.D., Hellstrom, E.E., Larbalestier, D.C., Eom, C.B., Lemberger, T.R.: Superfluid density measurement of Ba(Cox Fe1−x )2 As2 films near optimal doping. Phys. Rev. B 83, 104510 (2011) 316. Tai, T., Ghamsari, B.G., Kang, J.H., Lee, S., Eom, C.B., Anlage, S.M.: Localized GHz frequency electrodynamic behavior of an optimally-doped Ba(Fe1−x Cox )2 As2 epitaxial film. Physica C 532, 44 (2017) 317. Lee, S., Seo, Y.-S., Roh, S., Lee, N.H., Kang, W.N., Hwang, J.: Optical properties of Ba0.6 K0.4 Fe2 As2 thin film prepared by pulsed laser deposition and subsequent post-annealing process. Curr. Appl. Phys. 17, 976 (2017) 318. Baldassarre, L., Perucchi, A., Lupi, S., Dore, P.: Far infrared properties of the rare-earth scandate DyScO3 . J. Phys.: Condens. Matter 22, 355402 (2010) 319. Mattis, D.C., Bardeen, J.: Theory of the anomalous skin effect in normal and superconducting metals. Phys. Rev. 111, 412 (1958) 320. Zimmermann, W., Brandt, E.H., Bauer, M., Seider, E., Genzel, L.: Optical conductivity of BCS superconductors with arbitrary purity. Physica C 183, 99 (1991) 321. Charnukha, A.: Optical conductivity of iron-based superconductors. J. Phys.: Condens. Matter 26, 253203 (2014) 322. Gorshunov, B., Wu, D., Voronkov, A.A., Kallina, P., Iida, K., Haindl, S., Kurth, F., Schultz, L., Holzapfel, B., Dressel, M.: Direct observation of the superconducting energy gap in the optical conductivity of the iron pnictide superconductor Ba(Fe0.9 Co0.1 )2 As2 . Phys. Rev. B 81, 060509(R) (2010) 323. Nakamura, D., Akiike, T., Takahashi, H., Nabeshima, F., Imai, Y., Maeda, A., Katase, T., Hiramatsu, H., Hosono, H., Komiya, S., Tsukada, I.: Terahertz conductivity measurements of FeSe0.5 Te0.5 and Co-doped BaFe2 As2 thin films. Physica C 471, 634 (2011) 324. Pimenov, A., Engelbrecht, S., Shuvaev, A.M., Jin, B.B., Wu, P.H., Xu, B., Cao, L.X., Schachinger, E.: Terahertz conductivity in FeSe0.5 Te0.5 superconducting films. New J. Phys. 15, 013032 (2013) 325. Dordevic, S.V., Singley, E.J., Basov, D.N., Komiya, S., Ando, Y., Bucher, E., Homes, C.C., Strongin, M.: Global trends in the interplane penetration depth of layered superconductors. Phys. Rev. B 65, 134511 (2002) 326. Perucchi, A., Joseph, B., Caramazza, S., Autore, M., Bellingeri, E., Kawale, S., Ferdeghini, C., Putti, M., Lupi, S., Dore, P.: Two-band conductivity of a FeSe0.5 Te0.5 film by reflectance measurements in the terahertz and infrared range. Supercond. Sci. Technol. 27, 125011 (2014) 327. Fischer, T., Pronin, V., Wosnitza, J., Iida, K., Kurth, F., Haindl, S., Schultz, L., Holzapfel, B., Schachinger, E.: Highly anisotropic energy gap in superconducting Ba(Fe0.9 Co0.1 )2 As2 . Phys. Rev. B 82, 224507 (2010) 328. Karakozov, A.E., Zapf, S., Gorshunov, B., Ponomarev, Ya.G., Magnitskaya, M.V., Zhukova, E., Prokhorov, A.S., Anzin, V.B., Haindl, S.: Temperature dependence of the superfluid density

376

329. 330.

331.

332.

333. 334.

335.

336.

337.

338.

339.

340.

341.

342.

343.

344.

345.

6 Thin Film Studies Under Focus as a probe for multiple gaps in Ba(Fe0.9 Co0.1 )2 As2 : manifestation of three weakly interacting condensates. Phys. Rev. B 90, 014506 (2014) Xi, X., Dai, Y.M., Homes, C.C., Kidszun, M., Haindl, S., Carr, G.L.: Evidence of a full gap in LaFeAsO1−x Fx thin films from infrared spectroscopy. Phys. Rev. B 87, 180509 (2013) Wen, Y.-C., Wang, K.-J., Chang, H.-H., Luo, J.-Y., Shen, C.-C., Liu, H.-L., Sun, C.-K., Wang, M.-J., Wu, M.-K.: Gap opening and orbital modification of superconducting FeSe above structural transition. Phys. Rev. Lett. 108, 267002 (2012) Shi, Y., Lian, J., Feng, Z., Zhao, M., Jin, K., Song, H., Wei, M., Dai, K., Jiang, Q., Fang, J.: Obtaining the scattering rate of different Tc0 FeSe thin films via spectroscopic ellipsometry. J. Vac. Sci. Technol. B 37, 052907 (2019) Zhang, Y., Xu, W., Feng, Z., Lin, Z., Jin, K., Zhang, J., Zhou, S., Liu, Z., Guan, C., Chen, T., Wang, J., Ding, L., Zhang, S.: Near-infrared reflectivity of superconducting FeSe thin films. IEEE Photonics J. 11, 6500609 (2019) Yuan, R.H., Kong, W.D., Yan, L., Ding, H., Wang, N.L.: In-plane optical spectroscopy study on FeSe epitaxial thin film grown on SrTiO3 substrate. Phys. Rev. B 87, 144517 (2013) Nakajima, M., Yanase, K., Nabeshima, F., Imai, Y., Maeda, A., Tajima, S.: Gradual Fermisurface modification in orbitally ordered state of FeSe revealed by optical spectroscopy. Phys. Rev. B 95, 184502 (2017) Yoshikawa, N., Takayama, M., Shikama, N., Ishikawa, T., Nabeshima, F., Maeda, A., Shimano, R.: Charge carrier dynamics of FeSe thin film investigated by terahertz magneto-optical spectroscopy. Phys. Rev. B 100, 035110 (2019) Bonavolontá, C., Parlato, L., Pepe, G.P., de Lisio, C., Valentino, M., Bellingeri, E., Pallecchi, I., Putti, M., Ferdeghini, C.: Ultrafast quasiparticle relaxation dynamics in high quality epitaxial FeSe0.5 Te0.5 thin films. Supercond. Sci. Technol. 26, 075018 (2013) Wang, M.J., Luo, J.Y., Huang, T.W., Chang, H.H., Chen, T.K., Hsu, F.C., Wu, C.T., Wu, P.M., Chang, A.M., Wu, M.K.: Crystal orientation and thickness dependence of the superconducting transition temperature of tetragonal FeSe1−x thin films. Phys. Rev. Lett. 103, 117002 (2009) Imai, Y., Nabeshima, F., Nakamura, D., Katase, T., Hiramatsu, H., Hosono, H., Maeda, A.: Ultralow-dissipative conductivity by Dirac fermions in BaFe2 As2 . J. Phys. Soc. Jpn. 82, 043709 (2013) Perucchi, A., Baldassarre, L., Lupi, S., Jiang, J.Y., Weiss, J.D., Hellstrom, E.E., Lee, S., Bark, C.W., Eom, C.B., Putti, M., Pallecchi, I., Marini, C., Dore, P.: Multi-gap superconductivity in a BaFe1.84 Co0.16 As2 film from optical measurements at terahertz frequencies. Eur. Phys. J. B 77, 25 (2010) Perucchi, A., Baldassarre, L., Joseph, B., Lupi, S., Lee, S., Eom, C.-B., Jiang, J., Weiss, J.D., Hellstrom, E.E., Dore, P.: Transmittance and reflectance measurement at terahertz frequencies on a superconducting BaFe1.84 Co0.16 As2 ultrathin film: an analysis of the optical gaps in the Co-doped BaFe2 As2 pnictide. Eur. Phys. J. B 86, 274 (2013) Valdés Aguilar, R., Bilbro, L.S., Lee, S., Bark, C.W., Jiang, J., Weiss, J.D., Hellstrom, E.E., Larbalestier, D.C., Eom, C.-B., Armitage, N.P.: Pair-breaking effects and coherence peak in the terahertz conductivity of superconducting BaFe2−2x Co2x As2 thin films. Phys. Rev. B 82, 180514(R) (2010) Maksimov, E.G., Karakozov, A.E., Gorshunov, B.P., Prokhorov, A.S., Voronkov, A.A., Zukova, E.S., Nozdrin, V.S., Zhukov, S.S., Wu, D., Dressel, M., Haindl, S., Iida, K., Holzapfel, B.: Two-band Bardeen-Cooper-Schrieffer superconducting state of the iron pnictide compound Ba(Fe0.9 Co0.1 )2 As2 . Phys. Rev. B 83, 140502(R) (2011) Zapf, S., Gorshunov, B., Wu, D., Zhukova, E., Nozdrin, V.S., Haindl, S., Iida, K., Dressel, M.: Intra-gap absorption in superconducting Ba(Fe1−x Cox )2 As2 thin films studied by a FabryPérot resonant technique. J. Supercond. Nov. Magn. 26, 1227 (2013) Perucchi, A., Capitani, F., Di Pietro, P., Lupi, S., Lee, S., Kang, J.H., Jiang, J., Weiss, J.D., Hellstrom, E.E., Eom, C.B., Dore P.: Electrodynamics of superconducting pnictide superlattices. Appl. Phys. Lett. 104, 222601 (2014) Ran, Y., Wang, F., Zhai, H., Vishwanath, A., Lee, D.-H.: Nodal spin density wave and band topology of the FeAs-based materials. Phys. Rev. B 79, 014505 (2009)

References

377

346. Richard, P., Nakayama, K., Sato, T., Neupane, M., Xu, Y.-M., Bowen, J.H., Chen, G.F., Luo, J.L., Wang, N.L., Dai, X., Fang, Z., Ding, H., Takahashi, T.: Observation of dirac cone electronic dispersion in BaFe2 As2 . Phys. Rev. Lett. 104, 137001 (2010) 347. Liu, C., Zhao, J.L., Wang, J.O., Qian, H.J., Wu, R., Wang, H.H., Zhang, N., Ibrahim, K.: Correspondence between the electronic structure and phase separation in a K-doped FeSe system. J. Phys.: Condens. Matter 29, 395503 (2017) 348. Kong, W.-D., Liu, Z.-G., Wu, S.-F., Wang, G., Qian, T., Yin, J.-X., Richard, P., Yan, L., Ding, H.: Growth of high-quality superconducting FeSe0.5 Te0.5 thin films suitable for angleresolved photoemission spectroscopy measurements via pulsed laser deposition. Chin. Phys. Lett. 32, 087401 (2015) 349. Zhang, Y., Yi, M., Liu, Z.-K., Li, W., Lee, J.J., Moore, R.G., Hashimoto, M., Nakajima, M., Eisaki, H., Mo, S.-K., Hussain, Z., Devereaux, T.P., Shen, Z.-X., Lu, D.H.: Distinctive orbital anisotropy observed in the nematic state of a FeSe thin film. Phys. Rev. B 94, 115153 (2016) 350. Shen, B., Feng, Z.-P., Huang, J.-W., Hu, Y., Gao, Q., Li, C., Xu, Y., Liu, G.-D., Yu, L., Zhao, L., Jin, K., Zhou, X.J.: Electronic structure and nematic phase transition in superconducting multiple-layer FeSe films grown by pulsed laser deposition method. Chin. Phys. B 26, 077402 (2017) 351. Feng, Z., Yuan, J., He, G., Hu, W., Lin, Z., Li, D., Jiang, X., Huang, Y., Ni, S., Li, J., Zhu, B., Dong, X., Zhou, F., Wang, H., Zhao, Z., Jin, K.: Tunable critical temperature for superconductivity in FeSe thin films by pulsed laser deposition. Sci. Rep. 8, 4039 (2018) 352. Phan, G.N., Nakayama, K., Sugawara, K., Sato, T., Urata, T., Tanabe, Y., Tanigaki, K., Nabeshima, F., Imai, Y., Maeda, A., Takahashi, T.: Effects of strain on the electronic structure, superconductivity, and nematicity in FeSe studied by angle-resolved photoemission spectroscopy. Phys. Rev. B 95, 224507 (2017) 353. Yang, S., Sobota, J.A., Leuenberger, D., Kemper, A.F., Lee, J.J., Schmitt, F.T., Li, W., Moore, R.G., Kirchmann, P.S., Shen, Z.-X.: Thickness-dependent coherent phonon frequency in ultrathin FeSe/SrTiO3 films. Nano Lett. 15, 4150 (2015) 354. Gerber, S., Yang, S.-L., Zhu, D., Soifer, H., Sobota, J.A., Rebec, S., Lee, J.J., Jia, T., Moritz, B., Jia, C., Gauthier, A., Li, Y., Leuenberger, D., Zhang, Y., Chaix, L., Li, W., Jang, H., Lee, J.-S., Yi, M., Dakovski, G.L., Song, S., Glownia, J.M., Nelson, S., Kim, K.W., Chuang, Y.-D., Hussain, Z., Moore, R.G., Devereaux, T.P., Lee, W.-S., Kirchmann, P.S., Shen, Z.-S.: Femtosecond electron-phonon lock-in by photoemission and x-ray free-electron laser. Science 357, 71 (2017) 355. Mandal, S., Cohen, R.E., Haule, K.: Strong pressure-dependent electron-phonon coupling in FeSe. Phys. Rev. B 89, 220502(R) (2014) 356. Zhao, H.: Spectroscopic studies of high-temperature superconductors on planar tunnel junction devices and nanofabricated point contact junctions. University of Illinois at UrbanaChampaign: PhD thesis (2016) 357. Zheng, M.: Superconductivity in oxygen doped iron telluride by molecular beam epitaxy. University of Illinois at Urbana-Champaign: PhD thesis (2013) 358. Plecenik, T., Gregor, M., Sobota, R., Truchly, M., Satrapinskyy, L., Kurth, F., Holzapfel, B., Iida, K., Kus, P., Plecenik, A.: Surface transport properties of Fe-based superconductors: the influence of degradation and inhomogeneity. Appl. Phys. Lett. 103, 052601 (2013) 359. Naidyuk, Yu.G., Kvitnitskaya, O.E., Yanson, I.K., Fuchs, G., Haindl, S., Kidszun, M., Schultz, L., Holzapfel, B.: Point-contact study of ReFeAsO1−x Fx (Re = La, Sm) superconducting films. Supercond. Sci. Technol. 24, 065010 (2011) 360. Mehta, M., Sheet, G., Dikin, D.A., Lee, S., Bark, C.W., Jiang, J., Weiss, J.D., Hellstrom, E.E., Rzchowski, M.S., Eom, C.B., Chandrasekhar, V.: Conductance asymmetry in point-contacts on epitaxial thin films of Ba(Fe0.92 Co0.08 )2 As2 . Appl. Phys. Lett. 97, 012503 (2010) 361. Sheet, G., Mehta, M., Dikin, D.A., Lee, S., Bark, C.W., Jiang, J., Weiss, J.D., Hellstrom, E.E., Rzchowski, M.S., Eom, C.B., Chandrasekhar, V.: Phase-incoherent superconducting pairs in the normal state of Ba(Fe1−x Cox )2 As2 . Phys. Rev. Lett. 105, 167003 (2010) 362. Peng, H., De, D., Wu, Z., Diaz-Pinto, C.: Observation of multiple superconducting gaps in Fe1+y Te1−x Sex via a nanoscale approach to point-contact spectroscopy. J. Phys.: Condens. Matter 24, 455703 (2012)

378

6 Thin Film Studies Under Focus

363. Pecchio, P., Daghero, D., Ummarino, G.A., Gonnelli, R.S., Kurth, F., Holzapfel, B., Iida, K.: Doping and critical-temperature dependence of the energy gaps in Ba(Fe1−x Cox )2 As2 thin films. Phys. Rev. B 88, 174506 (2013) 364. Daghero, D., Tortello, M., Ummarino, G.A., Piatti, E., Ghigo, G., Hatano, T., Kawaguchi, T., Ikuta, H., Gonnelli, R.S.: Decoupling of critical temperature and superconducting gaps in irradiated films of a Fe-based superconductor. Supercond. Sci. Technol. 31, 034005 (2018) 365. Daghero, D., Pecchio, P., Ummarino, G.A., Nabeshima, F., Imai, Y., Maeda, A., Tsukada, I., Komiya, S., Gonnelli, R.S.: Point-contact Andreev reflection spectroscopy in Fe(Se, Te) films: multiband superconductivity and electron-boson coupling. Supercond. Sci. Technol. 27, 124014 (2014) 366. He, M.Q., Shen, J.Y., Petrovi´c, A.P., He, Q.L., Liu, H.C., Zheng, Y., Wong, C.H., Chen, Q.H., Wang, J.N., Law, K.T., Sou, I.K., Lortz, R.: Pseudogap and proximity effect in the Bi2 Te3 /Fe1+y Te interfacial superconductor. Sci. Rep. 6, 32508 (2016) 367. Blonder, G.E., Tinkham, M., Klapwijk, T.M.: Transition from metallic to tunneling regimes in superconducting microconstrictions: excess current, charge imbalance, and supercurrent conversion. Phys. Rev. B 25, 4515 (1982) 368. Naidyuk, Yu.G., Yanson, I.K.: Point-Contact Spectroscopy. Springer, Berlin (2005) 369. Arham, H.Z., Greene, L.H.: Point contact spectroscopy of Fe pnictides and chalcogenides in the normal state. Curr. Opin. Solid St. M. 17, 81 (2013) 370. Daghero, D., Tortello, M., Ummarino, G.A., Gonnelli, R.S.: Directional point-contact Andreev-reflection spectroscopy of Fe-based superconductors: Fermi surface topology, gap symmetry and electron-boson interaction. Rep. Prog. Phys. 74, 124509 (2011) 371. Sobota, R., Plecenik, T., Gregor, M., Truchly, M., Satrapinskyy, Vidis, M., Secianska, K., Kurth, F., Holzapfel, B., Iida, K., Kus, P., Plecenik, A.: Surface properties of Co-doped BaFe2 As2 thin films deposited on MgO with Fe buffer layer and CaF2 substrates. Appl. Surf. Sci. 312, 182 (2014) 372. Cho, K., Ko´nczykowski, M., Murphy, J., Kim, H., Tanatar, M.A., Straszheim, W.E., Shen, B., Wen, H.H., Prozorov, R.: Effects of electron irradiation on resistivity and London penetration depth of Ba1−x Kx Fe2 As2 (x ≤ 0.34) iron-pnictide superconductor. Phys. Rev. B 90, 104514 (2014) 373. Prozorov, R., Ko´nczykowski, M., Tanatar, M.A., Thaler, A., Bud’ko, S.L., Canfield, P.C., Mishra, V., Hirschfeld, P.J.: Effect of electron irradiation on superconductivity in single crystals of Ba(Fe1−x Rux )2 As2 (x = 0.24). Phys. Rev. X 4, 041032 (2014) 374. Van der Beek, C.J., Demirdi¸s, S., Colson, D., Rullier-Albenque, F., Fasano, Y., Shibauchi, T., Matsuda, Y., Kasahara, S., Gierlowski, P., Ko´nczykowski, M.: Electron irradiation of Co, Ni, and P-doped BaFe2 As2 iron-based superconductors. J. Phys.: Conf. Ser. 449, 012023 (2013) 375. Massee, F., Sprau, P.O., Wang, Y.-L., Davis, J.C.S., Ghigo, G., Gu, G., Kwok, W.-K.: Imaging atomic-scale effects of high-energy ion irradiation on superconductivity and vortex pinning in Fe(Se, Te). Sci. Adv. 1, e1500033 (2015) 376. Moore, J.D., Cohen, L.F., Yeshurun, Y., Caplin, A.D., Morrison, K., Yates, K.A., McGilvery, C.M., Perkins, J.M., McComb, D.W., Trautmann, C., Ren, Z.A., Yang, J., Lu, W., Dong, X.L., Zhao, Z.X.: The effect of columnar defects on the pinning properties of NdFeAsO0.85 conglomerate particles. Supercond. Sci. Technol. 22, 125023 (2009) 377. Kasaei, L., Manichev, V., Li, M., Feldman, L.C., Gustafsson, T., Collantes, Y., Hellstrom, E., Demir, M., Acharya, N., Bhattarai, P., Chen, K., Xi, X.X., Davidson, B.A.: Normal-state and superconducting properties of Co-doped BaFe2 As2 and MgB2 thin films after focused helium ion beam irradiation. Supercond. Sci. Technol. 32, 095009 (2019) 378. Ozaki, T., Wu, L., Zhang, C., Si, W., Jie, Q., Li, Q.: Enhanced critical current in superconducting FeSe0.5 Te0.5 films at all magnetic field orientations by scalable gold ion irradiation. Supercond. Sci. Technol. 31, 024002 (2018) 379. Eisterer, M.: Radiation effects on iron-based superconductors. Supercond. Sci. Technol. 31, 013001 (2017) 380. Fu, X.T., Song, W.D., Ho, H.W., Ji, R., Wang, L., Hong, M.H.: Anomalous phase change characteristics in Fe-Te materials. Appl. Phys. Lett. 100, 201906 (2012)

References

379

381. Ho, H.W., Branicio, P.S., Song, W.D., Bai, K., Teck, L. Tan, Ji, R., Yang, Y., Yang, P., Du, Y.H., Sullivan, M.B.: Uravelling the anomalous electrical and optical phase-change characteristics in FeTe. Acta Mater. 112, 67 (2016) 382. Janaki, J., Geetha Kumary, T., Mani, A., Amaladass, E.P., Raveendran, N.R., Magudapathy, P., Kalavathi, S., Sairam, T.N., Ravindran, T.R.: Characterization and low temperature study of iron telluride films upon ageing and oxygen ion irradiation. J. Supercond. Nov. Magn. 27, 2639 (2014) 383. Kar’kin, A.E., Wolf, T., Vasil’ev, A.N., Volkova, O.S., Goshchitskii, B.N.: Effect of neutron irradiation on the properties of the FeSe compound in the superconducting and normal states. Phys. Met. Metallogr. 113, 455 (2012) 384. Eisterer, M., Raunicher, R., Weber, H.W., Bellingeri, E., Cimberle, E., Pallecchi, I., Putti, M., Ferdeghini, C.: Anisotropic critical currents in FeSe0.5 Te0.5 films and the influence of neutron irradiation. Supercond. Sci. Technol. 24, 065016 (2011) 385. Ahmad, D., Choi, W.J., Seo, Y.I., Lee, S., Park, T., Mosqueira, J., Gu, G., Kwon, Y.S.: Effect of proton irradiation on the fluctuation-induced magnetoconductivity of FeSe1−x Tex thin films. New. J. Phys. 19, 093004 (2017) 386. Leo, A., Sylva, G., Braccini, V., Bellingeri, E., Martinelli, A., Pallecchi, I., Ferdeghini, C., Pellegrino, L., Putti, M., Ghigo, G., Gozzelino, L., Torsello, D., Pace, S., Nigro, A., Grimaldi, G.: Anisotropic effect of proton irradiation on pinning properties of Fe(Se, Te) thin films. IEEE Trans. Appl. Supercond. 29, 7300205 (2019) 387. Sylva, G., Bellingeri, E., Ferdeghini, C., Martinelli, A., Pallecchi, I., Pellegrino, L., Putti, M., Ghigo, G., Gozzelino, L., Torsello, D., Grimaldi, G., Leo, A., Nigro, A., Braccini, V.: Effects of high-energy proton irradiation on the superconducting properties of Fe(Se, Te) thin films. Supercond. Sci. Technol. 31, 054001 (2018) 388. Ozaki, T., Jaroszysnki, J., Li, Q.: Two-fold reduction of Jc anisotropy in FeSe0.5 Te0.5 films using low-energy proton irradiation. IEEE Trans. Appl. Supercond. 29, 7300403 (2019) 389. Leo, A., Grimaldi, G., Nigro, A., Ghigo, G., Gozzelino, L., Torsello, D., Braccini, V., Sylva, G., Ferdeghini, C., Putti, M.: Critical current anisotropy in Fe(Se,Te) film irradiated by 3.5 MeV protons. J. Phys.: Conf. Ser. 1559, 012042 (2020) 390. Nazir, M., Xu, Z., Peng, N.H., Akhtar, N., Papakonstantinou, P., Webb, R.P., Ma, Y., Zheng, D.: Enhancement of critical current density in helium ion irradiated Ba(Fe, Co)2 As2 thin films. Supercond. Sci. Technol. 33, 075012 (2020) 391. Tarantini, C., Iida, K., Sumiya, N., Chihara, M., Hatano, T., Ikuta, H., Singh, R.K., Newman, N., Larbalestier, D.C.: Effect of α-particle irradiation on a NdFeAs(O, F) thin film. Supercond. Sci. Technol. 31, 034002 (2018) 392. Phan, G.N., Nakayama, K., Kanayama, S., Kuno, M., Sugawara, K., Sato, T., Takahashi, T.: ARPES study of cesium-coated FeSe thin films on SrTiO3 . J. Phys.: Conf. Ser. 871, 012017 (2017)

Appendix A

Chronological Survey of Selected Publications

Until today most Fe-based superconducting thin films were grown by pulsed laser deposition (∼60% of publications), followed by molecular beam epitaxy (∼23%). Other methods, RF-sputter deposition, electrodeposition and chemical vapor deposition methods, for example, were only marginally exploited. This can be seen from the number of publications devoted to thin film growth of iron pnictides and iron chalcogenides that appeared since 2008. The dominant appearance of both methods can be explained by two facts: (i) Most thin film research groups, that entered the field of Febased superconductors, have used pulsed laser deposition and achieved reasonable results. (ii) Molecular beam epitaxy, was mainly used in the growth of monolayer FeSe films, which produced a lot of research output. Despite some drawbacks when it comes to the incorporation of volatile elements at high temperatures, both methods, pulsed laser deposition as well as molecular beam epitaxy, have demonstrated a great potential in the growth of the new Fe-based superconductors. Table A.1 provides a chronological list of the first thin film publication of each compound and also the arXiv-source, if available.

© Springer Nature Switzerland AG 2021 S. Haindl, Iron-Based Superconducting Thin Films, Springer Series in Materials Science 315, https://doi.org/10.1007/978-3-030-75132-6

381

382

Appendix A: Chronological Survey of Selected Publications

Table A.1 First publications of different Fe-based superconducting thin films in chronological order according to the journal publication. Methods: ED = electrodeposition, MBE = molecular beam epitaxy, MOCVD = metal-organic chemical vapor deposition, PLD = pulsed laser deposition. The onset critical temperatures do not necessarily correspond to the optimized values Date

Compound

Method

Tc,on (K)

2008 09 19

Sr(Fe1−x Cox )2 As2

PLD

20

Comment

2008 10 22

LaOFeAs

PLD

–

epitaxial

0808.1956

[2]

2008 11 04

LaO1−x Fx FeAs

2-stage

11

PLD & anneal.

0808.1864

[3]

2009 03 20

FeSea

PLD

2

–

[4]

2009 03 20

FeSe1−x Tex

PLD

13.2

–

[4]

2009 07 03

FeTex S y

PLD

5

–

[5]

2009 08 03

FeSe0.5 Te0.5

PLD

17

–

[6]

2009 08 28

NdOFeAs

MBE

–

–

[7]

2009 10 06

Ba(Fe1−x Cox )2 As2

PLD

20

0907.0666

[8]

2010 01 08

FeTea

PLD

13

0911.5282

[9]

2010 02 09

LiFeAs

ED

13

–

[10]

2010 05 15

Sr1−x Kx Fe2 As2

MBE

30.3

–

[11]

2010 05 18

Ba1−x Kx Fe2 As2

2-stage

40

1004.4751

[12]

2010 07 30

NdO1−x Fx FeAs

MBE

48

1005.0186

[13]

2011 12 16

SmO1−x Fx FeAs

MBE

57.8

–

[14]

2012 03 01

1 uc FeSe

MBE

53

1201.5694

[15]

2012 04 27

Ba1−x Lax Fe2 As2

PLD

22.4

1110.0045

[16]

2012 09 07

BaFe2 (As1−x Px )2

PLD

29

–

[17]

2012 12 13

Ba(Fe1−x Crx )2 As2

PLD

–

1302.0340

[18]

2012 12 20

Sr1−x Lax Fe2 As2

PLD

20.8

1302.0340

[19]

2013 07 08

Ba1−x Cex Fe2 As2

PLD

13.4

1307.0542

[20]

Ba1−x Prx Fe2 As2

PLD

6.2

PLD & anneal.

SrTiO3 substrate

arXiv:

Refs.

0808.1985

[1]

Ba1−x Ndx Fe2 As2

PLD

5.8

2014 07 17

KFe2 As2

2-stage

3.7

PLD & anneal.

–

[21]

2015 01 21

NdOFe1−x Cox As

2-stage

16

MOCVD & anneal.

–

[22]

2015 12 03

CaFe2 As2

MBE

1 (arithmetic crystal class 4/mmmI). Points and lines of symmetry are indicated. The irreducible wedge of the BZ is colored. Tetragonal BZ in the (kx , k y )-plane for (c) the 1-Fe unit cell (‘unfolded BZ’) and (d) the 2-Fe unit cell (‘folded BZ’) of Fe-based superconductors with two hole and two electron bands at the Fermi level. Folding lines and folding directions are indicated

References 1. Hiramatsu, H., Katase, T., Kamiya, T., Hirano, M., Hosono, H.: Superconductivity in epitaxial thin films of Co-doped SrFe2 As2 with bilayered FeAs structures and their magnetic anisotropy. Appl. Phys. Express 1, 101702 (2008) 2. Hiramatsu, H., Katase, T., Kamiya, T., Hirano, M., Hosono, H.: Heteroepitaxial growth and optoelectronic properties of layered iron oxyarsenide. LaFeAsO. Appl. Phys. Lett. 93, 162504 (2008) 3. Backen, E., Haindl, S., Niemeier, T., Hühne, R., Freudenberg, T., Werner, J., Behr, G., Schultz, L., Holzapfel, B.: Growth and anisotropy of La(O, F)FeAs thin films deposited by pulsed laser deposition. Supercond. Sci. Technol. 21, 122001 (2008) 4. Wu, M.K., Hsu, F.C., Yeh, K.W., Huang, T.W., Luo, J.Y., Wang, M.J., Chang, H.H., Chen, T.K., Rao, S.M., Mok, B.H., Chen, C.L., Huang, Y.L., Ke, C.T., Wu, P.M., Chang, A.M., Wu, C.T.,

Appendix B: Space Groups and Brillouin Zones

5.

6. 7.

8.

9. 10. 11. 12. 13.

14.

15.

16.

17.

18. 19.

20.

21. 22.

23.

385

Perng, T.P.: The development of the superconducting PbO-type β-FeSe and related compounds. Phys. C 469, 340 (2008) Mele, P., Matsumoto, K., Haruyama, Y., Mukaida, M., Yoshida, Y., Kiss, T.: Fabrication of Fe-Te-S superconducting epitaxial thin films by pulsed laser deposition. Appl. Phys. Express 2, 073002 (2009) Si, W., Lin, Z.-W., Jie, Q., Yin, W.-G., Zhou, J., Gu, G., Johnson, P.D., Li, Q.: Enhanced superconducting transition temperature in FeSe0.5 Te0.5 . Appl. Phys. Lett. 95, 052504 (2009) Kawaguchi, T., Uemura, H., Ohno, T., Watanabe, R., Tabuchi, M., Ujihara, T., Takenaka, K., Takeda, Y., Ikuta, H.: Epitaxial growth of NdFeAsO thin films by molecular beam epitaxy. Appl. Phys. Express 2, 093002 (2009) Katase, T., Hiramatsu, H., Yanagi, H., Kamiya, T., Hirano, M., Hosono, H.: Atomically-flat, chemically-stable, superconducting epitaxial thin film of iron-based superconductor, cobaltdoped BaFe2 As2 . Solid State Commun. 149, 2121 (2009) Han, Y., Li, W.Y., Cao, L.X., Wang, X.Y., Xu, B., Zhao, B.R., Guo, Y.Q., Yang, J.L.: Superconductivity in iron telluride thin films under tensile stress. Phys. Rev. Lett. 104, 017003 (2010) Chen, N., Qu, S., Li, Y., Liu, Y., Zhang, R., Zhao, H.: Synthesis of LiFeAs superconductor by electrochemistry at room temperature. J. Appl. Phys. 107, 09E123 (2010) Agatsuma, S., Yamagishi, T., Takeda, S., Naito, M.: MBE growth of FeSe and Sr1−x Kx Fe2 As2 . Phys. C 470, 1468 (2010) Lee, N.H., Jung, S.-G., Kim, D.H., Kang, W.N.: Potassium-doped BaFe2 As2 superconducting thin films with a transition temperature of 40 K. Appl. Phys. Lett. 96, 2020505 (2010) Kawaguchi, T., Uemura, H., Ohno, T., Tabuchi, M., Ujihara, T., Takenaka, K., Takeda, Y., Ikuta, H.: In situ growth of superconducting NdFeAs(O, F) thin films by molecular beam epitaxy. Appl. Phys. Lett. 97, 042509 (2010) Ueda, S., Takeda, S., Takano, S., Mitsuda, A., Naito, M.: Molecular beam epitaxy growth of superconducting Ba1−x Kx FeAs and SmFeAs(O, F) films. Jpn. J. Appl. Phys. 51, 010103 (2012) Wang, Q.-Y., Li, Z., Zhang, W.-H., Zhang, Z.-C., Zhang, J.-S., Li, W., Ding, H., Ou, Y.-B., Deng, P., Chang, K., Wen, J., Song, C.-L., He, K., Jia, J.-F., Ji, S.-H., Wang, Y.-Y., Wang, L.-L., Chen, X., Ma, X.-C., Xue, Q.-K.: Interface-induced high-temperature superconductivity in single unit-cell FeSe films on SrTiO3 . Chin. Phys. Lett. 29, 037402 (2012) Katase, T., Iimura, S., Hiramatsu, H., Kamiya, T., Hosono, H.: Identical effects of indirect and direct electron doping of superconducting BaFe2 As2 thin films. Phys. Rev. B 85, 140515(R) (2012) Adachi, S., Shimode, T., Miura, M., Chikumoto, N., Takemori, A., Nakao, K., Oshikubo, Y., Tanabe, K.: Pulsed laser deposition of BaFe2 (As, P)2 superconducting thin films with high critical current density. Supercond. Sci. Technol. 25, 105015 (2012) Engelmann, J., Müller, K.H., Nenkov, V., Schultz, L., Holzapfel, B., Haindl, S.: Metamagnetic effects in epitaxial BaFe1.8 Co0.2 As2 thin films. Eur. Phys. J. B 85, 406 (2012) Hiramatsu, H., Katase, T., Kamiya, T., Hosono, H.: Superconducting properties and phase diagram of indirectly electron-doped (Sr1−x Lax )Fe2 As2 epitaxial films grown by pulsed laser deposition. IEEE Trans. Appl. Supercond. 23, 7300405 (2013) Katase, T., Hiramatsu, H., Kamiya, T., Hosono, H.: Magnetic scattering and electron pair breaking by rare-earth-ion substitution in BaFe2 As2 epitaxial films. New J. Phys. 15, 073019 (2013) Hiramatsu, H., Matsuda, S., Sato, H., Kamiya, T., Hosono, H.: Growth of c-axis-oriented KFe2 As2 thin films. ACS Appl. Mater. Interfaces 6, 14293 (2014) Corrales-Mendoza, I., Bartolo-Pèrez, P., Sánches-Reséndiz, V.M., Gallardo-Hernández, S., Conde-Gallardo, A.: Growth of superconducting NdFe0.88 Co0.12 AsO films by metal-organic chemical vapor deposition and post arsenic diffusion. EPL 109, 17007 (2015) Hatano, T., Kawaguchi, T., Fujimoto, R., Nakamura, I., Mori, Y., Harada, S., Ujihara, T., Ikuta, H.: Thin film growth of CaFe2 As2 by molecular beam epitaxy. Supercond. Sci. Technol. 29, 015013 (2016)

386

Appendix B: Space Groups and Brillouin Zones

24. Richter, S., Aswartham, S., Pukenas, A., Grinenko, V., Wurmehl, S., Skrotzki, W., Büchner, B., Nielsch, K., Hühne, R.: Superconductivity in Ni-doped Ba-Fe-As thin films prepared from single-crystal targets using PLD. IEEE Trans. Appl. Supercond. 27, 7300403 (2017) 25. Fujiwara, K., Shiogai, J., Tsukazaki, A.: Fabrication of tetragonal FeSe-FeS alloy films with high sulfur contents by alternate deposition. Jpn. J. Appl. Phys. 56, 100308 (2017) 26. Matsumoto, J., Hanzawa, K., Sasase, M., Haindl, S., Katase, T., Hiramatsu, H., Hosono, H.: Superconductivity at 48 K of heavily hydrogen-doped SmFeAsO epitaxial films grown by topotactic chemical reaction using CaH2 . Phys. Rev. Mater. 3, 103401 (2019) 27. Haindl, S., Wurmehl, S., Büchner, B., Kampert, E.: PLD growth of iron-oxypnictides: Co- and F-substitution. Supercond. Sci. Technol. 33, 105004 (2020) 28. Aroyo, M.I. (ed.).: International Tables for Crystallography, vol. A. IUCr, pp. 486–487 (2016) 29. Aroyo, M.I. (ed.): International Tables for Crystallography, vol. A. IUCr, pp. 458–461 (2016) 30. Aroyo, M.I., Wondratschek, H.: Crystallographic viewpoints in the classification of spacegroup representations. In: Shmueli, U. (ed.): International Tables for Crystallography, vol. B. IUCr, pp. 175–192 (2010)

Index

A Activation energy, 254–257 Alkali metal dispenser, 67, 72, 79 Ambegaokar-Baratoff relation, 279, 282 Anderson’s theorem, 9 Andreev bound states, 309 Angle-Resolved Photoelectron Spectroscopy (ARPES), 338–341 Anion height, 17, 302 Annealing, 162, 176, 177 Anomalous Hall effect, 321 Aqueous solution, 115–118, 120, 126 As vapor, 67

B BaFe2 As2 , 2, 11, 196 electronic phase diagram, 294, 295 interface, 203, 213, 243, 245–248, 294 LEED, 179 optical spectroscopy, 332, 336 PLD, 52, 55, 192 SDW, 14 structure, 5, 8 surface, 169, 170 template, 193, 198 BaFe2 (As1−x Px )2 , 166 critical currents, 266, 267, 275 irradiation, 358 MBE, 85, 86 PLD, 58, 59 point-contact spectroscopy, 346 upper critical field, 315, 317 Ba(Fe1−x Cox )2 As2 , 161, 166, 167 critical currents, 268, 270, 275 © Springer Nature Switzerland AG 2021 S. Haindl, Iron-Based Superconducting Thin Films, Springer Series in Materials Science 315, https://doi.org/10.1007/978-3-030-75132-6

electronic phase diagram, 293, 294, 297 Hall effect, 320 interface, 211, 243, 246, 247 irradiation, 355, 356 LEED, 152 optical spectroscopy, 332, 333, 344 PLD, 3, 52–57, 202, 248, 249 point-contact spectroscopy, 345, 346 RHEED, 154, 155 surface impedance, 325 voltage noise, 321 vortex liquid, 253 Ba(Fe1−x Crx )2 As2 PLD, 57 Ba(Fe1−x Nix )2 As2 critical currents, 269 optical spectroscopy, 332, 337 PLD, 57, 58 vortex liquid, 253 BaFeO3−x , 55, 212, 248, 249, 269, 270, 325 (Ba1−x Kx )Fe2 As2 MBE, 84, 85 two-stage synthesis, 95–97 (Ba1−x Lax )Fe2 As2 , 295–298 PLD, 58 Band bending, 304–306 Band structure calculations, 11 (Ba1−x RE x )Fe2 As2 PLD, 58 BaZrO3 , 163, 167, 249, 250, 256, 257, 269, 272 BCS theory, 9, 15, 18, 327 Bean’s critical state, 260, 263 Bicrystal, 277–280, 282 BKT, 258–260 387

388 Blonder-Tinkham-Klapwijk theory, 344 Bohr magneton, 9 Bonding angle, 17, 159, 295, 302, 340 Buffer layer, 162, 163, 174, 193–198

C CaFe2 As2 MBE, 83, 84 Ca(Fe1−x Cox )2 As2 PLD, 60 Cathodic codeposition, 116 Cathodic metal deposition, 114 CeO2 , 162, 194, 195, 236–239, 260, 269, 270, 272–274, 353, 354 Charge fluctuations, 13 Charge transfer, 299, 301, 304–307 Chemical bath deposition (CBD), 126–129, 189 Chemical substitution, 6, 11 Coated conductor, 47, 56, 273–276 Cooper law fit, 105 Cracker cell, 66, 67 Critical currents, 260–264, 277 Critical temperature, 15, 105, 161, 299 Crystal field splitting, 4, 13 Cuprate superconductors, 18

D de Broglie wavelength, 149, 152 de Gennes extrapolation length, 302 Density of states, 11, 15 Depairing current, 260–263 Dielectric constant, 308 Dirac cone, 14, 302, 336, 339 Direct doping, 6, 295 Dislocations, 71, 167, 173, 178, 192, 204, 206, 207, 237, 239 Domain matching epitaxy, 34, 36, 62, 200 Drude-Lorentz model, 326 Drude term, 326

E Effusion cell, 66, 67, 100 Electric noise, 321, 322 Electrodeposition, 114–117, 119–121, 124, 189, 193 Electron-boson coupling, 312, 315, 333 Electron doping, 11, 295–298, 301, 302, 339 Electronic correlations, 13, 302, 340 Electronic phase diagram, 16, 287–291, 293–295

Index Electron-phonon coupling, 15, 327, 332, 340 interfacial, 16, 299, 304, 306

F Fe, 9, 10 buffer layer, 195, 196 electrodeposition, 116 ferromagnetism, 9 impurity, 55, 111 superconductivity, 10 Fe(CO)5 , 109 Fe1−x Cox Se MBE, 70 Fe3 O4 , 240, 249, 270, 352 Fermi surface, 11, 300, 339, 340 nesting, 14, 346 FeSe, 2, 13 ARPES, 338, 339 chemical bath deposition, 126–129 electrodeposition, 117, 119–121 FeSe1−x Tex , 161, 165, 167 Hall coefficient, 319 K:FeSe, 39 LEED, 150, 151 liquid phase deposition, 124–126 MBE, 69, 70 Mg:FeSe, 39 MOCVD, 109–112 PLD, 34, 36–39 spray pyrolysis, 129 sputter deposition, 103–105 structure, 6 two-stage synthesis, 95–97 upper critical field, 315 FeSe/Bi2 Se3 LEED, 151 FeSe1−x Sx electronic phase diagram, 291 PLD, 50, 51 FeSe/SrTiO3 (1 uc), 11, 298, 300, 302–310 energy gap, 300, 302 Fermi surface, 298, 300 LEED, 150 MBE, 72, 74–79 RHEED, 157, 158 STM, 176, 177 TRHEPD, 159 upper critical field, 314 FeSe1−x Tex conductivity fluctuations, 325 critical currents, 268 electronic phase diagram, 287–290

Index Hall coefficient, 319 irradiation, 353, 354 PLD, 43, 44, 46–48 point-contact spectroscopy, 345 RHEED, 154, 157, 158 sputter deposition, 106–108 two-stage synthesis, 96 upper critical field, 313 FeSe1−x Tex /SrTiO3 (1 uc) MBE, 78, 79 FeTe Hall coefficient, 319 irradiation, 352 MBE, 71, 72 oxygenation, 42, 71 PLD, 40–43 point-contact spectroscopy, 344 STM, 178 structure, 7 upper critical field, 313 FeTe/Bi2 Te3 point-contact spectroscopy, 344 upper critical field, 315 FeTe1−x Sx PLD, 48, 50 two-stage synthesis, 96 upper critical field, 313 FeTe/SiO, 94 FeTe/SrTiO3 (1 uc) MBE, 78 Fe-vacancy ordering, 72, 150, 151 Film bending, 166 Film texture, 160–163 Flash evaporation, 94 Fluorine source, 90–93 Flux creep, 253–257 Fuchs-Kliewer surface phonons, 192, 307 Fulde-Ferrell-Larkin-Ovchinnikov (FFLO), 313

G GaP, 67, 85, 86 Gap closing temperature, 299, 300 Ginzburg-Landau theory, 309 anisotropic, 310 coherence length, 309, 317 depairing current, 262 multiband effects, 313, 317 Grain boundaries, 48, 56, 277–280, 282 Growth methods (overview), 28, 93 Growth mode, 153, 154, 169, 171–173 Growth rate, 34, 105

389 H Hall coefficient, 318 Hall effect, 317–321 Halperin-Nelson formula, 258 Heterointerface, 3, 198–212, 214, 215, 218, 222, 225, 227, 235–248 High-Energy Positron Diffraction (HEPD), 159, 160 High gas pressure trap system, 96 Hillock formation, 127, 356 Hole doping, 11 H2 Se, 109, 111, 112, 121 Hund’s rule coupling, 13, 16, 302 Hund’s rules, 9 Hydrostatic pressure, 298

I IBAD technique, 47, 56, 57, 59, 163 Impurity phase, 38, 43, 55, 56, 58–61, 85, 90, 93, 96, 99, 104, 105, 111–113, 124 Indirect doping, 6, 295 In8 K4 , 67 Intercalated, 8, 51 Ionic liquid, 115, 121 Iron age, 1 Irradiation, 348 critical temperature, 350, 358 defect cascade, 350, 354 defect cluster, 350, 355 dpa, 351 fluence, 351 Frenkel defect, 349 implantation depth, 358 induced defects, 350 ion implantation, 352, 353 laser light, 351, 352 microcracks, 175 SRIM/TRIM, 351 stopping power, 348 Irreversibility field, 263, 265 Isovalent substitution, 11

K KFe2 As2 , 2 two-stage synthesis, 95–97 Kx Fe2−y Se2 , 39 electronic phase diagram, 291 MBE, 72 Kramer plot, 263, 265

390

Index

L LaOFeAs, 1, 11 PLD, 2, 60, 61 structure, 5, 7 LaOFe1−x Cox As PLD, 63 LaOFeP, 1, 11 LaO1−x Fx FeAs MBE, 86, 87 optical spectroscopy, 337 point-contact spectroscopy, 348 two-stage synthesis, 95–97, 99 upper critical field, 317 (La1−y Sm y )O1−x Fx FeAs upper critical field, 317 LiFeAs, 2, 8, 11, 27, 32 electrodeposition, 121, 124 growth mode, 173 MBE, 83 RHEED, 152 structure, 5, 7 surface morphology, 178 Li1−x Fex OHFeSe, 8 PLD, 51 Likharev limit, 259, 261 Liquid phase deposition, 124–126 Lorentz term, 327 Low-Energy Electron Diffraction (LEED), 149–152

NdOFeAs RHEED, 155–157 two-stage synthesis, 95–97 NdOFe1−x Cox As MOCVD, 112, 113 two-stage synthesis, 95–97 NdO1−x Fx FeAs irradiation, 356 MBE, 87–89 Nematicity, 14 Nematic transition, 14, 319, 320, 330, 338– 340 Non-Fermi liquid, 17, 327

M Magnetron, 102 Matthias rules, 9 Mattis-Bardeen theory, 327 Mechanical exfoliation, 94, 256, 258, 282, 345 Metal-Organic Chemical Vapor Deposition (MOCVD), 109, 110, 112 Metal-organic precursors, 109 Metastable compounds, 295–298 MgB2 , 18 Microbridge, 261 Microstructure, 350 Microwave spectroscopy, 324, 325 Molecular Beam Epitaxy (MBE), 66, 67, 69– 72, 74–94, 100 Mott transition, 13 Multilayer, 94

P Pairing mechanism, 19 Paramagnetic limit, 312 Passivation layer, 356 Pauli limit, 312, 313 Pauli’s exclusion principle, 9 Penetration depth, 322–325, 327, 328, 332, 334–337 Photoelectron Spectroscopy (PES), 338 Pinning force, 260, 263–266, 356 Point-contact spectroscopy, 342–346, 348 Postdeposition annealing, 94–97, 99, 100 Protection layer, 338 Proximity annealing, 95 Pulsed Laser Deposition (PLD), 28, 30–34, 36–39, 41–44, 46–48, 50–66 Pulsed magnetic fields, 309 P vapor, 67

N Nanobridge, 261–263 Nanoparticles, 269, 270

Q Quantum critical point, 315, 317

O Optical spectroscopy, 325–332, 334–338 Orbital fluctuations, 18 Orbital ordering, 291, 339 Orbital selective Mott phase, 13 Order parameter symmetry d-wave, 18, 302 s++ , 18 s± , 17, 332, 346 s-wave, 302, 325 Orthorhombic distortion, 13, 295, 307 O vacancies, 301, 302

Index R RABiTS, 47, 48, 120, 163, 193, 194, 273, 274 Reflection High-Energy Electron Diffraction (RHEED), 152–158 Replica bands, 299, 306–308 Rigid band shift, 11, 295 Rocking curve, 163–167

S Scotch-tape, 94 Se monoclinic (red), 120 sputter target, 103 Seed layer, 44, 193, 197, 198 Se etching, 74 Selenization, 94, 100, 101 Semimetal, 11, 110 Skin depth, 323, 324, 337 SmOFeAs PLD, 61, 62 SmO1−x Fx Fe1−y Co y As upper critical field, 317 SmO1−x Hx FeAs two-stage synthesis, 95, 96 SmOFe1−x Cox As PLD, 63 SmO1−x Fx FeAs MBE, 89–93 MOCVD, 113 PLD, 63–66 point-contact spectroscopy, 348 two-stage synthesis, 95, 96 upper critical field, 317 Solid Phase Epitaxy (SPE), 94 Spin Density Wave (SDW), 14, 287, 297, 319 Spin fluctuations, 10, 14, 16 Spin orbit coupling, 4, 302 Spin spiral state, 300 Spray pyrolysis, 129 Sputter deposition DC, 105 RF, 100, 102–104, 106–108 SQUID, 280 SrFe2 As2 , 14, 295 Sr(Fe1−x Cox )2 As2 PLD, 2, 52, 59, 60 upper critical field, 315, 317 (Sr1−x Kx )Fe2 As2 MBE, 84, 85 PLD, 84 (Sr1−x Lax )Fe2 As2

391 electronic phase diagram, 298 PLD, 60 Standard hydrogen electrode, 115 Stoichiometric transfer, 31–34, 97 Strain, 308, 320, 340 Structure anti-PbO-type, 6, 383 Cu2 Sb-type, 7, 383 NiAs-type, 6 PbClF-type, 7 ThCr2 Si2 -type, 8, 383 ZrCuSiAs-type, 7, 383 Substrate, 114, 189–193 Substrate pretreatment, 74–80 Superconducting gap, 328, 338 Superconductor-to-insulator transition, 356 Super-exchange interaction, 14 Surface Debye temperature, 150 Surface impedance, 322–325 Surface polarity, 169–171, 192 Surface reconstruction, 149–152, 155, 158, 169–171, 176, 177, 179 Surface roughness, 154–158 Surface termination, 192, 197

T Thermally Assisted Flux Flow (TAFF), 253– 257 Tinkham formula, 311 TlFe1.6 Se2 , 173 Tl1−x Fe1.6 Se2 , 8 PLD, 51 Topological insulator, 3, 240 Topological phase transition, 302 Topological quantum computers, 240 Topological superconductivity, 7 Topological surface states, 240 Two carrier model, 11, 319, 321 Two-stage synthesis, 95–97, 99, 100

U Upper critical field, 309 anisotropy, 311, 313, 317, 354 Fe-chalcogenides, 313 Fe-pnictides, 315 pseudo-isotropic, 313, 315

V Vacuum coating, 94 van der Waals bonding, 6, 200, 201 van der Waals engineering, 240

392 van der Waals epitaxy, 81, 190 Vapor pressures, 67 Verwey transition, 240 Vortex lattice, 309 Vortex liquid, 263

Index W Wet chemical deposition process, 124 Wexler’s formula, 342 WHH theory, 312, 315