Magnetic Properties of Metals: Magnetic and Electric Properties of Magnetic Metallic Multilayers: A Supplement to Landolt-Börnstein III/32 Series 366264908X, 9783662649084

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Yoshiyuki Kawazoe Ryunosuke Note

Magnetic Properties of Metals: Magnetic and Electric Properties of Magnetic Metallic Multilayers A Supplement to Landolt-Börnstein III/32 Series

MATERIALS.SPRINGER.COM

Magnetic Properties of Metals: Magnetic and Electric Properties of Magnetic Metallic Multilayers

Yoshiyuki Kawazoe • Ryunosuke Note

Magnetic Properties of Metals: Magnetic and Electric Properties of Magnetic Metallic Multilayers A Supplement to Landolt-Bo¨rnstein III/32 Series

With 1068 Figures and 130 Tables

Yoshiyuki Kawazoe Tohoku University Aoba-ku, Sendai, Japan

Ryunosuke Note Miyagi-gun, Japan

ISBN 978-3-662-64908-4 ISBN 978-3-662-64909-1 (eBook) https://doi.org/10.1007/978-3-662-64909-1 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer-Verlag GmbH, DE, part of Springer Nature 2022 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-Verlag GmbH, DE part of Springer Nature. The registered company address is: Heidelberger Platz 3, 14197 Berlin, Germany

Dedicated to Prof. Abe and Prof. Kaneko

Preface

In 1996, we published the first data book entitled Phase Diagrams and Physical Properties of Nonequilibrium Alloys as part of the Landolt-Boernstein (LB) series, which accumulates ternary metallic amorphous phase diagrams and makes them fairly simple. Although in the preface of the book I stated that the rest of the data books including this volume Magnetic and Electric Properties of Magnetic Metallic Multilayers will be published in the very near future, it was not an easy task to work on the physical properties of materials, and it took 26 years to publish a total of 12 books. Especially for magnetic properties, there are different types of notations and units to express physical properties, and these should be checked one by one. This is the main reason why it took so long to confirm all the data. We are a very rare group from Japan who collect, extract, and combine all data published in various journals and directly from researchers working on the subject. We have checked more than 2,500 published papers concerning magnetic materials and extracted necessary properties to construct a meaningful database for researchers all over the world. Finally, more than 60 kinds of magnetic and electric properties are listed in our data book for 25 species. We hope that this data book will be used by many researchers for a long time to come. We should not be selfish as a researcher and should inform what we know to other researchers. About 30 years ago when we started this data book project at the Institute of Materials Research, Tohoku University, I stated to my people working on this project that we should develop the LB series to serve all researchers equally along the lines of Martin Luther King, Jr.’s, famous speech “I have a dream,” where he expresses his idea of unification of black and white people in America. In the twenty-first century, it is regrettable that there are still major challenges for researchers in all fields of research, depending on the country of their origin, as there are several who do not have easy access to journals and therefore cannot obtain enough information for their research. Now is the time! We should overcome this difficult situation by providing a reliable database to accelerate their research work. In these 26 years, two of our collaborators, Professors Takejiro Kaneko and Shunya Abe, passed away. They were the main persons working on this very tedious work. We are very much thankful for their great contribution to achieve this final form. We also acknowledge a number of people who contributed to extract the papers from the journals; 26 years ago, there was no online database, and we had to vii

viii

Preface

visit the library and copy the papers one by one. Without the contributions of these hardworking colleagues, this data book could not have been realized. 15th October 2022 at Sendai, Japan

Editors

Contents

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Part I

1

Data

ScFe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9

TiFe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10

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

29

TiNi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

42

VCr . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

49

VMn . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

50

VFe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

51

VCo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

99

VNi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

108

VCu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

113

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

114

CrFe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

115

CrCo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

379

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

417

CrCu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

427

FeMn . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

436

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

450

MnNi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

471

MnCu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

482

TiCo

CrMn

CrNi

MnCo

ix

x

Contents

FeCo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

491

FeNi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

513

FeCu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

533

CoNi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

598

CoCu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

636

NiCu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1005 List of Magnetic Multilayers Collected

. . . . . . . . . . . . . . . . . . . . . . . . . 1053

Introduction

General Remarks The subject of this volume is to present both the numerical and graphical data on the magnetic and electrical properties of magnetic metallic multilayers which are composed with stacking up of double layers of thin films, one layer of which is at least the magnetic layer of 3d metals (M) or rare earth ones (R). Furthermore the data of the trilayers which have a top layer and bottom one of magnetic elements are also presented. In general, magnetic multilayers are classified into groups of five kinds with a difference of combinations of constituent elements as follows: (1) [Ml/M0 m]n, (2) [Ml/Xm]n, (3) [Ml/Rm]n, (4) [Rl/Xm]n, and (5) [Rl/R0 m]n, where M and M0 are 3d elements, R and R0 rare earth ones, and X non-magnetic ones, respectively. Among them, the multilayers of [Ml/M0 m]n are investigated extensively because they are the most useful multilayers. Therefore in this volume only the data for the multilayers of [Ml/M0 m]n are described in the form of figures and tables. For reference, all of the magnetic multilayers studied until now are given as a list of magnetic multilayers at the end of the book. Magnetic and electric data are presented in the one chapter per each magnetic multilayer of [Ml/M0 m]n. Each section consists of two subsections of (1) magnetic properties and (2) electrical properties. Each subsection then contains the items numbered as shown in the categories of magnetic and electric properties given at the following section “Categories of Magnetic Properties.” So each item contains the data of (1) magnetic field (H )-, (2) temperature (T )-, (3) layer thickness (t)-, and (4) annealing temperature (Tann)-dependence of magnetic properties or electric properties, respectively.

© The Editor(s) (if applicable) and The Author(s), under exclusive license to SpringerVerlag GmbH, DE, part of Springer Nature 2022 Y. Kawazoe, R. Note, Magnetic Properties of Metals: Magnetic and Electric Properties of Magnetic Metallic Multilayers, https://doi.org/10.1007/978-3-662-64909-1_1

1

2

Introduction

As an example of data presentation, a part of data for Cr/Co multilayers is shown below. Cr/Co Magnetization M vs. Magnetic Field H [Co(21 Å)/Cr(14 Å)]n (159), [Co(21 Å)/Cr(23 Å)]n (165), [Co(21 Å)/Cr(50 Å)]n (210). Relative magnetic hysteresis curves for (oxidized p-type Si(100))*/[Co (21 Å)/Cr(14 Å)]n (159)*, (oxidized p-type Si(100))*/[Co(21 Å)/Cr(23 Å)]n (165)*, and (oxidized p-type Si(100))*/[Co(21 Å)/Cr(50 Å)]n (210) multilayers at T ¼ 4.5 K under H || film plane. The number in the parenthesis is ttotal [Ǻ] of multilayers. The flattening of the hysteresis loops with decreasing Cr thickness is attributed to the AF alignment between regions of the Co layers in the multilayer film. Thicknesses tCo and tCr are the nominal values and ttotal denotes the average length in the direction of growth of the crystalline having a coherent multilayer structure [1: EBE*, 2: ~310 K, 3: ~5  1010 Torr*, 4: ~108 Torr*, 5: SQUID], [89SLG]* [90SCL, Fig. 3] The first line indicates an ordinary presentation of [Cr/Co] multilayer in the magnetic layers of [Ml/M0 m]n mentioned above, and the second line corresponds to the field dependence of magnetization as shown in the categories of magnetic and electric properties of the next section. At the top of the figure caption, the chemical formulae of magnetic multilayer are given like [Co(21 Å)/Cr(14 Å)]n (159) and so on. The substance of caption is then described, in which the substance of the figures is explained. Each caption carries a square bracket with some statements on the experimental conditions. The bracket is described, for example, like [1: EBE*, 2: ~310 K, 3: ~5  1010 Torr*, 4: ~108 Torr*, 5: SQUID], [89 SLG].*, where 1 shows the method of sample preparation, 2 the temperature of substrate, 3 base pressure, 4 pressure in the chamber during sample deposition, and 5 experimental method of magnetic properties. Data with note * are those from [89SLG]*. At the end of the caption, the original literature of the figure concerned is given like [90SCL, Fig. 3], where Fig. 3 means that the figure is Fig. 3 of the original literature [90SCL]. However, it is to be noted that the brackets with * do not appear in most of the brackets for other multilayers. References and Additional references are given after the presentations of the data in the item of the Cr/Co multilayers. In References, all the literatures cited in data presentations are given in chronological order. In Additional references, all the literatures collected for the Cr/Co multilayers which were studied up to now except the ones in References are provided. It is noted that in the field of magnetism, we are at a gradual transition stage from the use of cgs/emu units to SI units, confusing the readers of magnetic literature. However, the cgs/emu units are used in most literatures for magnetic multilayers. Thus in this volume the system of units, which was originally used by the authors of quoted work, was adopted as the units representing magnetic quantities. It is considered that this adoption of units will not inconvenience the users of the Landolt-Börnstein series, because there are a very few literatures using SI units.

Categories of Magnetic Properties

3

Of course, users of the tables and figures are benefitted in several ways as they can convert the data to the units which they are most familiar with, since they can use the list of definitions, units, and conversion factors for the magnetic quantities occurring most frequently.

Categories of Magnetic Properties In each section of the multilayer (A/B), the figures and tables are given in the following order: Magnetic Properties Magnetization M M vs. Magnetic Field H M vs. Temperature T M vs. Thickness t M vs. Annealing Tann Saturation Magnetization Ms Ms vs. T Ms vs. t Ms vs. Tann Remanent Magnetization Mr Mr vs. T Mr vs. t Mr vs. Tann Curie Temperature TC TC vs. H TC vs. t TC vs. Tann Permeability μ, Susceptibility χ μ vs. H, χ vs. H μ vs. T, χ vs. T μ vs. t, χ vs. t μ vs. Tann, χ vs. Tann Anisotropy Field HA HA vs. T HA vs. t HA vs. Tann Volume Anisotropic Constant Kv Kv vs. T Kv vs. t Kv vs. Tann

4

Introduction

Surface Anisotropic Constant Ks Ks vs. T Ks vs. t Ks vs. Tann Effective Anisotropic Constant Keff Keff vs. T Keff vs. t Keff vs. Tann Coercivity Hc Hc vs. T Hc vs. t Hc vs. Tann Exchange Energy J J vs. T J vs. t J vs. Tann Exchange Field HJ HJ vs. T HJ vs. t HJ vs. Tann Saturation Field Hs Hs vs. T Hs vs. t Hs vs. Tann Other Properties Electric Properties Resistivity R R vs. H R vs. T R vs. t R vs. Tann Magnetoresistance MR MR vs. H MR vs. T MR vs. t MR vs. Tann Hall Coefficient, Hall Resistivity ρH RH vs. H, ρH vs. H RH vs. T, ρH vs. T RH vs. t, ρH vs. t RH vs. Tann, ρH vs. Tann

List of Abbreviations

5

Magnetothermopower S S vs. H S vs. T S vs. t S vs. Tann Other Properties

List of Abbreviations ac, AC ACDF AF, AFM AFC AFM AGFM AP ASW BLS CAP CEMS CG CIP CPP CSDW dc, DC dc sp dHvA EB EBD EBE, EBV, EV ESR EXAFS F FM FC FC FIP FMR FPP FS FWHM GMR HAXRD

Alternating current AC driving force Antiferromagnetic (state) Antiferromagnetic coupling Atomic force microscope Alternating gradient field magnetometer Antiparallel (state) Augmented spherical waves Brillouin light scattering Current at an angle to the plane Conversion electron Mössbauer spectroscopy Corning glass Current in the plane Current perpendicular to the plane Commensurate spin density wave (states) Direct current Direct current sputtering de Haas-van Alphen Electron beam Electron beam deposition Electron beam evaporation, Electron beam vaporization, Electron vaporization Electron spin resonance Extended X-ray absorption fine structure spectroscopy Ferromagnetic (state) Ferromagnetic coupling Field cooling Field-in-plane Ferromagnetic resonance Field-perpendicular-plane FUCHS-Sondheimer Full width at half maximum Giant magnetoresistance High angle X-ray diffraction (continued)

6 HV IBS ISDW ITO LAXRD LHS MBE MFM ML MOKE MTEP NC ND NMR P P, PM PAC PMA PNR QPT rf, RF rf sp, RFS RHEED RHS rms RT SDW SEMPA SLIA SMOKE sp SQUID TEM TSDW UHV VD VSM XAFS XMCD XRD XRR YSZ ZFC μW

Introduction High vacuum Ion beam sputtering Incommensurate spin density wave (states) Indium tin oxide Low angle X-ray diffraction Left-hand side Molecular beam epitaxy Magnetic force microscope Multilayer Magneto-optic Kerr effect Magnetothermoelectric power Non coupling Neutron diffraction Nuclear magnetic resonance Parallel (state) Paramagnetic (state) Perturbed angular correlation Perpendicular magnetic anisotropy Polarized neutron reflectometry Quantum phase transition Radio frequency Radio frequency sputtering Reflection high energy electron diffraction Right-hand side Root mean square Room temperature Spin density wave Scanning electron microscopy with polarization analysis Sputtering in low-impurity atmosphere Surface magneto-optic Kerr effect Sputtering Superconducting quantum interference device Transmission electron microscope Transverse spin density wave propagating Ultra-high vacuum Vapor deposition Vibrating sample magnetometer X-ray absorption fine structure spectroscopy X-ray magnetic circular dichroism X-ray diffraction (pattern) X-ray reflectivity Yttrium-stabilized zirconium oxide Zero-field cooling Microwave

List of Symbols

7

List of Symbols a, b, c AFF AFM AMR d DR f H HA Hc Hflip Hj,HJ Hs Hsw I IB J J K K⊥ Ks Ku Kv , Kl kB M m MAE Mr MR MRs MRS Ms n p p, P pr , m r ps , ms R R0 RH Rs S

Å, nm

Å, nm Å/s Hz Oe, A/m Oe, A/m Oe, A/m Oe, A/m Oe, A/m Oe, A/m Oe, A/m A A erg/cm2, J/m2 erg/cm2, J/m2 erg/cm, J/m, (J/atom) erg/cm, J/m erg/cm2, J/m2 erg/cm3, J/m3 erg/cm3, J/m3 J/K G, T μB/atom, G cm3 erg, J, eV G, T

Oe-1 G, T μB, J/T, (μB/atom) Torr, bar, Pa μB μB Ω Ω Ω m/T, m3/c Ω V/K

Lattice parameter Antiferromagnetic fraction Antiferromagnetic ratio Anisotropic magnetoresistance Interplanar spacing Deposition rate Frequency Magnetic field Anisotropy field Coercivity Flip field Exchange coupling field Saturation field Switching field Electrical current Beam current Interlayer exchange coupling Interlayer coupling Anisotropy constant (per atom) Perpendicular anisotropy constant Surface anisotropy constant Uniaxial anisotropy constant Volume(cubic) anisotropy constant Boltzmann constant Magnetization Magnetic moment per atom Magnetic anisotropy energy Remanence Magnetoresistance Saturation magnetoresistance Magnetoresistance sensitivity Saturation magnetization Bilayer number Magnetic moment (per atom) Pressure Remnant magnetic moment Saturation magnetic moment Resistance Resistance in zero field Hall coefficient Saturation resistance Thermopower (continued)

8 T t, λ Tann TC TCR TN VB α δ η θ, φ κ λ λ μB ρ ρ0 ρH ρs σ σ σ, σ rms σR σs χ

Introduction K,  C Å, nm K,  C K,  C K-1 K,  C V K-1 Å, nm Å, nm Deg W/mK Å, nm Å, nm J/T Ω cm Ω cm Ω cm Ω cm G cm3/g (Ω m)-1 Å, nm G cm3/g G cm3/g cm3

Temperature Thickness, spacing Annealing temperature Curie temperature Temperature coefficient of resistance Néel temperature Deposition beam voltage Temperature coefficient of resistivity Dead layer thickness Roughness amplitude Angle Thermal conductivity Bilayer thickness Periods BOHR magneton Resistivity Resistivity in zero field Hall resistivity Saturation resistivity Magnetization per unit mass Electrical conductivity Root-mean-square roughness Remanence per unit mass Saturation magnetization per unit mass Susceptibility

ScFe

No available data given by figures and tables for this system in the references below.

References [91CSA] Chumakov, A.I., Smirnov, G.V., Andreev, S.S., Salashchenko, N.N., Shinkarev, S.I.: JETP Lett. 54 (1991) 216 (Pis’ma Zh. Eksp. Teor. Fiz. 54 (1991) 220) [92CSA] Chumakov, A.I., Smirnov, G.V., Andreev, S.S., Salashchenko, N.N., Shinkarev, S.I.: JETP Lett. 55 (1992) 509 (Pis’ma Zh. Ekps. Teor. Fiz. 55 (1992) 495) [93CSB] Chumakov, A.I., Smirnov, G.V., Baron, A.Q.R., Arthur, J., Brown, D.E., Ruby, S.L., Brown, G.S., Salashchenko, N.N.: Phys. Rev. Lett. 71 (1993) 2489 [94RKJ] Reddy, B.V., Khanna, S.N., Jena, P., Press, M.R., Jaswal, S.S.: J. Magn. Magn. Mater. 130 (1994) 255 [00GBK] Gebele, O., Bohm, M., Krey, U., Krompiewski, S.: J. Magn. Magn. Mater. 214 (2000) 309

© The Editor(s) (if applicable) and The Author(s), under exclusive license to SpringerVerlag GmbH, DE, part of Springer Nature 2022 Y. Kawazoe, R. Note, Magnetic Properties of Metals: Magnetic and Electric Properties of Magnetic Metallic Multilayers, https://doi.org/10.1007/978-3-662-64909-1_2

9

TiFe

Magnetization M vs. Magnetic Field H

Fig. 1 [Fe(tFe)/Ti(tTi)]n. Magnetic hysteresis loops for glass/[Fe(tFe)/Ti(tTi)]n multilayers at room temperature under H || film plane, where (a) [tFe ¼ 1.1 nm, tTi ¼ 9.4 nm, n ¼ 19]; (b) [tFe ¼ 2.8 nm, tTi ¼ 9.4 nm, n ¼ 14]; (c) [tFe ¼ 11.4 nm, tTi ¼ 9.4 nm, n ¼ 11]; (d) [tFe ¼ 2.8 nm, tTi ¼ 1.5 nm, n ¼ 40]; (e) [tFe ¼ 2.8 nm, tTi ¼ 2.8 nm, n ¼ 30] [1: EBE, 2: ---, 3: ---, 4: 2  104 Pa, 5: VSM] [98ZPL, Fig. 5]

© The Editor(s) (if applicable) and The Author(s), under exclusive license to SpringerVerlag GmbH, DE, part of Springer Nature 2022 Y. Kawazoe, R. Note, Magnetic Properties of Metals: Magnetic and Electric Properties of Magnetic Metallic Multilayers, https://doi.org/10.1007/978-3-662-64909-1_3

10

Saturation Magnetization Ms vs. Thickness t

11

Saturation Magnetization Ms vs. Thickness t

Fig. 2 [Fe(tFe)/Ti(tTi)]n (tFe total ¼ 1000 Å). Saturation magnetization 4πMs vs. Fe thickness tFe for SiO2/[Fe(tFe)/Ti(tTi)]n (tFe total ¼ 1000 Å) multilayers (the first and last layers were Ti ones so that every Fe layer was sandwiched by Ti ones) with tTi ¼ 12, 23, 53, 106, 212 Å and Fe single layer, at room temperature [1: sp, 2: 25  C, 3: ---, 4: 2 mTorr (Ar), 5: VSM] [89ONN, Fig. 4-2]

Fig. 3 [Fe(tFe)/Ti(53 Å)]n (tFe total ¼ 1000 Å). Saturation magnetization 4πMs vs. Fe thickness tFe for SiO2/[Fe(tFe)/Ti(53 Å)]n (tFe total ¼ 1000 Å) multilayers (the first and last layers were Ti ones so that every Fe layer was sandwiched by Ti ones) as deposited, annealed at 220  C and 400  C for 1 h, measured at room temperature [1: sp, 2: 25  C, 3: ---, 4: 2 mTorr (Ar), 5: VSM] [89ONN, Fig. 5-2]

12

TiFe

Fig. 4 [Fe(tFe)/Ti(tTi)]n (ttotal ≈ 240 nm). Saturation magnetization μ0Ms vs. bilayer thickness λ for glass/[Fe(tFe)/Ti(tTi)]n (ttotal ≈ 240 nm) multilayers with tTi [nm]/tFe [nm] (¼β) ¼ 1.0 and 1.5 [1: rf sp, 2: ---, 3: 1  105 Pa, 4: 0.7 Pa (Ar), 5, VSM] [97KSC, Fig. 7-2]

Fig. 5 [Fe(~6 Å)/Ti(tTi)]n (n ¼ 400). Spontaneous magnetization Ms (open squares: lefts axis) and coercivity Hc (closed triangles: right axis) vs. Ti thickness tTi for [Fe(~6 Å)/Ti(tTi)]n (n ¼ 400) multilayers at RT. H || film plane [1: sp, 2: ---, 3: 107  108 Torr, 4: 105 (Kr), 5: VSM] [97SAS, Fig. 2]

Saturation Magnetization Ms vs. Thickness t

13

Fig. 6 [Fe(tFe)/Ti(~40 Å)]n (n  580). Spontaneous magnetization Ms (closed squares: left axis) and coercivity Hc (closed triangles: right axis) vs. Fe thickness tFe for [Fe(tFe)/Ti(~40 Å)]n (n  580) multilayers, measured at room temperature. H || film plane [1: sp, 2: ---, 3: 107  108 Torr, 4: 105 (Kr), 5: VSM] [97SAS, Fig. 5]

Fig. 7 [Fe(tFe)/Ti(1 nm)]n (n ¼ 10  120). Fe layers magnetization multiplied by bilayer thickness MFeλ vs. Fe thickness tFe for glass/[Fe(tFe)/Ti(1 nm)]n/Ti(10 nm) (n ¼ 10  120) multilayers (see Table 2.1 [98FJT, Table 2] for the structure, Ms and MFe of each multilayer), measured at T ¼ 300 K, where MFe ¼ MFeλ/tFe. H || film plane, H ⊥ film plane[1: rf sp, 2: 300 K, 3: ---, 4: ---, 5: VSM] [98FJT, Fig. 6]

14

TiFe

Fig. 8 (a) [Fe(tFe)/Ti(9.4 nm)]n. (b) [Fe(2.8 nm)/Ti(tTi)]n. (a) Magnetic moment pFe vs. Fe thickness tFe for glass/[Fe(tFe)/Ti(9.4 nm)]n multilayers (see Table 2.2 [98ZPL, Table 1] for bilayer number n), measured at room temperature. The dotted line shows that pFe (bulk α-Fe) ¼ 2.15 μB. (b) Magnetic moment pFe vs. Ti thickness tTi for glass/[Fe(2.8 nm)/Ti(tTi)]n multilayers measured at room temperature [1: EBE, 2: ---, 3: ---, 4: 2  104 Pa, 5: VSM] [98ZPL, Fig. 6]

Table 1 [Fe(tFe)/Ti(1 nm)]n. Magnetic data for glass/[Fe(tFe)/Ti(1 nm)]n/Ti(10 nm) multilayers at T ¼ 300 K. Ms is the saturation magnetization and MFe the Fe magnetization, where MFe ¼ Msλ/tFe with λ to be the bilayer thickness [1: rf sp, 2: 300 K, 3: ---, 4: ---, 5: VSM] [98FJT, Table 2] tTi [nm] 1 1 1 1 1 1

tFe [nm] 1 2 3 3 4 6

N 120 60 40 30 30 20

Ms [T] 0.207 0.565 0.502 0.693 0.804 0.894

MFe [T] 0.415 0.850 0.697 0.922 1.005 1.041

Saturation Magnetization Ms vs. Annealing Temperature Tann

15

Table 2 [Fe(tFe)/Ti(tti)]n. Magnetic moment per Fe atom pFe for glass/[Fe(tFe)/Ti(tti)]n multilayers at room temperature [1: EBE, 2: ---, 3: ---, 4: 2  104 Pa, 5: VSM] [98ZPL, Table 1] Multilayer [Fe(1.1 nm)/Ti(9.4 nm)]19 [Fe(2.8 nm)/Ti(9.4 nm)]14 [Fe(3.7 nm)/Ti(9.4 nm)]15 [Fe(6.6 nm)/Ti(9.4 nm)]13 [Fe(11.4 nm)/Ti(9.4 nm)]11 [Fe(2.8 nm)/Ti(1.5 nm)]40 [Fe(2.8 nm)/Ti(2.8 nm)]30 [Fe(2.8 nm)/Ti(4.1 nm)]24 [Fe(2.8 nm)/Ti(7.0 nm)]18

pFe [μB] 0.05 1.42 1.61 1.81 1.78 1.63 1.35 1.31 1.50

See also Figs. 2.17 and 2.18.

Saturation Magnetization Ms vs. Annealing Temperature Tann

Fig. 9 [Fe(52 Å)/Ti(53 Å)]n (tFe total ¼ 1000 Å). Saturation magnetization 4πMs (open circles: left axis) and coercivity Hc (open triangles: right axis) vs. annealing temperature Tann for 1 h for SiO2/[Fe (52 Å)/Ti(53 Å)]n (tFe total ¼ 1000 Å) multilayer (the first and last layers were Ti ones so that every Fe layer was sandwiched by Ti ones), measured at room temperature [1: sp, 2: 25  C, 3: ---, 4: 2 mTorr (Ar), 5: VSM] [89ONN, Fig. 6-2]

See also Fig. 2.19.

16

TiFe

Anisotropy Field HA vs. Thickness t Table 3 [Fe(tFe)/Ti(1 nm)]n. Anisotropy field μ0HA for glass/[Fe(tFe)/Ti(1 nm)]n/Ti(10 nm) multilayers at T ¼ 300 K [1: rf sp, 2: 300 K, 3: ---, 4: ---, 5: VSM] [98FJT, Table 2] tTi [nm] 1 1 1 1 1 1

tFe [nm] 1 2 3 3 4 6

n 120 60 40 30 30 20

μ0HA [T] 0.45 1.25 1.25 1.40 1.65 1.65

Effective Anisotropy Constant Keff vs. Thickness t

Fig. 10 [Fe(tFe)/Ti(1 nm)]n (n ¼ 10  120). Effective anisotropy constant multiplied by Fe thickness KefftFe vs. tFe for glass/[Fe(tFe)/Ti(1 nm)]n/Ti(10 nm) (n ¼ 10  120) multilayers at T ¼ 300 K (see Table 2.3 [98FJT, Table 2] for the structure of each multilayer). The effective anisotropy constant Keff was evaluated by Keff ¼ KA  MFe2/2 μ0, where KA ¼ (μ0HAMFe)/2 (see Table 2.3 [98FJT, Table 2] for the values of μ0HA). The phenomenological relationship between the interface (Ks), volume (Kv), and the effective (Keff) anisotropy constants is usually given as KefftFe ¼ 2Ks + KvtFe. From the plot in the figure, it comes out that the interfacial perpendicular (the positive value) magnetic anisotropy constant Ks ¼ 0.11 mJ/m2 and the volume contribution Kv ¼ 0.28 mJ/m3. H || film plane, H ⊥ film plane [1: rf sp, 2: 300 K, 3: ---, 4: ---, 5: VSM] [98FJT, Fig. 7]

Coercivity Hc vs. Thickness t

17

Coercivity Hc vs. Thickness t

Fig. 11 [Fe(tFe)/Ti(tTi)]n (tFe total ¼ 1000 Å). Coercivity Hc vs. Fe thickness tFe for SiO2/[Fe(tFe)/Ti (tTi)]n (tFe total ¼ 1000 Å) multilayers (the first and last layers were Ti ones so that every Fe layer was sandwiched by Ti ones) with tTi ¼ 12, 23, 53, 106, 212 Å and Fe single layer, measured at room temperature [1: sp, 2: 25  C, 3: ---, 4: 2 mTorr (Ar), 5: VSM] [89ONN, Fig. 4-1]

18

TiFe

Fig. 12 [Fe(tFe)/Ti(53 Å)]n (tFe total ¼ 1000 Å). Coercivity Hc vs. Fe thickness tFe for SiO2/[Fe(tFe)/ Ti(53 Å)]n (tFe total ¼ 1000 Å) multilayers (the first and last layers were Ti ones so that every Fe layer was sandwiched by Ti ones) as deposited, annealed at Tann ¼ 200  C and 400  C for 1 h, measured at room temperature [1: sp, 2: 25  C, 3: ---, 4: 2 mTorr (Ar), 5: VSM] [89ONN, Fig. 5-1]

Coercivity Hc vs. Thickness t

19

Fig. 13 [Fe(tFe)/Ti(53 Å)]n (tFe total ¼ 1000 Å*). Coercivity Hc vs. Fe thickness tFe for SiO2*/[Fe (tFe)/Ti(53 Å)]n (tFe total ¼ 1000 Å*) multilayers deposited at Ts ¼ 25, 200 and 400  C, measured at room temperature*. *[89ONN] [1: sp, 2: 25  400  C, 3: ---, 4: 2 mTorr (Ar), 5: VSM] [91NN(1), Fig. 1-1]

20

TiFe

Fig. 14 [Fe(tFe)/Ti(50 Å)]n (tFe total ¼ 1000 Å*). Coercivity Hc vs. Fe thickness tFe for SiO2*/[Fe (tFe)/Ti(50 Å)]n (tFe total ¼ 1000 Å*) multilayers T ¼ 25  C *. *[89ONN] [1: sp, 2: 25  C, 3: ---, 4: 2 mTorr (Ar), 5: VSM] [91NN(1), Fig. 3; 91NN(1), Fig. 6]

Fig. 15 [Fe(tFe)/Ti(tTi)]n (ttotal ≈ 240 nm*). (a) Coercivity Hc vs. Fe thickness tFe for glass/[Fe(tFe)/ Ti(tTi)]n (ttotal ≈ 240 nm*) multilayers with tFe [nm]/tTi [nm] (¼β) ¼ 1.0 and 0.67. (b) Coercivity Hc vs. Fe average grain size DFe for glass/[Fe(tFe)/Ti(tTi)]n (ttotal ≈ 240 nm*) multilayers with tFe [nm]/tTi [nm] (¼β) ¼ 1.0 (tFe ¼ 2.5  40 nm*) and 0.67 (tFe ¼ 2  32 nm*). *[97KSC] [1: rf sp, 2: ---, 3: 1  105 Pa*, 4: 0.7 Pa* (Ar), 5, VSM*], *[97KSC] [96CSK(1), Fig. 3]

Coercivity Hc vs. Thickness t

21

Fig. 16 [Fe(tFe)/Ti(tTi)]n (ttotal ≈ 240 nm). (a) Coercivity Hc vs. bilayer thickness λ for glass/[Fe (tFe)/Ti(tTi)]n (ttotal ≈ 240 nm) multilayers with tTi [nm]/ tFe [nm] (¼β) ¼ 1.0 and 1.5. (b) Coercivity Hc vs. Fe grain size DFe for glass/[Fe(tFe)/Ti(tTi)]n (ttotal ≈ 240 nm) multilayers with tFe [nm]/tTi [nm] (¼β) ¼ 1.0 (tFe ¼ 2.5  40 nm) and 0.67 (tFe ¼ 2  32 nm) [1: rf sp, 2: ---, 3: 1  105 Pa, 4: 0.7 Pa (Ar), 5, VSM] [97KSC, Fig. 7-1]

22

TiFe

Fig. 17 [Fe(~6 Å)/Ti(tTi)]n (n ¼ 400). Coercivity Hc (closed triangles: left axis) and saturation magnetization Ms (open squares: right axis) vs. Ti thickness tTi for [Fe(~6 Å)/Ti(tTi)]n (n ¼ 400) multilayers at RT. H || film plane [1: sp, 2: ---, 3: 107  108 Torr, 4: 105 (Kr), 5: VSM] [97SAS, Fig. 2-1]

Fig. 18 [Fe(tFe)/Ti(~40 Å)]n (n  580). Coercivity Hc (closed triangles: left axis) and spontaneous magnetization Ms (closed squares: right axis) vs. Ti thickness tTi for [Fe(tFe)/Ti(~40 Å)]n (n  580) multilayers at room temperature. H || film plane[1: sp, 2: ---, 3: 107  108 Torr, 4: 105 (Kr), 5: VSM] [97SAS, Fig. 5-1]

Table 4 [Fe(tFe)/Ti(1 nm)]n. Coercivity μ0Hc for glass/[Fe(tFe)/Ti(1 nm)]n/Ti(10 nm) multilayers at T ¼ 300 K [1: rf sp, 2: 300 K, 3: ---, 4: ---, 5: VSM] [98FJT, Table 2] tTi [nm] 1 1 1 1 1 1

tFe [nm] 1 2 3 3 4 6

n 120 60 40 30 30 20

μ0Hc [mT] 1.7 6.7 5.1 4.8 4.7 5.4

Coercivity Hc vs. Annealing Temperature Tann

23

Table 5 [Fe(tFe)/Ti(tti)]n. Coercivity Hc for glass/[Fe(tFe)/Ti(tti)]n multilayers at room temperature [1: EBE, 2: ---, 3: ---, 4: 2  104 Pa, 5: VSM] [98ZPL, Table 1] Multilayer [Fe(1.1 nm)/Ti(9.4 nm)]19 [Fe(2.8 nm)/Ti(9.4 nm)]14 [Fe(3.7 nm)/Ti(9.4 nm)]15 [Fe(6.6 nm)/Ti(9.4 nm)]13 [Fe(11.4 nm)/Ti(9.4 nm)]11 [Fe(2.8 nm)/Ti(1.5 nm)]40 [Fe(2.8 nm)/Ti(2.8 nm)]30 [Fe(2.8 nm)/Ti(4.1 nm)]24 [Fe(2.8 nm)/Ti(7.0 nm)]18

Hc [Oe] – 16 19 9 15 5 12 24 32

See also Figs. 2.5 and 2.6.

Coercivity Hc vs. Annealing Temperature Tann

Fig. 19 [Fe(52 Å)/Ti(53 Å)]n (tFe total ¼ 1000 Å). Coercivity Hc (open triangles: left axis) and saturation magnetization 4πMs (open circles: right axis) vs. annealing temperature Tann for 1 h for SiO2/[Fe(52 Å)/Ti(53 Å)]n (tFe total ¼ 1000 Å) multilayer (the first and last layers were Ti ones so that every Fe layer was sandwiched by Ti ones), measured at room temperature [1: sp, 2: 25  C, 3: ---, 4: 2 mTorr (Ar), 5: VSM] [89ONN, Fig. 6-1]

See also Fig. 2.9.

24

TiFe

Saturation Field Hs vs. Thickness t

Fig. 20 (a) [Ti(20 nm)/Fe(tFe)/Ti(20 nm)]. (b) [Ti(tTi)/Fe(20 nm)/Ti(tTi)]. (c) [Fe(2.5 nm)/Ti(tTi)/Fe (2.5 nm)]. (d) [Fe(tFe)/Ti(tTi)/Fe(tFe)] (tFe ¼ 5, 10 nm). (a) Saturation field Hs vs. Fe thickness tFe for [Ti(20 nm)/Fe(tFe)/Ti(20 nm)]/carbon(10 nm) trilayers at room temperature under H || film plane. (b) Saturation field Hs vs. Ti thickness tTi for [Ti(tTi)/Fe(20 nm)/Ti(tTi)]/carbon(10 nm) trilayers at room temperature under H || film plane. (c) Saturation field Hs vs. Ti thickness tTi for [Fe(2.5 nm)/Ti(tTi)/ Fe(2.5 nm)]/carbon(10 nm) trilayers at room temperature under H || film plane. (d) Saturation field Hs vs. Ti thickness tti for [Fe(tFe)/Ti(tTi)/Fe(tFe)]/carbon (10 nm) (tFe ¼ 5 nm, tFe ¼ 10 nm) trilayers at room temperature under H || film plane [1: sp, 2: ---, 3: 109 Torr, 4: ~104 Torr (Ar), 5: Kerr effect] [00SKK(2), Fig. 1]

Resistivity R vs. Thickness t

25

Resistivity R vs. Thickness t

Fig. 21 [Fe(tFe)/Ti(tTi)]n (ttotal ≈ 240 nm). Electrical conductivity σ vs. inverse bilayer thickness 1/λ for glass/[Fe(tFe)/Ti(tTi)]n (ttotal ≈ 240 nm) multilayers with tTi [nm] /tFe [nm] (¼β) ¼ 1.0 and 1.5 at room temperature. The curves are according to the equation as follows: σ ¼ σλam  6Z Fe ð0Þ þ FFe ½tFe  2Z Fe ð0Þ þ FTi ½tTi  4Z Fe ð0Þ , where ZFe(0) ¼ 1 nm is the initial thickness of the crystalline Fe sublayer which was reduced by the thickness of the amorphous interface sublayer. Fi ¼ [Ri + 1 + fi(1  Ri)]/[Ri + 1  fi(1  Ri)] is the crystalline distribution function where grains are in the form of very thin cylinders (two-dimension model) in sublayer i (i ¼ Fe, Ti), Ri ¼ ρi/ρam (ρam ¼ 200 μΩcm, ρTi ¼ 130 μΩcm, ρFe ¼ 30 μΩcm), and fi(λ) ¼ Vi(C)/Vi(tot) (determined from XRD and CEMS measurements) is the relative amount of crystalline phase in the crystalline sublayer i. If fi ¼ 0, then σ ¼ σ am; if 1/λ ! 0 and fi ¼ 1, then the above equation transforms into one for a parallel connection of resistances and σ ¼ (βσ Fe + σ Ti)/(1 + β). The solid and dashed lines, calculated by using the above equation, for β ¼ 1.0 and 0.67, respectively, show good agreement with σ measured for λ  40 nm [1: rf sp, 2: ---, 3: 1  105 Pa, 4: 0.7 Pa (Ar), 5: ---] [96CSK(1), Fig. 4; 97KSC, Fig. 9; 98SCK, Fig. 2]

26

TiFe

Magnetoresistane MR vs. Thickness t

Fig. 22 [Fe(tFe)/Ti(tTi)]n (ttotal ≈ 240 nm). Saturation magnetoresistance MRs vs. bilayer thickness λ for glass/[Fe(tFe)/Ti(tTi)]n (ttotal ≈ 240 nm) multilayers at room temperature with tTi [nm]/t Fe [nm] (¼β) ¼ 1.0 and 1.5 [1: rf sp, 2: ---, 3: 1  105 Pa, 4: 0.7 Pa (Ar), 5: ---] [97KSC, Fig. 8]

Fig. 23 [Fe(tFe)/Ti(tTi)]n (ttotal ≈ 240 nm*). Saturation magnetoresistance MRs vs. Fe thickness tFe for glass/[Fe(tFe)/Ti(tTi)]n (ttotal ≈ 240 nm*) multilayers with tFe [nm]/tTi [nm] (¼β) ¼ 1.0 and 0.67 at room temperature. H || film plane, I || film plane, H⊥I. *[97KSC] [1: rf sp, 2: ---, 3: 1  105 Pa*, 4: 0.7 Pa* (Ar), 5: ---], *[97KSC] [98SCK, Fig. 3]

Symbols and Abbreviations

27

Hall Coefficient RH and Hall Resistivity rH vs. Thickness t

Fig. 24 [Fe(tFe)/Ti(tTi)]n (ttotal ≈ 240 nm*). Anomalous Hall constant RH vs. Fe thickness tFe for glass/[Fe(tFe)/Ti(tTi)]n (ttotal ≈ 240 nm*) multilayers with tFe [nm]/tTi [nm] (¼β) ¼ 1.0 and 0.67 at room temperature. The lines are a guide for the eye. *[97KSC] [1: rf sp, 2: ---, 3: 1  105 Pa*, 4: 0.7 Pa* (Ar), 5: ---], *[97KSC] [98SCK, Fig. 4]

Symbols and Abbreviations Short form M H Ms t μ0Ms λ Hc p Tann HA Keff K K⊥ Ks σ

Full form magnetization magnetic field saturation magnetization thickness saturation magnetization bilayer thickness coercivity magnetic moment (per atom) annealing temperature anisotropy field effective anisotropy constant anisotropy constant (per atom) perpendicular anisotropy constant surface anisotropy constant electrical conductivity (continued)

28 MR MRs RH rH

TiFe magnetoresistance saturation magnetoresistance Hall coefficient Hall resistivity

References [85BPT] Brenier, R., Perez, A., Thevenard, P., Treilleux, M., Capra, T.: Mater. Sci. Eng. 69 (1985) 83 [86HNM(1)] Hirvonen, J.P., Nastasi, M., Mayer, J.W.: Appl. Phys. Lett. 49 (1986) 1345 [86HNM(2)] Hirvonen, J.P., Nastasi, M., Mayer, J.W.: J. Appl. Phys. 60 (1986) 980 [89ONN] Ono S., Nitta M., Naoe M.: IEEE Trans. Magn. 25 (1989) 3872 [90BR] Bourret A., Rouviere J.L.: Philos. Mag. B 62 (1990) 415 [90RHL] Rodmacq B., Hillairet J., Laugier J., Chamberod A.: J. Phys.: Condens. Matter 2(1990) 95 [91ESJ] Eymery, J., Senillou, C., Joud, J.C., Chamberod, A.: Appl. Surf. Sci. 47 (1991) 127 [91NN(1)] Nakagawa, S., Naoe, M.: J. Appl. Phys. 70 (1991) 6424 [92BZC(1)] Bai, H.Y., Zhang, Y., Chen, H., Wang, W.K.: Chin. Sci. Bull. 37 (1992) 1342 [92BZC(2)] Bai, H.Y., Zhang, Y., Chen, H., Wang, W.K.: J. Mater. Sci. Lett. 11 (1992) 469 [92DDP] Dupuy, J.C., Dubois, C., Prudon, G., Brenier, R., Thevenard, P.: Nucl. Instrum. Methods Phys. Res. Sect. B 64 (1992) 636 [93BCZ] Bai, H.Y., Chen, H., Zhang, Y., Wang, W.K.: Phys. Status Solidi A 137 (1993) 125 [94RKJ] Reddy, B.V., Khanna, S.N., Jena, P., Press, M.R. Jaswal, S.S.: J. Magn. Magn. Mater. 130 (1994) 255 [95LJW] Liu, M.S., Jiang, E.Y., Wang, Z.J., Zhang, X.X., Liu, Y.G.: J. Magn. Magn. Mater. 140144 (1995) 537 [96CSK(1)] Czapkiewicz, M., Stobiecki, T., Kopcewicz, M.: J. Magn. Magn. Mater. 160 (1996) 357 [97KSC] Kopcewicz, M., Stoviecki, T., Czapkiewicz, M., Grabias, A.: J. Phys.: Condens. Matter 9 (1997) 103 [97SAS] Stetsenko, P.M., Antipov, S.D., Smirnitskaya, G.V., Kolumbaev, A.L., Goryunov, G.E.: JETP Lett. 65 (1997) 375 [98FJT] Fnidiki, A., Juraszek, J., Teillet, J., Duc, N.H., Danh, T.M., Kaabouchi, M., Sella, C.: J. Appl. Phys. 84 (1998) 3311 [98SCK] Stobiecki, T., Czapkiewicz, M., Kopcewicz, M., Zuberek, R., Castano, F.J.: Thin Solid Films 317 (1998) 306 [98ZPL] Zhang, M., Pan, F., Liu, B.X.: J. Magn. Magn. Mater. 182 (1998) 89 [99TO] Tanaka, K., Otsuka, M.: Int. J. Hydrog. Energy 24 (1999) 891 [00SKK(2)] Shalygina, E.E., Karsanova, M.A., Kozlovskii, L.V.: Tech. Phys. Lett. 26 (2000) 146 [00SS(3)] Shalyguina, E.E., Shin, K.H.: J. Magn. Magn. Mater. 220 (2000) 167 [01WW] Wang, W., Wen, L.S.: J. Mater. Sci. Technol. 17 (2001) 521

TiCo

Magnetization M vs. Magnetic Field H

Fig. 1 [Ti(52 Å)/Co(82 Å)]50. Magnetic hysteresis loops for sapphire/[Ti(52 Å)/Co(82 Å)]50 multilayer at room temperature. —: H || film plane and ---: H ⊥ film plane [1: dc sp, 2: ---, 3: ≈1
107 Torr, 4: ≈7.5 mTorr (Ar), 5: VSM] [90VED, Fig. 2]

© The Editor(s) (if applicable) and The Author(s), under exclusive license to SpringerVerlag GmbH, DE, part of Springer Nature 2022 Y. Kawazoe, R. Note, Magnetic Properties of Metals: Magnetic and Electric Properties of Magnetic Metallic Multilayers, https://doi.org/10.1007/978-3-662-64909-1_4

29

30

TiCo

Fig. 2 [Co(34 Å)/Ti(66 Å)]15. (a) Magnetic hysteresis loops for NaCl/[Co(34 Å)/Ti(66 Å)]15 multilayers as deposited, measured at room temperature. H || film plane and H ⊥ film plane. (b) Enlarged figure of (a) under H || film plane [1: sp, 2: water cool (~30  C), 3: 2
104 Pa, 4: 0.4 Pa (Ar), 5: VSM] [97WJW(1), Fig. 5]

Magnetization M vs. Magnetic Field H

31

Fig. 3 (a) [Co(17 nm)/Ti wedge (1.25 nm)/Co(17 nm)], (b) [Co(17 nm)/Ti(2.3 nm)/Co(17 nm)]. (a) Relative magnetic hysteresis loop for glass/[Co(17 nm)/Ti wedge (1.25 nm; .a slope of 0.125 nm/mm)/Co(17 nm)] trilayer at room temperature. H || film plane. (b) Hysteresis loop for glass/[Co(17 nm)/Ti wedge (2.3 nm; a slope of 0.125 nm/mm)/Co(17 nm)] trilayer at room temperature. H || film plane [1: dc sp for Co, rf sp for Ti, 2: RT, 3: 5
1010 mbar, 4: ---, 5: MOKE] [99S(5), Fig. 3]

Fig. 4 [Co(2.2 nm)/Ti(2 nm)]n (tCo total ≈ 100 nm). Relative magnetic hysteresis loop for (Si(111) or glass)/[Co(2.2 nm)/Ti(2 nm)]n (tCo total ≈ 100 nm) multilayer at room temperature under H || film plane, showing the 90 interlayer (negative biquadratic) coupling [1: dc sp for Co, rf sp for Ti, 2: RT, 3: 5
1010 mbar, 4: ---, 5: MOKE] [99S(5), Fig. 5; 00SS(1), Fig. 1-2]

32

TiCo

Saturation Magnetization Ms vs. Thickness t

Fig. 5 [Ti(49  3 Å)/Co(tCo)]50. Saturation magnetization multiplied by bilayer thickness Msλ vs. Co thickness tCo for sapphire/[Ti(49  3 Å)/Co(tCo)]50 multilayers at room temperature. The solid line is a least-square fit through data from the five magnetic multilayers indicated by the solid circles. The multilayer shown by the open circle has a thinner Ti layer and was not included in the fit. The magnetization of the Ti/Co multilayers can be described by a simple model. Each Ti layer is nonmagnetic. Each Co layer of thickness tCo is divided into a nonmagnetic layer of thickness tnm at each Ti interface and a magnetic layer of thickness tm at the center of Co layer with in-plane magnetization. The magnetization of the multilayer Ms can be related to that of each Co layer MCo as follows: Msλ ¼ MCotm ¼ MCo(tCo  2tnm), where Ms is the in-plane saturation magnetization. From the linear regression fit to the data for tCo > 24 Å, it is obtained MCo ¼ 1480  100 G and tnm ¼ 11.3  1.3 Å. This value of MCo was determined relative to the magnetic moment measured for pure Co films with thicknesses of 960 Å and 1400 Å. H || film plane [1: dc sp, 2: ---, 3: ≈1
107 Torr, 4: ≈7.5 mTorr (Ar), 5: VSM] [90VED, Fig. 3]

Saturation Magnetization Ms vs. Thickness t

33

Fig. 6 [Co(tCo)/Ti(23  2 Å)]30. Saturation magnetization multiplied by Co thickness MstCo vs. tCo for glass/Ti(50 Å)/[Co(tCo)/Ti(23  2 Å)]30 multilayers at room temperature. The magnetization of the multilayer Ms can be related to that of each Co layer MCo as follows: Ms ¼ MCo(1  2 t0/tCo), where Ms is the in-plane saturation magnetization and t0 is the dead layer thickness. From the linear regression fit to the data, it is obtained MCo ¼ 1398 G and t0 ≈ 5.5 Å [1: sp, 2: water cool, 3: ~2
105 Pa, 4: ~0.4 Pa (Ar), 5: VSM] [97WJB(1), Fig. 5; 97WJW(2), Fig. 4]

34

TiCo

Fig. 7 [Co(18  2 Å)/Ti(tTi)]30. Saturation magnetization Ms vs. Ti thickness tTi for glass/Ti(50 Å)/ [Co(18  2 Å)/Ti(tTi)]30 multilayers at room temperature. H || film plane [1: sp, 2: water cooling, 3: ~2
105 Pa, 4: ~0.4 Pa (Ar), 5: VSM] [97WJB(1), Fig. 6; 97WJW(2), Fig. 5]

Fig. 8 [Co(tCo)/Ti(2 nm)]n (tCo total≈100 nm). Saturation magnetization Ms multiplied by Co thickness tCo relative to magnetization of pure 100 nm Co (M100), (MstCo)/M100, vs. tCo for (Si (111) or glass)/[Co(tCo)/Ti(2 nm)]n (tCo total ≈100 nm) multilayers at room temperature. From linear fit, the magnetization Ms can be written as Ms/M100 ¼ (tCo  2tnm)/tCo. The effective non-magnetic Co layer thickness at the Co/Ti interface, tnm, is estimated to be tnm ≈ 0.5 nm [1: dc sp for Co, rf sp for Ti, 2: RT, 3: 5
1010 mbar, 4: ---, 5: VSM, MOKE] [99S(5), Fig. 2-2]

Anisotropy Field HA vs. Thickness t

35

Anisotropy Field HA vs. Thickness t

Fig. 9 [Ti(49  3 Å)/Co(tCo)]50. Magnetic anisotropy field HA vs. inverse magnetic Co thickness 1/tCo for sapphire/[Ti(49  3 Å)/Co(tCo)]50 multilayers at room temperature. See Fig. 5 [90VED, Fig. 3] for the definition of tm (thickness of magnetic layer). The uniaxial anisotropy coefficient Ku of a multilayer can be modeled using the equation Ku ¼ [(2πMCo2  Kv)tm  2Ks]/λ, where 2πMCo2 is the shape anisotropy of the Co, Kv is the volume anisotropy constant due to the magnetocrystalline and magnetoelastic effects, and Ks is the interface anisotropy constant. In this sign convention, positive anisotropy constants are due to perpendicular anisotropy while negative anisotropy constants are due to in-plane anisotropy. Using the above equation and the equation in Fig. 5 [90VED, Fig. 3], the anisotropy field HA ¼ 2Ku/Ms can be written as HA ¼ 2Kv/MCo + 4πMCo – (4Ks/MCo)tm. HA was determined from the hysteresis data by linear extrapolation of the perpendicular loop to its intersection with the saturated value of the in-plane loop (see Fig. 1 [90VED, Fig. 2]). Ks ¼ 0.23  0.04 erg/cm2 and Kv ¼ (3.5  0.8)
106 erg/cm3 using the MCo ¼ 1480  100 G (see Fig. 5 [90VED, Fig. 3]) [1: dc sp, 2: ---, 3: ≈1
107 Torr, 4: ≈7.5 mTorr (Ar), 5: VSM] [90VED, Fig. 4]

36

TiCo

Coercivity Hc vs. Thickness t

Fig. 10 (a) [Co wedge (tCo)/Ti(tTi)]n (tTi ¼ 2, 3 nm, ttotal < 70 nm), (b) [Co wedge (tCo)/Ti(2 nm)]n (ttotal < 70 nm). (a) Coercivity Hc vs. Co thickness tCo for glass/[Co wedge (tCo)/Ti(tTi)]n (tTi ¼ 2, 3 nm, ttotal < 70 nm) multilayers as deposited, measured at room temperature. tTi ¼ 2 nm and tTi ¼ 3 nm. (b) Hc vs. tCo for glass/[Co wedge (tCo)/Ti(2 nm)]n (ttotal < 70 nm) multilayers as deposited, annealed at Tann ¼ 423, 473, 523 and 573 K for 1 h, measured at room temperature [1:dc sp, 2: ---, 3: ---, 4: ---, 5: magnetooptical Faraday hysteresisograph] [96CDG, Fig. 1]

Coercivity Hc vs. Thickness t

37

Fig. 11 [Co wedge (tCo)/Ti(2 nm)]n (tCo total ≈ 100 nm). Coercivity Hc vs. Co thickness tCo for (Si (111) or glass)/[Co wedge (tCo)/Ti(2 nm)]n (tCo total ≈ 100 nm) multilayers, determined from hysteresis loops at room temperature under H || film plane. A significant drop of the coercivity -typically from Hc ~ 1.8 to Hc ~ 0.2 kA/m – can be observed at a critical Co thickness tcrit ~ 3 nm [1: dc sp for Co, rf sp for Ti, 2: RT, 3: 5
1010 mbar, 4: ---, 5: VSM, MOKE] [99S(5), Fig. 1; 00SS (1), Fig. 1-1]

Fig. 12 [Co(17 nm)/Ti wedge (tTi)/Co(17 nm)]. Coercivity Hc vs. Ti thickness tTi for glass/[Co (17 nm)/ Ti wedge (tTi with a slope of 0.125 nm/mm)/Co(17 nm)] trilayers at room temperature. H || film plane. It is observed two different coercivities Hc1 and Hc2 for the trilayers with tCo > ~1.9 nm (see Fig. 3 [99S(5), Fig. 3] for the hysteresis loops) [1: dc sp for Co, rf sp for Ti, 2: RT, 3: 5
1010 mbar, 4: ---, 5: MOKE] [99S(5), Fig. 4; 02S(1), Fig. 2-1]

38

TiCo

Fig. 13 [Co wedge (tCo: slope 0.05–0.125 nm/mm)/Ti(tTi)]n (ttotal ≈ 50 nm). Coercivity Hc vs. Co thickness tCo for SiO2(101)/[Co wedge (tCo: slope 0.05–0.125 nm/mm)/Ti(tTi)]n (tTi ¼ 2, 3 nm, ttotal ≈ 50 nm) multilayers at room temperature. H || film plane. tTi ¼ 2 nm and tTi ¼ 3 nm [1: dc sp for Co, rf sp for Ti, 2: RT, 3: 5
1010 mbar, 4: ---, 5: MOKE] [00SSN, Fig. 1]

Fig. 14 [Co wegde (tCo)/Ti(tTi)]10. Coercivity Hc vs. Co thickness tCo for SiO2(101)/[Co wegde (tCo: slope 0.05–0.125 nm/mm)/Ti(tTi)]10 (tTi ¼ 2, 5 nm) multilayers at room temperature. H || film plane. tTi ¼ 2 nm and 5 nm. A significant drop of the coercivity with decrease in Co thickness -from Hc ~ 1.8–2.1 kA/m to Hc ~ 0.1–0.2 kA/m -- can be observed at a critical Co thickness tcrit ~ 3 nm for tTi ¼ 2 nm and 3.3 nm for tTi ¼ 5 nm. For the Co/Ti multilayers with polycrystalline Co sublayers (tCo > tcrit ~ 3 nm), a small in-plane, highly dispersed uniaxial anisotropy (HA ~ 1–2 kA/m) was observed. The multilayers with nanocrystalline Co sublayers (tCo < tcrit) showed a well-defined in-plane uniaxial anisotropy (HA ~ 2–4 kA/m) [1: dc sp for Co, rf sp for Ti, 2: RT, 3: