Ferromagnetic Shape Memory Alloys [1 ed.] 9783038132141, 9780878493708

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Ferromagnetic Shape Memory Alloys

Ferromagnetic Shape Memory Alloys Selected, peer reviewed papers from the International Conference on Ferromagnetic Shape Memory Alloys, held at S.N.Bose National Centre for Basic Sciences, Kolkata, India, November 14-16, 2007

Editor

Lluís Mañosa Convenors

P.K. Mukhopadhyay and S.R. Barman

TRANS TECH PUBLICATIONS LTD Switzerland • UK • USA

Copyright  2008 Trans Tech Publications Ltd, Switzerland All rights reserved. No part of the contents of this book may be reproduced or transmitted in any form or by any means without the written permission of the publisher. Trans Tech Publications Ltd Laubisrutistr. 24 CH-8712 Stafa-Zurich Switzerland http://www.ttp.net Volume 52 of Advanced Materials Research ISSN 1022-6680 Full text available online at http://www.scientific.net

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Editor’s Note

This volume contains the Proceedings of the International Conference on Ferromagnetic Shape Memory Alloys (FSMA2007) held in Kolkata, India, on 14-16 November, 2007. The Proceedings contain 27 papers pertaining to both oral (invited) and poster contributions to FSMA2007. The papers have been grouped in the following 6 sections according to the main topic covered by the manuscripts: Sample Preparation, Thermal Treatments and Phase Stability, Magnetic and Structural Characterization, Microscopic Studies of Magnetic Shape Memory Alloys, Effects of External Fields and Coupled effects: Magnetoresistance and Magnetocaloric effects. All papers were peer reviewed. The Editorial Committee selected the referees among reputed experts in the community of shape memory alloys. On behalf of the Editorial Committee, I would like to express my gratitude to all the authors and reviewers.

Lluís Mañosa Chairman, Editorial Committee FSMA2007

List of Sponsors Governmental: S.N.Bose National Centre for Basic Sciences, Kolkata Department of Science and Technology, New Delhi Council of Scientific and Industrial Research, New Delhi Defence Metallurgical Research Laboratory, Hyderabad

Commercial Sector: Icon Analytical Equipment Pvt. Ltd., Kolkata Vico Scientific Sales Pvt. Ltd., New Delhi Specialise Instruments Marketing Company, Mumbai Aimil Ltd., Kolkata Stirling Cryogenics India Pvt. Ltd., New Delhi Con-Serv Enterprises, Mumbai

Committees International advisory committee G.H.Wu, PRC T.Lograsso, USA L.Mañosa, Spain V.Chernenko, Ukraine A.Planes, Spain L.Schultz, Germany National organizing committee P.K.Mukhopadhyay, Jt. Convenor, SNBNCBS, Kolkata S.R.Barman, Jt. Convenor, CSR Indore centre, Indore A.Srinivasan, IIT/G, Guwahati D.Pandey, BHU, Banaras S.N.Kaul, Central University, Hyderabad P.Chaddah, CSR Indore centre, Indore A.Mitra, NML, Jamshedpur A.Basumallik, BESU, Shibpur R.Gopalan, DMRL, Hyderabad Local organizing committee P.K.Mukhopadhyay, SNBNCBS D.Das, CSR Kolkata Centre R.Chaudhury, SNBNCBS B.Rajini Kanth, SNBNCBS SNBNCBS: S.N.Bose National Centre for Basic Sciences, Kolkata, India CSR: UGC DAE Centre for Scientific Research, India NML: National Metallurgical Laboratory, Jamshedpur, India BHU: Banaras Hindu University, Banaras, India BESU: Bengal Engineering and Science University, Shibpur, India DMRL: Defence Metallurgical Research Laboratory, India IIT/G: IIT Guwahati, India

Preface In the quest for engineering better or more versatile materials, one encounters a unique class of materials, called shape memory alloys (SMA). These have a special property that allows them to retain memory of their shapes under certain external conditions – and regain their original shape on their own even if they are beaten out of their shapes, if their original external conditions are restored. That is why they are called smart materials too. They also have another interesting property called super-elasticity. These unique properties have been exploited in some recent commercial and military applications. Advent of ferromagnetic shape memory alloys (FSMA) about a decade ago is an important milestone in the development of shape memory alloys. FSMA provide an additional handle in the property manipulations possible in SMA. Furthermore, the response times of these materials are much shorter than the conventional SMA. These alloys are also known to possess enhanced magneto caloric properties, which has many potential applications. Finally, huge amounts of magnetostriction can be achieved in FSMA, which is much more than known in electrostrictive materials. These properties place FSMA as potential next generation smart materials. Realizing their importance in the cutting edge technology of tomorrow, scientists all over the world are working on FSMA to understand their basic physical nature and to develop new materials with tailored properties. In addition, people are working on thin films and composite materials of these systems in order to full unravel their device potential. In India, there are now some groups that have started working on these systems in recent times. Not only are they actively working on the Ni2MnGa systems and their derivatives (the most well studied material at present) they are also working on many similar systems. The geographical distribution is also interesting. We seem to have more representatives from the East (including North East), West and South than from the North. Apart from the diversity of sample systems, there is also a variety of experimental methods that are used. In spite of these well directed efforts, these are mainly confined to an individual scale. There is not much coordination among the workers, and except for a few personal contacts and familiarity through publications in the literature, there is hardly any mission-type coordination among the various groups. So, we conceived the idea of organising a conference on FSMA sometime during the end of 2006, to provide a forum to bring in all the scientists working in this topic together so that there is a sharing of thoughts and expertise. We also wanted to have scientists from abroad too, to listen to the pioneers on their own work. We hope that this conference will provide a road map for

future concrete cooperation among various groups in India, and even abroad. Last but not the least, we were pleasantly surprised to learn that this is the first international conference solely on this topic. We are very happy to say that the conference went on well on the appointed schedule, despite some natural and human disturbances. In all, we had about 50 participants from India and abroad, including students and young scientists. There were 21 oral and 20 poster presentations. Going by the remarks made by the participants in the concluding session of the conference, ICFSMA-2007 has achieved the primary goal of bringing in the researchers on FSMA together and to provide a forum to initiate future collaborations among the community. We would now thank all the participants for making it a success. We are especially grateful to people who had to find their own money to finance their travel to India or within India, since our conference budget was small. We took all the pains to arrange for local hospitality for all participants. The sponsors who chipped in with cash and kind are acknowledged in separate pages. We thank them again, for their support. Finally, our heartfelt thanks go to Prof. L. Mañosa who agreed to be the editor for this particular volume and undertook the arduous job of getting all these papers refereed in time. Last but not the least we would thank the Director of S.N. Bose National Centre for Basic Sciences, the host institute for extending us all the help to arrange the conference – especially with timely suggestions every now and then. Mr. T. Wohlbier, Vice President of M/s. Trans Tech Publication has taken personal interest in getting the proceedings published in the Advanced Material Research. But for his generosity, this special volume would not have seen the light since we had serious budget constraints. We hope this special edition will be beneficial for all our intended and even for a casually interested reader, Let the quest for developing materials for the benefit of mankind continue.,

P.K.Mukhopadhyay S.R.Barman (Jt. Convenors, ICFSMA 2007)

Table of Contents Editor Sponsors Committees Preface

Inaugural Talk Concepts and Physical Phenomena in Magnetic Shape Memory Science V.A. Chernenko

3

I. Sample Preparation Development of Ni-Mn-Ga Based Ferromagnetic Shape Memory Alloy by Rapid Solidification Technique A. Mitra and A.K. Panda Magneto-Mechanical Behaviour of Textured Polycrystals of NiMnGa Ferromagnetic Shape Memory Alloys S. Roth, U. Gaitzsch, M. Pötschke and L. Schultz Magnetization and Domain Patterns in Martensitic NiMnGa Films on Si(100) Wafer V.A. Chernenko, R. López Antón, S. Besseghini, J.M. Barandiarán, M. Ohtsuka, A. Gambardella and P. Müllner

17 29 35

II. Thermal Treatments and Phase Stability Intermartensitic Transformations in Ni-Mn-Ga Alloys: A General View C. Seguí, E. Cesari and J. Pons Martensite Transformation and Magnetic Property Dependence on the Annealing Temperature in Ni-Rich Ni-Mn-Ga Alloy R.K. Singh and R. Gopalan Influence of Annealing Temperature on the Properties of Co-Ni-Ga Ferromagnetic Shape Memory Alloy S. Sarma and A. Srinivasan Textural Ordering in NiTi, Ni-Fe-Ti, and Ni-Mn-Ga Shape Memory Alloys - Kinetics of Intra- and Inter-Domain Processes A.M. Awasthi, S. Bhardwaj, S. Banik and S.R. Barman Effect of Site Disorder on Martensitic Transformation in Ferromagnetic Ni55Fe20Al25 Alloy as Inferred from Magnetic and Magneto-Transport Measurements A.C. Abhyankar, B.A. D'Santhoshini, S.N. Kaul and A.K. Nigam

47 57 63 69 77

III. Magnetic and Structural Characterization Acoustic Energy Absorption in Ferromagnetic Ni-Mn-Ga Shape Memory Alloy Polymer Composites M. Mahendran, J. Feuchtwanger and R.C. O'Handley Co-Ni-Ga Alloys with Room Temperature Ferromagnetic Martensite Phase A. Srinivasan and S. Sarma Structural Characterization of Co70-xNixGa30 Ferromagnetic Shape Memory Alloys S. Sarma and A. Srinivasan Structural Studies on Mn Excess and Ga Deficient Ni-Mn-Ga S. Banik, P.K. Mukhopadhyay, A.M. Awasthi and S.R. Barman Mapping of Magnetic Domains by MFM in Ni2MnGa D. Jain, S. Banik, L.S. Sharath Chandra, S.R. Barman, R. Nath and V. Ganesan

87 95 103 109 115

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Ferromagnetic Shape Memory Alloys

Transformation Behavior of Ni-Mn-Ga Ferromagnetic Shape Memory Alloy K. Pushpanathan, R. Senthur Pandi, R. Chokkalingam and M. Mahendran Effect of Stress Relaxation on Quenched NiFeAl Ferromagnetic Shape Memory Alloy R.B. Kanth, P.K. Mukhopadhyay and S.N. Kaul Lattice Thermal Expansion of the Shape Memory Alloys Cu-Al-Ni, Cu-Al-Zn, Cu-Al-Be and Cu-Al-Pd S. Potharay Kuruvilla and C.S. Menon

121 129 135

IV. Microscopic Studies of Magnetic Shape Memory Alloys Magnetic Compton Scattering Study of Shape Memory Alloys B.L. Ahuja, V. Sharma and Y. Sakurai Hybridization Effects in Ni-Mn Based Shape Memory Alloys: XAFS Study K.R. Priolkar, P.A. Bhobe and P.R. Sarode Electronic and Structural Properties of Ferromagnetic Shape Memory Alloys Studied by Density Functional Theory A. Chakrabarti and S.R. Barman Signature of Austenitic to Martensitic Phase Transition in Ni2MnGa in Mn and Ni K-Edge XANES Spectra V.G. Sathe, S. Banik, A. Dubey, S.R. Barman, A.M. Awasthi and L. Olivi A Charge Compton Profile Study of Ni2MnGa: Theory and Experiment G. Ahmed, B.L. Ahuja, N.L. Heda, V. Sharma, A. Rathor, B.K. Sharma, M. Itou, Y. Sakurai and S. Banik

145 155 165 175 181

V. Effects of External Fields Effect of External Fields on the Martensitic Transformation in Ni-Mn Based Heusler Alloys X. Moya, L. Mañosa, A. Planes, S. Aksoy, M. Acet, E.F. Wassermann and T. Krenke Effect of Magnetic Field on Martensite to Intermediate Phase Transformation in Ni2MnGa T. Fukuda and T. Kakeshita

189 199

VI. Coupled Effects: Magnetoresistance and Magnetocaloric Effects Magneto-Transport and Magnetic Properties of Ni-Mn-Ga S. Banik, R. Rawat, P.K. Mukhopadhyay, B.L. Ahuja, A. Chakrabarti and S.R. Barman Magnetic Investigations on Ni-Mn-Sn Ferromagnetic Shape Memory Alloy S. Chatterjee, S. Giri, S.K. De and S. Majumdar Magnetocaloric and Shape-Memory Properties in Magnetic Heusler Alloys A. Planes, L. Mañosa, X. Moya, J. Marcos, M. Acet, T. Krenke, S. Aksoy and E.F. Wassermann

207 215 221

Inaugural Talk

Advanced Materials Research Vol. 52 (2008) pp 3-14 © (2008) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/AMR.52.3

Concepts and Physical Phenomena in Magnetic Shape Memory Science V. A. Chernenko1,2 1

Institute of Magnetism, Vernadsky str. 36-b, Kyiv 03142, Ukraine 2

CNR-IENI, C.Promessi Sposi, 29, Lecco 23900, Italy [email protected]

Keywords: Ferromagnetic shape memory effect, Ni-Mn-Ga alloys, martensitic transformation, twin rearrangement, magnetoelastic mechanism

Abstract. The magnetically weakly anisotropic cubic Ni-Mn-Ga Heusler alloys exhibit martensitic transformation resulting in martensitic phases with elastically soft crystal lattices and strong magnetocrystalline anisotropies. The magnetic state of these martensites is coupled with a highly mobile twin structure through the ordinary magnetoelastic interactions giving rise to a giant magnetic-field-induced-strain effect. This effect is the key ingredient of a new scientific field. In the present article, the basic phenomena and concepts of this field, such as lattice instability, soft-mode behavior, electron concentration, ferromagnetic shape memory effect, magnetic-field-induced superelasticity, twinning strain-induced change of magnetization, and magnetoelastic mechanism of magnetostress are briefly reviewed. Introduction It is well-known that some ferromagnetic metallic compounds, such as X2YZ Heusler compounds (X is 3d-metal, Y is usually Mn but could be some other 3d-metal or rare-earth element, Z is one of the elements from groups III or IV of the periodic table), the Fe3Pt and Fe-Pd alloys exhibit quite mobile twin interfaces in the martensitic phase. The crystallographic twinning structure is formed in these materials as a result of inherent lattice instability towards a thermoelastic martensitic transformation (MT). Alongside a conventional shape memory effect (SME) (e.g.,[1]), the ferromagnetic martensites in the aforementioned materials show a prominent feature: the ferromagnetic shape memory effect (FSME) (e.g., [2]). Whereas SME is due to the reverse MT and consists in a heat-activated shape recovery of a sample, which was previously mechanically deformed in the martensitic state, true FSME consists in a magnetic field-induced twin rearrangement in the martensitic phase, whereby a strain of the order of martensitic spontaneous distortion is reversibly generated depending on the mutual orientation of the magnetic field and the hard magnetic direction of the twin variant. The novel practical importance of both effects in a number of engineering applications is summarized, e.g., in Refs.[3,4]. The best-working Ni-Mn-Ga Heusler alloys [5], as prototypes of FSME materials, show recordbreaking magnetic field-induced strains (MFIS) of 5-10% [6-9]. These MFIS values correspond to the complete magnetic/mechanical stress-induced conversion of one crystallographic twin variant into the other, which is accompanied by a strain release almost equal to the spontaneous martensitic lattice distortion. In order to exhibit these effects on a macroscale, the FSME materials, such as the mentioned Ni-Mn-Ga alloys, must have particular physical properties as the necessary prerequisites. Then, the sufficient condition is deduced from the balance of these properties. Generally, it was suggested in Ref. [2] that any FSMA must be an easy-twinned and mechanically soft martensitic material with enhanced magnetoelastic interaction. In this context, the lattice instability, low-elastic shear modulus (~1 GPa) and low twinning stress (~1 MPa) of the high magnetostrictive crystal lattice (λ ~10-4) and high enough absolute value of magnetization are considered as the necessary prerequisites of a large MFIS. The sufficient condition of a large MFIS

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is the criterion by which magnetically-induced equivalent mechanical stress (magnetostress) must exceed the twinning stress [2,4]. The effect of giant MFIS (4% in a field of 10 T at 4.2 K) was first measured by using single crystals of Dy and Tb and explained by the magnetic field-induced mechanical twinning mechanism [10,11]. This effect gained a great deal of renewed interest after the discovery of Ni-Mn-Ga martensitic alloys [5] showing a giant magnetostriction (comparable to TERFENOL-D) at nearroom temperature [12]. Considering the burst of activity and publication records [2,4], the magnetic shape memory science may be counted as a well-established interdisciplinary research field in smart materials and solid state physics, which has been going on over last 10 years, while the elaboration of its basic knowledge started some 20 years before. Many aspects of the FSME/FSMA activity have been already brought to the light in a number of review articles [4,13-23] and recent Special Topic book [2]. The present paper highlights some phenomena related to the FSME science from the viewpoint of their conceptual treatment and underlying physics. The main phenomena/concepts in the FSME field such as lattice instability, soft-mode behavior, electron concentration, ferromagnetic shape memory effect, magnetostress, magnetomechanical mechanism, magnetomechanics in a rotating magnetic field, magnetic-field-induced superelasticity and twinning-strain-induced change of magnetization are briefly summarized using integral information on Ni-Mn-Ga FSMAs as a model alloy system. Lattice instability The phenomenon and concept of lattice instability plays a key role in the unusual and technologically important properties exhibited by Ni-Mn-Ga FSMAs. This instability implies a free energy surface with several shallow minimums corresponding to relatively stable phases, that allow the system to be easily transformed from one phase to another. The tendency of Ni atoms to occupy more stable natural FCC lattice positions is, probably, a source of the lattice instability of Ni-MnGa Heusler alloys, where Ni atoms, have instead a BCC-type environment [23]. This instability is mainly related to a (110)[1 1 0] uniform shear often accompanied by shuffling in the same system (e.g.,[24-29]). It belongs to a Zener-type instability typical of β-alloys ([27,30-32] and references therein) when a parent phase with BCC open lattice transforms during cooling into a lowersymmetry close-packed martensitic phase as a result of a spontaneous invariant-plane Bain deformation. In order to accommodate stresses due to the large Bain strains, secondary invariantlattice strains occur involving the same shear system, so that a twinned microstructure is formed. Different aspects of the lattice instability can be considered. Generally, one should distinguish between the instabilities in vibrational and electronic spectra although a strong connection between these two degrees of freedom exists in solids. Because of this, for instance, the electronic instabilities very often trigger structural transitions. The vibrational properties of Ni-Mn-Ga alloys have been a subject of intense examination since the very beginning of FSMA studies. Particularly, measurements of the temperature dependencies of elastic moduli (e.g., [28,33]) and phonon spectra (e.g. [26,34]) have revealed two types of instabilities of the initial cubic phase towards (i) soft-mode freezing resulting in the premartensitic phase and (ii) martensitic transformation. Additionally, some of these measurements demonstrated that ferromagnetic ordering in the cubic phase makes those instabilities more pronounced [28,34]. The premartensitic transition is caused by freezing of the soft 1/3[110]TA2-phonon. For pure a soft mode mechanism, Cochran’s theory yields ω 2 ∝ (T − TI ) , where ω is the frequency of the aforementioned phonon, and TI is the premartensitic transition temperature [35]. The softening of this mode in the cubic phase is accompanied by a lowering in the energy of the whole TA2 branch, which is a clear manifestation of the anharmonicity of vibrational modes [26,28,33-36]. The modulus stiffening in the premartensitic phase [28] does not prevent the crystal lattice to be

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globally unstable with respect to the mechanism of its uniform distortion at MT. Thus, the martensitic transformation cannot be directly controlled by the phonon mechanism of instability. Theoretical work revealed that a soft mode behavior is governed by electron-phonon coupling and Fermi surface nesting [37,38] alongside the essential contributions of ferromagnetic ordering [34,39] and possible interactions between optical and acoustic phonon branches [23,40]. The (110)[1 1 0] uniform shear accompanying the MT in Ni-Mn-Ga is characterized by a low restoring force, that is to say, the shear elastic modulus C′ is very small. Moreover, C′ has an abnormal temperature dependence on cooling in the cubic phase and reaches a minimum of a few GPa near MT [28,33]. A Landau-type thermodynamics provides C ' ∝ (T − Tt ) (Tt is a transition temperature) for the phase transitions close to second order [41], which has a broad implications for the thermoelastic MTs, e.g., in In-Tl or Ni-Mn-Ga [23,42-46]. Note that studies of the elastic and thermomechanical properties of Ni-Mn-Ga alloys show that the martensitic state is, in turn, unstable and can be represented, at least, by three different crystallographic structures which could exhibit mutual intermartensitic transformation(s) [46-49]. Experiment and ab-initio calculations evidence that the ground state belongs to a non-modulated tetragonal martensitic phase, 2M [23,49,50]. Electronic instabilities in the density of states and their influence on the structural and magnetic state of Ni-Mn-Ga alloys have been explored experimentally and theoretically in a number of publications ([23,51,52] and references therein). Particularly, some experimental findings about the electron concentration dependence of the properties and information about the density-of-states near the Fermi level are presented in the next section. What follows from this activity is that MT in Ni-Mn-Ga alloys is currently considered to be a result of a band Jahn-Teller effect [50,51]. The Jahn-Teller effect consists in the spontaneous distortion of a lattice into a lower symmetry configuration as a consequence of the electron-lattice coupling (e.g., [53]). This occurs when the total energy can be reduced by a distortion-induced split of the degenerate electronic levels. The value of distortion amplitude depends on both the nature of electronic states and the related loss of elastic energy. The occurrence of a Jahn-Teller distortion can be illustrated by the simple electronlattice Hamiltonian: H el − lat = aq + bq 2 , which comprises the linear and quadratic terms in the normal mode coordinate q describing lattice distortion. A decrease of the linear term competes with the quadratic increase due to ionic repulsion, which produces level splitting. This results in turn in a minimum of energy for the lower level at some q0 indicating the amount of spontaneous distortion. In the case of Ni-Mn-Ga, the band Jahn-Teller tetragonal distortion is related to the splitting of degenerate Ni spin-down bands and crossing of the Fermi level by the new electronic states [51]. Valence electron concentration Composition dependence of the lattice instability is considered as an important ingredient to clarify many properties of the Ni-Mn-Ga alloy system. It was found that the valence electron concentration concept is a convenient and physically sound representation of this dependence in Ni-Mn-Ga [31], similarly to what happens in the other martensitic Hume-Rothery alloys [13,54]. Nowadays, the valence electron concentration, e/a, is widely accepted, both empirically and theoretically, to be a basic characteristic which controls lattice, magnetic and electronic instabilities of the Ni-Mn-Ga alloy system [55-60]. Fig. 1 compiles experimental e/a dependencies reflecting the aforementioned instabilities. All properties, such as transformation temperatures, electronic specific heat coefficient and Debye temperature, elastic modulus in the austenitic state, lattice tetragonal ratio c/a and magnetic moment exhibit a regular behavior as a function of e/a. The lowest and highest limits of e/a in Fig.1 roughly correspond to the Ni-Mn-Ga alloys in which every element varies up to 10 at.% around its content in the stoichiometric Ni2MnGa [5,31]. All the alloy compositions involved are chemically quasihomogeneous, their high temperature cubic phase is implied to have L21 atomic order [5].

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Ferromagnetic Shape Memory Alloys

Fig. 1(a) depicts a phase diagram with a strong almost linear dependence of the martensitic transformation temperature, Tm. Tm varies from about 0 K up to 700 K and crosses the curve of

Fig.1. Effect of the valence electron concentration on the lattice, electronic and magnetic instabilities in Ni-Mn-Ga alloy system: (a) phase diagram representing dependencies of the transformation temperatures of martensitic, Tm, premartensitic, TI, and ferromagnetic ordering, TC, transformations [28,31]; (b) Debye temperature and Sommerfeld coefficient for four alloys obtained from low-temperature specific heat measurements (see Ref.[62] and text for details), curves are guides for the eyes; (c) low-frequency elastic modulus measured around 323 K in the case of alloys with e/a7.8 for poly- and single-crystalline austenitic samples, the curves are a polynomial approximation; (d) tetragonality ratio, c/a, of the martensitic lattice [65]; (e) saturation magnetic moment, the dashed line is a linear fit to the experimental data and the solid line is the theoretical prediction (adopted from Ref.[59]).

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Curie temperatures, TC , below the critical concentration e/a ≈ 7.7. The alloys at the crossing point have merged Tm and TC temperatures. These alloys are currently under intense study ([23] and references therein). The existence of a crossing point has important implications on the other behaviors of Ni-Mn-Ga alloys {see, e.g., Fig.1(c) and (d)}, which justifies their conventional classification into three basic groups as suggested in Refs.[28,31]. The phase diagram in Fig. 1(a) also comprises a premartensitic transition line, TI(e/a), exhibited by the alloys of Group I [28]. Fig.1(a) shows that TI and Tm lines are independent, which indicates that the lattice instability towards uniform martensitic distortion scarcely depends on the lattice instability towards a soft mode freezing [28,61]. Recently, the electronic and vibrational properties of Ni-Mn-Ga alloys were found to be dependent on e/a, Fig.1(b) [62]. Measurements of low-temperature specific heat were carried out for four alloys exhibiting in the low-temperature range a cubic premartensitic phase, I, (alloy 1) and the martensitic phases: 10M for alloys 2 and 3 and 2M for alloy 4, alloys numbers are indicated in Fig.1(b). In alloys 1 and 2, soft-phonon condensation is responsible for the formation of I-phase. This phase is stable in alloy 1 while in alloy 2 it transforms martensitically during cooling. Alloys 3 and 4 do not exhibit I-phase. In this case, the austenitic phase transforms directly into martensite. All these features evidence that I-phase formation cannot be considered as a precursor for the martensitic transformation [61]. Debye temperature, θD, appears to be an increasing function of e/a while the values of the Sommerfeld coefficient, γ, which vary from 2.9 to 3.4 mJ/molK2, appear to be increasing in the martensitic region only. A high density of electronic states near the Fermi level (DOS) for the martensitic phase can be deduced from the above magnitudes of Sommerfeld coefficient. This high DOS is expected, indeed, to be smaller than the one for the austenite, because martensite formation is associated with a DOS peak splitting (e.g.,[23,54,56]). An extrapolation of the θD vs e/a curve to e/a = 7.35 in Fig.1(b) supports this assertion. The obtained high values of DOS favor the JahnTeller transformation mechanism discussed above. A considerable growth of θD as a function of e/a suggests an increase in the relative stability of the martensitic state as a function of e/a increment, which is correlated with the phase diagram on Fig.1(a). Moreover, the largest θD value for 2Mmartensite is in line with the first-principle calculations, showing an absolute minimum of energy 2 measured in the low-temperature for this phase [59,63]. Also, the values of elastic moduli E ~ θ D range elsewhere [28] confirm the trend of relative stability of martensitic phases found in specific heat measurements. The graphs in Fig.1(c) show e/a dependencies of the low-frequency elastic modulus measured in the vicinity of 323 K for mono- and poly-crystalline samples in the austenite phase. The data for alloys with e/a>7.8 were taken at temperatures of (Tm+70)K for each alloy. Temperature dependencies of elastic modulus were measured by a dynamical mechanical analysis using the three-point-bending method [64]. The polynomial approximation of results in Fig. 1(c) is shown to demonstrate a trend of minimal values of modules for Ni-Mn-Ga alloys exhibiting a merged loss of stability related to soft-mode freezing and MT. According to Fig.1(c), this minimum roughly corresponds to the concentration range of 7.55-7.70. Fig. 1(d) shows the electron concentration dependence of tetragonality ratio. A jump-like change from the oblate unit cell with tetragonality ratio of c/a1 is observed in the vicinity of e/a ~7.7. More systematic measurements show that the regions of appearance of these martensites are actually overlapped: either martensite can exist in the e/a range of 7.61 – 7.71 depending on Mn/Ni ratio [58]. Different tetragonal lattice distortions affect magnetic anisotropy significantly: the tetragonal martensites with c/a < 1 correspond to the easyaxis type of ferromagnetic ordering while the alloys with c/a> 1 are the ferromagnets of the easyplane type. As follows from Fig.1(e), the magnetic properties of Ni-Mn-Ga alloys also depend regularly on e/a (see Ref.[59] for details]). Both the experiments and theory show that the maximum of the

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saturated magnetic moment corresponds to the stoichiometric composition (e/a=7.50). Note, that Curie temperature in Fig.1(a) also exhibits a small broad maximum near the same concentration range. It is worth noting that all the composition-dependent properties discussed above are relevant to the magnetic field-induced shape memory effect in the Ni-Mn-Ga alloy system. Ferromagnetic shape memory effect The main phenomenon distinguishing the Ni-Mn-Ga ferromagnetic shape memory alloys from the other functional materials is an occurrence of the ferromagnetic shape memory effect which combines the features of an ordinary shape memory effect and magnetostriction. This effect is commonly referred to as the giant magnetic-field-induced-strain, MFIS. As mentioned in the Introduction, the MFIS is comparable in value with a spontaneous deformation of the crystal lattice during the MT, εm. From the conceptual point of view, this term captures the phenomenon of the magnetic field-induced twin boundary motion causing twin rearrangements in the martensitic state [2,6-12,14,15,18]. Besides, by virtue of the magnetoelastic nature of Ni-Mn-Ga materials, the magnetic field acts as an uniaxial equivalent-mechanical compression which is called a magnetostress [2,4,43,66-69]. The simplified schematic in Fig. 2 illustrates this equivalence in the sense that the same twin rearrangement mechanism resulting in the same

Fig. 2. Schematic of the deformation process when compressive load (white arrows) created either mechanically (full part of curve 1) or magnetically (curve 2) is applied along a-axis of the onedomain single twin variant of the Ni-Mn-Ga tetragonal 10M-martensite. Dash part of curve 1 represents strain in the subsequent tensile test. Different shading is used to distinguish two twin variants. Black arrows denote magnetization vectors. See text for details. Fig.3. Magnetization process along the field direction accompanying a cyclic uniaxial magnetic field loading shown in Fig.2. The irreversible abrupt change of magnetization corresponds to the plateau region of ε versus H dependence.

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maximum possible twinning-detwinning strain εm is produced during uniaxial compressive loading of the sample (white arrows) either mechanically (upper part of curve 1) or magnetically (upper part of curve 2). With regard to the geometry of loading, several practically important cases are highlighted below. Uniaxial loading Fig.2 depicts uniaxial stressing by mechanical or magnetic field loading. Let the sample with all {100} edges consist of single twin variant of martensite which is also a single domain. The crystallographic short c-axis is an easy-axis for the magnetization vector (black arrow) aligned perpendicularly to the loading direction: configuration (a) in Fig.2. The initial loading up to the threshold stress σc or threshold field Hc corresponds to the elastic response of the sample which should obey Hooke’s law [2]. Configuration (b) showing the event of an one-interface twinningdetwinning process corresponds to the plateau region in both ε versus σ and ε versus H dependencies. At this instant, the sample is assumed to consist of two magnetic domains divided by a nearly 900 domain wall. In configuration (c), a martensitic twin variant is formed with a short caxis along the compressive force. A removal of the mechanical or magnetic compression to zero is accompanied by the recovery of only the elastic part of the total accumulated strain. A difference between the action of magnetic field and mechanical stress appears when mechanical or magnetic loading changes sign. While the subsequent mechanical tension leads to the reverse reconfiguration of the sample and its strain recovery (dash part of curve 1, see also experimental confirmation in Ref.[70]), no structural changes are involved in the subsequent ramping of magnetic field, following which only the ordinary magnetostriction takes place (small loop in the dependence 2). The latter behavior is due to the magnetoelastic nature of magnetostress which is proportional to the square of magnetic field. Particularly, the relationship σc = const· H c2 with a prescribed value of the constant parameter was obtained in Ref. [71]. Fig.3 schematically illustrates the behavior of magnetization recorded along the field direction and accompanying a cyclic uniaxial magnetic field loading as shown in Fig.2, curve 2. The deformation process corresponding to the plateau seen in the ε versus H dependence gives rise to an abrupt change in magnetization (Fig.3). Both effects are present only during the first increasing of the magnetic field. The value of Hc is the same in Figs. 2 and 3. The magnetization behavior of NiMn-Ga alloy shown in Fig. 3 is studied both experimentally and theoretically, e.g., in Ref.[71]. Biaxial loading It is important for many applications that the giant MFIS (upper curve of dependence 2 in Fig.2) is recoverable after removal of the magnetic field or mechanical stress. This condition can be met by a simultaneous orthogonal loading of the sample. In the majority of available publications, such loading is realized by a simultaneous orthogonal application of magnetic field and mechanical compression. Moreover, it is more common that the reversible giant strain is obtained by variation of a magnetic field while compressive stress is kept constant [6,7]. Fig.4 schematically reproduces an opposite situation when the magnetic field Hx is kept constant during the stress-strain cycle. Let the sample shown in Fig.4 be polytwinned and similarly oriented with regard to both the crystallographic axes and the mechanical compressive force (directed along y-axis) as the sample in Fig. 2. It was found that a step-wise increase of Hx raises the σc values up to a value where the irreversible strain {dash curve in Fig.4(a)} becomes reversible as shown by a full loop in Fig.4(a) [9,68,69,72]. The reversible giant strain in the martensitic phase at a constant orthogonal magnetic field is referred to as a phenomenon of magnetic-field-induced

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Ferromagnetic Shape Memory Alloys

Fig. 4. Schematic of the compression stress-strain curves showing irreversible strain at zero field (uniaxial loading, dash line) and reversible strain in a constant orthogonal magnetic field of appropriate value (biaxial loading) (a); and corresponding reversible change of magnetization along x-direction of sample (b). Two configurations of a polytwinned sample corresponding to the ( x)

magnetization values M 1 top.

( x)

(left) and M 2 (right) are shown at the

superelasticity and described in detail in Ref.[69]. The concept of magnetostress [66,67] is substantiated by direct measurements of this key parameter σM as shown in Fig.4(a) [69]. Fig.4(b) schematically illustrates a behavior of the magnetization recorded along the field direction (x-axis) and accompanying a loading-unloading path along the superelastic loop shown in Fig.4(a). The prototype dependence can be found in Ref. [68]. This effect firstly observed in Ref.[68] is a reverse one to the giant MFIS effect. It is referred to as a twinning-strain-induced change of magnetization. The strain-induced change of twin and magnetic configuration of a sample shown in the upper section of Fig.4 unequivocally demonstrates a reduction of net magnetization registered along the x-axis. The total reversible strain change in Fig.4(a) corresponds ( x)

( x)

to the change of magnetization between the M 1 and M 2 values {Fig.4(b)}. In this experiment, a Ni-Mn-Ga sample being deformed about 2% exhibits a 30% of magnetization change, which is quasi-linear without hysteresis (see [68] for detail). Different engineering applications of the reverse effect are already suggested in Refs.[74,75]. Rotating loading In practice, high-frequency periodic actuation of the Ni-Mn-Ga sample can be produced by the magnetic field only. In the case of an electromagnetically generated periodic magnetic field, its influence on the sample is uniaxial so, the deformation can be obtained in the first cycle only, as the dependence 2 in Fig.2 evidences. A biasing mechanical force is needed for the periodic actuation of sample in this case [76]. The second option is to use a rotating magnetic field with a constant amplitude. In this case, the sample is loaded periodically along all possible axes in the rotation plane. The field rotation produces a continuous mutual change of volume fraction of two twin variants whereby the deformation versus magnetic field is a periodic function being reminiscent to the sinusoidal one. By using this method, the sample training effect and cyclic stability of magnetostrain (fatigue) were studied in detail [9,77]. Magnetoelastic mechanism of magnetostress The magnetostress can be defined as an equivalent mechanical stress produced in the sample by a magnetic field [2,43,66,67]. In the experiment, a magnetostress, σM, is measured as a difference between yield stress in a zero field stress-strain curve and in a curve obtained in the orthogonal field (Fig.4 and Refs.[4,68,69]). This key parameter is conceptually deduced from an analysis of the anisotropic magnetoelastic interactions in the framework of the magnetoelastic model of ferromagnetic martensite ([2,4,75] and references therein). Briefly, the magnetoelastic interaction in

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a free energy expansion is described by terms like M2ε where M and ε are the appropriate components of magnetization vector and strain tensor, respectively. These terms arise because spin exchange and spin-orbit interactions between the electrons depend on the atom coordinates. The core structure of the free energy for ferromagnetic tetragonal martensite can be written as follows: 1 1 (1), F = C ′ε ii2 + AM i2 + δM i2ε ii − M i H i 2 2 where C ′ is the elastic modulus, A ~ δ (1 − c / a ) is the magnetic anisotropy parameter, δ is a magnetoelastic energy parameter, and H is the magnetic field. Eq.(1) is obtained after minimization of the Landau potential for cubic-tetragonal MT in the ferromagnetic solid [4,43,66, 69,71]. Note, that the elastic and magnetoelastic energies in Eq.(1) are expressed as in the cubic phase due to negligible ‘tetragonal corrections’[4,43]. The fundamental equation of thermodynamics σ ik = (∂F / ∂εik ) T yields:

σ ii = C ′ε ii + δM i2

(2),

where a sum of the mechanical stress (first term) and magnetostress (second term) represents a generalized Hooke’s law for a stressed i-variant of the ferromagnetic martensite. Eq. (2) shows that the magnetoelastic coupling is responsible for the occurrence of magnetostress. The proportionality between stress and magnetization square confirms the magnetoelastic nature of the field-induced stress which is in line with an experiment [69]. It is worth noting that the mechanical stress acts in the same way in all the twin variants present in a sample, while a magnetic field generates compressive stress only in those variants in which the magnetization vector is not aligned parallel to the magnetic field [4,69]. It is also important that the same value of magnetostress may cause different strains in the cubic or martensitic phase giving rise to the ordinary magnetostriction in the former phase or an additional large MFIS in the latter. From this viewpoint, it becomes clear that the origin of the large MFIS and magnetostriction is basically the same and their difference lies in the appearance of large microstructural changes (in the case of MFIS). The magnetostrictive origin of MFIS was also shown [2] to be compatible with the crystallographic Wechsler–Liberman–Read theory of martensitic transformations [78]: the small changes in lattice parameters due to magnetostrictive deformation trigger the appreciable reorientation of the twin boundaries. Acknowledgments The financial support of Fondazione Cariplo (project 2004.1819-A10.9251) is greatly acknowledged. The author is grateful to S. Besseghini and V.Lvov for the discussions and A.Gambardella, S. Pittaccio and G. Carcano for technical help. References [1] Shape memory materials, edited by K.Otsuka and C.M. Wayman (Cambridge University Press, Cambridge, 1998). [2] Advances in Shape Memory Materials, edited by V.A. Chernenko (TTP, Switzerland, 2008). To be published. [3] M. Kohl: Shape memory microactuators. (Springer-Verlag, Berlin, Heidelberg, 2004). [4] V.A. Chernenko and S. Besseghini: Sensors and Actuators A,vol. 142, 2008, pp. 542–548. [5] V.A. Chernenko, E.Cesari, V.V. Kokorin and I.N. Vitenko: Scr.Met.et Mat. Vol.33 (1995), p. 1239.

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[6] S. J. Murray, M. Marioni, S. M. Allen, R. C. O’Handley and T. A. Lograsso: Appl. Phys. Lett. Vol. 77 (2000), p. 886. [7] O. Heczko, A. Sozinov and K. Ullakko: IEEE Trans. Magn. Vol. 36(2000), p.3266. [8] A.Sozinov, A.A. Likhachev, N.Lanska and K.Ullakko: Appl.Phys. Lett.Vol. 80 (2002), p.1746. [9] P.Müllner, V.A.Chernenko and G.Kostorz: J.Appl. Phys. Vol.95 (2004), p.1531. [10] H.H. Liebermann and C.D. Graham: Acta Metall. Vol. 25 (1976), p.715. [11] H.H. Liebermann and C.D. Graham: AIP Conference Proceedings, No.29, edited by H.C. Wolfe (AIP, New York, 1976), p. 598. [12] K. Ullakko, J. K. Huang, C. Kantner, R. C. O’Handley and V. V. Kokorin: Appl. Phys. Lett. Vol. 69 (1996),p. 1966. [13] Ll. Manosa and A.Planes: Adv. Sol.Stat.Phys. Vol.40 (2000), p.361. [14] R. C. O’Handley and S. M. Allen: in Encyclopedia of Smart Materials, edited by M. Schwartz ( Wiley, New York 2002), p.936. [15] T. Kakeshita and K. Ullakko: MRS Bull. Vol. 27 (2002), p.105. [16] A. N. Vasil’ev, V. D. Buchel’nikov, T. Takagi, V. V. Khovailo and E. I. Estrin: Phys.-Usp. Vol. 46 (2003), p. 559. [17] E. Cesari, J. Pons, R. Santamarta, C. Segui and V. A. Chernenko: Archives Metal. Mater. Vol. 49 (2004), p.791. [18] O. Söderberg, A. Sozinov and V. K. Lindroos: in Encyclopedia of Materials: Science and Technology Vol.1, edited by J. Buschow (Elesevier,2004), p.1. [19] E.Cesari, J.Pons, C.Seguí and V.A. Chernenko: Applied Crystallography, edited by H. Moraviec and D. Stróz (World Scientific 2004), p. 128. [20] P. Müllner, Z. Clark, L. Kenoyer, W. B. Knowlton and G. Kostorz: Mater. Sci. Eng. A (2007), doi:10.1016/j.msea.2006.12.215 [21] G.Kostorz and P. Müllner: Z. Metallk. Vol.96 (2005), p.703. [22] P. Müllner: Z. Metallk.Vol.97 (2006), p.205. [23] P. Entel, V. D. Buchelnikov, V. V. Khovailo, A. T. Zayak,W. A. Adeagbo, M. E. Gruner, H. C. Herper and E. F. Wassermann: J. Phys. D: Appl. Phys. Vol. 39 (2006), p.865. [24] P. J. Webster, K. R. A.Ziebeck, S. L.Town and M. S. Peak: Phil. Mag. B Vol.49 (1984), p. 295. [25] I.K. Zasimchuk, V.V. Kokorin, V.V. Martynov, A.V. Tkachenko and V.A. Chernenko: Phys. Met. Metall., No. 6 (1990), p. 104. [26] A. Zheludev, S.M. Shapiro, P. Wochner and L.E. Tanner: Phys.Rev. B. Vol. 54 (1996), p. 15045. [27] J.Pons, V.A.,Chernenko, R.Santamarta and E.Cesari: Acta Mater. Vol. 48 (2000), p.3027. [28] V.A. Chernenko, J.Pons, C.Segui and E.Cesari: Acta Mater.Vol. 50 (2002), p.53. [29] J.Pons, R.Santamarta, V. A. Chernenko and E.Cesari: J. Appl. Phys. Vol.97 (2005) 5083516. [29] L. Righi, F. Albertini, L. Pareti, A. Paoluzi and G. Calestani: Acta Mater. Vol. 55 (2007), p. 5237. [30] C. Zener: Elasticity and anelasticity (University of Chicago Press, Chicago, 1948). [31] V.A. Chernenko: Scr. Mater. Vol. 40 (1999), p. 523.

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[32] A. Planes and Ll. Manosa: Sol.State Phys. Vol.55 (2001), p.159. [33] M. Stipcich, Ll. Mañosa, A. Planes, M. Morin, J. Zarestky, T. Lograsso and C. Stassis: Phys. Rev.B Vol. 70 (2004) 054115. [34] Ll. Manosa and A. Planes: Phys.Rev.B Vol. 64(2001) 024305. [35] R. Blinc and B.Zeks: Soft modes in ferroelectrics and antiferroelecrics (Amsterdam: North Holland, 1974). [36] Ll.Manosa, A.Gonzales-Comas, E.Obrado, A.Planes, V.A.Chernenko, V.V.Kokorin and E. Cesari: Phys.Rev.B Vol.55 (1997 – I), p.11068. [37] Y. Lee, J. Y. Rhee and B. N. Harmon: Phys. Rev.B Vol.66 (2002) 054424. [38] C. Bungaro, K. M. Rabe and A. Dal Corso: Phys. Rev.B Vol. 68 (2003) 134104. [39] A. Planes, E. Obrado, A. Gonzales-Comas and Ll. Manosa: Phys. Rev. Lett. Vol.79 (1997) p. 3926. [40] A. T. Zayak, P. Entel, K. M. Rabe, W. A. Adeagbo and M. Acet: Phys. Rev.B Vol.72 (2005) 054113. [41] L. D. Landau and E. M. Lifshitz: Statistical Physics I, 3rd edition (Pergamon, Oxford, 1980). [42] V.A. Chernenko and V.A. L'vov: Phil. Mag. A Vol.73 (1996), p. 999. [43] V.A.Chernenko, V.A.L’vov, S.P.Zagorodnyuk and T.Takagi: Phys.Rev.B Vol.67 (2003) 064407. [44] D.J. Gunton and G.A. Saunders: Sol. Stat. Commun. Vol.14 (1974), p. 865. [45] Y. Murakami: J. Phys. Soc. Jap. Vol.38 (1975), p. 404. [46] V. V. Martynov and V. V. Kokorin: J. Physique III 2 (1992),p.739. [47] V.A.Chernenko, C. Segui, E. Cesari, J. Pons and V.V.Kokorin: Phys.Rev. B Vol.57 (1998-I) p.2659. [48] C.Seguı´, V.A.Chernenko, J.Pons, E. Cesari, V.Khovailo and T.Takagi: Acta Mater. Vol. 53 (2005), p. 111. [49] V.A.Chernenko, J.Pons, E.Cesari and K. Ishikawa: Acta Mater. Vol.53(2005), p. 5071. [50] A. Ayuela, J. Enkovaara, K. Ullakko and R. M. Nieminen: J. Phys.: Condens. Mat. Vol.11 (1999), p. 2017. [51] P.J. Brown, A. Y. Bargawi, J. Crangle, K.-U. Neumann and K.R.A.Ziebeck: J. Phys. Condens. Mat. Vol.11 (1999), p. 4715. [52] S. Banik, Aparna Chakrabarti, U. Kumar, P. K. Mukhopadhyay, A. M. Awasthi, R. Ranjan, J. Schneider, L. Ahuja and S. R. Barman: Phys.Rev.B Vol.74 (2006) 085110. [53] F.Agullo-Lopez, C.R.A. Catlow and P.D. Townsend: Point defects in materials (Academic Press, 1988). [54] T. Krenke, X. Moya, S. Aksoy, M. Acet, P. Entel, Ll. Manosa, A. Planes,Y. Elerman, A. Yucel and E.F. Wassermann: J. Magn. Magn. Mater. Vol. 310 (2007), p. 2788. [55] K. Tsuchia, H. Nakamura, D.Ohtoyo, H. Nakayama, M. Umemoto and H. Ohtsuka: J. Phys.IV France Vol. 11 (2000), p.Pr8-263. [56] K. Yamaguchi, S. Ishida and S. Asano: Mater. Trans. Vol.43 (2002), p.846.

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[57] X. Jin, M. Marioni, D. Bono, S. M. Allen, R. C. O’Handley and T. Y. Hsu: J. Appl. Phys. Vol. 91 (2002), p.8222. [58] N. Lanska, O. Soderberg, A. Sozinov, Y. Ge and K. Ullakko: J.Appl. Phys. Vol.95 (2004), p.8074. [59] J. Enkovaara, O. Heczko, A. Ayuela and R. M. Nieminen: Phys.Rev. B Vol.67 (2003) 212405. [60] A. T. Zayak, W. A. Adeagbo, P. Entel and K. M. Rabe: App. Phys.Let. Vol. 88(2006) 111903. [61] J. I. Pérez-Landazábal, V.Sánchez-Alarcos, C.Gómez-Polo, V.Recarte and V. A. Chernenko: Phys. Rev. B Vol. 76 (2007) 092101. [62] V.A. Chernenko,A. Fujita, Magn.Mater.(2008), in print.

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[63] J. Enkovaara, A. Ayuela, L. Nordstrom and R. M. Nieminen: J. Appl.Phys. 91(2002), p. 7798. [64] C. Segui, V.A. Chernenko and E. Cesari: unpublished. [65] V.A.Chernenko, V.A.L’vov, E.Cesari, J.Pons, R.Portier and S.P. Zagorodnyuk: Proc. Fourth Pacific Rim Int. Conf. on Advanced Materials and Processing (PRICM4), Vol.II, edited by S.Hanada, Z.Zhong, S.W.Nam and R.N.Wright (The Japan Institute of Metals, 2001), p.1653. [66] V. A. L'vov, S. P. Zagorodnyuk and V. A. Chernenko: Eur. Phys. J. Vol. B27(2002), p. 55. [67] P.Müllner, V.A.Chernenko, M.Wollgarten and G.Kostorz: J.Appl. Phys. Vol. 92 (2002), p. 6708. [68] P.Müllner, V.A.Chernenko and G.Kostorz: Scr. Mater. Vol. 49 (2003), p.129. [69] V.A.Chernenko, V. A. L’vov, P.Müllner, G.Kostorz and T.Takagi: Phys. Rev.B Vol. 69 (2004) 134410. [70] O. Soderberg, L. Straka, V. Novak, O. Heczko, S.-P. Hannula and V.K. Lindroos: Mat. Sci. Eng.A Vol.386 (2004), p. 27. [71] M.Pasquale, C.P. Sasso, G. Bertotti, V. L'vov, V. Chernenko and A. De Simone: J. Appl. Phys. Vol. 93 (2003), p. 8641. [72] A .Sozinov, A.A. Likhachev, N. Lanska, O. Soderberg, K. Ullakko and V.K. Lindroos:Mat. Sci.A Vol.378 (2004), p.399. [73] P.Müllner, V.A. Chernenko and G. Kostorz: J. Magn.Magn.Mat. Vol. 267 (2003), p. 325. [74] I. Suorsa, J. Tellinen, K. Ullakko and E. Pagounis: J.Appl.Phys. Vol.95 (2004), p.8054. [75] V. A. Chernenko, S. Besseghini, P. Müllner, G. Kostorz, J. Schreuer and M. Krupa: Sensor Lett. Vol. 5(2007), p. 229. [76] J. Tellinen, I. Suorsa, A. Jääskeläinen, I. Aaltio and K. Ullakko: Actuator 2002 Conference Vol. 8 (Bremen, Germany, 2002), p. 566. [77] P. Müllner, V.A. Chernenko and G. Kostorz: Mater.Sci. Eng. A 387–389 (2004),p. 965. [78] D. S. Liberman, T. A. Read and M. S. Wechsler: J. Appl. Phys.Vol. 28(1957), p. 532.

I. Sample Preparation

Advanced Materials Research Vol. 52 (2008) pp 17-27 © (2008) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/AMR.52.17

Development of Ni-Mn-Ga based Ferromagnetic Shape Memory Alloy by Rapid Solidification Technique Amitava Mitraa and A.K.Pandab National Metallurgical Laboratory, Jamshedpur 831007, India a email: [email protected] b email: [email protected]

Abstract Rapid solidification route by melt spinning has been adopted for preparation of a Ni52.5Mn24.5Ga23 (at %) ferromagnetic shape memory alloy in the form of ribbons. In the as-spun state, the ribbon revealed a predominant austenitic L21 structure in combination with martensitic feature as observed from x-ray diffraction studies. Transmission electron microscopic (TEM) evaluation showed these features in the form of martensitic plates. At low temperature, martensite to austenite transformation was exhibited by an increase in magnetization during heating cycle. The reverse effect was observed during cooling cycle. Annealing temperature and magnetising field was also found to effect this transformation. Keywords: Shape memory alloy, Melt-spun ribbons, martensitic transformation, Magnetisation 1. Introduction Highly adaptive structures called “Smart Materials” typically include shape memory alloys, piezoelectric ceramics, piezoelectric polymer films, ferroelectrics and fiber optics. One of the frontline areas of research amongst different smart materials is on shape memory alloys (SMAs) due their potential application as actuator material. Some of the conventional SMAs include Cu-, NiAl-, NiTi- based alloy systems revealing shape recovery with thermal environments. In these materials the shape memory effect is based on reorientation of the twin variants of the martensitic phase by thermal stresses involving the actuation between heating and cooling cycles. Since in these materials the mode of actuation is thermally controlled hence the response time is delayed. Therefore the need for smarter actuators have led to the introduction of magnetically controlled shape memory alloys which are supposed to be faster actuator materials than thermally controlled ones. In this new class of materials called Ferromagnetic Shape Memory Alloys (FSMAs) the overall change of shape under an applied magnetic field rests on the fundamental basis of field induced martensite to austenite transformation and its reverse [1]. Such transformations typically between the tetragonal and cubic geometry in the crystal lattice in martensite and austenite states respectively are directly evidenced form strain variations in these two states. The earliest of the known ferromagnetic shape memory alloys, belonged to Heusler’s NiMnGa alloy system exhibiting high recoverable magnetic field induced strain in the range of 6 – 9.5 % [2]. In view of such high

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Ferromagnetic Shape Memory Alloys

magneto-strain, these ferromagnetic shape memory alloys find applications in aircrafts, biomedical, robotics etc. In view of their large displacement induced by magnetic fields, new applications in the area of magnetic micro-electro-mechanical systems (MagMEMS) transducers are envisaged. Inspite of potential properties of the Heusler type NiMnGa ferromagnetic shape memory alloys as magnetically controlled actuators; they bear utmost limitations due to their production route. The materials are conventionally prepared by crystal growth techniques that require longer processing time with additional concern towards crystal defects. At the same time these crystals are either expensive or brittle in manufacturing in the form of thin plate type actuators. Hence, stems up the need for convenient processing routes. In the recent years rapid solidification routes are being explored to develop FSMAs by using different techniques out of which melt spinning is one of the most convenient method for faster preparation of larger quantities in ribbon geometry. Melt spinning technique for FSMA preparation has been found effective in not only getting ribbon shaped materials but also in achieving the desired structure. It is known that Co-Ni-Al alloys on cooling result into γ precipitation. However, recent reports have shown that in Co–Ni–Al alloys, melt spinning has been successful in retaining only the β phase amongst the high temperature (γ +β) phase [3]. This retention in these alloys is particularly important as their shape memory effect occurs between the β (bcc type B2) to L10 martensitic ordering. In an another example, it is known that the formation of a large fraction of melt-ingots of γ phase in Ni–Fe–Ga can be impeded by rapid solidification using melt spinning leading to the formation of only the L21 phase [4]. The interesting reports have prompted our present investigation in the development of NiMnGa alloy in the form of melt spun ribbons and evaluating their martensite to austenite reversible transformation which is responsible for its shape memory effect. For this study, a composition has also been selected which is supposed to have transformations close to room temperature, desirable from application point of view. 2. Experimental Pure elements were used to prepare master alloy with a nominal composition of Ni52.5Mn24.5Ga23 (at %) by vacuum arc melting. This alloy composition bears number of electrons per atom (e/a) equal to 7.655 which is chosen so as to achieve close to room temperature austenitic start (or martensitic start during cooling) [5], desired for practical applications. The arc melting in argon atmosphere was carried out in argon atmosphere for effective homogenization. Subsequently, the master alloy ingot (fig-1a) was induction melted and rapidly quenched by melt spinning

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technique into ribbons (fig-1b) using a single roll Cu-wheel rotating at a wheel speed of 2000rpm and melt ejection pressure of 10psi.

(b)

(a)

Fig-1: Photograph of the (a) master alloy ingot and (b) melt spun ribbons The evolution of the phases in the ribbons was identified using an x-ray diffractometer (Philips D500) with a Cu-Kα radiation. The morphology of the as-quenched ribbon and also the elemental distribution was studied using Scanning Electron Microscope (SEM, Jeol 400) and Energy dispersive x-rays (EDX) analysis. The structure of as-spun ribbons was also observed using Transmission Electron Microscopy (Philips CM-200). The magnetization studies were carried out using a Vibrating Sample Magnetometer (VSM, Lakeshore: 7404). 3. Result and discussion: The microstructure of the alloy ingot and the as-spun ribbons was observed using scanning electron microscope and is shown in fig-2a and b. SEM micrograph revealed acicular needle shape structure distributed in the matrix while the ribbon sample showed granular structure with distinct grain boundaries. Some pitting in the granular structure was attributed to over etching of the ribbon during sample preparation for microscopy. Energy dispersive x-ray (EDX) analysis of the

(a)

(b)

Fig-2: Scanning electron micrograph of (a) alloy ingot and (b) as-spun ribbon

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Ferromagnetic Shape Memory Alloys

microstructures was done to analyse the elemental distribution in alloy ingot as well as as-spun ribbon and shown in table-I and table-II respectively. As shown in table-I elemental distribution did not reveal any drastic changes in the concentration of Ni, Mn and Ga between the matrix and the acicular sites. This indicated that the elements were homogeneously distributed with a slight higher concentration of Ga in the matrix. However, melt spinning of the alloy ingot distinctly modified Table-I: Microstructural analysis of alloy ingot showing elemental distribution: Elements Nickel Manganese Gallium

Matrix 62.55 23.78 13.67

Composition (at %) At acicular sites 65.24 24.00 10.76

the distribution of elements. It was observed that at the grain boundary there was a relative increase in the Nickel and Manganese concentration. Noticeably, the Gallium concentration decreased drastically at the grain boundary as also reported for the Ni56Mn18.8Ga24.5Gd0.7 alloy [6]. Table-I: Microstructural analysis of As-spun ribbon showing elemental distribution: Elements Nickel Manganese Gallium

Composition (at %) Grain Matrix Grain Boundary 67.45 79.5 10.35 11.26 22.2 9.24

To study the phase evolution, x-ray diffractograms were obtained for the alloy ingot and the as-spun ribbon and is shown in fig-3. Both the samples indicated diffraction peaks at identical positions. The interesting feature was that the peak intensities of the as-spun ribbons revealed an ordered L21 (cubic) austenite structure [7], typically of a Heusler alloy. In contrast to the alloy ingot, the highly ordered L21 cubic structure in the as-spun ribbons was evidenced from their proportionally decaying intensities as proceeding from (220) to (440) reflections. The lattice constants ‘a’ derived from the primary reflection d220 for the alloy ingot and the as-spun ribbon has been found to be 5.7672A and 5.8039A respectively. The values have been found to be close to 5.821A reported for the Ni50Mn27Ga23 alloy with an L21 austenitic structure [7]. It is interesting to note that in the as-spun ribbon the (220) reflection showed splitting about its original position (inset of fig-3). Such splitting has been attributed to the existence of some tetragonal feature (martensitic) that may be in small volume fraction to suppress the cubic L21 structure [8]. This was also supported by the higher

21

(220)

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Intensity (A.U)

42

44

Intensity (A.U)

46

Degrees (2θ)

48

(440)

40

As-Cast Ribbon

(422)

(400)

(220)

A s-Cast Ribbon

A lloy Ingot

40

60

80

100

Degrees (2 θ ) Fig-3: X-ray diffractogram of as-spun ribbon and alloy ingot. Inset shows splitting of primary peak in the as-spun ribbon.

content of element Ga in the grain matrix (table-II) as compared to the grain boundary. The higher clustering of Ga atoms in the matrix was also the cause of such splitting of the x-ray primary reflections [9].

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Ferromagnetic Shape Memory Alloys

The as-spun ribbon was subjected to Differential thermal analysis (DTA) at a scan rate of 2K/min. The same as-spun ribbon sample was subjected to consecutive heating cycles and the plots are shown in fig-4. The first and the second heating cycles showed endothermic transformations. Endothermic Heat flow (W/g)

0.36

Martensite

Austenite nd

2 Heating Cycle 0.34

AS2= 307 K

0.26 st

1 Heating Cycle AS1= 305K 0.24

310

320 Temperature (K)

330

Fig-4: Differential Thermal Analysis plots of as-Spun ribbon showing martensite to austenite transformation. Heating rate 2K/min. These endothermic peaks indicated reverse martensitic transformation (martensite to austenite) with the austenitic start temperature AS1 and AS2 revealed during the first and second heating cycles being 305 K and 307K with their enthalpy of transformation being 1.11 J/g and 1.01 J/g respectively. The slightly lower AS temperatures compared to similar compositions [10] may be attributed to differences in quenching process parameters. The Transmission electron microscopy was carried out for the as-spun ribbon. The micrograph shown in fig-5a indicated granular structure with the grain

Martensitic plates

(a)

(b)

0.1µm

Fig-5: TEM micrograph showing (a) Grains interface (SAD at inset for grain matrix) and (b) grain boundary region

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interior indicating an L21 austenitic matrix as shown in from the SAD pattern (inset of fig-5a). As the ribbon had indicated different elemental distributions at the grain matrix and the grain boundary therefore examination was carried out for the grain boundary and it was interesting to find welldefined stripe like morphology typically of martensitic phase [11] as shown in fig-5b. The phase boundary between the martensite plates was straight and also distinct. TEM examination showed that a low volume fraction of textured martensite phase was accommodated within the austenite L21 structure as observed from XRD studies (fig-3). The thermal variation of magnetisation of as-spun ribbon at a low magnetising field of 2.0 kA/m was obtained using Vibrating Sample Magnetometer and is shown in fig-6. During the heating cycle, the magnetisation initially increased which is attributed to change from martensitic state to an austenitic state with long range ferromagnetic ordering [12]. This is also attributed to due to change from martensitic state with some non-ferromagnetic components (possibly of antiferromagnetic origin) to an austenitic state with long range ferromagnetic ordering [12]. Subsequently, the magnetization dropped indicating the ferromagnetic to paramagnetic transition (Curie temperature, Tc) of the austenitic state occurring at 302K. The Curie temperature was found to be lower compared to the reported values [10] and may be attributed to the fraction of quenchedin L21 austenitic state. The reversibility of austenite to martensitic state was also observed from the cooling cycle with a drop in magnetization indicating a martensitic start (Ms) occurring around 300K. Similar magnetisation behaviour was also observed in heat-treated samples.

As-Spun Ribbon

-3

Magnetisation, Tesla (x 10 )

2.5

Magnetising field = 2.0 kA/m

2.0

1.5 Heating Cycle Cooling

1.0

Cycle

TC = 302 K 300

320

340

Temperature (K)

Fig-6: Thermal variation of magnetisation of as-spun ribbon at magnetising field of 2 kA/m

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Ferromagnetic Shape Memory Alloys 2.5

As Spun Ribbon

-3

Magnetisation, Tesla (x 10 )

2.0 1.5 1.0

TC = 302 K Annealed at 775K / 5 hrs

20 15 10 5

= 305 K 300

320

340

Temperature (K) Fig-7: Thermal variation of magnetisation of (a) As-spun ribbon and (b) Annealed at 775K for 5hrs. Magnetising field of 2 kA/m As compared to the as-spun ribbon, the magnetisation level was much higher in the case of annealed sample as shown in fig-7.

(400)

(220)

(422)

Intensity (Arb.Unit)

(220)

Annealed at 775K/5hrs

(422)

(400)

As-Cast

40

50

60

70

Degrees (2 θ )

80

Fig-8: X-ray diffractogram of as-cast ribbon and after annealing at 775K for 5hrs.

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This is attributed to the increase in the L21 austenitic ferromagnetic ordering after annealing at 775K for 5 hours which is also evident from the relative increase in the high angle peaks as observed from the x-ray diffractogram shown in fig-8. Transmission electron microscopy of this annealed ribbon sample showed granular matrix with a highly ordered austenitic phase. The SAD pattern shown in the inset of fig-9a indicated super lattice spots indicative of a highly ordered L21 structure. The

(a)

(b)

Fig-9: TEM micrograph of sample annealed at 775K for 5hours showing (a) Grains interface (SAD at inset for grain matrix) and (b) grain boundary region

-3

Magnetisation, Tesla (x 10 )

150

Magnetising field = 400 kA/m

100 50 0

= 40 kA/m

60 40 20 0

= 2.0 kA/m

2

1

300

320 340 Temperature (K)

Fig-10: Effect of magnetizing field on the thermal variation of magnetisation of as-spun ribbon

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Ferromagnetic Shape Memory Alloys

granular structure shown in fig-9b indicated discrete distribution of martensitic fraction more prominently in the grain boundary. In addition to the annealing effect, an increasing intensity of magnetic field on the martensite to austenite transformation was also observed as shown in fig-10. With increasing magnetizing field, the distinct initial rise in magnetisation above 295K was not observed. This effect can be attributed to the critically low magnetic fields bringing about detwinning of the martensitic variants in polycrystalline materials having randomly oriented magnetic domains [13]. At higher applied fields such de-twinning effect occurs in a spontaneous way and thus the rise in magnetization was not observed. Conclusion Ferromagnetic shape memory alloy with a nominal composition of Ni52.5Mn24.5Ga23 (at %) prepared in the form of ribbons by melt spinning technique revealed martensite to austenite transformation and its reverse. The as-spun ribbon revealed granular morphology with L21 austenitic (cubic) structure in combination with martensitic phase. Effect of magnetizing field on martensite to austenite transformation was also observed. Acknowledgement The authors express their profound gratitude to Director, National Metallurgical Laboratory, Jamshedpur, India for kindly giving necessary permission to publish this work. Reference: [1]. K.Ullako, J.K.Huang, V.V.Kokorin and R.C.O’Handley: Appl.Phys Lett., Vol.69 (1996), p.1133 [2]. S.J.Murray, M.Marioni, S.M.Allen, R.CO’Handley and T.A.Lograsso: Appl.Phys. lett, Vol.77 (2000), p. 886 [3]. Z.H Liu, X.F Dai, Z.Y Zhu, H.N Hu, J.L Chen, G.D Liu and W.H. Wu: J Phys D: Appl Phys Vol. 37(2004), p. 2643 [4]. Z.H. Liu, M. Zhang, Y.T. Cui, Y.Q. Zhou, W.H. Wang, G.H. Wu, X.X. Zhang and G. Xiao: Appl. Phys. Lett. Vol.82 (2003), p. 424 [5]. S.K.Wu and S.T.Yang: Materials Letters, Vol.57 (2003), p. 4291 [6]. Z.Zeyu, L.Yi, D.Jingfang, H.Peng, W.Guangheng and C.Yongqin: J.Rare Earths, Vol.24 (2006), p. 579 [7]. C.Jiang, Y.Muhammad, l.Deng, W.Wu and H.Xu: Acta Materialia, Vol.52 (2004), p. 2779 [8]. P.J.Webster, K.R.A.Ziebeck, S.L.Town and M.S.Peak: Philos.Mag.B, Vol.49 (1984), p. 295 [9]. G.D. Liu, Z.H.Liu, X.F.Dai, S.Y.Yu, J.L.Chen and G.H.Wu: Science and Technology of

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Advanced Materials, Vol.6 (2005), p. 772 [10]. V.Recarte, J.I.Perez-Landazabal, C.Gomez-Polo, C.Segui, E.Cesari and P. Ochin: Mater.Sc Engg A, Vol.438 (2006), p. 927 [11]. H.B.Xu, Y.Li and C.B Jiang: Mat.Sc.Engg. A, Vol.438-440(2006), p. 1065 [12]. T.Krenke, E.Duman, M.Acet, E.F.Wassermann, X.Moya, L.Manosa and A.Planes: Nature Materials, Vol.4 (2005), p. 450 [13]. J.Gutierrez, J.M.Barandiaran, P.Lazpita, C.Segui and E.Cesari: Sensors and Actuators A, Vol.129 (2006), p. 163

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Advanced Materials Research Vol. 52 (2008) pp 29-34 © (2008) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/AMR.52.29

Magneto-mechanical behaviour of textured Polycrystals of NiMnGa ferromagnetic Shape Memory Alloys S. Roth1, a, U. Gaitzsch1, b, M. Pötschke1, c, and L. Schultz1, d 1 a

IFW Dresden, Institute for Metallic Materials, P.O.B. D-01117 Dresden, Germany

[email protected], b [email protected], c [email protected], d [email protected]

Keywords: textured polycrystal, NiMnGa-alloy, magnetic field induced strain.

Abstract. Textured polycrystalline NiMnGa alloys were prepared by directional solidification. Alloys were chosen to have either the 7M or the 5M modulated martensitic structure after proper heat treatment. Mechanical training allowed to reduce the twin boundary pinning stress to below the magnetically induced stress. Thus, magnetic field induced changes in the mechanical behaviour could be demonstrated. The conditions of preparation and mechanical training will be discussed together with their influence on structure, microstructure, and the magneto-mechanical behaviour. Introduction Single crystals of NiMnGa show magnetic-field-induced strain (MFIS) due to twin boundary motion [1]. This effect is found in low temperature martensitic phases, which form from a cubic L21 phase arising upon cooling at around 750 °C. Prerequisites for MFIS are a uniaxial magnetic anisotropy and highly mobile twin boundaries [2]. Both features depend not only on composition but also on structure details on all scales. The goal of the present paper is to investigate the conditions under which magnetic field induced twin boundary movement can be achieved in polycrystalline NiMnGa. There are three different types of martensite which may exist in NiMnGa: Nonmodulated (NM) martensite with tetragonal symmetry and c/a>0, modulated martensite with five unit cells modulation length (5M) with tetragonal symmetry and c/aa

202 220

45

50

022

55

530 °C 24 h, 15 K/min "orthorhombic" => 7M

60

65

70

2theta, deg.

Fig. 2: Influence of final annealing on the martensite type of Ni50Mn30Ga20

Fig. 3: XRD spectrum of Crushed Ni50Mn30Ga20 in the as crushed state.

had turned out that neither the second annealing step at 700 0C nor the water quenching is essential for the formation of the 7M phase. Rather the last final annealing step had proven to be mandatory

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31

Intensity, a. u.

in order to promote the formation of the 7M phase. If the bulk sample is crushed to powder a transformation of the 7M martensite to NM martensite (Fig. 3) is observed. Recovery to practically single-phase 7M martensite was achieved after annealing at 600 °C for 14 h (Fig. 4). Therefore, we

45

50

55

60

65

70

75

80

85

90

2theta, deg.

Fig. 4: Crushed Ni50Mn30Ga20 after annealing at 600 °C for 14 h

Fig. 5: The relation between composition, c/a-ratio, and martensite type (data taken from [5]).

assume that the transformation of the 7M martensite to NM martensite is stress induced [4]. Preparation of 5M Martensite. According to Lanska et al. [5] a lower valence electron number per atom favours the formation of the 5M martensite (cf. Fig. 5). Therefore, we changed the composition from Ni50Mn30Ga20 with e/a = 7.70 to Ni50Mn29Ga21 with c/a = 7.66. It turned out that the martensite is of 5M structure for this composition nearly independent on the thermal treatment. Preparation of Austenite. As mentioned above nearly all technological means to influence the microstructure have to be applied in the austenitic state. Therefore, we prepared samples which are cubic at room temperature in order to be able study the influence of preparation on microstructure without passing the austenite – martensite transformation [6, 7]. The composition Ni48Mn30Ga22 with Tmart ≈ -5°C fulfils these requirements.

direction of solidification

Changing the Microstructure As cast Microstructure. The principle of the experimental set up is displayed in Fig. 6. A hot mold is mounted on a cooling copper plate. To avoid heating of the cooling plate by the hot mold, an insulation ring is placed between the mold and the plate. When the melt is cast into the mold, a temperature gradient and thereby a heat flow through the melt toward the bottom is generated, which causes a directional solidification in opposite direction. The texture is supposed to occur along the direction of the heat flow,

20°C 10 mm

Fig. 6:Principle of directional solidification, q : direction of heat flow, ds: direction of solidification

800°C

1000°C

1100°C

1200°C+ insulation

Fig. 7: Influence of the mold temperature on the as-cast microstructure. The given mold temperatures are at begin of the casting process.

32

Ferromagnetic Shape Memory Alloys

-20

0 T in °C

20

40

-40

-20

0 T in °C

20

40

10 mm

-40

heat flow endo up

heat flow endo up

preferentially in [100] direction [8]. The influence of various casting and annealing parameters was demonstrated in [9].The influence of different mold temperatures on the as-cast microstructure can be seen from the optical micrographs in Fig. 7. Four different regions of the microstructure of the samples it can be distinguished. In the first very narrow zone at the bottom of the mold fine almost globular grains are observed. This is due to the high cooling rate at the beginning of the solidification. In this region also a grain selection takes place. In the second zone columnar grains can be seen. The size of this zone depends on the casting parameters, especially the mold temperature. With increasing mold temperature the area of elongated grains becomes larger. At the top of this zone a conical region can be seen, where in the centre still columnar grains can be observed whilst globular grains are on the rim of the sample. There the solidification direction changes gradually from unidirectional (to the copper plate) to radial (to the mold). Above this cone in zone 3 all the grains are globular. In the fourth zone sink holes and other cavities due melt shrinkage are observed. Effect of Annealing. Annealing at 1000 °C for 48 h in Ar-5% H2 atmosphere causes grain coarsening and homogenization cf. Fig. 8. In the DSC curves in Fig. 8 the transformation peaks become sharper after the annealing process. This is due to homogenization, stress relaxation and possible ordering during cooling. Is to be mentioned that the martensite transition temperature does not vary for small samples taken along the direction of solidification [9]. This demonstrates, that the

Direction of solidification

10 mm

Fig. 8: Microstructure and DSC curves of the as-cast (left) and the annealed sample (right).

deviation of [100] from solidification direction

EBSD

Fig. 9: EBSD picture of a sample (right) and histogram (left) with the orientations of grains of the marked area.

chemical composition of the ingot does not vary significantly along its length. EBSD measurements on annealed samples showed, that the columnar grains are preferably aligned along the direction of solidification with an [100] axis. Mechanical training and magneto-mechanical response Mechanical training. Plastic deformation of martensitic NiMnGa alloys by dislocation movement is not possible. Dislocation movement is hampered strongly due to atomic ordering and the low crystal symmetry of theses alloys. Therefore, the main source of plastic deformation observed in such alloys is the movement of twin boundaries. Magnetic field induced strain (MFIS) in ferromagnetic shape memory alloys is also a result of twin boundary movement in the special case as a result of an external magnetic field. Thus, plastic deformation provides information about the mobility of the grain boundaries. Furthermore, it is expected, that cyclic plastic deformation increases the mobility of the twin boundaries. Cubes of 5 to 7 mm edge length were cut from the columnar region of directionally solidified and annealed ingots. Such cubes were cooled through the martensitic transformation under 30 MPa load. A strain of typically 1–2% is achieved by this procedure which means that many twins remained in the sample, since a detwinned sample would cause a strain of εtrans = 5% during the martensitic

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33

transformation (εtrans = 1 _ aaust/cmart). The samples were successively compressed along all three axes in order to cause maximum deformation. This means a sample that was compressed along axis 1 is pressed along directions 2 and 3, before the next compression along axis 1 is performed. (Fig 10). The influence of successive training is given in Fig.11 for a 7M martensite [10].For clarity,

Fig. 10: Directions of compressive stress during mechanical training

only the curves of compression along one Fig. 11: Stress and strain for successive compression along all three axis for 7M martensite. Curves are direction are displayed in Fig. 11. A clear given for one axis only. effect of the training can be observed. The residual strain increases to 8%, which is rather close to the crystallographic strain limit εmax = 1 - c/a ≈ 10%. It becomes also evident that most of the strain is produced at comparably small loads. However, the strain at 2 MPa, which is approximately the stress an external magnetic field can generate [11], is very low. The effect of training a 5M martensite is given in Fig. 12. Training of the 5M martensite is much more efficient. It is possible to apply a large number of training cycles without any harm to the samples. The maximum stress which can be generated by a magnetic field is about σmag,max ≈ 2.6 MPa for the 5M martensite. This value is higher than the corresponding value of the 7M martensite due to the lower crystallographic strain of the 5M martensite which is εmax = 1 - c/a ≈ 6%. There is a considerable large amount of strain at stress values smaller than σmag,max for the 5M martensite. Therefore, we can expect an effect of a magnetic field on the stress – strain curve of such samples.

Fig. 12: Stress and strain for successive compression along all three axis for 5M martensite. Curves are given for one axis only.

Fig. 13: Stress release with and without magnetic field for trained 5M martensite. The inset gives the direction of load and magnetic field.

Magneto-mechanical response. Trained samples of the 5M martensite were subjected to mechanical testing with and without a magnetic field. The axis of the magnetic field was perpendicular to the axis of the mechanical load. The axis of the columnar grains was parallel to the load axis. I turned out, that there is a considerable influence of the magnetic field on the mechanical

34

Ferromagnetic Shape Memory Alloys

behaviour. Fig. 13 shows unloading curves for a sample made from trained 5M martensite. The initial load was 2 MPa and the strain upon stress release was recorded. The strain observed during stress release with a magnetic field of 0.7 T is about 0.5 % larger than the strain observed when no magnetic field is applied. Thus, a MFIS of 0.5 % was found for the trained 5M martensite. Summary Magnetic field induced strain was demonstrated for a textured polycrystalline Ni50Mn29Ga21 alloy with 5M structure. In order to achieve this, structure and microstructure have to be adjusted. Furthermore, mechanical training was applied to reduce the twinning stress to a level which is lower than the stress which can be exerted by a magnetic field. Texture was achieved by directional solidification. A large grained columnar microstructure with a fibre texture developed this way. Homogenization and stress relief was achieved during annealing at 1000°C/48 h. The bottom of the ingot had to be removed in order to prevent giant grain growth and loss of the texture. Mechanical training of cubic samples was performed by compressing along all three axes successively with various loads. It was not possible to achieve magnetic field induced strain in NiMnGa with 7M structure. Acknowledgement Financial support of the German ministry of education and research (BMBF, code 03X4005E) and the German foundation for research (DFG, code RO 962/5-1) is kindly acknowledged. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]

K. Ullakko, J.K. Huang, C. Kantner, R.C. O’Handley, and V.V. Kokorin, Appl. Phys. Lett. 69 (1996) 1966. R.C. O'Handley, J. Appl. Phys. 83 (1998) 3263-3270. J. Pons, V.A. Chernenko, R. Santamarta, and E. Cesari, Acta Mater. 48 (2000) 3027. U. Gaitzsch, M. Pötschke, S. Roth, N. Mattern, B. Rellinghaus, and L. Schultz, J. Alloys Comp. 443 (2007) 99—104. N. Lanska, O. Söderberg, A. Sozinov, A. Ge, K. Ullakko, and V. K. Lindroos, J. Appl. Phys 95 (2004) 8074 V.A. Chernenko, Scr.Mater. 40 (1999) 523. X. Jin, M.Marioni, D. Bono, S.M. Allen, and R.C. O’Handley, J. Appl. Phys..91 (2002) 8222. R.C. O'Handley, S.J. Murray, M. Marioni, H. Nembach, and S.M. Allen, J. Appl. Phys. 87 (2000) 4712. M. Pötschke, U. Gaitzsch, S. Roth, B. Rellinghaus, and L. Schultz, J. Magn. Magn. Mater. 316 (2007) 383. U. Gaitzsch, M. Pötschke, S. Roth, B. Rellinghaus, and L. Schultz, Scr. Mater. 57 (2007) 493 A.A. Likhachev, A. Sozinov, K. Ullakko, Mater. Sci. Eng. A 378 (2004) 513.

Advanced Materials Research Vol. 52 (2008) pp 35-43 © (2008) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/AMR.52.35

Magnetization and domain patterns in martensitic NiMnGa films on Si(100) wafer V.A. Chernenko1, 3,a, R. Lopez Anton 2,b, S. Besseghini3,c, J. M. Barandiaran4,d, M. Ohtsuka5,e, A. Gambardella3,f and P. Müllner6,g 1

Institute of Magnetism, Vernadsky str. 36-b, Kyiv 03142, Ukraine

2

ISIS , STFC Rutherford Appleton Laboratory, Didcot, OX11 0QX, UK 3

CNR-IENI, C.Promessi Sposi, 29, Lecco 23900, Italy

4

Universidad del Pais Vasco, Dept. de Electricidad y Electronica, PO Box 644, Bilbao 48080, Spain 5

IMRAM, Tohoku University, Sendai 980-8577, Japan

6

Boise State University, 1910 University Dr., Boise, ID 83706, USA

a

[email protected], [email protected], [email protected], d [email protected], [email protected], [email protected], g [email protected]

Keywords: Ferromagnetic shape memory alloys, NiMnGa/Si(100) thin film composites, magnetization, magnetic domain structure.

Abstract. A series of Ni51.4Mn28.3Ga20.3 films sputter-deposited on Si(100) wafer (with 500 nm thick buffer layer of SiNx) and annealed at 800 oC for 1h. are investigated with respect to their transformation behavior and magnetic properties. The film thickness, d, varies from 0.1 to 5.0 µm. Resistivity measurements reveal martensitic transformation above room temperature for all the films except for 0.1µm-thick film which is transforming at much lower temperature. The magnetic characteristics of martensitic films such as susceptibility and anisotropy field extracted from the inplane and out-of-plane magnetization curves show film thickness dependence likewise Curie temperature obtained from the resistivity curves. The surface topography and micromagnetic structure are studied by scanning probe microscopy. A stripe magnetic domain pattern featuring a large out-of-plane magnetization component is found in the films. The domain width, δ, depends on the film thickness, d, as δ ~ d . Introduction It is well-known that the magnetically weakly anisotropic cubic Ni2MnGa Heusler alloy and its offstoichiometric derivatives exhibit a thermoelastic martensitic transformation (MT) resulting in a number of martensitic phases with the elastically soft crystal lattices and strong magnetocrystalline anisotropies. The magnetic state of these martensites is coupled with a highly mobile twin structure through the ordinary magnetoelastic interactions giving rise to the giant magnetostrain effect and related phenomena. While the ferromagnetic shape memory properties in the bulk are well addressed in the literature, the relationship between the martensitic and magnetic structures on the micro(nano)scale is still rather unexplored research area. In this area, the thin film technologies can play prime importance alongside opening up new technical applications. The submicron thin films of NiMnGa ferromagnetic shape memory alloys sputter-deposited on different substrates are recently in the focus of interest (see, e.g., [1-12]) since they represent promising materials for the (micro)nanosystem applications. Properties of such films depend very much on the substrate nature, film thickness and technological details (see [4] and references

36

Ferromagnetic Shape Memory Alloys

therein). The results on structure [2-5,7-9,11], texture [9], transformation behavior [1-11], and magnetic anisotropy [5-8,10,12] are worth mentioning. The thickness dependencies of the structural and magnetic properties of the martensitic NiMnGa/substrate submicron film composites, where substrate is alumina ceramic or Mo foil, have been studied in our previous works (see, e.g., [4-6,8,9]). On the other hand, a silicon technology may offer a fast possibility of integration of the newly elaborated functional materials into microsystems, so some efforts have been already undertaken to produce and characterize the NiMnGa/Si(100) film composites but these studies are at the beginning [1,2,9,11]. In particular, the significant film thickness dependence of both the MT temperature and residual stress have been found in such films [9]. In addition, a strong 220 fiber texture was also observed experimentally [9]. Meanwhile, the texture of polycrystalline films giving rise to the certain martensitic twin structure is a prerequisite of the occurrence of perpendicular magnetic anisotropy [5,8,12], the latter one being one of the most important properties for the applications. In the present work, the magnetic properties and magnetic domain patterns of NiMnGa/Si(100) films are studied and their film thickness dependence is determined. The origin of perpendicular magnetic anisotropy is briefly discussed. Experimental method A series of Ni51.4Mn28.3Ga20.3 thin films were sputter-deposited on the Si(100) wafer with 500 nmthick amorphous buffer layer of SiNx. The film thicknesses vary from 0.1 to 5 µm. The substrate temperature was kept about 50 oC. The experimental details of films preparation by radio-frequency magnetron sputtering can be found elsewhere [4-9]. Then, the samples were annealed in vacuum (2x10-4 Pa) at 800°C for 1 hour and cleaved to a size of about 4 mm x 4 mm. A cross-sectional EDS profile of the film composites measured with the SEM excluded a possible diffusion of Si into the Ni-Mn-Ga films. It has to be noted that due to the large difference in the thermal expansion coefficients of film and substrate, the films thicker than 2 µm are subject of peeling of the substrate after annealing. The structural characterization was carried out at room temperature with an X-ray diffractometer (Rigaku RINT2200, CuKα radiation) in the angle range of 20◦ < 2θ < 90◦ with a step of 0.04◦ and a holding time of 2 s for each step. The transformation behavior was characterized by the temperature dependencies of electrical resistivity which were precisely measured by the four-probe method using set-up controlled with LabView software. In the course of these measurements, a sample was immersed inside the oil bath, a thermocouple was attached directly to the sample. In-plane and out-of-plane magnetization loops at room temperature were studied by a SQUID magnetometer (Quantum Design MPMS). The magnetic field-induced signal from the substrate was recorded separately in order to correct the data. The magnetic force microscopy, MFM, and atomic force microscopy, AFM, measurements were performed with a Digital Instrument 3100 AFM/MFM probe microscope. Topographic (height contrast) and magnetic (phase contrast) images were obtained in tapping and tapping-lift mode using standard non-magnetic and magnetic tips. Magnetized CoCr coated etched silicon probe magnetic tips with resonant frequency 70 kHz were used. The lift scan height was in the range 50– 120 nm depending on the sample. Each sample was measured in remanent state after applying a 1 T field with a magnet. X-ray results Previous X-ray synchrotron studies have shown that in the parent phase stable at 150 oC, our films exhibited a strong 220 fiber texture which is inherited by the martensitic phase at room temperature [5-9]. The film composition and heat treatment ensure the formation of 10M- and/or 14M-

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martensitic phase with c/a < 1 type of lattice distortion. This is in line with the X-ray powder diffraction patterns where a limited number of small peaks clustering near the intense broad 202M/022M maximum is observed (Fig.1). Because 220M reflection is not observed, this indicates the preferential formation of two martensite variants with the unit cell parameter a parallel to the film plane and the short parameter c inclined to the film plane by 45o. Thus, the twinning planes of these variants are parallel to the film plane (e.g.,[12]). Such martensitic microstructure has important consequences on the micromagnetic structure of films, which will be discussed below. In Fig.1, the 2θ positions of the peaks which can be still distinguished are labeled by italic characters at the figure top. The X-ray spectra contain very intense (220)C-peak of austenitic phase [e-peak at 2θ=44.4o(2)] and several weak reflections which number is dependent on the film thickness. Although rigorous analysis of XRPD pattern in Fig.1 is impossible, some crystallographic features may be inferred by taking into account non-diffraction data of this work and the literature results [4, 15]. The 0.1 µm thick film displays only the (220)C-peak [besides the (200)Si peak of the substrate]. For this film, the (220)C-peak is significantly narrower than for all other films suggesting that 0.1 µm thick film could be entirely cubic. For the other film thicknesses, this peak overlaps with d-peak of the martensitic phase, presumably (0,0,10) of 10M-martensite. The presence of c- and f-peaks might be also attributed to the 10M monoclinic phase [4,15] although it cannot be excluded that due to residual stresses or composition fluctuation, the 14M-martensite is also formed. Generally, the occurrence of the peculiar cluster of peaks near (220)C intense maximum such as visible in Fig.1 qualitatively indicates modulated character of the crystal lattice of martensitic phase in Ni-Mn-Ga alloys, while the periodicity of modulation is hardly discernible [4]. The a- and b-peaks in the lowangle range can be attributed to the L21 and B2 atomic ordering of cubic phase, respectively.

Fig. 1. X-ray diffraction patterns for Ni51.4Mn28.3Ga20.3 thin films of different thicknesses deposited on the Si(100)/SiNx wafer. XRPD for the wafer is also shown. CuKα radiation is used. Exact positions of peaks are labeled on a top by the italic characters a… f.

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Ferromagnetic Shape Memory Alloys

Transformation behavior and magnetic properties Fig. 2 shows selected electrical resistivity curves for the films of different thicknesses. Basically, the structural and ferromagnetic transformations in the heat-treated (HT) well-ordered Heusler alloys are readily detected by the measurements of the anomalies on the temperature dependencies of electrical resistivity. Instead, as-deposited non-heat-treated (NHT) submicron films show in the investigated temperature range of -30 – +180 oC an almost linear dependence of electrical resistivity with some slope depending on the film thickness (Fig. 2). Such dependencies stem from the quasiamorphous state and various degree of the structural and magnetic disorder in the as-deposited samples. The aforementioned behavior changes drastically after heat treatment.

Fig. 2. Temperature dependencies of resistivity for as-deposited non-heat-treated (NHT) and heat-treated NiMnGa/Si(001) films (HT). Films in annealed state show thermal hysteresis typical for the martensitic transformation and kink due to ferromagnetic ordering. Film thicknesses are indicated near curves. Arrows point to the transformations temperatures.

The well-pronounced hysteretic anomaly reflects the presence of the martensitic transformation (MT) at TM, which is the MT temperature, while kink-like anomaly at the elevated temperatures is an unequivocal signature of the Curie temperature, TC. This kink is related to the appearance of electron scattering on magnetic fluctuations in the paramagnetic phase. A perfectly reversible character of the martensitic transformation and small temperature hysteresis width are observed also for other film thicknesses, except for the smallest thickness of d=0.1 µm. The last film is not transforming martensitically down to -30 oC but in the additional low-field magnetization measurements carried out to lower temperatures, the MT, indeed, is observed at about -73 oC (see Fig. 3). Thus, the resistivity results demonstrate the presence of martensites at room temperature (except of 0.1 µm film) which is an important precondition for development of micro- and nanodevices. The Curie temperature extracted from the resistivity curves does not show a thickness evolution [Fig. 4(a)]. In studied thickness range, TC only fluctuates within 1 oC. It has to be recalled that TC was reduced by about 25 oC for 0.1 µm thick film compared to the 5 µm thick one in the same NiMnGa film deposited on alumina ceramic [6]. The thickness dependence of TC

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Fig.3. Magnetization measured at 100 Oe as a function of temperature for annealed NiMnGa/Si(100) film composite with film thickness 0.1 µm. Arrows point to the temperatures of martensitic transformation and ferromagnetic ordering.

of film deposited on alumina can be probably related with long annealing time 10h. Such a thickness-dependent trend may be presumably explained by two possible reasons. One is an

Fig.4. Thickness dependencies of the magnetic characteristics for annealed NiMnGa/Si(100) film composites: Curie temperature, TC, determined from resistivity curves (a); magnetic susceptibility, χ, determined as slopes of the initial linear part of the magnetisation curves measured parallel to the film plane (b); anisotropy field, Ha, determined from magnetisation curves measured perpendicularly to film plane direction (c); effective magnetic anisotropy parameter, Keff, calculated as area between in-plane and out-of-plane magnetisation curves (d) and coercive field, Hc (e). The symbol size is correspondent to the uncertainty, error bars are shown in section (c). Lines are guides for the eye.

exchange integral decreasing due to increasing of Mn - Mn distances in the course of the enlargement of in-plane tension of film. Other reason can be related to the general trend towards superparamagnetic behavior when decreasing size of the ferromagnetic entities. In the case of films on Si(100) studied in this work, these factors appeared not pronounced. Fig. 5 shows typical examples of relative change of magnetization as a function of the magnetic field, M(H), measured in the perpendicular (PE) to film plane direction and parallel (PA) to it.

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Ferromagnetic Shape Memory Alloys

Curves are shifted for clarity. Perpendicular measurements clearly show different values of anisotropy fields, Ha, for the different film thicknesses. Ha is tentatively taken at the point of deviation of M(H) curve from the extrapolated high-field linear dependence. The parallel measurements demonstrate slow changing values of Ha for the different thicknesses but

Fig.5. Typical examples of the relative change of magnetization as a function of the magnetic field measured at 25 oC in the perpendicular to film plane direction (PE) and parallel to it (PA) (Inset). Films are in the martensitic state. Curves are shifted for clarity. Arrows point to the values of anisotropy field. The film thicknesses are indicated near the curves.

quite different values of the initial magnetic susceptibility, χ, much larger than in the case for the perpendicular geometry. An in-plane magnetic anisotropy was not found in our measurements which is consistent with a fiber texture of films. The thickness dependencies of the values of perpendicular Ha, parallel χ and coercive field Hc are plotted in different sections of Fig. 4. The perpendicular data for 5 µm film were not accessible since specimens were peeled off substrate due to heat treatment whereby having tube-like shape. Note that coercive field Hc ≈ 100 Oe was approximately the same for in-plane and out-plane configuration. Fig. 4(d) contains the values of the magnetic anisotropy, Keff, calculated as the areas between in-plane and out-of-plane M(H) curves (see [5,6,8]). The results shown in the sections (b,c) of Fig. 4 are qualitatively similar to the ones obtained for the NiMnGa/substrate composites where substrate is alumina [4-6] or Mo foil [8]. In fact, all the described data and literature results show thickness dependence of the magnetic

Fig.6. Magnetization curves for 0.1 µm film measured at 25 oC (austenite state) and at -193 o C (martensitic state) in the parallel to film plane direction (PA). Different saturation fields can be seen.

parameters in the submicron range. Contrary to the films on alumina and Mo foil, Keff for NiMnGa/Si(100) demonstrates slight decrease as the film thickness increases [Fig.4(d)]. This disagreement is related to the ambiguity in the absolute value of the calculated saturation magnetization. The irregular geometry of the samples obtained by cleavage and the uncontrollable variation of film thickness could be the reasons of such ambiguity. The magnetic results shown in Figs.4 and 5 are related to the studied films with thicknesses larger than 0.1 µm. They exhibit ferromagnetic martensite at room temperature. For comparison

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sake, two magnetization curves for 0.1 µm film exhibiting a ferromagnetic cubic austenite at 25 oC and ferromagnetic martensite below -73 oC are depicted in Fig. 6. Both two M(H) curves were measured in parallel configuration. The curves in Fig. 6 reflect the well-known for the bulk NiMnGa alloys fact that the magnetic anisotropy of martensitic phase is much larger than one of austenite. The temperature dependence of the magnetic anisotropy in the textured martensitic NiMnGa thin films is unknown and must be clarified in future. Scanning probe microscopy Fig. 7 illustrates a surface topography and corresponding images of the micromagnetic structure of the same film areas for the films of different thicknesses. MFM image for austenitic 0.1 µm film (not shown in Fig.7) contains very irregular features much reminiscent to the ones observed in the surface relief implying that magnetic moments in this case are aligned in film plane.

Fig.7. AFM topographic images (upper side) and corresponding MFM magnetic domain patterns (bottom side) of the same areas for the annealed NiMnGa/Si(001) film composite of different film thicknesses indicated below. Like in the case of NiMnGa/substrate thin film composites where substrate is alumina [5] or Mo foil [8], the films deposited on Si(100) wafer in remanent state reveal a stripe domain pattern mismatching the surface relief (Fig.7). This pattern is produced by the perpendicular component of macroscopic magnetization directed up and down to the film surface. This component is resulting from the 220 fiber texture and a preferable orientation of two tetragonal martensitic variants with easy-magnetization c-axis inclined to the film plane by 45o as described above in the section Experimental Method. According to Fig. 8, the average stripe domain periodicity varies considerably depending on the film thickness. The values of averaged width δ of magnetic domains measured from the images in Fig. 7 are plotted in Fig.8 in accordance to the simple expression (see [5,8] and references therein):

δ =ξ d .

(1)

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Ferromagnetic Shape Memory Alloys

Fig. 8. Film thickness dependence of the averaged magnetic domain width, δ, determined from the MFM images shown in Fig. 7, as a function of film thickness. The straight line shows a linear fit to the experimental data made according to Eq.(1).

In Eq.(1), the parameter ζ is a function of anisotropy and exchange energy. Linear approximation in Fig. 8 demonstrates that the magnetic domain pattern of the 220 fiber textured submicron NiMnGa films deposited on Si(100) wafer (alumina ceramic or Mo foil) is described by simple onedimensional model of a conventional domain wall. The reason for the occurrence of the stripe domains is a perpendicular magnetic anisotropy Kperp. In a textured film which is the present case, Kperp is assumed to consist of several competitive constituents such as magnetostatic anisotropy due to the film shape, Kd ≈ 2πM s2 (Ms is the saturation magnetization), magnetocrystalline uniaxial anisotropy, Ku, and magnetoelastic stress-induced anisotropy, Kλ ≈ -3/2λσ (λ and σ are the magnetostriction and in-plane residual stress, respectively). The magnetocrystalline and/or magnetoelastic anisotropies may compete with the shape anisotropy, particularly if the film is textured [12] as in the present case. Numerical approximate estimations can be done using the following reasonable parameter variations: Ms ≈ 300 – 450 emu/g for saturation magnetization of films [5,8,10]; λ ≈ -50 ppm for the magnetostriction [13], and 0.4 – 1.0 GPa for the in-plane tensile residual stress [9]. Rough estimations and averaging result in Kd ≈ 8×105 erg/cm3 and Kλ ≈ -5×105 erg/cm3. The sum (Kd + Kλ) is much lower than value Ku ≈ -2×106 erg/cm3 [14], thus ensuring a perpendicular magnetic anisotropy of film due to major role of Ku. Summary The magnetization behavior and micromagnetic domain structure of martensitic Ni51.4Mn28.3Ga20.3 films sputter-deposited on Si(100) have been characterized. The thickness dependencies of both the magnetic anisotropy parameters of the films and magnetic stripe domain width are identified. The perpendicular magnetic anisotropy in the studied martensitic films is explained by major contribution of the magnetocrystalline anisotropy due to 220 fiber texture and martensitic twin preferable orientation. The results of this work suggest that Si technology is promising for the implementation of ferromagnetic martensites into functional microsystems.

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Acknowledgments VAC, SB and AG are grateful to Fondazione Cariplo for financial support (project 2004.1819A10.9251). PM acknowledges partial support through DARPA contract N66001-01-C-80345. Authors thank to Dr. H.Rumpf for providing a silicon wafer. References [1] M. Wuttig, C. Craciunescu and J. Li: Mater. Trans. JIM.Vol. 41 (2000), p. 933 [2] A. Hakola, O. Heczko, A. Jaakkola, T. Kajava and K. Ullakko: Appl. Surf. Sci.,Vol. 238 (2004), p. 155. [3] W. Dong, Q. J. Xie, J. Lu, C. Adelmann, C.J. Palmstrøm, J. Cui, Q. Pan, T.W. Shield, R.D. James and S. McKernan: J. Appl. Phys. Vol. 95 (2004), p.2593. [4] V.A. Chernenko, M. Ohtsuka, M. Kohl, V.V. Khovailo and T. Takagi: Smart Mater. Struct. Vol.14 (2005), p.S245. [5] V.A. Chernenko, R. Lopez Anton, M. Kohl, M. Otsuka, I. Orue and J.M. Barandiaran: J. Phys. Condens. Matter. Vol. 17 (2005), p. 5215. [6] M. Kohl, V.A. Chernenko, M. Ohtsuka, H. Reuter and T.Takagi: Mater. Res. Soc. Symp. Proc. Vol.855E, W2.8.1 (2005). [7] M. Kohl, A. Agarwal, V.A. Chernenko, M. Ohtsuka and K. Seemann: Mater. Sci. Eng. A. Vol. 438–440 (2006), p.940. [8] V.A. Chernenko, R. Lopez Anton, M. Kohl, J.M. Barandiaran, M. Ohtsuka, I. Orue and S. Besseghini: Acta Mater. Vol. 54 (2006), p.5461. [9] S.Besseghini, A. Gambardella, V.A. Chernenko, M. Hagler, C. Pohl, P. Müllner, M. Ohtsuka and S. Doyle: to be published in European Physical Journal-Special Topics (2008). [10] J. Dubowik and I. Goscianska: J. Magn. Magn. Mater. Vol. 316 (2007), p. 599. [11] C.Li, J.Sun, G.Sun, G. Yao, and Z.Chen: Surf.&Coat.Techn. Vol.201(2007), p.5348. [12] V.A.Chernenko, M. Hagler,P. Müllner, V.M. Kniazkyi, V.A. L’vov, M. Ohtsuka and S. Besseghini: J. Appl. Phys. Vol.101 (2007) 053909. [13] V.A. Chernenko, V.A. L’vov, M. Pasquale, S. Besseghini, C. Sasso and D.A. Polenur: Int. J. Appl. Electromag. Mech. Vol. 12 (2000), p. 3. [14] O. Heczko and L. Straka: JMMM. Vol. 272–276 (2004), p. 2045. [15] Y. Ge, O. Söderberg, N. Lanska, A. Sozinov, K. Ullakko and V. K. Lindroos: J. Phys.IV France. Vol. 112 (2003), p.921.

II. Thermal Treatments and Phase Stability

Advanced Materials Research Vol. 52 (2008) pp 47-55 © (2008) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/AMR.52.47

Intermartensitic Transformations in Ni-Mn-Ga alloys: a general view C. Seguí1,a, E. Cesari1,b and J. Pons1,c 1

Departament de Física, Univ. de les Illes Balears, E-07122 Palma de Mallorca, Spain a

[email protected], [email protected], [email protected]

Keywords: Ferromagnetic shape memory alloys; Intermartensitic transformation; Ageing; Ordering

Abstract. Off-stoichiometric Ni2MnGa ferromagnetic shape memory alloys undergo a martensitic transformation (MT) from the L21 cubic phase to a martensitic crystal lattice consisting, in the majority of cases, of a periodic stacking sequence of nearly closed-packed planes with periodicity of 5, 7 or 2 planes, denoted as 10M (five layered tetragonal), 14M (seven layered orthorhombic) and 2M (non-modulated tetragonal). In addition to the parent to martensite transformation, Ni-Mn-Ga alloys tend to show stress or temperature induced intermartensitic transformations (IMTs) towards the most stable 2M phase, through the sequences 10M→14M→2M or 14M→2M depending on the first formed martensite. The IMTs reported in the literature show a variety of characteristics such as reversibility, completeness, hysteresis and temperature of occurrence, but, as a general trend, the role of internal stresses in favouring the occurrence of IMTs is recognised. Recently it has been shown that the L21 order degree favours the occurrence of the intermartensitic transformation from 14M to 2M martensite, stabilising the non modulated martensite through a decrease of its free energy with respect to the layered martensite. From this point of view, the occurrence of intermartensitic transformations in Ni-Mn-Ga alloys appears as a “chemical“ free energy effect. Aiming to go deeply into this aspect, in this work the occurrence of IMTs and their properties have been examined for an extensive set of off-stoichiometric Ni2MnGa. The results show the existence of a relationship between the IMTs temperatures and the alloys composition, as well as the dependence of all observed IMTs (i.e., 10M→14M, 14M→2M and their corresponding reverse transformations) on the L21 order degree.

Introduction Ferromagnetic shape memory alloys (FSMA) have received increasing interest, mainly due to the giant magnetic field induced strain (MFIS) that they can show [1,2]. Such MFIS is based on the rearrangements of the crystallographic domains –i.e., twin variants-. Among FSMA, close to stoichiometric Ni2MnGa Heusler-type alloys, are the most studied. The ferromagnetic Ni-Mn-Ga alloys undergo, on cooling or under applied stress, a thermoelastic martensitic transformation (MT), which characteristics depend highly on composition [3]. Particularly, the transformation temperature (TM) has been found to increase as the electron to atom ratio, e/a [4,5] while the Curie temperature (TC) is located around 350 K and less composition dependent, slightly decreasing for increasing e/a [3,4]. The austenite phase of off-stoichiometric Ni2MnGa alloys has L21 ordered cubic structure, and the crystal lattice of the martensite is, in the majority of cases, a periodic stacking sequence of nearly closed-packed planes with periodicity of 5, 7 or 2 planes, denoted as 10M (five layered tetragonal), 14M (seven layered orthorhombic) and 2M (non-modulated tetragonal) [5,6]. Aside from those structures and their mixtures, stacking sequences with periodicity of six, eight, ten or twelve planes have been occasionally observed [5-7].

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Among the above described martensite structures, the non-modulated 2M appears as the most stable, since, in addition to the parent to martensite transformation, stress or temperature induced intermartensitic transformations (IMTs) towards the 2M phase have been observed in several NiMn-Ga alloys [8-13], often in the sequence 10M→14M→2M if the first formed martensite is 10M, or 14M→2M if austenite is transformed into seven layered martensite [14]. It is worth noting that, since big magnetic field induced strains have been only observed in the modulated five or seven layered martensites, it is essential to establish the region of existence of such martensite structures, as a function of composition as well as a function of temperature; if, for example, the desired structure forms directly from the (ferromagnetic) parent phase, a subsequent intermartensitic transformation would give the lower temperature limit for which such structure exists. Thus detailed knowledge and understanding of the mechanisms driving the occurrence of intermartensitic transformations seem to be a major affair concerning the applicability of FMSA. Indeed, this phenomenon has been reported in the literature for diverse compositions, but a general picture is yet lacking. The apparent scattering of the experimental results concerning IMTs hinders the building of such a picture. Recently it has been shown that the L21 order degree favours the occurrence of the intermartensitic transformation from 14M to 2M martensite, stabilising the non modulated martensite through a decrease of its free energy with respect to the layered martensite [15]. From this point of view, the occurrence of intermartensitic transformations in Ni-Mn-Ga alloys appears as a “chemical“ free energy effect. Aiming to go deeply into the knowledge of IMTs, in this work the occurrence of IMTs and their properties have been examined for an extensive set of off-stoichiometric Ni2MnGa. The results show the existence of a relationship between the IMTs temperatures and the alloys composition, as well as the dependence of all observed IMTs (i.e., 10M→14M, 14M→2M and their corresponding reverse transformations) on the L21 order degree.

Experimental Procedures Off-stoichiometric Ni2MnGa alloys, with nominal compositions given in Table 1 have been used. The samples were subjected to an initial annealing consisting of 24 h ageing at 1100 K followed by air cooling to room temperature (annealed condition). The transformation sequences on cooling and heating were mainly recorded by means of Dynamic Mechanical Analysis (Perkin-Elmer DMA-7), a technique which has proven to be very sensitive to the occurrence of structural changes which, as it happens with IMTs, are hardly detected by other conventional techniques such as DSC. DMA outputs are the internal friction (IF, measured as the phase lag between the sinusoidal applied stress and the strain response) and the elastic modulus (E, obtained as the real part of the complex modulus, see [16] for more details). Plate like specimens of appropriate size were spark cut from the rods and the measurements were performed in three point bending configuration at 1 Hz frequency, 3 MPa stress amplitude (corresponding to strain amplitudes in the range 10-4) and temperature rate 5 K/min. The Curie temperature TC was also obtained from DMA measurements in which a small permanent magnet was placed below the sample; the change of magnetic interaction between the sample and the magnet when crossing TC causes apparent changes of the elastic modulus. Although the Curie temperatures determined by this method are affected by a considerable uncertainty, they are reliable enough to account for relative changes in the position of the magnetic transition. Additional Differential Thermal Analysis (DTA) and Differential Scanning Calorimetry (DSC) measurements were also performed. Structural changes and phase identification was made by means of a TEM electron microscope Hitachi H-600 100 kV, equipped with single tilt cooling and heating stages. Thin foil specimens

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were prepared by double jet electro-polishing in an electrolyte composed of 30% nitric acid in methanol at ~ 250 K. For some of the studied alloys the effect of gradual ageing at 570 K (well above the reverse transformation finish temperature) after water quench from 1070 K on the structural and magnetic phase transitions was also studied.

Alloy# G17 G42 G43 G44 G45 G46 G30 G28 G12 G9

SC PC PC PC PC PC SC SC SC PC

Ni 52.6 50.5 48 51 49.5 52.5 53.1 51.2 59 58.3

Mn 23.6 30 31 28 30.5 24.5 26.6 31.1 19.4 15.9

Ga 23.8 19.5 21 21 20 23 20.3 17.7 21.6 25.8

e/a TM1 7.626 283 7.735 360 7.6 263 7.69 338 7.685 389 7.655 301 7.781 380 7.828 413 7.906 570 7.717 518

TM2 183 257 204 263 346 263 349 348

TM3 TC 163 354 341 343 348 183 353 186 341 396 355 321 333

Table 1.- Nominal compositions [at%], electron to atom ratio and transformation temperatures [K] for the studied alloys in the annealed condition. See text for details. SC are single crystalline and PC polycrystalline alloys.

Results The IF and E–modulus evolutions during cooling and heating runs of some of the studied alloys (G17, G44 and G30) in the annealed state are shown in Figs. 1, 2 and 3. As it was previously established in [12] and [15], the stages which can be observed both in the IF and the modulus behaviour are due to the occurrence of a sequence of martensitic and intermartensitic transformations. In the case of the single crystalline alloy G17 (Fig. 1) two IMTs are observed on cooling, corresponding to the sequence L21→10M→14M→2M, the reverse sequence being observed on heating [12]. The temperatures of the maxima of internal friction are taken as representative of the structural transformations, and are labelled as TM1 and TA1 (forward and reverse MT), TM2 and TA2 (first intermartensitic transformation) and TM3 and TA3 (second IMT).

0.5

20 TM1 TA2

0.35 0.3

0.15

16 14 12

0.25 0.2

18 TA1

0.4

10

TM2

8

TM3 TA3

6

0.1

4

0.05

2

0 0 100 125 150 175 200 225 250 275 300 325 350 375 Temperature (K)

E-Modulus (GPa)

Internal Friction (tan d)

0.45

Fig. 1.- Internal friction (symbols) and elastic modulus (continuous line) vs. temperature curves for a complete cooling/heating cycle of alloy G17 in the annealed condition.

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Ferromagnetic Shape Memory Alloys

0.2

70 60 TM1

TA1

50

TA2

0.12

40 30

0.08 TM2

20

E-Modulus (GPa)

Internal Friction

0.16

Fig. 2.- Internal friction (symbols) and elastic modulus (continuous line) vs. temperature curves for a complete cooling/heating cycle of alloy G44 in the annealed condition.

0.04 10 0

0 200

225

250

275

300

325

350

375

400

Temperature (K)

0.2

60

TA

0.16

40 0.12 30 0.08

T M2

20

Fig. 3.- Internal friction (symbols) and elastic modulus (continuous line) vs. temperature curves for a complete cooling/heating cycle of alloy G30 in the annealed condition.

T M1 0.04

10 0 275

Internal Friction

Elastic Modulus (GPa)

50

300

325

350 375 Temperature (K)

400

425

0 450

Polycrystalline alloy G44 (Fig. 2) undergo at temperature TM1 on cooling the L21→14M martensitic transformation, followed on further cooling by the intermartensitic 14M →2M occurring at TM2. The reverse transformations occur at TA2 and TA1 on heating, as indicated in Fig. 2. Also the single crystalline alloy G30 (Fig. 3) exhibits 14M as the first formed martensite, experiencing an intermartensitic transformation towards the 2M structure on cooling at lower temperatures. In this case, however, the reverse transformation on heating takes place in a single step from 2M to austenite [see 15]. DSC cooling and heating runs performed on samples of the above alloys confirm the sequence of structural, first order, transformations [12,15]. The above mentioned transformation sequences have been confirmed by TEM observations performed during in situ cooling and heating [12,15]. An important fact is, however, that the martensite phases observed in the thin foils often consist of a mixture of structures, the transformation events producing (significant) changes in the fraction of the present structures instead of leading to a single phase. As an example, thin foils of alloy G17 undergo, on in situ cooling, a MT from the parent L21 to 10M martensite (see Fig. 4(a)); on further cooling, another transformation event leads to a mixture of 14M and 2M structures, with residual presence of 10M. At the lowest attainable temperature (≈ 110 K) still the three above mentioned martensitic phases are present (see Fig. 4 (b) and (c)), although 2M is the major component and 10M appears only scarcely [12].

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While the presence of regions of anomalous or unexpected phases can be due, at least to some extent, to the thin foil condition, yet the IMTs seem to be incomplete as a single martensite structure is seldom observed. In Table 1 other Ni-Mn-Ga alloys showing one or two IMTs are quoted, and the corresponding transformation temperatures are indicated, together with other alloys showing the MT solely.

(a)

(b)

(c)

Fig. 4.- Selected area diffraction patterns of alloy G17 obtained upon in-situ cooling, corresponding to 10M (a), 14M (b) and 2M (c) martensites.

0.15

0.12 Internal Friction

TQ=1070 K 0.09

TQ=970 K

Fig. 5.- Internal Friction vs. temperature cooling curves obtained for alloy G30 after quenching from different TQ temperatures.

TQ=870 K 0.06

TQ=770 K TQ=670 K

0.03

initial astreatment received 0 250

275

300

325

350

375

400

425

450

Temperature (K)

Thermal treatments performed to the studied alloys have been found to modify the temperatures at which the structural –and magnetic- transitions occur. For instance, Fig. 5 shows the IF vs. temperature curves obtained during cooling after water quenching alloy G30 from different TQ temperatures between 670 and 1070 K. It can be seen that, while the highest temperature IF peak, which corresponds to the MT L21→14M, occurs at almost constant temperature, the second IF peak, corresponding to the intermartensitic 14M→2M, shifts toward lower temperatures with increasing TQ. After water quench from 1070 K, no IF peak related to the IMT is observed even cooling down to 120 K. On its turn, the single step reverse transformation observed for G30 remains almost unchanged when varying TQ. Along with this temperature evolution, the IF peaks shape show changes that are indicative of changes in the transformation dynamics. Ageing at 570 K (well in parent phase) after water quench from TQ=1070 K allows for recovering of the IMT, its temperature of occurrence increasing with ageing time until reaching a constant value –similar to that of the annealed condition- after about 1 hour ageing. On their turn, the temperatures of the IF peaks corresponding to the forward MT and to the reverse single step are much less affected by

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ageing. Similarly, neither the quench temperature nor ageing after quench affect significantly the Curie temperature TC. The above behaviour, summarised in Fig. 6, reflects the effect of L21 ordering: quenching from TQ=1070 K (above the B2↔L21 ordering temperature, determined by DTA experiments to be of 1030 K for alloy G30) leads to significant disorder, and the L21 order degree improves upon austenite ageing; L21 ordering has little effect on the forward and reverse MT temperatures while favouring the occurrence of the intermartensitic transformation.

400

450

350

300

Temperatures (K)

Temperatures (K)

400

350

300

250

200

150

250 1.E+00

TQ=1070 K

1.E+01

1.E+02

1.E+03

1.E+04

Ageing time (min)

Fig. 6.- Martensitic (forward ■ and reverse □) and intermartensitic (●) transformation temperatures and Curie temperature (∆) of alloy G30 as a function of ageing time at 570 K after a previous quench from 1070 K.

100 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05

TQ=1070 K

Ageing time (min)

Fig. 7.- Martensitic (■), first (●) and second (
) intermartensitic transformation temperatures and Curie temperature (∆) obtained on cooling alloy G17 as a function of ageing time at 570 K after a previous quench from 1070 K.

The effect of thermal treatments has been also studied on several of the alloys presented in Table 1. In all cases the results have confirmed the above conclusion. It is worth to mention that, if two intermartensitic transformations occur on cooling below the MT, both of them are suppressed by water quench from 1070 K, and both are progressively recovered upon austenite ageing at 570 K. This is illustrated in Fig. 7, where the evolution of the transformation temperatures as a function of ageing time is plotted for alloy G17.

Discussion and conclusions The occurrence of a sequence of martensitic and intermartensitic transformations on cooling has been already recognised and analysed in the literature for a wide set of Ni-Mn-Ga [7,10-15,17] and some other FSMA [18-20]. In spite of the large number of reported cases, the phenomenon of IMTs has not been boarded as a general issue of phase stability in this alloy system. The lack of a general approach can be, at least partially, due to the apparent scattering of the experimental results concerning IMTs. As a matter of fact, the IMTs reported in the literature exhibit a big variety of characteristics, such as undercooling below the MT, temperature extent, hysteresis, etc. Along with

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this variability the role of internal stresses favouring the occurrence of IMTs is widely recognised [11,12,20]. To find, if any, a systematic relationship between the composition of Ni-Mn-Ga and the occurrence and properties of intermartensitic transformations, the available data has been plotted as a function of the electron to atom ratio (e/a). A graph has been built using as starting point the MT and Curie temperatures for a large set of off-stoichiometric Ni2MnGa alloys, listed and depicted as a function of e/a in [21], to which the data concerning IMTs, given in Table I, corresponding to the alloys in the “ordered” state, has been added. In order to produce a picture as general as possible, IMTs data extracted from the literature [9-11, 17, 20, 22, 23] have also been included. The result is shown in Fig. 8.

600

Temperatures (K)

500 400 300 200 100 0 7.3

7.5

e/a

7.7

7.9

Fig. 8.- Characteristic temperatures for the martensitic (■, □), first (●, ○) and second (▲,∆) intermartensitic transformations, Curie temperature (+, x) as a function of the electron concentration for the studied alloys. The open symbols correspond to data extracted from the literature. The uncertainty for e/a is indicated by an error bar. The lines are just a guide for the eyes, while the dotted line indicates the temperature of the premartensitic transformation observed for close to stoichiometric Ni-Mn-Ga alloys.

As it can be seen in Fig. 8, despite the large scatter, the temperatures corresponding to the IMTs increase with increasing e/a. Moreover, the occurrence of IMTs seems to be limited to the electron to atom ratio values roughly ranging from 7.6 to 7.8. Besides the uncertainty for e/a, indicated by the error bar in Fig. 8, several sources contribute to blur the picture: on the one hand, the uncertainty in the determination of the transformation temperatures, which can be related to the use of different experimental techniques with different sensitivity to the mechanisms underlying IMTs; on the other hand, the thermal (and mechanical) treatments performed on the samples can influence the martensite structure, thus the subsequent intermartensitic transformations sequence, and, as it has been shown, the transformation temperatures depend on the resulting order degree; finally, considering the proven influence of internal stresses on the occurrence of IMTs, the austenite microstructure is likely another factor that should be accounted for. The recent finding of the effect of L21 ordering on the intermartensitic transformations is a further indication of the prevalence of the “chemical” free energy terms in driving the occurrence of IMTs. This issue was studied in detail in [15] for alloys G28 and G30, showing the transformation sequence L21→14M→2M, being concluded that while L21 ordering has little effect on the forward and reverse martensitic transformation temperatures, it favours the occurrence of the

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Ferromagnetic Shape Memory Alloys

intermartensitic transformation from 14M to non-modulated martensite, stabilising the non modulated martensite through a decrease of its free energy with respect to the seven-layered martensite. The change in the free energy difference between the two martensitic phases which brings about a shift δTM2 of the IMT temperature can be approached as δ∆G14M → 2M = ∆S 14M → 2M ⋅ δTM 2

(1)

where ∆S14M→2M is the entropy change associated to the intermartensitic transformation. It has to be taken into account that the different martensite structures (14M and 2M) are energetically very close to each other, as proven by the very low values of the related entropy changes (determined by DSC for both G30 and G28 alloys), thus small changes of the relative free energy in [7] as –0.2 J mol ⋅ K

are enough to cause considerable shifts of the intermartensitic transformation temperatures; as a matter of fact, Fig. 6 reveal displacements of TM2 around 50 K, which, according to (1), would be caused by a free energy change of only –10 J/mol. Instead, the entropy change associated to the martensitic transformation, |∆SP→14M|, takes considerably higher values (1.5 and 1.6 J for mol ⋅ K

alloys G30 and G28 respectively, according to [7]), meaning that much bigger free energy changes would be necessary to produce comparable displacements of the corresponding transformation temperature. The above estimation of the relative free energy change can not be extrapolated to the martensitic transformation, since the free energy of the related phases can be affected by ordering to a different extent, but it is worth to note that variations around –10 J/mol would be expected to produce shifts of only ~ 6 K in the martensitic transformation temperature TM1. The study of the effect of L21 ordering on the IMTs has now been extended to the transformation sequence L21→10M→14M→2M, as undergone by alloy G17. As it can be seen in Fig. 7, both the 10M→14M and the 14M→2M intermartensitic transformations are favoured by improvement of the L21 order degree, while the martensitic and the magnetic transitions are much less affected by austenite ageing, as indicated by the different shifts of the corresponding transformation temperatures. Therefore, the argument of the change of the relative stability of the martensite phases brought about by L21 ordering is still valid in the case in which the full L21→10M→14M→2M sequence is observed. The closeness of the free energies of the different martensite structures can help to understand the importance of internal stresses on the occurrence and reversibility of intermartensitic transformations referred to in the literature [11,13,17], since the elastic energy developed in the first formed martensite can be enough to change the relative stability of the phases. Acknowledgements: Financial support from DGI of Spain (Project MAT2005-00093) and from CAIB (PCTIB-2005-CC2-02) is acknowledged.

References [1] T. Kakeshita and K. Ullakko: MRS Bull. 27 (2002) p. 105 [2] R. Tickle, R.D. James, T. Shield, M. Wuttig and V.V. Kokorin: IEEE Trans. Magn. 35 (1999) p. 4301 [3] V.A. Chernenko, E. Cesari, V.V. Kokorin and N.I. Vitenko: Scripta Mater. 33 (1995) p. 1239 [4] V.A. Chernenko: Scripta Mater. 40 (1999) p. 523 [5] J. Pons, V.A. Chernenko, R. Santamarta and E. Cesari: Acta Mater. 48 (2000) p. 3027 [6] J. Pons, R. Santamarta, V.A. Chernenko and E. Cesari: J. Appl. Phys. 97 (2005) p. 083516

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[7] V.A. Chernenko, C. Seguí, E. Cesari, J. Pons and V.V. Kokorin: Phys. Rev. B 57 (1998) p. 2659 [8] J. Pons, V.A. Chernenko, E. Cesari and V.A. L’vov: J. Phys. IV Paris 112 (2003) p. 939 [9] O. Heczko and K. Ullakko: IEEE Trans. Magn. 37 (2001) p. 2672 [10] L. Straka, O. Heczko and N. Lanska: IEEE Trans. Magn. 38 (2002) p. 2835 [11] W.H. Wang, Z.H. Liu, J. Zhang, J.L. Chen, G.H. Wu, W.S. Zhan, T.S. Chin, C.H. Chen and X.X. Zhang: Phys. Rev. B 66 (2002) p. 052411 [12] C. Seguí, V.A. Chernenko, J. Pons, E. Cesari, V. Khovailo and T. Takagi: Acta Mater. 53 (2005) p. 111 [13] V.A. Chernenko, J. Pons, E. Cesari and K. Ishikawa: Acta Mater. 53 (2005) p. 5071 [14] V.A. Chernenko, V.V. Kokorin, O.M. Babii and I.K. Zasimchuk: Intermetallics 6 (1998) p. 29 [15] C. Seguí, J. Pons and E. Cesari E. Acta Mater. 55 (2007) p. 1649 [16] E. Cesari, V.A. Chernenko, V.V. Kokorin, J. Pons and C. Seguí: Acta Mater 45 (1997) p. 999 [17] Y. Xin, Y. Li, L. Chai and H. Xu: Scripta Mater. 54 (2006) p. 1139 [18] H.X. Zheng, M.X. Xia, J. Liu and J.G. Li : J. Alloys & Compd. 385 (2004) p. 144 [19] H.X. Zheng, M.X. Xia, J. Liu, Y. Huang and J. Li: Acta Mater. 53 (2005) p. 5125 [20] V.V. Khovailo, R. Kainuma, T. Abe, K. Oikawa and T. Takagi: Scripta Mater. 51 (2004) p. 13 [21] V.A. Chernenko, J. Pons, C. Seguí and E. Cesari: Acta Mater. 50 (2002) p. 53 [22] V.V. Kokorin, A.O. Perekos, , A.A. Tshcherba, O.M. Babiy and T.V. Efimova: J. Magn. Mag. Mat. 3023 (2006) p. 34 [23] V.K. Srivastava, R. Chatterjee, A.K. Nigam and R.C. O’Handley: Sol. State Comm. 136 (2005) p. 297.

Advanced Materials Research Vol. 52 (2008) pp 57-62 © (2008) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/AMR.52.57

Martensite transformation and magnetic property dependence on the annealing temperature in Ni-rich Ni-Mn-Ga alloy R. K. Singh1,a and R. Gopalan2,b 1,2

Defence Metallurgical Research Laboratory, Hyderabad 500058, India a email: [email protected], bemail: [email protected]

Keywords: Martensite transformation; Ni-Mn-Ga alloy; Curie temperature; Annealing

Abstract: The effect of annealing temperature on martensite transformation temperature and magnetic properties has been investigated in a polycrystalline Ni53.69Mn26.06Ga20.25 alloy. The significant variation of the martensite transformation temperature and the magnetic properties is observed as a function of annealing temperature. Introduction Ferromagnetic shape memory alloys (FMSAs) are new class of smart materials which exhibit high magnetic field induced strains (MFIS) with faster response as compared to conventional shape memory alloys (SMAs) due to the rearrangement of martensite variants under a magnetic field [1]. The Ni-Mn-Ga Heusler alloys have been extensively studied as FMSA in recent years since the single crystals of these alloys shows MFIS up to 6-10% making them potential material system for the device application such as actuators and sensors [2]. Ni-Mn-Ga alloys exhibit thermoelastic martensite transformation which involves transformation of ordered cubic L21 austenite phase to a low-symmetry non-modulated tetragonal or modulated (5M,7M) martensite phase on cooling [3]. In Ni-Mn-Ga alloys the martensite transformation temperature (TM) strongly depends on the composition or the valence electron to atom ratio (e/a) whereas the Curie temperature (TC) is reported to be less sensitive to the alloy composition [4]. Based on TM and TC, Ni-Mn-Ga alloys are classified into three different groups (i) TMTc. Results are discussed in the light of models available for tip-sample interactions that track the local magnetization. Introduction Shape memory alloys are technologically important materials because of their wide range of potential applications. These alloys undergo a reversible austenite phase (cubic) to martensitic phase (tetragonal or orthorhombic or monoclinic) transformation, which is a diffusionless first order paraelastic to ferroelastic transition. This results in the appearance of ferroelastic twin type domains in martensitic phase. Ferromagnetism in shape memory alloys make them more effective in the sense that they can be tuned by varying temperature, stress as well as magnetic field and are called as ferromagnetic shape memory alloys (FSMA). Ferromagnetic transition and martensitic transformation are the two transformations that these ferromagnetic shape memory alloys are expected to show. This creates the possibility for the occurrence of field induced phase transitions and field induced variant rearrangements [1]. Ni2MnGa is the most studied ferromagnetic shape memory alloy because of broad range of tunability of structural (Tm) and ferromagnetic (Tc) transitions by varying compositions. In these alloys the ferromagnetic Weiss domains are magnetoelastically coupled to and superimposed upon ferroelastic twin domains that are formed upon undergoing a martensite phase transformation [2]. In order to study the evolution of ferroelastic and ferromagnetic domains across the transformation temperatures (Tc and Tm), MFM with a temperature variation attachment is well suited because it is capable of high resolution imaging of micro magnetic structures with topography. Since Ni-Mn-Ga is known to display spectacular magnetic domains, it is considered as a good test specimen. The micro-magnetic structures and their evolution across the martensitic phase has been a subject of interest for past few years [2,4,5,6,7,8]. Simultaneous observation of magnetic domains and twin domains by optical microscope as a function of magnetic field clearly established a magnetic field induced twin boundary motion in these alloys as well as the underlying strong magneto-elastic coupling [2]. In a similar technique using Differential Interference Contrast (DIC), magnetic domains were mapped as a function of temperature and fields to establish the evolution of twin as well Weiss domains in this system [4]. Compared to the well-known powerful DIC technique, MFM seems to play a vital role in understanding the magnetic domains in a more quantitative fashion. Micro-magnetic study of domains in Ni-Mn-Ga using temperature variation of

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MFM in the presence of fields shows various evolution schemes of twin and Weiss domains across the martensite – austenite transition. They include surface relief seen at zero fields, wiping out of such relief at 2kOe. Between 2-8.5KOe, observed features include fir tree patterns, fir patterns localized at twin boundaries, single domains and a de-twined interior on higher fields [6]. In the present paper we report the coupled influence of matensitic and ferromagnetic transition on the domain structures in Ni2MnGa. Experimental Well-characterized poly crystalline sample having bulk composition Ni2.23Mn0.8Ga named as sample (A), and Ni2.35Mn0.66Ga0.98 named as sample (B) was used in present study [3]. Transition temperatures as estimated from Differential Scanning Calorimeter (DSC) are, for sample A (Tm~354K and Tc~370K) and sample B (Tm = 537K, Tc = 320K). Magnetic Force Microscopy (MFM) imaging was carried out at different temperature using multimode Nanoscope-IV from Veeco-Digital Instruments USA with a high temperature attachment option. Topographic and magnetic images are obtained with the instrument being operated in the tapping mode and lift mode using the standard MFM CoCr coated Si tips having spring constant 3N/m, resonance frequency 78 KHz and a typical lift height of 80nm. In the tapping mode cantilever oscillate in its resonance frequency and taps the sample surface at the bottom of the swing, which enables to track morphology. When the lift mode is activated, the tip is lifted by certain amount (~80nm) and the frequency shift is measured at the same locations as that of morphology. Since the tip is lifted, it is common that only long-range forces like that of magnetic origin are contributing. MFM image is constructed by measuring the resonance frequency shift of cantilever because of magnetic interaction between tip and sample at each point (pixel). Contrast between the frequency shifts is proportional to the magnetic gradient of the surface and is normally shown in units of Hz. Results and Discussion Figure 1 shows evolution of MFM images of both the samples as a function of temperature for sample A (333-393K) and for sample B (303-353K) for heating and cooling cycles. It is to be remembered that for sample A: Tm~354K and Tc~370K and sample B: Tm = 537K, Tc = 320K. In all the frames the left side shows the topography while the right side shows the MFM images. One can clearly see the evolved well-contrasted magnetic domains. Typical dimensions of the large domains are 8-10µm and the corresponding magnetic contrast is 7-8 Hz. Such large domains are characteristic of twin formation while crossing the maternsitic transition. One can also see certain fine structure inside these domains that are attributed to the magnetic Weiss domains. Typical dimensions of these fine structures are ~6µm in AFM & ~3Hz in MFM for sample A and ~4 µm in AFM & ~3Hz in MFM for sample B. The observed features at room temperature are well representatives of the results discussed above. The large contrast can be understood by the fact that sample B has a Tm well above room temperature while Tc is just above room temperature. As a result, while twins are already well formed, the magnetic order just started settling in and the effects of partial coherence are reflected in tiny and fine Weiss structures seen. In sample A, they are absent because Tc is very large and higher than Tm. In order to understand more about these structures, certain quantitative estimates are made from the observed patterns. MFM images correspond to a shift in resonance frequency of cantilever due to magnetic tip - sample interaction. The difference in domain contrast across the domain wall δf is related to the magnetic interaction force derivative F′ by F′ = 2k.δf/f where k is the spring constant and f is the resonance frequency of the cantilever. The magnetic tip sample interaction force derivative is given by F′= m x (δ2B/δz2), where m is tip magnetization and B is the sample magnetic field in z direction. By measuring this force derivative as a function of temperatures at a given morphological place (domain wall) a plot is made. This is carried out for both the samples and for heating and cooling cycles. The temperature variation of the frequency shift seems to follow a

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trend, which looks like the usual magnetization behavior across the Curie transition. We have used this shift as a magnetic order parameter and data is fitted to the usual form (1-(T/Tc))n. with n as critical exponent, which turned out to be 0.33. This is as expected for a ferromagnetic transition. Such plots are shown in Figure 2. It is interesting note that both heating and cooling show a similar trend. The difference in patterns while cooling and heating may be attributed to the reduced magnetic contrast due to several reasons inclusive of surface oxidation, in spite of argon flow used while heating.

333K

353K

373K

303K

393K

323K

353K 373K

323K 353K

303K 333K

(A) (B) Figure1. Topography (Left) and Magnetic Force Microscope (Right) images depicting the evolution of Magnetic domains across (A) the Tc (370K) and Tm (354K) in Ni2.23Mn0.8Ga and (B) the Tc (320K) in the martensitic phase of Ni2.35Mn0.66Ga0.98. Scan sizes are for (A) 57µm x 57µm.and for (B) 50µm x 50µm.

-3

Force Derivative(10 N/m)

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Ferromagnetic Shape Memory Alloys

1.4

Ni2.23Mn0.8Ga (A) = Heating = Cooling Tc ~ 374K n=0.33

1.2 1.0

Ni2.35Mn0.66Ga0.98(B) heating cooling Tc~325K n=0.33

0.7 0.6 0.5

0.8 0.4 0.6 0.3 0.4 0.2 0.2 0.1 0.0 300

320

340

360

380

400 300

320

340

360

380

Temperature(K) Figure 2. The force derivative as a function of temperature and the corresponding fittings (lines) based on the conventional magnetic order parameter variation. For sample (A) the Tc (370K) and for (B) the Tc (320K). 3.4

(Sample B)

Frequency Shift(Hz)

3.2 3.0 2.8 2.6 2.4 2.2 2.0 -8

5.0x10

-7

-7

-7

1.0x10 1.5x10 2.0x10 Tip-Surface Seperation z (meter)

Figure 3. The maximum frequency shift across the domains as a function of tip surface separation. One can also estimate the magnetization of a particular section of a domain using the point probe approximation of MFM and measurement of MFM signal as a function of tip to sample distance [9,10 ]. This measurement is shown in Figure 3 for sample B where finer size domains are seen. As we know, the magnetic tip sample interaction force derivative is given by F′ = m x (δ2H/δz2), and F′= 2k*∆f/f. where m is tip magnetic dipole moment oriented in z direction, and H is the sample magnetic field in z direction. Considering that, magnetic domains can be represented by disk of radius b and magnetization M along the z direction at a distance d from the tip, domain stray field is given as H=2πM (1-(d/(b2 +d2)(1/2))) [9]. Now making d=(z+h) the domain tip distance is equal to the domain tip surface distance plus the distance of position of dipole in the tip. Then final relation is given as: ∆f =3πb2fMm(z+h)/k[(z+h)2+b2]5/2 This equation is used to fit the MFM signal as a function of tip domain separation. To obtain the magnetization M of the sample, we need to know the several parameters in this equation. m =

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1156.57 x b2.8 and h = 61.002 x b1.31 are given for commercially available MESP tip [11]. Domain radius b ~390nm for a typical small domain considered here, then ‘m’ and ‘h’ turn out to be 9.1 x 10-16Am2 and 200nm respectively. Using these values and k = 3 N/m, f = 78.78 kHz, we obtain the sample magnetization M~7 x 103A/m. Conclusion In conclusion, the evolution martensitic twin domains along with magnetic Weiss domains have been investigated in two samples of Ni-Mn-Ga alloy system. The temperature variation option with MFM enables to map the evolution across the Curie temperature. The compositions chosen are such that in one sample Tm < Tc, while Tm > Tc in the other. Significant result is the quantitative observation of frequency shifts that scales the magnetization. Observed frequency shift upon lift heights suggests a variation that may be quantified to yield either strength of the domain magnetization or domain sizes by assuming either of them. Acknowledgement Authors would like to acknowledge Dr. P. Chaddah and Prof. Ajay Gupta for their encouragement and Mr. Mohan Gangrade for his technical assistance. DJ and LSSC would like to thank CSIR, India for their support in the form of a fellowship. SRB is thankful to DST for RFRG grant. References [1] C.M.Craciunescu, and M.Wuttig J. Optoelectronics and Adv. Mat. Vol.5(2003), p.139. [2] Harsh Deep Chopra, Chunhai Ji, and V. V. Kokorin, Phys. Rev. B., Vol. 61 (2000), p. R14913. [3] S. Banik, Aparna Chakrabarti, U. Kumar, P. K. Mukhopadhyay, A. M. Awasthi, R.Ranjan, J. Schneider, B. L. Ahuja and S. R. Barman Phys. Rev. B,Vol. 74 (2006), p.085110. [4] Matthew R.Sullivan and Harsh Deep Chopra, Phys. Rev. B., Vol.70 (2004), p.094427. [5] Matthew R.Sullivan, Ashish A. Shah and Harsh Deep Chopra, Phys. Rev. B., Vol.70 (2004), p. 094428. [6] Qi Pan and R.D.James , J. Appl. Phys. Vol.87 (2000), p.4702. [7] Qi Pan J.W.Dong, C.J. Palmstrom, J. Cui and R.D.James , J. Appl. Phys. Vol.91 (2002), p.7812. [8] Nariaki Okamoto, Takashi Fukuda, Tomoyuki Kakeshita, Tetsuya Takeuchi, Kohji Kishio, Science and Technology of Advance Materials, Vol.5 (2004), p.29. [9] B.R.A. Neves and M.S.Andrade, Appl. Phys. Lett., Vol.74 (1999), p.2090. [10] K.H.Han and P.Esquinazi, Journal of Applied Physics, 96, 1581(224). [11] J.Lahau, S.Kirsch, A.Carl, G.Dumpich and E.F.Wassermann, Journal of Applied Physics, 86, 3410, (1999)].

Advanced Materials Research Vol. 52 (2008) pp 121-128 © (2008) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/AMR.52.121

Transformation behavior of Ni-Mn-Ga Ferromagnetic Shape Memory Alloy K.Pushpanathan1,a, R.Senthur Pandi2,b, R.Chokkalingam3,c and M. Mahendran4,*,d 1,2,3,4

Department of Physics, Thiagarajar College of Engineering, Madurai 625 015, India a

*, d

email: [email protected] b

email: [email protected]

c

email: [email protected]

Corresponding author email: [email protected]

Keywords: Magnetic Materials, Martensitic Temperature, Actuators

Abstract Ni-Mn-Ga Ferromagnetic Shape Memory Alloy (FSMA) has been prepared by melt casting technique. The alloy was annealed at different temperatures. The samples are characterized in prepared condition and after three different annealing treatments. Microstructure of the alloy has been investigated using SEM at room temperature. Microstructure study reveals that the magnetic domains run diagonally across the surface. Differential Scanning Calorimetry (DSC) result shows the ferromagnetic transition temperature of the alloy is 105°C. In-situ study of structure during heating has revealed that the martensite to austenite transformation takes place in the temperature range of 28°C to 36°C. The present study focuses the effect of annealing on phase transformation and magnetic transformation temperature of Ni-Mn-Ga alloy. It has been observed that the thickness of the martensite plate increases as the alloy is annealed at 950°C for 30 hrs. Introduction The term Shape Memory Alloy (SMA) is applied to certain groups of intermetallic compounds having superlattice structure with metallic – ionic – covalent characters. They demonstrate the ability to return to their original shape, i.e, it will “remember” the shape it had before cooling. Generally, these materials can be plastically deformed at some relatively low temperature (martensite phase) and upon exposure to high temperature (austenite) they will return to their shape prior to deformation. This effect is known as shape memory effect and the materials that exhibit this effect is said to be shape memory alloys (SMAs). Shape memory effect (SME) is the result of reversible, diffusionless and first-order transformation from austenite to martensite. During this transformation strains are produced in the alloys. This effect has been found in Ni-Ti, Cu-Al-Zn, Cu-Al-Ni , Ni-Mn-Ga and Fe3Pd alloys. Of these Ni-Ti, Cu-Al-Zn, Cu-Al-Ni are known as

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conventional shape memory alloys, in which strain is produced by thermomechanical treatment. Ni-Mn-Ga and Fe3Pd are said to be ferromagnetic shape memory alloys, in which the strain is caused by the magnetic field [1, 2].

The strain induced in conventional shape memory alloys is very low of the order of 0.1%. Due to low thermomechanical strain and slow response, conventional SMA’s find only limited applications in actuator and sensors. Though a number of alloys exhibit shape memory effect, only those alloys that can produce considerable amount of strain (or) force are having great importance. Robert C. O’ Handley group has shown the magnetic field induced strain of 0.2% in a single crystal Ni2-Mn-Ga by the application of magnetic field of 0.8T at –8°C [1-5]. As a result, a remarkable increase in the magnetic field induced strain of 0.57% in single crystal Ni-Mn-Ga alloy was reported when the alloy was subjected to a magnetic field 0.5T at room temperature [3]. As of now, the maximum field induced strain of 10% is demonstrated in a orthorhombic single crystal Ni-Mn-Ga alloys [4]. In Ni-Mn-Ga alloys, within 10ms, a field-induced strain level of 6% has been obtained in tetragonal modulated structure and 10% in modulated orthorhombic structure by the orientation of martensite structure. It is believed that the field-induced strain, produced in these materials, is due to microscopic twin boundary movement in the martensite, which causes a macroscopic change in dimension [6].

The stoichiometric alloy Ni-Mn-Ga shows a ferromagnetic transition at 376K and the thermoelastic martensitic transformation at 202K [6]. On the other hand, the transformation temperature of stoichiometric Ni-Mn-Ga alloys can be modified by compositional changes, e.g., the martensitic transformation temperature is found to raise to the order of 85K/ atomic percent for Ga replaced by Ni. It is also demonstrated that the magnetocrystalline anisotropy energy [4] and saturation magnetization [5] are strongly composition dependent. Moreover, the martensitic transition temperature is a function of valence electron to atom ratio e/a .It has been shown that in Ni-Mn-Ga alloys with e/a range between 7.6 and 7.62, martensitic transformation takes place below ferromagnetic transition temperature Tc. Many researchers are working towards the co-occurrence of both martensitic and magnetic transition temperature. The possibility of the co-occurrence of the structural and magnetic transition is expected at e/a = 7.7 [6]. However, the co-occurrence of martensitic and magnetic transition is reported in Ni2.19Mn0.81Ga composition [7]. Interesting results on Ni-Mn-Ga have been reported in literatures, but most of them are related to single crystals and thin films; only a few papers are available on polycrystalline alloy. The shape memory effect is high, when the material is single crystalline in nature. It is mainly dependent on the orientation of the magnetic domains with respect to the crystallographic axes. In single crystal

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Ni-Mn-Ga, the maximum strain is observed when the magnetic field orients along the [001] crystal axis. [1, 2]. But in polycrystalline sample the [001] direction will vary from grain to grain. Hence the strain observed in polycrystalline sample is less than in single crystal. Most of the researchers study single crystal Ni-Mn-Ga alloy, as they their properties are not affected by the microstructural phenomenon like the variation of crystallographic direction from grain to grain, and that they are more ductile. For commercial purpose, polycrystalline alloy is preferred cost wise, even if the fieldinduced strain in these materials is somewhat lower than in the single crystal. Besides, the formation of intergranular fracture and the brittle nature of polycrystalline SMA is one of the demerits that prevent the use of polycrystalline Ni-Mn-Ga FSMAs for engineering applications. For the present study, we have used the sample of polycrystalline Ni-Mn-Ga FSMA prepared by low cost tabular furnace. The main focus of this article is the study of phase transformation and the effect of annealing on the thickness of the microstructure. In addition to this, we have discussed the crystal structure and magnetic properties of Ni-Mn-Ga.

Experimental Methods

The sample is prepared by melting high purity elements Nickel (99.99%), Manganese (99.8%) and liquid gallium (99.99%) in the form of powders, in a ceramic crucible. These powders are mixed and grained manually at room temperature using the mortar and pestle. The specimen of about 8g is used to fabricate the alloy. The sample is melted in a heating tabular furnace under argon atmosphere and maintained at 1000°C for 5 hrs. Initially, the sample temperature is raised step by step from 500°C for 30 min, 700°C for 40 min and 750°C for 60 min. Finally the temperature is kept constant at 1000° C, and the sample is melted for 15 hrs followed by water quenching. The alloy has been remelted several times and cooled down to room temperature to ensure the compositional homogeneity. This cycle of operation is carried out for 15 days by maintaining the temperature at 700°C.

The sample is cut into three pieces for further study. Then the alloy has been annealed at different temperatures to study the changes in the thickness of the martensite plates. The sample is polished for microscopic observation. Solution of 2% nitric acid and 98% ethanol has been used as etchants. The effect of annealing on microstructure and in martensitic transformation temperature is studied. The microstructure of both the cast and annealed alloys are analyzed using optical microscope (Unilab). The microstructure of the sample has also been observed using the Scanning Electron Microscope (JEOL 5000). Au is used as the reference material. The transformation temperature is

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measured using a Differential Scanning Calorimeter (Perkin-Elmer). Crystal structure of both martensite and austenite phases are analyzed by means of powder X-ray diffraction pattern, recorded between 30 and 70˚ in 2θ, with scanning rate of “5” min-1”, using Rigaku RINT 2500 with CuKα radiation (λ=1.5416˚A). Kβ was filtered with Ni.

Results and Discussion Many of the physical properties of ferromagnetic Ni-Mn-Ga alloys are mainly depend on their crystal structure of martensite [8-11]. In order to determine the crystal structure and lattice parameters, X-ray diffraction pattern is recorded from the powder specimen of the alloy. The diffracted lines observed are identified as martensite superlattice reflections and indexed on the tetragonal phases, shown in Fig. 1. Two XRD peaks, one at (220) at 42o indicates the alloy has body centered cubic structure (BCC) with lattice constant 5.752A°, and the other (110) at 49o infers that the alloy is in the martensite phase with tetragonal structure: a = b=5.830 A° and c = 5.424 A° (c/a= 0.93). The BCC structure is stable at high temperature above 800 K [12] can be retained at a lower temperature by fast cooling. The long-range atomic order [13] is maintained in the metastable BCC structure, which causes the unpaired electron spin to line up parallel to each other within the domain. The long range atomic order favors ferromagnetic property [14]. The width of the XRD peaks is attributed to the size of the powder particles. The diffraction peaks are slightly broadened

(111)

in both austenite and martensite. It is due to particle size variation in powder sample [13].

Figure 1 XRD Pattern for Ni-Mn-Ga shape memory alloy

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The effect of annealing is different in different form of ferromagnetic shape memory alloys. Annealing a sample at high temperature for a long time makes the sample more homogeneous in composition and microstructure. Annealing increases both Tc and Tm in ribbon form of Ni-Mn-Ga alloy [15]. In thin films, annealing helps to regain the bulk composition and the surface is identified as Ni rich [16], whereas in polycrystalline Ni-Mn-Ga long time annealing decreases the coercive field in hysteresis curve and makes the martensite and austenite peaks very sharp [17]. Fig. 2 shows the results of DSC measurement, where the forward and reverse martensitic transitions are clearly highlighted as large exothermic and endothermic peaks. Measured transformation temperatures As = 36˚C, Af = 38˚C, Ms = 31˚C, Mf = 28˚C, implies that the specimen is fully martensite at room temperature. Curie temperature is estimated as Tc = 105˚C. In the beginning, the sample is heated to 250°C to complete the reverse martensite. This indicates that at room temperature, the studied alloy is fully austenite. The martensitic transformation temperature of the stoichiometric alloy Ni-Mn-Ga is 70°C, and its electron to atom ratio (e/a) is 7.5. The substitution of Ni and Mn in place of Ga leads to decrease in unit cell volume and an increase in e/a concentration. As a result an increase of the martensitic transformation temperature and the appearance of the martensitic structure at room temperature are observed. Upon heating, the temperature ranges for the reverse orthorhombic phase and martensite phase overlapped and hence only one endothermic peak is observed. The observed narrow thermal hysteresis of 6°C indicates that the crossing point between the austenite and martensite phases is easily movable upon cooling and heating [15]. The increase of the elastic and the surface energies during the martensitic transformation are attributed to thermal hysteresis and large exothermic and endothermic peaks. 1 cooling

0.8

heating

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Heat Flow (mW) 0 0

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Figure 2 DSC Curve for Ni-Mn-Ga shape memory alloy

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Optical microscope observation of the sample after polishing and etching provides the evidence for the presence of martensitic plates. While heating the sample at 850°C for 20 hrs, the martensitic plates of thickness 5µm are found to run diagonally through the entire sample in the form lines, closely parallel to each other. After annealing the sample for 20 hrs, again the composition has been analyzed. There is no appreciable change in the composition. So the sample annealed at 900°C has been used for the study. We have reported the typical diagonal flow of the martensitic in our previous work [18, 19]. No such a martensitic plate is observed when the sample is annealed at 850°C for 10 hours. The thickness of some martensitic plates has increased from 5µm to 20µm and some others have remained unchanged as the sample was annealed at 950°C for 30hrs (Fig. 3). It indicates that annealing plays a major role, which determines the thickness of martensitic plate. The possible reasons for the formation of the cracks are (i) water quenching or internal stress result of long time annealing and (ii) movement of twin

20µm

Figure:3 Microstructure of Ni-Mn-Ga shape memory alloy

dislocation. The direction of flow of martensitic bands is the same on either side of the crack; this indicates that the crack could have been formed after the formation of martensitic plates. For the formation of cracks in the Ni-Mn-Ga shape memory alloys martensitic, a model is proposed [9] in which the cracks are nucleated along the direction of martensitic plates due to the movement of twin dislocations. But we observed the crack in a direction almost perpendicular to the direction of propagation of martensitic plates. It is confirmed that the observed crack may not be due to the movement of twin dislocation. The presently reported brittleness in Ni-Mn-Ga may be due to long time annealing at high temperature.

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Conclusion We have fabricated Ni51-Mn26-Ga23 ferromagnetic shape memory alloy using low cost furnace and studied the phase transformation and ferromagnetic transformation characteristics.

From our

observation we conclude that the annealing an off-Stoichiometric compound will increase the thickness of the martensitic plates considerably. Also it is concluded that the annealing will decrease the difference between martensite start and finish temperature range due to twin boundary rearrangements. An increase of the martensitic transformation temperature and the appearance of the martensitic structure at room temperature are observed in the Ni-Mn-Ga.

Acknowledgement The authors thank Prof. Robert C. O’ Handley, MIT for his scholarly suggestions.

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K. Ullakko, J. K. Huang, C. Kantner, and R.C. O’ Handley: Appl. Phys. Lett Vol. 69 (1996), p.1966

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K. Ullakko, J. K. Huang, V. V. Kokorin, and R. C. O’ Handley: Scripta. Metall Vol. 36 (1997), p.1133

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S. J. Murray, M. Marioni, S. M. Allen, and R.C. O’ Handley: Appl. Phys. Lett Vol.77 (2000), p.886

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S. J. Murray, R. Hayashi, M. Marioni, S. M. Allen, and R. C. O’ Handley: SPIE Vol.25 (1999), p.3675

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X. Jin, M. Marioni, D. Bono, S.M. Allen, R.C. O’ Handley, and T.Y. Hsu: J. Appl. Phys Vol.91 (2002), p.8222

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L. Pareti, M. Solzi, F. Albertim, and A. Paoluzi: Eur. Phys. J Vol.B32 (2003), p.307

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I. Takeuchi, O.O. Famodu, J. C. Read, M. A. Aronova, K-S.Chang, C. Craciunescu, S. E. Lofland, M. Wuttig, F. C. Wellstood, L. Knauss, and A. Orozco: Nature Mater Vol.180 (2003)

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C. Biswas and S. R. Barman: Appl. Surf. Sci Vol.252 (2006), p.3380

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P. Mullner, V.A.Chernenko, and D. Mukherji: MRS Proc Vol.D122 (2004), p.785

[11]

Z.H. Liu, M. Zhang, Y. T. Cui, Y.Q. Zhou, W. H. Wang, G.H. Wu, X. X. Zhang and Gang Xiao: App. Phys. Lett Vol. 82 (2003), p.424

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[12]

T. Kanomatta, K. Shirakawa, H. Yasui, and T. Kanako: J. Magn. Magn. Mater Vol. 68 (1987), p. 286

[13]

H.Hosoda, T. Sugimoto, K. Ohkubo, S. Miura, T. Mohri, and S. Miyazaki: Internat. J. Appl. Electromag. Mech. Vol.12 (2000), p. 9

[14]

T. Kakeshita, T. Fukuda and T. Takeuchi: Mater. Sci. Engg A Vol. 438-440 (2006), p.12

[15]

A. Sozinov, A.A. Likhachev, and K. Ullakko: IEEE Trans. Magn. Vol.38 (2002), p. 2814

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J. Pons, C. Segui, V.A. Chernenko, E. Cesari, P. Ochin, and R. Portier: Mater. Sci. Engg. A Vol.273 – 275(1999), p.315

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M. Pasquale, C. Sasso, S. Besseghini, F. Passaretti, E. Villa, and A. Sciacca: IEEE Trans. Magn Vol.36 (2000), p.3263

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M. Mahendran: Smart Mater. Struct Vol.14 (2005), p.1403

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M. Mahendran and K. Pushpanathan: J. Syn. Reac. Metal Org. Nano-Metal Chem. Vol.83 (2006), p.36

Advanced Materials Research Vol. 52 (2008) pp 129-133 © (2008) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/AMR.52.129

Effect of Stress Relaxation on Quenched NiFeAl Ferromagnetic Shape Memory Alloy B. Rajini Kanth 1, a, P. K. Mukhopadhyay 1, b and S. N. Kaul 2, c 1

2

LCMP, S.N.Bose National Center for Basic Sciences, Salt Lake, Kolkata 700 098, India School of Physics, University of Hyderabad, Central University P.O., Hyderabad – 500 046, Andhra Pradesh, India a b [email protected], [email protected], c [email protected]

Keywords: Stress Relaxation, Ferromagnetic Shape Memory Alloy, Sound Velocity and Internal Friction

Abstract: In this paper, we report on the effect of stress on the mechanical relaxation in the quenched Ni55Fe20Al25 Ferromagnetic Shape Memory Alloy (FSMA). The sound velocity and internal friction measurements were carried out using a vibrating reed setup. The results of such measurements on this system with varying stress amplitudes are presented. The present study provides a new insight into the stress amplitude and temperature dependence of the damping process and their bearing on the structural changes in the FSMAs. Introduction: Ferromagnetic Shape Memory Alloys (FSMAs) are attracting a lot of attention from the past few decades, as they exhibit shape memory and high mechanical damping in the martensite phase [1-3]. Several investigators have reported the results of detailed but diverse measurements on the NiMnGa system [4-8]. However, this material is brittle and hence difficult to use for practical applications. Thus there is a need for a new shape memory material which can fulfill the requirements of the materials industry. Recognizing this need, many other alloys such as CoNiAl, NiFeGa and CoNiGa have been studied [9-11]. Out of these systems, the ferromagnetic shape memory alloys NiFeGa, CoNiAl and NiFeAl, hold a great promise because their properties can be tailored for practical applications [12]. Thermoelastic martensitic transformation from face-centered-cubic (fcc) austenite (hightemperature) phase to tetragonal martensite (low-temperature) phase in a new ternary ferromagnetic alloy system Ni-Fe-Al (“prepared” in different states of site disorder) had been recently reported [12] based on the results of a detailed neutron diffraction (ND), electrical resistivity, ρ(T), and magnetization, M(T, H), studies. The effect of site disorder, in this alloy system, is to (i) promote ductility, (ii) narrow down the temperature range over which austenite and martensite phases coexist (and hence sharpen the martensitic phase transition) and (iii) shift the martensitic transition temperature to higher temperatures. In the melt-quenched sample of Ni55 Fe20 Al 25 (henceforth referred to as q-Fe20), which has the highest degree of site disorder, the thermoelastic martensitic phase transition is sharp and occurs near the Curie temperature TC ≅ 225 K . The martensitic transformation (MT) is evidenced by the thermal hysteresis exhibited by electrical resistivity as a function of temperature, ρ(T), when a given sample undergoes thermal cycling. An elaborate analysis of the ρ(T) data yields the characteristic temperatures for the beginning, TMb (TAb), and end, TMe (TAe), of the growth of martensite (austenite) phase at the expense of austenite (martensite) phase while cooling (heating) as TM b ≅ 260 K and TMe ≅ 150 K ( TAb ≅ 170 K and TAe ≅ 280 K ) for the q-Fe20 sample. These values for the characteristic temperatures are consistent with those deduced from the ND data. Previously we have reported on the dynamic elastic properties and magnetic susceptibility across the Austenite-Martensite transformation in this system at a constant stress [13]. Recognizing that the thermoelastic martensitic transformation causes the shape memory effect (SE) and the thermoelastic nature of MT is directly reflected in the elastic property measurements across the Austenite-Martensite phase transformation, extensive measurements of sound velocity and attenuation under varying stress amplitude, on the q-Fe20 sample, were undertaken using the vibrating reed technique [14-15].

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There is no report in the literature on the effect of stress relaxation on the martensite phase of the NiFeAl shape memory alloys. Therefore, we have chosen to study the temperature variation of sound velocity and internal friction at different stress amplitudes. The results of the effect of stress relaxation on the NiFeAl shape memory alloy are presented in this paper. Experimental: Ultra high pure (99.999%) Ni, Fe and Al were taken in the requisite proportion so as to arrive at the composition Ni55Fe20Al25 and polycrystalline rods of 10 mm diameter and 100 mm length were prepared by radio-frequency induction melting technique. A portion of these rods was melt-quenched to form 2 mm wide, 2 cm long and 30 µm thick crystalline ribbons, labeled as q-Fe20. The details of the sample preparation were furnished elsewhere [16]. Vibrating reed experiments were performed on the ribbon shaped samples for measuring sound velocity and attenuation. In the reed experiment, one end of the sample was clamped firmly to the base plate of the cryostat while a flexural resonance was set up at the other (free) end by an electrostatic drive via an electrode placed near that end. Another matching electrode (biased at 45 V and connected to the Lock-in Amplifier) was placed against the opposite face of the reed and it picked up the oscillations by electrostatic coupling. The reference input to the lock-in amplifier came from the same generator that feeds the drive electrode with sine wave amplitude variation, but locked to the second harmonic. As the stress (force) varies as square of drive voltage for the present sample arrangement, it is possible to have an order of magnitude change in stress amplitudes by just varying the drive voltages. In this work, we selected 2, 5 and 11V drive voltages so as to vary the stress levels by 1: 6 : 30 times. In order to meet the main motivation of the present study, the temperature was varied between 240 K to 300 K with the intention of monitoring the transformations taking place just below the martensitic start temperature, TMs, and the way these transformations react to the applied varying stress amplitudes. At room temperature, the resonance curve was obtained by measuring the amplitude of vibration of the free end as a function of the driving frequency. From the resonance curve, so measured, the absolute value of internal friction, Q-1 = ∆υ/υ res (where ∆υ is the width of the resonance curve between the points at which the amplitude has the value Amax / √2, if Amax is the maximum amplitude at the resonance frequency υres) at room temperature was deduced as Q-1 (T = 293.7K ) = 6.5 x 10-3. Subsequently, the resonance was phase-locked and tracked as the sample temperature was varied. The sound velocity, V, as a function of temperature was obtained from the fundamental (resonance) vibration frequency, υ, using the relation υ = (d / 4π √3) (1.875 / l)2 V, where d and l are the thickness and length of the sample reed. Note that we could measure only the relative changes in sound velocity, δV/V, with respect to its value at room temperature because the unknown clamping yield caused a large uncertainty in the measurement of actual effective l. This is a standard problem with the vibrating reed measurements. In the present experiments, the relative change in sound velocity and internal friction could not be resolved better than 100 ppm and 5%, respectively. Results and Discussion: Figure 1 (a, b) shows the temperature variations of δV/V and Q-1 for the present sample, measured at different stress, when the sample was cooled down to 260 K (near TMb). As the sample temperature decreases, δV/V declined while Q-1 increased. This decline (rise) in δV/V (Q-1) signaled phonon “softening” in the premartensitic regime. The rate of decline in δV/V or equivalently, increase in Q-1 slowed down at the on-set temperature for the growth of the martensitic phase.

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4 0.000

2V 260K 5V 260K 11V260K

-0.005 -0.010

3

-0.015 -0.020

2V 260K 5V 260K 11V 260K

-0.035

2 -1

-0.030

Q

δV/V

-0.025

-0.040

1

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265

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290

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Fig. 1(a) Fig. 1(b) -1 Fig.1(a, b). Temperature variations of δV/V and Q for the q-Fe20 sample, measured at the drive voltages of 2V, 5V and 11V, when the sample is cooled down to 260K. Figure 2(a, b) shows the temperature variations of δV/V and Q-1, measured at different stress amplitudes when the sample was cooled down to 250 K (just below TMb). The onset temperature for the growth of martensite phase, TMb, (end temperature for the growth of austenite phase, TAe) is found to be ≅ 260 K ( ≅ 277 K), ≅ 255 K ( ≅ 277 K) and ≅ 252 K ( ≅ 273 K) at drive voltages 2 V, 5 V and 11V, respectively. 3

0.00

2V 250K 5V 250K 11V 250K

-0.02

-0.06

Q

δV/V

2V 250K 5V 250K 11V 250K

-1

2

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1

-0.08

-0.10 0

-0.12 250

260

270

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Fig. 2(a)

290

250

260

270

280

290

Temperature (K)

Fig. 2(b)

Fig.2(a, b). Temperature variations of δV/V and Q-1 for the q-Fe20 sample, measured at the drive voltages of 2V, 5V and 11V, when the sample is cooled down to 250K. Figure 3(a, b) displays the variations of δV/V and Q-1 with temperature, measured at different stress amplitudes when the sample was cooled down to 240K (well below TMb). In this case, we find that TMb, (TAe) is found to be ≅ 265 K ( ≅ 280 K), ≅ 248 K ( ≅ 274 K) and ≅ 248 K ( ≅ 265 K) at drive voltages 2 V, 5 V and 11V, respectively. TMb and TAe, reminiscent of unstressed ribbon, can be seen in both the δV/V and Q-1 curves for lower stresses. Lower the stress, higher are the TMb and TAe. These observations permit us to conclude that the martensitic as well as the austenite growth temperatures can be shifted down with the application of stress. We have also calculated the stress and estimated the Young’s modulus based on the dimensions of the samples

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and vibrating reed apparatus specifications [17]. The values are tabulated in table 1. From the entries in table 1, it is evident that as the driving voltage increases, the stress also increases due to the increase in the force applied by the electric field. The strain increases in proportion to the stress so that the Young’s modulus has a constant value of 6.8 GPa, independent of the drive amplitude. 25

0.00 -0.02

20

-0.04

2V 240K 5V 240K 11V 240K

15

Q

-1

-0.06

δV/V

2V 240K 5V 240K 11V 240K

-0.08 -0.10

10

5

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260

270

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Temperature(K)

Fig. 3(a) Fig. 3(b) -1 Fig.3(a, b). Temperature variations of δV/V and Q for the q-Fe20 sample, measured at the drive voltages of 2V, 5V and 11V, when the sample is cooled down to 240K. Table.1. Stress data obtained from vibrating reed measurements Sl.No 01 02 03

Drive Voltage(V) 2 5 11

Resonance Frequency(Hz) 186 187 188

Stress (MPa) 2.2 13.8 67.2

Strain 3.3x10-4 20.4x10-4 99.3x10-4

Young’s Modulus (GPa) 6.8 6.8 6.8

Conclusions: From the present study, it can be concluded that the sound velocity and internal friction measurements clearly demonstrate as to how the Austenite-end and Martensite-begin temperatures get shifted with stress. Therefore, such studies have the potential of providing new physical insight into the structural mechanisms prevalent in the shape memory alloys. Acknowledgements: Financial assistance from the Department of Science and Technology, India, vide project No: SR/S2/CMP-24/2006 is gratefully acknowledged. References [1] K.Ullako, J.K.Huang, V.V.Kokorin, R.C.O’Handley: J.Appl Phys, Vol. 69 (1996), p. 1966. [2] S. J. Murray, M. Marioni, S. M. Allen, R.C.O’Handley, T. A. Lograsso: Appl Phys Lett Vol.77 (2000), p. 886. [3] P. J. Brown, K. Ishida, R. Kainuma, T. Kanomata, K. –U. Meumann, K. Oikawa, B. Ouladdiaf and K. R. A. Ziebeck : J. Phys.: Condens. Matter Vol. 17 (2005), p.1301. [4] N. Okamoto, T. Fukuda, T. Kakeshita and T. Takeuchi: Mater. Sci. Eng. A Vol. 948 (2006), pp 438-440. [5] T. Krenke, E. Düman, M. Acet, E.F. Wassermann, X. Moya, L. Mañosa, A. Planes, E. Suard, B. Ouladdiaf: Phys. Rev. B Vol. 75 (2007), p. 104414. [6] J. Pons, V. A. Chernenko, R. Santamarta, E. Cesari: Acta Mater. Vol. 48 (2000), 3027. [7] P. Entel, et al: J. Phys. D: Appl. Phys. Vol. 39 (2006), 865.

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[8] Rajeev Ranjan, S. Banik, S. R. Barman, U. Kumar, P. K. Mukhopadhyay and Dhananjai Pandey: Phys. Rev. B Vol. 74 (2006), p.224443. [9] H. Morito, A. Fugita, K. Fukamichi, R. Kainuma, K. Ishida and K. Oikawa: Appl. Phys. Lett. Vol. 83 (2003), 4993. [10] R. Kainuma, Y. Imano, W. Ito, Y. Sutou, H. Morito, S. Okamoto, O. Kitakami, K. Oikawa, A. Fujita, T. Kanomata and K. Ishida: Nature Lett. Vol. 439 (2006), p. 957. [11] M. Zhang, E. Brück, F. R. de Boer and G. Wu: J. Phys. D: Appl. Phys. Vol. 38 (2005), p.1361. [12] S. N. Kaul, B.Annie D’Santhoshini, A.C.Abhyankar, L.Fernandez Barquin and Paul Henry: Appl. Phys. Lett. Vol. 89 (2006), p. 093119. [13] P.K.Mukhopadhyay and S.N.Kaul : Appl. Phys. Lett. Vol. 92 (2008), p. 101924. [14] P. K. Mukhopadhyay and A. K. Raychaudhuri: J. Phys. C: Solid State Vol. 21 (1988), L385; J. Appl. Phys. Vol. 67 (1990), 5235. [15] K. Balakrishnan and S. N. Kaul: Phys. Rev. B Vol. 65 (2002), p.134412. [16] B.Annie D’Santhoshini and S.N.Kaul: J. Phys.: Condens. Matter Vol.15 (2003), p.4903. [17] P.K.Mukhopadhyay, Ph.D Thesis, IISc Bangalore (1989), pp. 32-35.

Advanced Materials Research Vol. 52 (2008) pp 135-142 © (2008) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/AMR.52.135

Lattice Thermal Expansion of the Shape Memory Alloys Cu-Al-Ni, Cu-Al-Zn, Cu-Al-Be And Cu-Al-Pd. Santhosh Potharay Kuruvilla and Menon C S* School of Pure and Applied Physics, Mahatma Gandhi University Kottayam, Kerala, INDIA. 686 560. [email protected] Keywords: Elastic Constants, Thermal Expansion, Copper based Shape Memory Alloy

Abstract. Theoretical and experimental investigations are being carried out on Cu based alloys due to their technologically important shape memory properties and pseudo-elasticity, which are intimately associated with the martensitic transformation. The transition between the two phases, martensite to austenite, is of continued interest in academics and in industry. The shape memory effect, superelastic properties and biocompatibility are being applied in a variety of fields. Cu based SMA system has large vibrational entropy, high damping capacity and good economic viability. All these make it a potential candidate in the field of sensors and actuators. The concurrent knowledge of the second order elastic constants (SOEC) and third order elastic constants (TOEC) enables a better understanding of the nonlinear elasticity exhibited by these alloys. We have used a model based on deformation theory and Keating’s potential scheme to obtain the expressions for TOEC of the above alloys. In this paper we have calculated the complete sets of six non-vanishing TOEC of Cu-Al-Ni, Cu-Al-Zn, Cu-Al-Be and Cu-Al-Pd and are presented along with the available experimental data. It is remarkable that all the third order elastic constants are negative, indicating an increase in the vibrational frequencies under stress, giving rise to an increase in the strain-free energy. The absolute values of the TOEC are large. This means that the bcc phase observed is considerably anharmonic. The TOEC C144 representing the shear mode has a smaller value than C111. Hence, the effect of pressure is much greater on longitudinal wave velocity than on the shear wave velocity in the above Cu based SMA. The mode Grüneisen parameters of the acoustic waves are determined based on the quasi-harmonic approximation method. The low temperature limit of the lattice thermal expansion and the Anderson– Grüneisen parameter of these alloys are also obtained. Introduction Shape memory alloys (SMA), which form an important part in the category of ‘smart materials’ are alloys, which exhibit unique properties viz pseudo elasticity and shape memory effect [1,2]. These unusual properties are being employed to a wide variety of applications [3,4]. The transition between the two phases, martensite to austenite, is of continued interest both in academics and industry [5]. The shape memory effect, superelastic properties and bio-compatibility are used in space shuttles, thermostats, aerodynamics, solar panels, cryogenic valves and medicine. Austenite phase of Cu based SMA have bcc lattice [4]. Moreover these alloys are efficient because of their high damping capacity, favorable working temperature, large vibrational entropy and economic viability [6,7,8]. All these make them potential candidates in the field of sensors and actuators. The concurrent knowledge of the second order elastic constants (SOEC) and third order elastic constants (TOEC) enables a better understanding of the nonlinear elasticity exhibited by these alloys. In this paper, we determine the second and third-order potential parameters, the complete set of second and third-order elastic constants and the pressure derivatives of second-order elastic constants of these alloys. The values obtained are compared and are in agreement with the experimental results. We have determined the mode Gruneisen parameters (GPs) of the acoustic waves propagating in different orientations in the crystal lattice, low temperature limit of thermal expansion along with the Anderson– Gruneisen parameter.

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Theory Higher order elastic constants. We have used a model based on deformation theory and Keating’s potential scheme [9] to obtain the SOEC and TOEC of these alloys. Elastic constants of higher orders can be obtained as algebraic functions of potential parameters [10]. Considering Keating’s approach, the potential energy of the alloy is written as the sum of the potential energy contributions due to two-body and three-body interactions. φ = φ ( 2 ) + φ ( 3) . (1) r Let R (Lµ , L ′µ ′) be the vector distance between the atom µ in the cell L and the atom µ ′ in the r cell L ′ in the unstrained state and R ′ (Lµ , L ′µ ′) , the corresponding vector in the deformed state. Then the contribution to the potential energy of the crystal from the two-body interaction among them in the deformed state is written as r r r 2 1 r′  ′ ′ ′ ′ ′ ′ ′ α µ µ µ µ µ µ ⋅ − ⋅ R ( L , L ) . R ( L , L ) R ( L , L ) R ( Lµ , L ′µ ′)   1   φ ′ ( 2 ) = φ ( 2) + ∑  2  .(2) r r r r 3 2 Lµ , L′µ ′′  1 ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ + β R ( Lµ , L µ ) ⋅ .R ( Lµ , L µ ) − R( Lµ , L µ ) ⋅ R( Lµ , L µ )   6 

[

]

[

]

Here α and β are the two-body potential parameters. Similarly the potential due to the three-body interaction among the triplet of atoms µ in the cell L , µ ′ in the cell L ′ and µ ′′ in the cell L ′′ in the strained state is written as

φ ′ ( 3) = φ ( 3 )

[

]

r r r 2  1 r′ ′ ′ ′ ′ ′ ′ ′ ′ ′ λ µ µ µ µ µ µ R ( L , L ) . R ( L , L ) R ( L , L ) R ( Lµ , L ′′µ ′′)  ⋅ − ⋅  1 2  +   ,(3) ∑ r r r r 3 2 Lµ , L′µ , L′′µ ′′  1 + ζ R ′( Lµ , L ′µ ′) ⋅ .R ′( Lµ , L ′′µ ′′) − R( Lµ , L ′µ ′) ⋅ R( Lµ , L ′′µ ′′   6 

[

]

where, λ and ζ are the three-body potential parameters. In homogeneous deformation [11] the components of the interatomic vectors are altered as Ri′(Lµ , L ′µ ′) = Ri (Lµ , L ′µ ′) + ∑ ε ij R j (Lµ , L ′µ ′) + Wi (1 − δ µµ ′ ) ,

(4)

j

where Wi are the components of the internal displacements of the sub-lattices which are found to vanish. ε ij are deformation parameters related to the macroscopic Lagrangian strains ηij by





ηij = 12 ε ij + ε ji + ∑ ε ik ε jk  . 

k

(5)



Therefore, the scalar product in (2) and (3) can be written using (4) and (5) as r r r r R ′( Lµ , L ′µ ′) ⋅ .R ′( Lµ , L ′′µ ′′) = R ( Lµ , L ′µ ′) ⋅ R ( Lµ , L ′′µ ′′) + 2∑η ij Ri ( Lµ , L ′µ ′).R j ( Lµ , L ′′µ ′′) .(6) ij

Substituting for the change in scalar product in (2) and (3) from (6) and summing all the contribution to the potential energy, we obtain the strain energy per unit volume as

∆φ = (φ ′ − φ ) / V z .

(7)

where Vz is the volume of the unit cell. In the present work, two body interactions up to the second neighbors and three body interactions among the nearest neighbors of each atom in the unit cell are

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considered to obtain the strain energy density of the alloy. The fourth and higher powers of the interatomic displacements are neglected. Comparing ∆φ thus obtained with the strain energy from continuum model approximation [12] given by U=

1 1 C ij ,klη ijη kl + ∑ C ij ,kl , mnη ijη klη mn + L ∑ 2! ijkl 3! ijklmn

(8)

(where Cij,kland Cij,kl,mn are the second and third-order elastic constants evaluated at constant entropy), we get the expressions for the second and third elastic constants of the alloy systems in Voigt’s notation as C11 = (4α + 3λ + 8σ )a ,

(9.1)

C12 = (4α − λ )(a 4 / V z ) ,

(9.2)

C 44 = (4α + λ )(a 4 / V z ) ,

(9.3)

C111 = ( β + ζ + 16υ )(4a 6 / V z ) ,

(9.4)

C112 = ( β + ζ )(4a 6 / V z ) ,

(9.5)

C123 = ( β − 3ζ )(4a 6 / V z ) ,

(9.6)

C144 = ( β − ζ )(4a 6 / V z ) ,

(9.7)

C155 = ( β + ζ )(4a 6 / V z ) ,

(9.8)

C 456 = β (4a 6 / V z ) ,

(9.9)

where a is the lattice parameter of the unit cell. Cij and Cijk are SOEC and TOEC of Cu based shape memory alloys under study. Here σ and ν are the second and third order potential parameters of two body interactions in connection with the second neighbour respectively. In the above equations, the numerical prefactors are entirely derived from the crystal structure. For an isotropic substance, the elasticity tensor scheme yields C11–C12=2C44. We have calculated A, the anisotropy factor along with the shear modulus C’[= (C11–C12)/2]. We have used finite strain theory [12] to obtain the effective second-order elastic constants of a strained cubic crystal in terms of the second-order and third-order elastic constants. Let a cubic crystal be subjected to a hydrostatic pressure p. The coordinates of the material particles in the initial state change after applying the pressure. The expression for the pressure derivatives of second order elastic constants is obtained to the first order in η as, ∂C11 −1 = [C111 + 2C112 + 2C11 + 2C12 ] , (10.1) ∂p C11 + 2C12 ∂C12 −1 = [C123 + 2C112 − C11 − C12 ] , ∂p C11 + 2C12

(10.2)

∂C44 −1 = [C144 + 2C155 + C11 + 2C12 + C44 ] . ∂p C11 + 2C12

(10.3)

Grüneisen parameters and lattice thermal expansion: The thermal expansion of a solid is a property arising due to the anharmonicity of the lattice. A simple method of taking this into account

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Ferromagnetic Shape Memory Alloys

is the quasi-harmonic approximation. Here the interatomic forces and hence the lattice frequencies are assumed to be functions of the strain components in the lattice. The thermal energy of a simple lattice is treated as the energy of a spectrum of elastic waves, having any temperature at a certain maximum frequency of vibration. The GPs γ j (θ , φ ) for the j th acoustic mode propagating in the direction (θ , φ ) can be defined as; ∂v j (θ , φ ) 1 γ j (θ , φ ) = − , v j (θ , φ ) ∂ε

(11)

where vj (θ , φ ) is the natural velocity of the j th acoustic mode propagating in the direction (θ , φ ) , when the lattice is homogeneously strained by a uniform longitudinal strain ε [13]. The evaluated second-order and third-order elastic constants are used to obtain the Grüneisen functions γ j (θ , φ ) of the acoustic modes using (11). The results of GPs for the corresponding elastic wave velocities at different angles θ are drawn. At very low temperatures according to Debye theory the number of −3

normal modes excited in the j th acoustic branch is proportional to v j (θ ,φ ) . Hence the Grüneisen function at very low temperature becomes a constant designated as the low temperature limit of thermal expansion which is given by, 3

γL =

∑∫v

−3 j

(θ , φ )γ j (θ , φ )dΩ

j =1

3

∑∫v

. −3 j

(12)

(θ , φ )dΩ

j =1

Here Ω is the solid angle. The low temperature limit γ L is evaluated using the GPs of the acoustic modes by numerical integration. The Anderson- Grüneisen parameter which account for the intrinsic variation of the GP with pressure [13] is given by  dK   − 1 , δ =  (13)  dp  where K is the bulk modulus of the strained cubic crystal which is given by

K = (C11 + 2C12 ) / 3 .

(14)

Thus using (10), (13) and (14), we calculate the Anderson– Grüneisen parameter in terms of SOEC and TOEC as

δ = −1 −

(C111 + 6C112 + 2C123 ) . (3C11 + 2C12 )

(15)

Results and Discussion.

In this paper we have calculated the second-order and third-order potential parameters of alloys with composition Cu-14.3% Al-4.1% Ni (wt.%), Cu-66.5% Al-12.7% Zn (wt.%), Cu-74.1% Al23.1% Be (wt.%) and Cu-67.5% Al-23.1% Pd (wt.%) at room temperature and tabulated in table 1. The values of the second order potential parameters are estimated by best fitting with the reported experimental values. It is to be noted that α , σ , β and ν are related to the stretching of bonds while λ and ζ are linked with the distortion of the angle between two adjacent bonds in the lattice.

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Table 1. Second-order and third-order potential parameters. Alloy

α ′ [GPa]

λ ′ [GPa]

σ ′ [GPa]

β ′ [TPa]

ζ ′ (TPa)

ν ′ (TPa)

Cu-Al-Ni

27.45

-14.52

9.51

-0.59

-0.05

-0.06

Cu-Al-Zn

23.33

-8.95

6.24

-0.96

-0.02

-0.07

Cu-Al-Be

27.1

-11.7

7.6

-0.49

0.01

-0.06

Cu-Al-Pd

27.59

-18.97

11.43

-0.82

0.03

-0.06

The SOEC, CL (=(C11+C12+2C44)/2), bulk modulus K and shear modulus C’(=(C11-C12)/2) are collected in table 2. The Cauchy pressure P (=C12-C44) is also determined which can be related to the brittle or ductile properties of materials as suggested by Chen et al [14]. Table 2. Second order elastic constants (C11, C12, C44, CL), bulk modulus (K), shear modulus (C') and Cauchy pressure (P) [GPa]. Alloy

C11

C12

C44

CL

C’

K

P

A

Cu-Al-Ni

142.32

124.32

95.28

228.60

9.00

130.32

29.04

10.59

Cu-Al-Zn

116.39

102.27

84.37

193.70

7.06

106.98

17.90

11.95

Cu-Al-Be

134.10

120.10

96.70

223.80

7.00

124.80

23.40

13.80

Cu-Al-Pd

144.89

129.33

91.39

228.50

7.78

134.52

37.94

11.80

The complete set of six non-vanishing TOEC along with the reported values are presented in table 3 [15,7,16,17]. It is to be noted that the alloy composition used by Gonzalez-Comas et al [7], Nagasawa et al [17] are different. The TOEC C144 representing the shear mode has a smaller value than C111. Hence, the effect of pressure is much greater on longitudinal wave velocity than on the shear wave velocity in these alloys. It is remarkable that all the third order elastic constants are negative for these alloys, indicating an increase of the vibrational frequencies under stress, giving rise to an increase in the strain-free energy. Also the absolute values of the TOEC are large. This means that the bcc phase observed is considerably anharmonic [17].

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Ferromagnetic Shape Memory Alloys

Table 3. Third order elastic constants [TPa]. Alloy

Reference

C112

C123

C144

C155

C456

Present work

-1.68 -0.64 -0.44 -0.54 -0.64 -0.59

[15]a

-1.65 -0.62 -0.48 -0.60 -0.69 -0.56

[7]b

-1.79 -1.05 -0.98 -0.93 -1.08 -0.60

Present work

-2.10 -0.98 -0.90 -0.94 -0.98 -0.96

[16]c

-2.08 -1.06 -0.92 -1.02 -1.02 -0.66

[17]d

-1.548 -0.703 -0.836 -0.762 -0.760 -0.501

Present work

-1.44 -0.48 -0.52 -0.50 -0.48 -0.49

Present work

-1.75 -0.79 -0.91 -0.85 -0.79 -0.82

[18]e

-1.78 -0.78 -0.94 -0.94 -0.93 -0.63

Cu-Al-Ni

Cu-Al-Zn

Cu-Al-Be

C111

Cu-Al-Pd a

Pulse-echo measurements by Landa et al (2004). Ultrasonic phase sensitive detection by Gonzalez-Comas and Manosa (1996). c Pulse-echo measurements by Verlinden et al (1984) d Pulse-echo overlap detection by Nagasawa et al(1982) e Ultrasonic measurements by Nagasawa et al (1992) b

The wave velocities at high pressures are inextricably related to elastic constants and we have obtained the pressure derivatives of the second-order elastic constants of these Cu based alloys and presented in table 4. Reported values are only available for Cu-Al-Be [18]. The pressureinduced variations in the longitudinal elastic constants are relatively large compared with those for the shear and off-diagonal constants. Table 4. Pressure derivative of second order elastic constants. Alloy

dC11/dp

dC12/dp

dC44/dp

Cu-Al-Ni

6.21

5.08

3.41

Cu-Al-Zn

11.29

9.59

7.77

Cu-Al-Be [19]

5.05

4.63

2.64

5.0

4.6

2.6

Cu-Al-Pd

6.89

6.85

4.80

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141

Generalized Grüneisen parameters are also calculated using the second- and third-order elastic constants and a typical curve for Cu-Al-Zn is shown in fig.1. The mode gammas are all positive, ranging from 3.0 to 13.4. The transverse acoustic mode of GP, γ 1 assumes a minimum value of 3.0 at angle θ = 350 and has a maximum value of 4.9 at θ = 900. The transverse acoustic mode γ 2 varies from 4.3 to 6.0 as the angle changes from 00 to 900. The longitudinal acoustic mode γ 3  ranges from 4.9 at 00 to 13.4 at 550. This mode shows the maximum anisotropy among the GPs for these alloys. It is to be noted that the longitudinal acoustic modes are much less anisotropic compared to the longitudinal mode for all the four alloys.

Fig. 1. Variation of the generalized Gruneisen parameter for the three acoustic branches as a function of the angle to the c-axis of Cu-Al-Zn. The low temperature limits γ L of these alloys are positive and hence we expect the thermal expansion to be positive down to absolute zero. In the quasi-harmonic approximation, the vibrations are considered to be harmonic about the new equilibrium positions of the atoms corresponding to the strained state. The Anderson– Grüneisen parameter is introduced to account for the intrinsic variation of the Grüneisen parameter with respect to pressure. The low temperature limits of thermal expansion along with the Anderson– Grüneisen parameter is calculated and presented in table 5.

Table 5. Low temperature limit of lattice thermal expansion ( γ L ) and Anderson-Gruneisen parameter ( δ ) . Alloy

Cu-Al-Ni

Cu-Al-Zn

Cu-Al-Be

Cu-Al-Pd

γL

4.5

8.5

3.5

6.1

δ

8.5

16.7

7.4

11.0

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Ferromagnetic Shape Memory Alloys

Acknowledgement: We extend our sincere feeling of gratitude to Government of India, State Government of Kerala and B. P. C. College, Piravom, for the award of fellowship under FIP of UGC to complete this work. References: [1] L.Delaey: Phase Transformations in Materials, edited by Haasen P, VCH, Weinheim, (1991) p 339. [2] K. Otsuka, C.M. Wayman: Shape Memory Materials (Cambridge University Press) (1998) p 143. [3] J.J. Wang, T. Omori, Y. Sutou, R. Kainuma and K. Ishida: Journal of Electronic Materials, 33 (2004) 1098. [4] A. Planes and L. Manosa: Solid State Physics 55 (2001) 159. [5] J.V. Humbeeck and S. Kustov: Smart Mater. Struct. 14 (2005) S171. [6] A. Planes, L. Manosa, E. Vives, J.R. Carvajal, M. Morin, G. Guenin, and J. L. Macqueron: J. Phys.: Condens. Matter 4 (1992) 553. [7] A. Gonzalez-Comas and L.Manosa: Phys. Rev. B 54 (1996) 6007. [8] P. Sedlak, H. Seiner, M. Landa, V. Novak, P. Sittner and L. Manosa: Acta Materialia 53 (2005) 3643. [9] P.N. Keating: Phys. Rev. 145 (1966) 637. [10] P.K. Santhosh And C.S. Menon: Smart Mater. Struct. 15 (2006)1974-1978. [11] M. Born, K. Huang: Dynamical Theory of Crystal Lattice, Oxford University Press, N.Y. 1962. [12] F. D. Murnaghan: 1951 Finite Deformation of an elastic solid, Wiley, New York. [13] K.P. Jayachandran and C.S. Menon: Physica C, 382 (2002) 303. [14] K. Chen, L.R. Zhao and J.S. Tse: J. Appl. Phys. 93( 2003) 2414. [15] M. Landa, V. Novac, P. Sedlak and P. Sittner: Ultrasonics 42 (2004) 519. [16] B. Verlinden, T. Suzuki, L. Delaey, G. Guenin: Scripta Met. 18 (1984) 975. [17] A. Nagasawa, T. Makita and Y. Takagi: J. Phys. Soc. Jpn.51 (1982) 3876. [18] Nagasawa, A. Kuwabara, Y. Morri, K. Fuchizaki and S. Funahashi: Mater. Trans. JIM 33, 203 (1992). [19]M.A Jurado, M.Cankurtaran, L. Manosa and G.A. Saunders: Phys. Rev. B 46 (1992) 14174.

IV. Microscopic studies of Magnetic Shape Memory Alloys

Advanced Materials Research Vol. 52 (2008) pp 145-154 © (2008) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/AMR.52.145

Magnetic Compton scattering study of shape memory alloys B.L. Ahuja1,a, Vinit Sharma1,b and Y. Sakurai2,c 1

Department of Physics, M. L. Sukhadia University, Udaipur 313001, India.

2

Experimental Research Division, Japan Synchrotron Radiation Research Institute (JASRI), SPring8, Mikazuki, Hyogo 679-5198, Japan.

a

email: [email protected], bemail: [email protected], cemail: [email protected]

Keywords: Magnetic Compton scattering, Electronic structure, Band structure calculations, Shape memory alloys

Abstract The Compton profile, projection of electron momentum density distribution along the scattering vector, is very sensitive to the behavior of valence electrons in a variety of materials. In this paper theoretical aspects related to measurement of spin momentum densities of magnetic materials using Compton scattering is reviewed. To highlight the potential of the magnetic Compton scattering, the spin momentum densities in Ni-Mn-Ga Heusler alloys at various temperatures and magnetic fields are presented. The magnetic Compton profiles are mainly analyzed in terms of the contribution from the 3d electrons of Mn. A comparison of the magnetic Compton data with other magnetization studies illustrates its importance in exploring the magnetic effects in ferro- or ferri-magnetic materials. Introduction The scattering of a photon by a stationary electron is known as Compton scattering [1]. In this type of scattering, wavelength shift (∆λ) that is independent of the nature of scatterer can be written in terms of angle of scattering θ as follows:

∆λ = λ2 − λ1 =

h (1 − cos θ ). m0 c

(1)

Here λ1 and λ2 are the wavelengths of the photon before and after the scattering. The Eq. 1 is based on two simple assumptions: the electron is free and is at rest. The electron can be considered as free if the recoil energy is larger than the binding energy of the electron in the atom. In real materials, the electrons cannot be at rest due to inevitable motion of the target electrons. The position of Compton peak deduced by Eq. 1 remains the same as the experimentally observed position, but the Compton line width is broadened because of Doppler broadening due to motion of the target electrons. After incorporating the electron’s motion [2], Eq. 1 becomes

∆λ ==

h (1 − cos θ ) + 2 λ1 λ2 m0 c

 pz   θ    sin   m c  0  2

(2)

where pz is the component of electron’s ground state linear momentum along the scattering vector (z-axis). Within the impulse approximation (infinitesimally short duration of electron-photon interaction), the Compton profile J(pz) is related to the scattering cross section as d 2σ = C (ω1 , ω 2 , θ , p z ) J ( p z ) (3) dΩ dω 2

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Ferromagnetic Shape Memory Alloys

The quantity ‘C' which is a function of photon’s energy before ( ω1 ) and after the scattering ( ω 2 ), θ and pz was calculated by Eisenberger and Reed [3] for 1800 scattering angle. Moreover, Ribberfors [4] has derived an expression within the impulse approximation that relates the relativistic Compton cross-section to the momentum distribution of bound electron states. Theoretically, J(pz) is expressed as J ( pz ) =

∫ ∫ ρ ( p) dp dp x

(4)

y

px p y

where ρ ( p) is the electron momentum density and is given by

ρ (p ) = ∑ χ n ( p) ∝ ∫ψ n (r )exp (− i p.r) 2

2

(5)

n

where ψ n (r ) is the position space wave function for the electron in the nth state.

k 2 ,ω 2 , ε 2

θ k = k1 − k 2

( )

p2 e−

θ

k 1,ω1 , ε1

( )

p1 e−

Fig. 1: Schematic diagram of Compton scattering with an incident photon of energy ω1, wave vector k1 and polarization ε1, scattered through an angle θ from a moving electron with initial momentum p1. The subscript 2 refers to the scattered photon. The wavelength λ1 (λ2) corresponds to energy ω1 (ω2).

In the magnetic Compton scattering (MCS), the magnetic field associated with the incident electromagnetic wave interacts with the magnetic moment of the electron [2, 5]. Magnetic Compton scattering is not a new phenomenon. It was employed four decades ago as the basis of a Compton polarimeter to measure the degree of circular polarization of the γ -rays emitted after beta decay, as a part of the study of neutrino helicity [6]. The first attempt to study spin density distribution of iron via Compton effect employed cooled beta emitters as the radiation sources [7]. These β γ -ray sources had to be kept at very low temperatures (mK). To limit self-heating effects within the sources, their intensity was kept extremely low. Therefore, due to poor statistics, such measurements could be used for little more than a demonstration of the effect. During the last two decades, polarized synchrotron radiations source (SR) have been applied to perform magnetic X-ray scattering experiments [2, 5]. In such experiments, one requires a beam of circularly polarized X-rays. Since the Compton scattering is an incoherent process, the technique is sensitive to spin directions summed over the electron distribution. Therefore, only ferro- or ferrimagnetic materials can be studied. Adopting the nomenclature used in the inset of Fig. 2, the double differential cross-section for spinpolarized electrons can be written as [5],

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147

 ω   m   d 2σ  ω   m1J ( pz ) + m 2 1 2  Pc F (α ) J mag( pz )  = r02  2   dΩ dω 2  mc    ω 1   2h k 

(6)

where m 1 =

(ω 1 − ω 2 ) 2

(1 − cos θ ) + Pl sin 2θ + cos 2θ + 1

mc m2 = −(1 − cos θ )

(7)

and   ω F (α ) = σˆ  cos α cos θ + 2 cos(θ − α )  ω1  

In these equations, r0 is the classical electron radius while Pl and Pc are the degrees of linear and circular polarization of the incident photons, respectively. As shown in the inset of Fig. 2, the direction of spin can be reversed by the use of external magnetic field; the interference term contributes positively or negatively to the charge scattering. The same would be true if one could reverse the handedness of circular polarization of the photons, which is currently impractical. Since only the F (α ) expression changes its sign on reversing the direction of the electron spin ( σˆ is ± 1), the following expression is derived from the difference in cross-sections when spins are reversed: +

−

 d 2σ   d 2σ    −  ∝ J mag ( p z )  d Ω dω 2   d Ω dω 2 

(8)

The symbols + and – denote spin-up and spin-down, respectively and the magnetic Compton profiles (MCP) Jmag(pz) is a projection of the difference in the momentum densities between ground-state electrons with spin-up (+) and spin-down (-) to the scattering vector. The MCP can be obtained experimentally by subtracting the data sets taken with the magnetizing field direction or handedness reversed. Although Jmag(pz) is only one-dimensional projection of the spin momentum density, it is strongly direction dependent. Theoretically, Jmag(pz) is written as 2 2  J mag ( p z ) = ∫∫  ∑ χ n+ ( p) − ∑ χ n− ( p)  dp x dp y n  n 

=

∫∫ [ρ (p ) − ρ (p )]dp +

−

x

dp y

In the absence of spin polarization

(9)

∑χ n

+ n

( p)

2

=

∑χ

− n

( p)

2

which leads to Jmag(pz) = 0

n

One can conclude that MCP builds up from the unpaired electrons, involved in the ferri- or ferromagnetism. The normalization condition in MCS experiments leads to +∞

∫J

mag

( p z ) dp z

= µs

(10)

−∞

where µ s is the number of unpaired electrons or the spin moment per formula unit. Experimental methodology In any MCS experiment, the basic requirements are (a) a high-energy monochromatic, circularly polarized primary X-ray beam (b) a magnetized sample and (c) an energy sensitive X-ray detector.

148

Ferromagnetic Shape Memory Alloys

Experimental set-up for MCS as being used at SPring-8 is shown in Fig. 2. Currently, the peak brightness of the synchrotron radiation (SR) from elliptical multipole wiggler is about 1.4 × 1017 ph.s-1 mrad-2mm-2 per 0.1% BW with critical energy 42.6 keV. The beam size at the sample position can be even of the order of 1mm2. The energy of SR is tunable upto 300 keV and Pc is about 0.5. The backscattered radiations (1780 scattering angle) are energy analyzed with a high purity tensegmented Ge detector and separate spectrum analysis hardware consisting of spectroscopy amplifiers, high voltage power supplies, analog to digital converters and spectrum stabilizers, etc.

Liq. He condenser

To magnet power supply

gas liq.

10 elements Ge-SSD

SR

(Sample) R. T. to 10 K To He-gas compressor

α

B

B α θ θ ω2 , k 2

sample ω1 , k 1

-k

Fig. 2: The experimental arrangement for magnetic Compton scattering measurements at BL08W, SPring8, Japan. In the inset, schematic diagram of the magnetic Compton scattering process is shown. The applied magnetic field (B) alternates between being parallel and antiparallel to the scattering vector k. α is angle between incident beam and the applied magnetic field.

The magnetic field in the sample is reversed using a super conducting magnet ( ± 5 T) in a sequence like + - - + + - - + … where (+) and (-) represent the relative direction of the magnetic field and the scattering vector [(+) being parallel and (-) antiparallel]. A switching time of 3 to 6 sec. (depending upon the applied magnetic field) and data acquisition time of 60 sec are usually taken to ensure a good signal averaging. At SPring8, multi-array Ge crystals (10 crystals each of 100 mm2 effective area) are circularly arranged around a hole (11 mm Dia.) to collect the scattered photons. The pulses coming out from the multi elements of detector are first fed into independent preamplifiers (for impendence matching and immediate amplification) and then to the spectroscopy amplifiers. Very special amplifiers are required to ensure that a linear relation between the input and output signals is maintained. Finally, these pulses are transferred to multichannel analyzers, which designate the pulses into channel numbers. Other experimental details are available in Ref. [8, 9]. The energy spectrum of Ni2.03Mn0.97Ga (hereafter referred as Ni2MnGa) at 110 K with 2 T field as measured at SPring8, Japan is shown in Fig. 3. In this figure, spin-up and spin-down spectra are almost overlapped because of small differences between them. The raw MCP data (difference of spin-up and spin-down data) are also shown in Fig. 3.

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149

+ Raw J Raw J + Raw (J -J ) x 20

4

counts x 10

5

3

2

1

0 3800

4000

4200

4400

Channel No.

+ Fig. 3: Raw Compton profiles (J and J ) measured for the opposite magnetization of the sample (with 2 T) at + + 110 K for Ni2MnGa. The J and J are not distinguishable on the present scale. The difference J - J , which results in raw magnetic Compton profile, is multiplied by a factor of 20 (in order to be visible).

Data processing To derive a true magnetic Compton profile, numerous systematic corrections have to be taken into account [5]. The most important are (i) beam decay correction (ii) energy dependent correction for the absorption of the photons in the sample (iii) energy dependence of the Compton cross-section and (iv) multiple scattering correction. In such experiments, the background contribution cancels out in taking the difference between spin-up and spin-down profiles. One crucial factor in the data reduction is to have the same intensity of the incident radiations for two opposite directions of magnetization. In the SR sources, the intensity of the incident photons changes during the course of the experiment and has to be monitored so that one can normalize the data for the same number of primary photons. Experimentally, the beam decay correction factor a can be calculated using the elastic line (which exists in the data) as a=

Intensity of elastic peak for spin - up direction Intensity of the same elastic peak for spin - down direction

The magnetic effect, which is ratio of magnetic to charge signals, is defined as I + − aI − R= + I + aI −

(11)

where I + and I − are the integrated Compton intensities for parallel and antiparallel magnetic field directions. Since the value of a remains close to 1, assuming a =1, the error in the magnetic effect (∆R) can be given as

∆R =

1 I +I−

(12)

+

As evident from Fig. 3, in such measurements, it is seen that I + ≈ I − ≈ I then

∆R =

1 2I

(13)

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Ferromagnetic Shape Memory Alloys

Moreover, the statistical error in magnetic Compton profile ∆J mag ( p z ) is given as ∆J mag ( pz ) =

J mag ( p z )

(14)

2I ×R

Progress of MCS in case of shape memory alloys (i) MCPs of Ni2MnGa: A representative case In Fig. 4, the onset of MCPs at a fixed temperature 294K at different sample-magnetizing fields is shown. At low external field ( 1, the reverse happens. For c/aTM. So, to find the stability of the ferromagnetic state, the difference in Etot between the paramagnetic and the ferromagnetic states has been calculated in the austenitic phase. This difference is 322 meV/atom for Ni2MnGa. In contrast, in Ni2.25Mn0.75Ga, TM>TC and the magnetic

169

170

Ferromagnetic Shape Memory Alloys

transition occurs in the martensitic phase. Ni2.25Mn0.75Ga show that TM>TC and the magnetic transition occurs in the martensitic phase and Etot turns out to be 219 meV/atom. Since Ni2MnGa satisfies the Stoner condition of ferromagnetism, it is possible to approximately relate TC to Etot by kBTC~ Etot [5]. We use this expression to find the relative variation. Thus, if TC = 376 K for x= 0; for x= 0.25, TC should be 256 K. So, although the experimental value (351 K) is higher, the qualitative trend of the decrease in TC with increasing x is obtained from theory. Larger difference of Etot between the austenitic and martensitic phases (δEtot) would imply greater stability of the martensitic phase and enhanced TM. Considering the experimental TM and δEtot for different FSMA’s, an approximate linear correlation is obtained. Conceptually, this is understandable since larger δEtot implies higher stability of the martensitic phase. This implies that higher temperature (TM) will be required to overcome the potential barrier for transition to the austenitic phase. For Ni2MnGa in the ferromagnetic state, Etot is 3.6 meV/atom. For x= 0.25 in the paramagnetic state, Etot is 39 meV/atom. Thus, the martensitic phase is more stable compared to the austenitic phase in Ni2.25Mn0.75Ga, i.e., the Ni excess composition. This is consistent with the experimentally observed higher TM with Ni doping (Fig. 4).The calculated magnetic moments for

x= 0, Ni2MnGa TMTC PC 39 PT 253 219

3.6

FT

Fig. 4: The middle panel shows the phase diagram of Ni2+xMn1-xGa from Ref.18; TM and TC are the martensitic start and Curie temperatures, respectively. The numbers (in meV/atom) shown in the left and the right panels are the total energy difference between two phases (as indicated by arrows) obtained from the total energy calculation for x= 0 and 0.25.

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Fig. 5: (a) The structure of Mn2NiGa the austenitic phase; blue, green, red, and brown spheres represent Ni, MnI, MnII and Ga, respectively. (b) The calculated total energies (Etot) of Mn2NiGa as a function of a (top axis) in the cubic austenitic phase; and as a function of c/a (bottom axis) in the tetragonal martensitic phase. (c) Three dimensional plot of the spin magnetic moment (in unit of eÅ-3) distribution of Mn2NiGa in the (110) plane in the martensitic phase [19]. (d) Experimental photoemission valence band (VB) spectrum of Mn2NiGa in the martensitic phase, compared with theoretical VB calculated from the DOS in Ref. 19. The experimental spectrum has been shifted along the vertical axis. Ni2.25Mn0.75Ga and Ni2MnGa are in good agreement with the experimental moments determined by magnetization and magnetic Compton scattering studies [20]. The structure of Mn2NiGa in the austenitic phase is cubic L21 (Fig. 5a). However, while in Ni2MnGa, the Ni atoms are at equivalent 8f positions: (0.25, 0.25, 0.25) and (0.75, 0.75, 0.75), in Mn2NiGa the two Mn atoms are at inequivalent positions: one Mn atom is at (0.5, 0.5, 0.5) (referred to as MnII), while the other (MnI) is at (0.75, 0.75, 0.75) position (Fig. 5a). From our powder x-ray diffraction studies on Mn2NiGa, we find c/a= 1.21 from the Rietveld fitting and the pattern can be indexed by a tetragonal unit cell, in agreement with an earlier study [2]. To understand the origin of the martensitic phase in Mn2NiGa, Etot in both phases have been calculated as function of lattice parameters in the lowest energy magnetic state (Fig. 5b). Since the magnetism in Mn2NiGa may be somewhat complicated, detailed calculations have been performed to determine the lowest energy magnetic state: Etot has been calculated with various possible starting MnI and MnII magnetic moment combinations for three electrons in Mn 3d κ= -3 state. κ is the relativistic quantum number given by -s(j+1/2), where s is the spin quantum number and j= l + s/2 [12]. The maximum occupancy of the κ= -3 state is 6, i.e. 3 for each spin. The occupancy of Mn 3d κ= 2 state is kept unchanged, with one electron each in majority and minority-spin state. Similar calculations have been done for both the phases, and the results are shown for the martensitic phase in Table I. We find that the

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self consistent field runs with anti-parallel starting MnI and MnII moments converge to the lowest Etot (0 meV in the martensite energy scale) and a ferrimagnetic solution is obtained. The spin magnetic moment distribution in the martensitic phase (Fig. 5c) for the lowest energy magnetic state clearly shows the anti-ferromagnetic alignment of MnI and MnII moments. So, we have used the starting MnI and MnII moments to be 3µB each with opposite alignment that converges to minimum Etot in both phases. In all cases, the starting Ni moment is taken to be zero and it develops a small moment aligned along MnII after convergence. For the martensitic (austenitic) phase, our calculated spin magnetic moments for the lattice constant optimized lowest energy magnetic state are -2.21 (-2.44), 2.91 (3.18), 0.27 (0.31), 0.01 (0.01) µB/f.u. for MnI, MnII, Ni, and Ga, respectively. Parallel starting MnI and MnII moments converge to higher energy local minimum and a ferromagnetic solution is obtained (see Table I). For example, Etot local minimum around 171 meV/atom is obtained for starting moments of 3µB each in parallel configuration, which converge to moment values of 2.58 and 2.83 µB for MnI and MnII, respectively. Interestingly, for starting MnI and MnII magnetic moments of 1 and 3 µB, respectively, we obtain the MnI moment to be small (0.4 µB) converging at a Etot local minimum of 109 meV. This indicates that there might be a local minima in the Etot hyperspace where one Mn atom moment is small, and such moments have been reported in Ref.2. So, we performed calculations starting with the converged Mn and Ni moments from Ref.2 and find that Etot converges to a local minimum at 194 meV/atom (see Table I, last but one row). Converged MnI, MnII and Ni moments are 1.38, -0.12 and 0.01 µB, respectively that are quite similar to Ref.2. A calculation with 3 and 0µB Mn starting moments, converges to 180 meV/atom with 2.48 and -0.19 and 0.03µB on MnI, MnII and Ni, respectively. Thus, quenching of MnII and Ni moment is possible for certain starting Mn moment configurations. However, it is clear that this is an artefact of the calculation, caused by convergence to a local minimum. Table I clearly shows that it is indeed possible to converge to different local minima at considerably higher energy and obtain completely different Mn moments. In Ref.2, calculations with different starting Mn moments are not reported, and the starting Mn moments that have been used are also not mentioned. Thus, it is likely that they have performed their calculation with a particular starting Mn moment combination that has converged to a local minimum. Etot in the austenitic phase and the above described magnetic state has been calculated as a function of the cubic lattice constant a. It exhibits a parabolic behavior and the minimum determines the optimized lattice constant (a= 11.055 a.u.) (Fig. 5b). The agreement is excellent: within 1% of with the experimental value of 5.907Å [2]. For the martensitic phase, in the first step, equilibrium unit cell volume (= 1330 a.u.3) is calculated by varying the volume keeping c/a fixed at the experimental value of 1.21. Next, Etot is calculated as a function of c/a with the unit cell volume fixed at the equilibrium value. This gives the equilibrium c/a= 1.25 corresponding to the Etot global minimum and 6.6 meV/atom lower than the austenitic phase Etot minimum (Fig. 5b).

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This demonstrates that

Table I: Starting and converged Mn spin magnetic moments (the configuration i.e. the occupancy in the majority and minority-spin states in the starting Mn 3d κ=-3 state is shown in bracket separated by a comma) and the corresponding total energies (Etot) for the martensitic phase of Mn2NiGa. The lowest Etot is taken to be zero meV/atom as reference. Etot is minimized through a large tetragonal distortion (c/a= 1.25) and lowering of the total energy drives the structural transition resulting in the lower temperature martensitic phase. The optimized lattice constants (a= 5.402 and c= 6.753Å) are in very good agreement with the experimental lattice constants: a= 5.527 Å and c= 6.704 Å [2]. Note that martensitic Etot exhibits a local minimum around c/a= 1.176, which could be related to a metastable phase not identified so far. Such local minimum in the total energy curve has been reported for Ni2MnGa [6]. If we compare the δEtot (experimental TM) for Ni2MnGa, Mn2NiGa and Ni2.25Mn0.75Ga, these are found to be 3.6 (210 K), 6.8 (270 K) and 39 (434 K) meV/atom, respectively. Thus, it seems that a proportionality relation between TM and δEtot would hold. Photoemission spectroscopy is a direct probe of the occupied electron states. In Fig. 5d, we present the valence band (VB) spectrum of Mn2NiGa in the martensitic phase recorded with He I source at 190 K. The sample surface was cleaned in situ in ultra high vacuum (6×10-11 mbar) by mechanical scraping. The main peak in the VB spectrum appears at -1.4 eV, and is dominated by Mn 3d-Ni 3d hybridized states. The Fermi edge (EF) is at 0 eV. The VB is calculated by adding the martensitic phase Ni and Mn 3d partial DOS in proportion to their PES cross-section, multiplied by the Fermi function and convoluted by broadening parameters [21]. The position of the main peak at about -1.4 eV and the intensity at EF with respect to the main peak depict nice agreement between experiment and theory. Summary We have determined the optimized lattice constants and the electronic structure of Ni2MnGa using the full potential linearized augmented plane wave method. The optimized tetragonal martensitic phase with c/a= 0.97 has 3.6 meV/atom lower energy than the austenitic phase. By comparing the DOS of the two phases of Ni2MnGa, we

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find a splitting of the minority-spin states below EF. These states are predominantly Ni 3d-like, weakly hyrbidized with Ga p-like states. The minority-spin DOS at EF varies with c/a, while the majority spin DOS is unaffected. The total energies have been calculated by ab initio FPLAPW method for the different phases and compositions to explain the phase diagram. The theoretically calculated lattice constants and magnetic moments are in good agreement with the experimental values. This shows the reliability of density-functional theory based all-electron calculations using generalized gradient approximation to describe the structural and magnetic properties. Mn2NiGa is found to an itinerant ferrimagnet in both the austenitic and martensitic phase. We furthermore show that in Mn2NiGa a large tetragonal distortion (c/a= 1.25) decreases the total energy, stabilizing the lower-temperature martensitic phase. References [1] S. J. Murray, M. Marioni, S. M. Allen, R. C. O Handley and T. A. Lograsso: Appl. Phys. Lett. Vol. 77 (2000), p. 886; A. Sozinov, A. A. Likhachev, N. Lanska and K. Ullakko: Appl. Phys. Lett. Vol. 80 (2002), p. 1746. [2] G. D. Liu, J. L. Chen, Z. H. Liu, X. F. Dai, G. H. Wua, B. Zhang and X. X. Zhang: Appl. Phys. Lett. Vol. 87 (2005), 262504. [3] T. Krenke, T. E. Duman, E., M. Acet, E. F. Wassermann, X. Moya, L. Maňosa, A. Planes: Nature Mat. Vol. 4 (2005), p. 450; R. Kainuma, Y. Imano, W. Ito, Y. Sutou, H. Morito, S. Okamoto, O. Kitakami, K. Oikawa, A. Fujita, T. Kanomata, and K. Ishida: Nature Vol. 439 (2006), p. 957. [4] S. Fujii, S. Ishida, and S. Asano: J. Phy. Soc. Japan Vol. 58 (1989), p. 3657. [5] O.I. Velikokhatnyi and I. I. Nuamov: Phys. Solid State Vol. 41 (1999), p. 617. [6] V. V. Godlevsky and K. M. Rabe: Phys. Rev. B Vol. 63 (2001), p. 134407. [7] A. Ayuela, J. Enkovaara, K. Ullakko, and R. M. Nieminen: J. Phys. : Condens. Matter Vol. 11 (1999), p. 2017; A. Ayuela, J. Enkovaara, and R. M. Nieminen: J. Phys. : Condens. Matter Vol. 14 (2002), p. 5325. [8] A. T. Zayak, P. Entel, J. Enkovaara, and R. M. Nieminen: J. Phys.: Condens. Matter Vol. 15 (2003), p. 159. [9] S. R. Baman, S. Banik and A. Chakrabarti: Phys. Rev. B Vol. 72 (2005), p. 184410. [10] J. M. MacLaren: J. Appl. Phys. Vol. 91 (2002), p. 7801. [11] J. Enkovaara, O. Heczko, A. Ayuela, and R. M. Nieminen: Phys. Rev. B Vol. 67 (2003), p. 212405. [12] P. Blaha, K. Schwartz, and J. Luitz, WIEN97, A Full Potential Linearized Augmented Plane Wave Package for Calculating Crystal Properties (Karlheinz Schwarz, Tech. Universitat, Wien, Austria), 1999. ISBN 3-9501031-0-4. [13] J. P. Perdew, K. Burke, and M. Ernzerhof: Phys. Rev. Lett. Vol. 77 (1996), p. 3865. [14] P. J. Webster, K. R. A. Ziebeck, S. L. Town, and M. S. Peak: Philos. Mag. B Vol. 49 (1984), p. 295. [15] B. Wedel, M. Suzuki, Y. Murakami, C. Wedel, T. Suzuki, D. Shindo, and K. Itagaki: J. Alloys Comp. Vol. 290 (1999), p. 137. [16] S. Banik, R. Ranjan, A. Chakrabarti, S. Bhardwaj, N. P. Lalla, A. M. Awasthi, V. Sathe, D. M. Phase, P. K. Mukhopadhyay, D. Pandey, and S. R. Barman: Phys. Rev. B Vol. 75 (2007), p. 104107. [17] F. D. Murnaghan: Proc. Natl. Acad. Sci. USA Vol. 30 (1944), p. 244. [18] S. Banik, A. Chakrabarti, U. Kumar, P. K. Mukhopadhyay, A. M. Awasthi, R. Ranjan, J. Schneider, B. L. Ahuja, and S. R. Barman: Phys. Rev. B Vol. 74 (2006), p. 085110. [19] S. R. Barman, S. Banik, A. K. Shukla, C. Kamal and A. Chakrabarti: Europhys. Lett. Vol. 80 (2007), p. 57002; S. R. Barman and A. Chakrabarti: Phys. Rev. B (2008), in press. [20] B. L. Ahuja, B. K. Sharma, S. Mathur, N. L. Heda, M. Itou, A. Andrejczuk, Y. Sakurai, Aparna Chakrabarti, S. Banik, A. M. Awasthi, and S. R. Barman: Phys. Rev. B Vol. 75 (2007), p. 134403; C. Biswas, R. Rawat, and S. R. Barman: Appl. Phys. Lett. Vol. 86 (2005), p. 202508. [21] A. Chakrabarti, C. Biswas, S. Banik, R. S. Dhaka, A. K. Shukla, and S. R. Barman: Phys. Rev. B Vol. 72 (2005), p. 073103.

Advanced Materials Research Vol. 52 (2008) pp 175-180 © (2008) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/AMR.52.175

Signature of austenitic to martensitic phase transition in Ni2MnGa in Mn and Ni K-edge XANES spectra V.G. Sathe 1,a, Soma Banik1,b, Aditi Dubey1,c, S. R. Barman1,d A. M. Awasthi1,e and Luca Olivi2,f 1

UGC-DAE Consortium for Scientific Research, Khandwa Road, Indore, 452001, India. 2

ELETTRA Sincrotrone, 163,5 in AREA Science Park, 34012 Basovizza, Trieste ITALY.

a

[email protected], [email protected], [email protected], [email protected], e [email protected], [email protected]

Keywords: Martensitic Transformations, XANES, EXAFS, Shape memory alloy

Abstract. The XANES studies at Mn, Ni and Ga K-edge of Ni2MnGa compound have been carried out at room and low temperatures. The Mn K-edge and Ni K-edge spectra shows modulation in the post edge features when the sample is cooled below martensitic transition temperature. It is strongly reflected in the XANES of Mn K-edge where the peak after the edge gets totally suppressed when the sample is in martensitic phase. This peak shows a hysteretic behaviour when thermal cycling was done across the martensitic transition temperature. This clearly shows that the peak height is a measure of austenitic phase present at a particular temperature. This demonstrates the strong correlations of electronic states and crystal structures in these compounds. Introduction Ni-Mn-Ga is of recent interest because it exhibits shape memory effect (SME) that can be driven by the magnetic field. This makes it an important candidate for practical applications, since the response in magnetic field driven SMA is faster and more efficient than the conventional SME driven by temperature or stress [1,2]. Ni-Mn-Ga exhibits highest known magnetic field induced strain (MFIS) of up to 10%. Ni-Mn-Ga shows giant magnetocaloric effect and has large negative magnetoresistance [3–5]. The martensitic transition in Ni2MnGa was first reported by Webster and co-workers in 1984 [6]. Ni2MnGa has an L21 structure at room temperature. The martensitic start temperature (MS) is 205 K. The ferro to paramagnetic transition occurs at TC= 376K. The properties of Ni-Mn-Ga are highly sensitive to the composition [7-10]. The martensitic phase of Ni2MnGa assumes complicated modulated structures, which are referred to as 5M and 7M structures [2,6,8,9,11,12]. The 5M and 7M phases correspond to 5-layer and 7-layer modulations of the (110) atomic planes in [1⎯1 0] direction. From high resolution neutron powder diffraction pattern, Brown et al. have shown that Ni2MnGa in the martensitic phase has a 7-layered orthorhombic structure with Pnnm space group and showed that the modulations are sinusoidal [11]. On the other hand, high resolution transmission electron microscopy (HRTEM) images show that the modulation has a stacking sequence of (5⎯2) i.e. five atoms are linearly shifted in one direction and two in the other [8,13]. However, for certain compositions, a tetragonal phase that does not exhibit any modulation has been reported [8,9]. The origin of the modulation has been related to the softening of the phonon mode and the nesting of the Fermi surface. The crystal structure and the c/a ratio in particular, influences both the magnetic and mechanical properties including the extent of FSMA. In the present work, we report our study on Mn, Ni and Ga K-edge XANES carried out at as a function of temperature. The aim is to explore the changes in local environment around these metal ions across the martensitic transition.

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Experimental methods Polycrystalline ingot of Ni2MnGa was prepared by arc melting the appropriate quantities of the constituent metals of 99.99 % purity under Argon atmosphere. The subsequent homogenization of the ingot material was carried out by annealing at 827 oC for 9 days in sealed quartz ampules. The samples were subsequently quenched in ice water. The sample was characterized by using x-ray diffraction, energy dispersive analysis of x-rays, magnetization, resistivity, and x-ray photoelectron spectroscopy [10]. Differential scanning calorimetry (DSC) measurements were performed using Model 2910 from TA Instruments at a heating and cooling rate of 10 °C/min. For XANES, pieces cut from the ingot were manually ground into powder and internal residual stress was removed by annealing the powder at 500oC for 10 hours. Absorbers for the XANES experiments were made by spreading very fine powder on a scotch tape avoiding any pin holes and thickness inhomogeneity. Few such tapes coated with sample are fixed one on top of the other to give adequate thickness such that an absorption edge jump, Δμx≤1. XANES at Mn, Ga and Ni K-edges were recorded in the transmission mode at the EXAFS-1 beamline at ELETTRA Synchrotron Source using Si(111) as monochromator. The measurements were carried out at room temperature, many intermediate temperature across the martensitic transition down to liquid nitrogen temperature. For measurements carried out at intermediate temperatures, the measured quantity of samples was mixed thoroughly with Boron nitride powder by using a mortar and pestle. The mixture was packed in the form of a thin pellet. This pellet was mounted inside a Nitrogen cryostat with a Tantalum heater. A K-type thermocouple was used for monitoring the sample temperature. The temperature stability was within ±2 K. The incident and transmitted photon energies were simultaneously recorded using gas-ionization chambers filled with mixtures of He-N2 for Mn-edge, Ar-N2 for Ga edge and Ar-He-N2 for Ni edge. Measurements were carried out from 300 eV below the edge energy to 1200 eV above it with a step of 4 eV in the pre-edge region and a 0.5 eV step in the XANES region. Preliminary data reduction and normalization was carried out using the Artemis software program for EXAFS data reduction. Results and Discussion Fig. 1 shows the Mn K-edge, Ni K-edge and Ga K-edge XANES spectra (from top to bottom) of the Ni2MnGa sample recorded at room temperature (RT) and liquid nitrogen temperature (LT) respectively. The spectra are slightly shifted vertically for ease of comparison. XANES spectra at Ga K-edge at RT and LT shows similar structure apart from more sharper feature at LT compared to that at RT that can be attributed to thermal effects. The XANES spectra at Ni K-edge shows significant difference at LT when compared to RT spectra. This effect is seen more pronounced when one compares the RT and LT spectra at Mn K-edge. The very prominent peak just after the edge peak seen at room temperature is not at all seen in the LT spectra. Even the next peak is also smeared off at LT when compared to RT spectra. The differences are very distinct and the effect is opposite to what would be expected due to the thermal effects. Generally, it is expected that the peaks become broader and less prominent at higher temperature due to thermal effects. These changes can be related to the local structural changes. As mentioned in the introduction, Ni2MnGa undergoes an austenitic to martensitic transition when cooled down below the martensitic start temperature (MS= 205 K). This encouraged us to carry out temperature variation of this sample in both heating and cooling cycle. Fig. 2 shows the XANES spectra recorded at various temperatures in both heating and cooling cycle. The spectra are shifted vertically for clarity. The intensity under the square block marked by an arrow in the Fig. 2(a) at 6576 eV (33 eV from the edge) shows systematic variation as the sample temperature was cycled across the martensitic transition temperature. The intensity steadily decreased as the temperature is decreased and no sudden drop is observed, though the intensity is found to be extremely small as the martensitic transition temperature is approached. This indicates towards the pre-transitional effects reported by many workers in displacive phase transition.

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Fig. 1: The K-edge XANES at Mn, Ni and Ga of Ni2MnGa recorded at room temperature (RT) and low temperature (LT). The spectra are shifted vertically for ease of comparison.

A background is subtracted from the highlighted portion of the curves by subtracting a straight line and the resulting curves are plotted in the Fig. 2(b). A close look at this figure shows a hysteretic behaviour in the intensity as the spectra is recorded across MS. It is found that the peak intensity is higher in cooling cycle at a given temperature than compared to that in a heating cycle. It is worth mentioning here that earlier reports [14, 15] clearly shows a hysteretic behaviour in magnetic and thermal measurements with martensitic start temperature MS = 205, martensitic finish temperature of MF = 189 K in cooling cycle while austenitic start temperature AS= 216 and Austenitic finish AF= 234 K during heating cycle. This indicates that this peak is a hallmark of austenitic phase and is vanishing as soon as the phase is transformed to the martensitic phase. The X-ray absorption near edge structure (XANES) is known to reflect the local symmetry in terms of changes in first coordination number around the absorbing atom. Normally this is reflected in the pre-edge region. Also, if the coordination number around the absorbing ion and its valence is unaltered the XANES spectra are expected to be very similar. The strength of the XANES feature is

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(a)

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Fig. 2: (a) The temperature variation both in cooling and heating cycle of Mn K-edge XANES spectra. (b) The area highlighted by square in (a) is shown in zoom after background subtraction. represented by the so called Fermi “golden rule”, which is proportional to the strength of a Lorentz oscillator, from an initial state |i> to a final state |f>. It can be written as Ii→f ~ ||2ρfρi where ρi and ρf are densities of states for |i> and |f>, respectively. Here, the final state is the empty state available in continuum where the bound electron is excited due to absorption of incident xrays. Hence, XANES gives information about the density of empty states above the Fermi level.

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This clearly indicates that the density of empty states is getting modified as the sample is undergoing a structural phase transition. As these modifications are mostly observed at the Mn site, it is concluded that the Mn related unoccupied electronic states play a role in driving the martensitic transition. It is worth noting here that during the austenitic to martensitic transformation, the structural distortion changes nearest neighbour distances around the absorbing atom that may be responsible for the changes in the electronic structure at the Mn-site. Fig. 3 shows the thermal hysteresis curve obtained by the temperature variation of the mole fraction of the austenitic phase during heating and cooling cycles determined from the analysis of the DSC curves. From the cooling curve, the martensitic start temperature (MS) is 205 K. MS has been determined from the point of inflection on the cooling curve. We have determined the point of inflection to be the point of intersection of two straight lines fitted to data points on the two side of the inflection point (dotted lines in Fig. 3). Similarly, martensitic finish temperature MF is about 195 K. From the heating curve, austenitic start (AS) and austenitic finish (AF) temperatures are 216 and 231 K, respectively.

Fig. 3: Hysteresis curve showing the mole fraction of the austenitic phase as a function of temperature, determined from the analysis of the DSC curves; arrows indicate the direction of heating and cooling. When one compares this curve with the curve in figure 2(b) representing the intensity of the XANES peak in heating and cooling cycle, it is seen that the intensity of the peak shows the lowest value around 180 K during cooling while during heating it starts gaining strength above 215 K. As mentioned before this peak represents the fraction of the austenitic phase present in the compound at a given temperature and it exhibits hysteresis behaviour similar to one seen in DSC studies. Hence, during cooling this peak is expected to have higher intensity than during heating at any given temperature. This is indeed observed at all the temperatures, for example, at 210 K the intensity of the peak is higher during the cooling cycle than compared to the heating cycle (Fig. 2(b)). Summary The XANES studies at Mn, Ga and Ni K-edge of Ni2MnGa compound is carried out at room and low temperatures. The Mn K-edge and Ni K-edge spectra show modulation in the post edge

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features when the sample undergoes the martensitic transition. It is strongly reflected in the features of Mn K-edge where the peak after the edge gets totally suppressed when the sample is in martensitic phase. The intensity of this peak showed a hysteretic behaviour when thermal cycling was done across the martensitic transition temperature. This agrees with the hysteresis observed from other studies like differential scanning calorimetry, x-ray diffraction and ac-susceptibility. This clearly shows that the peak height is a measure of the austenitic phase present at a particular temperature. This also shows that the electronic structure of Ni2MnGa is correlated to its crystal lattice. Our results are in agreement with the observation of electron–phonon coupling and phonon-softening due to Fermi surface nesting in this compound [16]. References [1] S. J. Murray, M. Marioni, S. M. Allen, R. C. O’Handley, and T. A. Lograsso: Appl. Phys. Lett. Vol. 77 (2000), p. 886. [2]

A. Sozinov, A. A. Likhachev, N. Lanska and K. Ullakko: Appl. Phys. Lett. Vol. 80 (2002), p. 1746.

[3]

J. Marcos, L. Manosa, A. Planes, F. Casanova, X. Batlle and A. Labarta: Phys. Rev. B Vol. 68 (2003), p. 094401.

[4]

X. Zhou, W. Li, H. P. Kunkel, G. Williams: J. Phys.: Condens. Matter Vol. 16 (2004), p. L39.

[5]

C. Biswas, R. Rawat, and S. R. Barman: Appl. Phys. Lett. Vol. 86 (2005), p. 202508.

[6] [7]

P. J. Webster, K. R. A. Ziebeck, S. L. Town, M. S. Peak: Philos. Mag. B Vol. 49 (1984), p. 295. A. N. Vasilev, A. D. Bozhko, V. V. Khovailo, I. E. Dikshtein, V. G. Shavrov, V. D. Buchelnikov, M. Matsumoto, S. Suzuki, T. Takagi, and J. Tani: Phys. Rev. B Vol. 59 (1999), p. 1113.

[8]

J. Pons, V. A. Chernenko, R. Santamarta and E. Cesari: Acta Mater. Vol. 48 (2000), p. 3027.

[9]

N. Lanska, O. Söderberg, A. Sozinov, Y. Ge, K. Ullakko, and V. K. Lindroos: J. Appl. Phys. Vol. 95 (2004), p. 8074.

[10] S. Banik, A. Chakrabarti, U. Kumar, P. K. Mukhopadhyay, A. M. Awasthi, R. Ranjan, J. Schneider, B. L. Ahuja, and S. R. Barman: Phys. Rev. B Vol. 74 (2006), p. 085110. [11] P. J. Brown, J. Crangle, T. Kanomata, M. Matsumoto, K. U. Neumann, B. Ouladdiaf, and K. R. A. Ziebeck: J. Phys.: Condens. Matter Vol. 14 (2002), p. 10159. [12] A. Chakrabarti, C. Biswas, S. Banik, R. S. Dhaka, A. K. Shukla, and S. R. Barman: Phys. Rev. B Vol. 72 (2005), p. 073103; V. V. Martynov and V. V. Kokorin: J. Phys. III Vol. 2 (1992), p. 739. [13] J. Pons, R. Santamarta, V. A. Chernenko and E. Cesari: J. App. Phys. Vol. 97 (2005), p. 083516. [14] S. Banik, R. Ranjan, A. Chakrabarti, S. Bhardwaj, N. P. Lalla, A. M. Awasthi, V. Sathe, D. M. Phase, P. K. Mukhopadhyay, D. Pandey, and S. R. Barman: Phys. Rev. B Vol. 75 (2007), p. 104107. [15] R. Ranjan, S. Banik, S. R. Barman, U. Kumar, P. K. Mukhopadhyay, and D. Pandey: Phys. Rev. B Vol. 74 (2006), p. 224443. [16] L. Manosa and A. Planes, J. Zarestky, T. Lograsso, D. L. Schlagel, and C. Stassis: Phys. Rev. B Vol. 64 (2001), p. 024305.

Advanced Materials Research Vol. 52 (2008) pp 181-186 © (2008) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/AMR.52.181

A charge Compton profile study of Ni2MnGa: Theory and experiment G. Ahmed1,a, B.L. Ahuja1,b, N.L. Heda1,c, V. Sharma1,d, A. Rathor1,e, B.K. Sharma2,f, M. Itou3,g, Y. Sakurai3,h and S. Banik4,i 1

Department of Physics, M. L. Sukhadia University, Udaipur 313001, India. 2

Department of Physics, University of Rajasthan, Jaipur 302015, India.

3

Experimental Research Division, Japan Synchrotron Radiation Research Institute (JASRI), SPring8, Mikazuki, Hyogo 679-5198, Japan. 4

UGC-DAE Consortium for Scientific Research, Khandwa Road, Indore 452017, India.

a

email: [email protected], bemail: [email protected], cemail: [email protected] d email: [email protected], eemail: [email protected], femail: [email protected], gemail: [email protected], hemail: [email protected], iemail: [email protected]

Keywords: Compton scattering, Electronic structure, Band structure calculations, Shape memory alloys

Abstract We present the first ever theoretical and experimental charge Compton profiles of Ni2MnGa Heusler alloy. The measurements have been made using magnetic Compton spectrometer at SPring8, Japan. The Compton profiles and energy bands have been computed using Hartree-Fock, density functional theory with local density and generalized gradient approximations. It is seen that the Hartree-Fock based Compton profile is relatively in better agreement with the experimental profiles. In addition, we also report the energy bands, density of states and valence charge densities using full potential linearized augmented plane-wave method. Introduction The Heusler alloys with cubic L21 structure are of great interest in spin electronics. These alloys have drawn much attention in the recent years because they possess localized magnetic moment. In the Ni2MnGa Heusler alloy, a multistage structural transformation from high temperature cubic austenitic to ferromagnetic martensitic phase is observed. Particularly, the combination of ferromagnetic ordering and martensitic transformation enables the magnetically driven shape memory effect, thereby extending its technical applications. Among earlier studies, several workers have reported structural, electronic and magnetic properties including magnetic Compton profiles of Ni2MnGa [1-6]. Within the impulse approximation, the differential scattering cross-section is simply proportional to the charge Compton profile, J ( p z ) , which is related to the electron momentum density and hence the electronic properties of materials [7]. The J ( p z ) can be written as r r J ( p z ) = ∫∫ ρ ↑ ( p ) + ρ ↓ ( p ) dpx dp y (1)

(()

() )

Here ρ (↑) ( p ) and ρ (↓ )( p ) are the electron momentum densities for the majority and the minority spins, respectively. In this paper, we report the charge Compton profile of Ni2MnGa at T = 110 and 294 K using magnetic Compton spectrometer at Super Photon Ring 8 GeV (SPring8), Japan. To compare our experimental data, we have computed the Compton profiles and energy bands using Hartree-Fock and density functional theories. We have also derived the energy bands, density of states and spin r

r

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Ferromagnetic Shape Memory Alloys

densities using full potential linearized augmented plane wave (FP-LAPW) method within the framework of generalized gradient approximation. Experiment The preparation of sample is mentioned in an earlier paper [8]. The Compton profile measurements were performed at the high-energy inelastic scattering beam line at SPring8, Japan [5, 9]. The beam size at the sample position was 0.4 mm (h) x 1mm (w). The incident x-rays with energy of 176.8 keV were monochromatized using a Johann-type Si 620 reflection. The angle of Compton scattering in the present measurement was 1770. The scattered radiations were analysed using a ten-element high purity Ge detector. The overall momentum resolution obtained was 0.42 a.u. (1 a.u. = 1.99 x 10-24 kg m s-1). The raw data for charge Compton profiles were obtained by the addition of two Compton intensities I+ (pz) and I- (pz) with positive and negative applied magnetic field directions. The raw data (I+ + I- ) were corrected for the energy dependent corrections like Compton scattering cross-section, sample absorption and multiple scattering, etc. [10, 11]. In such experiments, it is very difficult to measure the background data. Our experience in this field guides us that in the high momentum region (pz > 5 a.u.), the major contribution in Compton line shapes is from the tightly bound core electrons. Since the core electrons are almost unaffected by the crystal environment, one can subtract out the linear and constant background along with a fixed free atom core contribution. In the present measurements, the background contribution was subtracted out by assuming that the valence Compton profile at pz = 6.0 a.u. becomes zero. Therefore, the experimental Compton profile at pz = 6.0 a.u. after the above mentioned data reduction was subtracted from the entire range of Compton data. Finally, keeping the baseline correction in mind, the data were normalized to 47.48 e-being the area of the corresponding free atom profile in the range 0-6 a.u. [12]. Due to reasonable statistics of raw Compton data from a single detector, the data of only one detector was used to derive the charge Compton profiles. Theory To compute the electronic structure of Ni2MnGa, we have employed the linear combination of atomic orbitals (LCAO) and FP-LAPW methods. The salient features of our calculations are given below. LCAO method The LCAO within CRYSTAL03 code of Torino group [13] includes a variety of self-consistent treatments of exchange and correlation namely the Hartree-Fock (HF), the local density and generalised gradient approximations (LDA and GGA, respectively) to density functional theory (DFT). In the LCAO technique the Bloch orbitals of the crystal are expanded using atom-centered Gaussian orbitals of s, p or d symmetry. In the B3LYP, hybrid functional (HF + DFT), the exchange and correlation part E XC is given as E XC = (1 − m0 ) E XLDA + m0 E XHF + m x ∆E XB 88 + mc ECLYP + (1− mc )ECVWN

(2)

where m x ∆E XB88 is Becke’s gradient correction to the exchange functional and the correlation functional (Ec) is a combination of the functionals due to Lee-Yang-Parr (LYP) and Vosko-WilkNusair (VWN) [13]. The standard values of the parameters m0, mx and mc were 0.20, 0.90 and 0.81, respectively. In the present calculations, the structure of Ni2MnGa was taken as fcc, having the space group number 225 (Fm3m). Accordingly, the atomic positions were taken as Ni = ¼, ¼, ¼ and ¾, ¾, ¾ ; Mn = ½, ½, ½; and Ga = 0, 0, 0. The value of lattice parameter a was taken as 5.854 Å. In the present DFT-LDA calculations, we have taken the exchange of Dirac-Slater [13] and correlations of Perdew-Zunger [14], while in case of DFT-GGA calculations exchange of Becke [13] and

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correlations of Perdew and Wang [15, 16] were taken. For a faster convergence of self-consistence field (SCF) cycles the BROYDEN scheme [17] was applied after ISTART-SCF iteration. The all electron Gaussian type orbitals (GTOs) basis sets for bulk Ni, Mn and Ga were downloaded from Ref. [18]. Following the default tolerances in the CRYSTAL03 code, self-consistency (SC) has r been performed at 328 k points in the irreducible Brillouin zone (BZ). FP-LAPW method The FP-LAPW has proven to be one of the most reliable prescriptions for the computation of the electronic structure of solids within the DFT [19]. In this method, the space is divided into interstitial regions and non-overlapping muffin-tin (MT) spheres centered at the atomic sites. The present computations were performed in the framework of GGA, recently suggested by Wu and Cohen [20]. The cut off for the charge density was Gmax = 12. The radial basis functions of each LAPW were calculated up to maximum l (l max ) = 10. The radius of MT spheres ( RMT ) was 2.35 a.u. for Ni and Mn and 2.20 a.u. for Ga. We have used an energy cut off for the plane wave expansion RMT K max = 7. The SC was achieved after 19 iterations. The BZ integration was r

performed using the modified tetrahedron method with 47 k (10x10x10) points in irreducible wedge of the BZ. Results and discussion The majority and minority band structures resulting from FP-LAPW and LCAO-DFT-GGA calculations are shown in Figs. 1-2.

Fig. 1: The FP-LAPW band structure of Ni2MnGa (Fm3m) along the high symmetry directions for (a) majority spin and (b) minority spin. In FP-LAPW calculations, as a reference level, the Fermi energy EF is shifted to 0 eV.

Fig. 2: Same as figure 1, except the scheme which is LCAO-DFT-GGA.

In the vicinity of EF, the overall topology of energy bands for majority and minority spins computed within GGA in both the schemes is almost the same. Due to similar topology of bands computed within the LCAO-HF, LCAO-DFT-LDA and B3LYP, these bands are not shown here. The lowest band in both the majority and minority spins, separated from the other valence bands, mainly arises from 4s contribution of Mn, Ni and Ga. The majority spin bands, as shown in figures 1(a) and 2(a), depict a hole pocket centered at Γ. The electronic density of states (DOS) for the majority and minority spins of the d electrons of Mn and Ni and total DOS are given in Figs. 3 (a-c). The contribution of 4s electrons of Mn, Ni and Ga in the energy range –10 to –5 eV is also visible in the Fig. 3(c). A close inspection of Figs. 1-3 reveals that in the majority bands, a number of flat bands below the Fermi level (EF) are mostly from the d bands of Mn and Ni. In case of minority states, the

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flat curves below (above) EF are dominated by the d-band of Ni (Mn) atoms. The overall shape of present energy bands and DOS agrees with the full potential spin-polarised linear combination of muffin tin orbitals calculations of Velikokhatnyĭ and Naumov [6]. Fig. 4 depicts the 3D spin density map in the (110) plane of Ni2MnGa. It is seen that in the spin-density map, the resulting three large peaks coincide with the location of Mn ions. It re-confirms that the magnetisation in the present NiMn-Ga system arises mainly from the Mn atoms. The magnitude of spin density at Ni and Ga sites is also consistent with the spin moments derived from the magnetic Compton profile data [5]. (b)

Mn (d)

(a)

0

(c)

Ni (d)

0

-10.0

-7.5

-5.0

-2.5

0.0

2.5

5.0

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10.0

Total

0

-10.0

-7.5

-5.0

-2.5

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-7.5

-5.0

-2.5

Energy (eV)

Energy (eV)

0.0

2.5

5.0

7.5

10.0

Energy (eV)

Fig. 3: FP-LAPW (GGA) based majority-spin (↑) and minority-spin (↓) densities (Arb. units) in Ni2MnGa for d electrons of (a) Mn and (b) Ni. In figure (c), the total of majority-spin and minority-spin densities in Ni2MnGa is shown. Mn Ni

Fig. 4: 3-dimensional plot of spin density in the (110) plane (linear scale in Å-3) using FPLAPW (GGA) for majorityminus-minority

Mn Mn Ni

Ni Ni Ga

Ga Ga

HF D FT- LD A D FT- GGA B3LYP

(a) J 111 - J 110

0.50

Ga

0.25

∆ J ( in e/a.u.)

-0.25 0.5

(b) J 111 - J 100

0.0 -0.5 -1.0

(c) J 110 - J 100

0.25 0.00 -0.25

HF DFT - L DA D F T - GGA B3 L YP

0.8

∆ J(Theory - Expt.) (in e/a.u.)

0.00

( a) 110K

1.2

0.4 0.0 -0.4 1.2

0

1

2

3

4

5

( b) 294K 0.8 0.4 0.0 -0.4

-0.50

0

1

2

3

4

5

6

p z (in a.u.)

Fig. 5: The differences in the directional Compton profiles of Ni2MnGa computed by various schemes namely HF, DFT with LDA and GGA and also by B3LYP of CRYSTAL03 code. The solid lines connecting the symbols are only to guide the eyes.

-0.8 0

1

2

3

4

5

pz ( i n a . u . )

Fig. 6: Difference between convoluted theoretical profiles computed using various schemes of CRYSTAL03 code and the isotropic experimental profiles for (a) T = 110 K and (b) T = 294 K. Statistical errors are within the size of symbols used.

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v The anisotropic part of ρ (p ) , which is free from systematical errors in the theory and the experiment, can be deduced by forming direction difference profiles (Jhkl – Jh’k’l’). To visualize the anisotropies in the electron momentum densities, we have plotted in Figs. 5 (a-c), the LCAO based directional differences between the low-indexed theoretical Compton profiles of Ni2MnGa. The fine structures in the anisotropies are consistent with the degeneracy of the energy bands and the holetype structures at the Γ point. To investigate specific features like shape of the profiles in the low momentum region and blurring of the Umklapp, experimental anisotropies are required. In Figs. 6 (a) and (b), we have shown the difference profiles between convoluted theory (HF, DFT with LDA and GGA and B3LYP) and our experiment at two different temperatures 110 and 294 K. The difference profiles at both the temperatures show that the HF theory gives a relatively better agreement in comparison to the other theories. It is also confirmed by χ2 fitting. Such a trend has also been observed in our earlier work on II - IV semiconductors [see for example, 21]. Conclusions

We have presented the charge Compton profile of Ni2MnGa alongwith its energy bands using the LCAO method. Our experimental Compton profiles are compared with the various LCAO based schemes namely HF, DFT with LDA and GGA and also hybridization of HF and DFT. The experimental profiles at 110 and 294 K are relatively in a better agreement with the HF profile. The energy bands, density of states and 3D spin densities using FP-LAPW are also reported. To confirm the theoretical anisotropy in the momentum densities, the experimental data on single crystalline Ni2MnGa are required. Acknowledgement

We are grateful to the authorities of SPring8 (JASRI), Japan for granting beam time under Proposal No. 2003A0055ND3-np. We also thank DST, New Delhi for financial support and Dr. S. R. Barman for his kind suggestions. References

[1] F. Zuo, X. Su and K.H. Wu: Phys. Rev. B Vol. 58 (1998), p. 11127 [2] A.N. Vasil’ev, A.D. Bozhko, V.V. Khovailo, I.E. Dikshtein, V.G. Shavrov, V.D. Buchelnikov, M. Matsumoto, S. Suzuki, T. Takagi and J. Tani: Phys. Rev. B Vol. 59 (1999), p. 1113 [3] J. Enkovaara, A. Ayuela, J. Jalkanen, L. Nordstrom and R.M. Nieminen: Phys. Rev. B Vol. 67 (2003), p. 054417 [4] A.T. Zayak, P. Entel, J. Enkovaara, A. Ayuela and R.M. Nieminen: Phys. Rev. B Vol. 68 (2003), p. 132402 [5] B.L. Ahuja, B.K. Sharma, S. Mathur, N.L. Heda, M. Itou, A. Andrejczuk, Y.Sakurai, A. Chakrabarti, S. Banik, A.M. Awasthi and S.R. Barman: Phys. Rev. B Vol. 75 (2007), p. 134403; also S.R. Barman, S. Banik and A. Chakrabarti: Phys. Rev. B Vol. 72 (2005), p. 184410 ( [6] O.I. Velikokhatny i and I.I. Naumov: Phys. Sol. State Vol. 41 (1999), p. 617 [7] M.J. Cooper: Rep. Prog. Phys. Vol. 48 (1985) p. 415 and references therein. [8] S. Banik, A. Chakrabarti, U. Kumar, P.K. Mukhopadhyay, A.M. Awasthi, R. Ranjan, J. Schneider, B.L. Ahuja and S.R. Barman: Phys. Rev. B Vol. 74 (2006), p. 085110

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[9] Y. Kakutani, Y. Kubo, A. Koizumi, N. Sakai, B.L. Ahuja, and B.K. Sharma: J. Phys. Soc. Japan Vol. 72 (2003), p. 599 [10] D.N. Timms: Ph. D. thesis (unpublished), University of Warwick, England (1989). [11] J. Felsteiner, P. Pattison and M.J. Copper: Phil. Mag. Vol. 30 (1974), p. 537 [12] F. Biggs, L.B. Mendelsohn and J.B. Mann: Atomic Data and Nuclear Data Tables Vol. 16 (1975), p. 201 [13] V.R. Saunders, R. Dovesi, C. Roetti, R. Orlando, C.M. Zicovich-Wilson, N.M. Harrison, K. Doll, B. Civalleri, I.J. Bush, Ph.D’Arco and M. Llunell: CRYSTAL03 User’s Manual, University of Torino, Torino, (2003); also C. Pisani and R. Dovesi: Int. J. Quantum Chem. Vol. 17 (1980), p. 501; also M.D. Towler, A. Zupan and M. Causa: Comp. Phys. Commun. Vol. 98 (1996), p. 181 [14] J.P. Perdew and A. Zunger: Phys. Rev. B Vol. 23 (1981), p. 5048 [15] J.P. Perdew and Y. Wang: Phys. Rev. B Vol. 33 (1986), p. 8800 [16] J.P. Perdew and Y. Wang: Phys. Rev. B Vol. 45 (1992), p. 13244 [17] D.D. Johnson: Phys. Rev. B Vol. 38 (1988), p. 12807 [18] Information on http://www.tcm.phy.cam.ac.uk/~mdt26/basis_sets. [19] P. Blaha, K. Schwarz and J. Luitz: WIEN code, An Augmented Plane Wave Plus Local Orbitals Program for Calculating Crystal Properties, Vienna University of Technology, Vienna, Austria (2001); also P. Blaha, K. Schwarz, P. Sorantin and S.B. Rickey: Comput. Phys. Commun. Vol. 59 (1990), p. 399 [20] Z. Wu and R. Cohen: Phys. Rev. B Vol. 73 (2006), p. 235116 [21] N.L. Heda, S. Mathur, B.L. Ahuja and B.K. Sharma: Phys. Stat. Sol. (b) Vol. 244 (2007), p. 1070

V. Effects of External Fields

Advanced Materials Research Vol. 52 (2008) pp 189-197 © (2008) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/AMR.52.189

Effect of external fields on the martensitic transformation in Ni-Mn based Heusler alloys Xavier Moya1 , Llu´ıs Ma˜ nosa1 , Antoni Planes1 , Seda Aksoy2 , Mehmet Acet2 , Eberhard F. Wassermann2 , Thorsten Krenke3 1 Departament

d’Estructura i Constituents de la Mat`eria. Facultat de F´ısica. Universitat de Barcelona. Diagonal 647, 08028 Barcelona, Catalonia 2 Experimentalphysik, Universit¨ at Duisburg-Essen, D-47048 Duisburg, Germany 3 ThyssenKrupp Electrical Steel, Kurt-Schumacher-Str. 95, D-45881 Gelsenkirchen, Germany

Keywords: Field-induced transformation, shape-memory alloys, ferromagnetism, Heusler alloys.

Abstract. In this paper, we discuss the possibility of inducing a martensitic transition by means of an applied magnetic field or hydrostatic pressure in Ni-Mn based Heusler shape memory alloys. We report on the shift of the martensitic transition temperatures with applied magnetic field and applied pressure and we show that it is possible to induce the structural transformation in a Ni50 Mn34 In16 alloy by means of both external fields due to: (i) the low value of the entropy change and (ii) the large change of magnetization and volume, which occur at the martensitic transition. Introduction Functional materials are materials that exhibit a strong response of some of their properties (mechanical, electric or magnetic) to changes in some external variable, such as temperature, pressure or electric/magnetic field. In many cases, this strong response is due to the proximity of the state of the system to a phase transition (magnetic, structural...). In addition, in some cases the interplay of several response variables in the same material leads to a multiple response to an external parameter, thus giving rise to the so-called multifunctional materials [1]. Over the last years, we have studied the magnetic and structural properties of Ni-Mn based Heusler alloys Ni-Mn-Sn [2] and Ni-Mn-In [3]. These alloys show martensitic transformations with a strong interplay between structural and magnetic degrees of freedom, leading to several interesting properties such as inverse magnetocaloric effect [4, 5] and magnetic superelasticity [6], which confer to these compounds interesting functional performances. Besides the properties arising from the application of a magnetic field, Ni-Mn-X Heusler alloys also show a noticeable dependence of the structural and magnetic properties on applied pressure [7, 8, 9, 10, 11]. This fact opens up the possibility of controlling magnetic and structural properties by means of an applied magnetic field and/or an applied pressure, a further step towards multifunctionality. In the present paper we study the influence of magnetic field and pressure on the martensitic transformation. In order to evaluate the necessary conditions to induce the structural transition by means of the application of an external field we should take into account the ClausiusClapeyron relation which is expected to be valid for equilibrium first order phase transitions

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Ferromagnetic Shape Memory Alloys

2 and provides the magnitude of the shift in the transition temperature caused by an external field. In general, it is expressed as: dTt ∆ψ =− , dφ ∆S

(1)

where Tt is the transition temperature, φ is the external field (magnetic field, H, or pressure, p, in our case), ψ is the corresponding conjugate variable (magnetization, M , or volume, v) and ∆S is the entropy change across the transition. Thus, in order to have a large shift of the transition temperature with the applied field, it is necessary to have (i) a small entropy change and/or (ii) a large change of the response variable ψ across the structural transition. The paper is organized as follows. First, we introduce the phase diagrams of the different studied systems and discuss the entropy change associated with the occurrence of a martensitic transition in specific compositional ranges. In the following two sections, we discuss the possibility of inducing the structural transformation by means of both applied magnetic field and hydrostatic pressure. Finally, we summarize the main results and conclude.

Transformation properties Figure 1 shows the phase diagrams (transition temperatures as a function of the valence electron concentration) for the prototypical ferromagnetic shape memory alloy (a) Ni-Mn-Ga, and for the two studied systems (b) Ni-Mn-Sn and (c) Ni-Mn-In. The martensitic start temperature (Ms ) increases almost linearly with increasing the valence electron concentration (decreasing the X element concentration) in all systems. However, in contrast to Ni-Mn-Ga, no structural transformation has been observed for compositions x ≥ 18 and x ≥ 16.5, for systems containing Sn and In, respectively. The main difference of the studied system compared to the prototypical Ni-Mn-Ga stands out when looking at the Curie temperature. While the Ga system shows similar (and weak) e/a dependencies of the Curie point in both austenite and martensite phases, Ni-Mn-Sn and Ni-Mn-In show a stronger e/a dependence of the Curie point in the martensitic state (TCM ) than in the cubic phase (TCA ). Thus, from the phase diagrams in figure 1, it can be inferred that there will be a noticeable change in the magnetic interactions in the studied alloys when the sample goes from the cubic to the martensitic phase. On the other hand, the entropy change at the martensitic transition (shown in the insets of figure 1) for the studied systems shows a similar behaviour as a function of e/a as the martensitic transition temperatures, i. e., ∆S increases as the electron concentration per atom increases [2, 3]. In order to fulfill the first condition related to the possibility of inducing the martensitic transition by an external field, we selected samples with low e/a values that transform martensitically. Specifically, we focused on Ni50 Mn35 Sn15 (e/a = 8.05) and Ni50 Mn34 In16 (e/a = 7.86) compositions. These alloys have small entropy-change values, especially the Inalloy. Additionally, these samples correspond to compositions close to the region where martensitic and magnetic transitions coincide. As stated above, in this region, magnetic interactions are expected to change considerably due to changes in the interatomic distances across the martensitic transition. In this situation, it is expected that the application of a magnetic field (which modifies the magnetic properties) and hydrostatic pressure (which basically modifies the interatomic distances) will lead to significant shifts in the transitions temperatures.

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191 3

(a) Ni-Mn-Ga

(b) Ni-Mn-Sn

1200

T (K)

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800

0 7.2

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(c) Ni-Mn-In

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Ms

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0 7.2

7.6

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0 7.6

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Fig. 1: Structural and magnetic transition temperatures as a function of the valence electron concentration, e/a, for: (a) Ni-Mn-Ga, (b) Ni-Mn-Sn and (c) Ni-Mn-In. In the case of the NiMn-Ga system, data are compiled from reference [14]; open square and open circle symbols stand for the premartensitic (TI ) and intermartensitic transition temperatures, respectively. Insets show the electron concentration dependence of the entropy change at the martensitic transition for each system; for Ni-Mn-Ga system, • are taken from reference [15] and ◦ from reference [16]. Effect of a magnetic field on the martensitic transformation Figure 2 shows the difference between the magnetization in the martensitic state and the austenitic state, ∆M = MM − MA , as a function of magnetic field for four selected compounds: (a) close-to-stoichiometric Ni49.5 Mn25.4 Ga25.1 [17], (b) off-stoichiometric Ni54.7 Mn20.3 Ga25.0 [18], (c) Ni50 Mn35 Sn15 and (d) Ni50 Mn34 In16 . This figure illustrates the main difference between the prototypical Ni-Mn-Ga and the studied Sn and In systems: while for Ni-Mn-Ga, the saturation magnetization of the martensitic state is larger than the saturation magnetization of the austenitic phase (thus, ∆Msat > 0), the opposite behaviour is observed in Ni-Mn-Sn and Ni-Mn-In, i. e., ∆Msat < 0. Actually, this behaviour is at the origin of the so-called inverse magnetocaloric effect observed in these compounds [4, 5]. It should be noted that close to stoichiometric composition the Ni-Mn-Ga alloy shows a peculiar non-monotonous behaviour which is due to the different length-scale of the coupling between magnetism and structure in this compound [19]. Additionally, the magnetization-change across the transition observed in the Ni-Mn-In alloy is the largest reported (in absolute value) more than twice the values of Ni-MnGa and Ni-Mn-Sn. This fact yields the second condition required by the Clausius-Clapeyron equation and thus makes this compound a serious candidate to exhibit magnetic-field-induced structural transformations. The effect of the magnetic field on the martensitic transition of magnetic shape memory alloys has been studied by using differential scanning calorimetry (DSC) under magnetic field

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Ferromagnetic Shape Memory Alloys

∆M (A m2/kg)

∆M (A m2/kg)

4 30 0 20 -10 10 -20

Ni49.5Mn24.5Ga25.1 (a)

Ni56.2Mn18.2Ga25.5 (b)

0

-30 0 0

Ni50Mn35Sn15 (c)

Ni50Mn34In16 (d) -20

-10 -40 -20 -60 -30 0

1

2

3

µ0H

(T)

4

5

0

1

2

3

µ0H

(T)

4

5

Fig. 2: Magnetic field dependence of the magnetization change associated with the martensitic transition, ∆M = MM −MA , corresponding to (a) Ni49.5 Mn25.4 Ga25.1 [17], (b) Ni54.7 Mn20.3 Ga25.0 [18], (c) Ni50 Mn35 Sn15 and (d) Ni50 Mn34 In16 . The solid line in (a) indicates the position of the zero, in (b) it is a guide for the saturated behaviour up to 5 T.

∆Tt (K)

20

0

-20

Ni2MnGa Ni53.5Mn19.5Ga27 Ni50Mn35Sn15 Ni50Mn34In16

-40

-60 0

1

2

µH

3

4

5

(T)

Fig. 3: Transition temperature as a function of magnetic field for the analyzed systems. Data for stoichiometric Ni2 MnGa is from Ref. [10] and for the nonstoichiometric NiMnGa from Ref. [12].

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and magnetization measurements on both Ni50 Mn35 Sn15 [21] and Ni50 Mn34 In16 alloys [3, 6]. The former technique is especially suited for studying magnetostructural transitions [20] since, not only transition temperatures are obtained, but also it is possible to estimate the effect of the field on entropy changes. The obtained results are summarized in figure 3, which shows the magnetic field dependence of the martensitic transition temperatures. As can be seen from this figure, Ni-Mn-Sn and Ni-Mn-In show monotonous shift towards lower temperatures on increasing the magnetic field. By contrast, for non-stoichiometric Ni-Mn-Ga alloys with higher electron concentration, the transition temperature shifts with field towards higher values. For stoichiometric Ni2 MnGa, there is a non-monotonous behaviour again due to the different length scale of the coupling between magnetism and structure in this alloy [19]. Actually, the magnetic field dependence of the transition temperatures is consistent with the Clausius-Clapeyron equation dTt ∆M = −µ0 , (2) dH ∆S where we have substituted the generic external field φ by the magnetic field H and the corresponding conjugate variable ψ by the magnetization M . DSC measurements under magnetic field have proved that ∆S is independent of magnetic field [21]. Therefore, we can integrate the previous expression as ∆Tt = −µ0

Z H ∆M 0

1 ZH dH = −µ0 ∆M dH . ∆S ∆S 0

(3)

Hence, the magnetic field dependence of the transition temperature is essentially controlled by the magnetization change at the phase transition: the magnetic field stabilizes the phase with higher magnetization. Thus, if the magnetization of the martensitic phase is larger than the magnetization of the austenitic state the magnetic field induces the forward martensitic transformation (austenite to martensite), and the opposite situation is found when MM < MA . Effect of hydrostatic pressure on the martensitic transformation Pressure is another intensive variable that could be modified in order to induce the martensitic transformation. In order to explore this possibility, significant volume changes across the structural transitions are needed. Effectively, if we take into account the Clausius-Clapeyron (equation 1) and consider the variables (p, −v) we can write dTt ∆v = . dp ∆S

(4)

Now, if we assume that the entropy change at the martensitic transition does not depend on the applied pressure (analogously to the magnetic field) and that the volume change across the phase transition does not strongly vary with hydrostatic pressure, we obtain the following expression: ∆Tt =

Z p ∆v 0

∆S

dp =

∆v Z p ∆v p. dp = ∆S 0 ∆S

(5)

Thus, the transition temperature is proportional to applied pressure and the sign of the transition temperature shift is controlled by the volume change at the phase transition: if the volume of the martensitic phase is lower than the volume of the austenite we will observe a positive shift of the transition temperatures and viceversa.

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6 Ms

∆l/l (%)

0

Ni50Mn27Ga23 Ni50Mn34.5Sn15.5 Ni50Mn34In16

Ms

Ms

-0.2

ε ε

-0.4

100

200

300

T (K) Fig. 4: Temperature dependence of the relative length change ∆l/l (with respect to the length at 300 K) for the analyzed systems. Vertical arrows indicate Ms . ε illustrates the length decrease across the martensitic transition. In order to estimate the volume change across the structural transition we carried out measurements of the sample-length as a function of temperature [22]. Figure 4 shows the temperature dependence of the relative length change ∆l/l (with respect to the length at 300 K) for the analyzed systems. As can be seen from this figure, Ni-Mn-Ga and the systems with Sn and In again exhibit marked differences. While in the prototypical Ni-Mn-Ga system a weak hysteretic feature in the temperature range corresponding to that of the martensitic transition (Ms is indicated by a vertical arrow) and no substantial difference in the macroscopic dimensions between the austenitic and martensitic states are found, a rapid drop (shown with ε) in ∆l/l at Ms is observed in the Ni-Mn-Sn and Ni-Mn-In alloys indicating a volume decrease. The presence of this volume decrease is sustained by temperature-dependent neutron diffraction experiments [23]. From the reported measurements, the relative volume change across the transition can be estimated as ∆v/v ≃ 3ε and we obtain volume changes of 0.20% and 0.54% for Ni-Mn-Sn and Ni-Mn-In, respectively. Again, the volume change in the Ni-Mn-In alloy is the largest observed. Thus, the substantial volume changes and the small entropy changes across the transition of Ni50 Mn34 In16 will enable considerable shifts of the transition temperatures with applied pressure (eq. 3). With the aim of studying the effect of the hydrostatic pressure on the martensitic transition of magnetic shape memory alloys, we carried out DTA and magnetization measurements under applied pressure (details of the experiments are given in reference [11]). The obtained results are summarized in figure 5 which shows the shift of the martensitic transition temperature as a function of the hydrostatic pressure for the studied compounds. In all cases, the martensitic transition temperature increases with increasing pressure as a consequence of the lower volume of the martensitic phase with respect to the cubic phase. For Ni-Mn-Ga alloys, the rate of change is smaller than for Ni-Mn-Sn and Ni-Mn-In. Such a difference is due to the fact that for this Ni-Mn-Ga alloy, the relative volume change is smaller than for Ni-Mn-Sn and Ni-Mn-In. By contrast, as was discussed in the previous section, the shift of the martensitic transition tem-

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40

Ni53.5Mn23Ga23.5 Ni50Mn36Sn14 Ni49.5Mn35.5In15 Ni50Mn34In16

35

∆Tt (K)

30 25 20 15 10 5 0 0

2

4

6

8

10

p (kbar) Fig. 5: Shift with pressure of the martensitic transition temperature for Ni53.5 Mn23 Ga23.5 (squares) [13], Ni50 Mn36 Sn14 (up triangles) [24], Ni49.5 Mn35.5 In15 (open circles) and Ni50 Mn34 In16 (solid circles). Lines are fits to the data. peratures with the magnetic field can be positive or negative. Despite this different behaviour, it is noteworthy that the rate of change in the transition temperature with both pressure and magnetic field for the sample with 16 at% In is much larger than in other Ni-Mn-X alloys. Such behavior is due to the lower entropy change in this alloy as compared to the entropy change in the other alloys, together with the significant changes of the variable response ψ across the transition. Therefore, for this alloy, it is easier to induce the martensitic transition by applying moderate hydrostatic pressure or magnetic field as opposed to the other compounds. This feature opens up a broad range of possible applications of the functional properties of this alloy such as magnetic superelasticity, caloric effects, magnetoresistance, etc., associated with a pressure-induced or a magnetic-field-induced martensitic transition.

Summary and conclusions We have explored the possibility of inducing a martensitic transition by means of both an applied field and hydrostatic pressure in Ni-Mn based Heusler alloys. We have shown that Ni50 Mn34 In16 is a good candidate for observing external field-induced martensitic transformations due to the large shift of the transition temperatures with both external fields, H and p. Such large values are a consequence of the low value of the entropy-change at the martensitic transition and the large change of magnetization and volume across the martensitic transition. The possibility of inducing the structural transformation by means of a magnetic field and/or hydrostatic pressure opens up a broad range of possible applications for the functional properties of this alloy.

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8 Acknowledgements This work has received financial support from CICyT (Spain), project MAT2007-61200, DURSI (Catalonia), Project No. 2005SGR00969 and Deutsche Forschungsgemeinschaft (No. SPP1239). X. M. acknowledges support from DGICyT (Spain). References [1] Magnetism and Structure in functional materials ed. A. Planes, L. Ma˜ nosa, A. Saxena, Materials Science Series, Vol. 79 (Springer-Verlag, Berlin 2005). [2] T. Krenke, M. Acet, E. F. Wassermann, X. Moya, L. Ma˜ nosa, A. Planes, Phys. Rev. B. 72, 014412 (2005). [3] T. Krenke, M. Acet, E. F. Wassermann, X. Moya, L. Ma˜ nosa, and A. Planes, Phys. Rev. B 73, 174413 (2006). [4] T. Krenke, M. Acet, E. F. Wassermann, X. Moya, L. Ma˜ nosa, A. Planes, Nat. Mater. 4, 450 (2005). [5] X. Moya, L. Ma˜ nosa, A. Planes, S. Aksoy, T. Krenke, M. Acet, E. F. Wassermann, Phys. Rev. B 75, 184412 (2007). [6] T. Krenke, E. Duman, M. Acet, E. F. Wassermann, X. Moya, L. Ma˜ nosa, A. Planes, E. Suard, B. Ouladdiaf, Phys. Rev. B. 75, 104414 (2007). [7] T. Kaneko, H. Yoshida, S. Abe, K. Kamigaki, J. Appl. Phys. 52, 2046 (1981). [8] S. Kyuji, S. Endo, T. Kanomata, F. Ono, Physica B 237-238, 523 (1997). [9] F. Albertini, J. Kamarad, Z. Arnold, L. Pareti, E. Villa, L. Righi, J. Magn. Magn. Mat. 316, 364 (2007). [10] J. Kim, F. Inaba, T. Fukuda, and T. Kakeshita, Acta Mater. 54, 493 (2006). [11] L. Ma˜ nosa, X. Moya, A. Planes, O. Gutfleisch, J. Lyubina, J. Tamarit, M. Barrio, S. Aksoy, T. Krenke, and M. Acet, Appl. Phys. Lett. 92, 012515 (2008). [12] S. Jeong, K. Inoue, S. Inoue, K. Koterazawa, M. Taya, and K. Inoue, Mater. Sci. Eng., A 359, 253 (2003). [13] J. Kim,T. Fukuda,T. Kakeshita, Mat. Sci. Forum 512, 189 (2006). [14] For Ni-Mn-Ga, data are compiled from a large number of papers. Original references are given in J. Marcos, PhD Thesis, Universitat de Barcelona, Barcelona, 2004. [15] V. V. Khovailo, K. Oikawa, T. Abe, and T. Takagi, J. Appl. Phys. 93, 8483 (2003). [16] V. A. Chernenko, E. Cesari, V. V. Kokorin, and I. N. Vitenko, Scripta Metall. Mater. 33, 1239 (1995). [17] J. Marcos, A. Planes, L. Ma˜ nosa, F. Casanova, X. Batlle, A. Labarta, and B. Mart´ınez, Phys. Rev. B 66, 224413 (2002). [18] L. Pareti, M. Solzi, F. Albertini, and A. Paoluzi, Eur. Phys. J. B 32, 303 (2003).

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[19] J. Marcos, L. Ma˜ nosa, A. Planes, F. Casanova, X. Batlle, A. Labarta, Phys. Rev. B 68, 094401 (2003). [20] J. Marcos, F. Casanova, X. Batlle, A. Labarta, A. Planes, and L. Ma˜ nosa, Review Sci. Inst. 74, 4768 (2003). [21] X. Moya, L. Ma˜ nosa, A. Planes, T. Krenke, E. Duman, M. Acet, E.F. Wassermann, J. Magn. Magn. Mat. 316, e572 (2007). [22] S. Aksoy, T. Krenke, M. Acet, E. F. Wassermann, X. Moya, L. Ma˜ nosa, A. Planes, Appl. Phys. Lett. 91, 251915 (2007). [23] P. J. Brown, A. P. Gandy, K. Ishida, R. Kainuma, T. Kanomata, K.-U. Neumann, K. Oikawa, B. Ouladdiaf, and K. R. A. Ziebeck, J. Phys.: Condens. Matter 18, 2249 (2006). [24] T. Yasuda, T. Kanomata, T. Saito, H. Yosida, H. Nishihara, R. Kainuma, K. Oikawa, K. Ishida, K.-U. Neumann, K.R.A. Ziebeck, J. Magn. Magn. Mat. 310, 2770 (2007).

Advanced Materials Research Vol. 52 (2008) pp 199-203 © (2008) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/AMR.52.199

Effect of magnetic field on martensite to intermediate phase transformation in Ni2MnGa Takashi Fukudaa and Tomoyuki Kakeshitab Department of Materials Science and Engineering, Graduate School of Engineering, Osaka University, 2-1, Yamdaoka, Suita, Osaka 565-0871, Japan a

[email protected], [email protected]

Keywords: martensite, variant, ferromagnetic shape memory alloy, magnetization

Abstract We have investigated the martensitic transformation behavior in a single crystal of Ni2MnGa under various magnetic field. The single crystal used in the present study exhibits an intermediate phase (I-phase) transformation at TI = 250 K and a martensitic transformation at TM = 202 K. Since the martensite phase (M-phase) of Ni2MnGa has a large magnetocrystalline anisotropy, the effect of magnetic field depends significantly on the direction of magnetic field. We have measured the reverse (i.e., M-phase to I-phase) transformation start temperature As from a single variant state to examine the effect of magnetic field because the forward (I-phase to M-phase) transformation usually forms a multivariant state of the M-phase. When the magnetic field is applied parallel to the easy axis, As increases linearly with increasing magnetic field. On the other hand, when the magnetic field direction is not parallel to the easy axis, As decreases in a low field region and then increases on further increasing the magnetic field. Such behavior of magnetic field dependencies of As are quantitatively explained by the Clausius-Clapeyron equation, where we have assumed that the magnetic field dependence of As agrees with the magnetic field dependence of the equilibrium temperature.

Introduction The martensite phase of Ni2MnGa ferromagnetic shape memory alloy has a large magnetocrystalline anisotropy[1,2]. This anisotropy is one of the most important feature through which very interesting effect of magnetic field appears in the material. One interesting effect is the large magnetic field-induced strain associated with rearrangement of martensite variants[3,4]. In this case, the variant with the lowest magnetocrystalline anisotropy energy is selected to grow under a magnetic field. Another interesting effect is an unusual magnetic field dependence of martensitic transformation temperature, which has been reported in a previous paper[5]. In the paper, we have reported that the equilibrium temperature T0, between the martensite and the intermediate phases of Ni2MnGa, decreases with increasing field in a low field range and then increases on further increasing magnetic field. This behavior is quite different from most iron based alloys[6,7], in which the martensitic transformation temperature increases monotonically with increasing magnetic field. We have explained such unusual behavior of T0 from the difference in magnetic moment between the martensite phase (M-phase) and intermediate phase (I-phase). That is, in the low field region, the magnetic moment of the M-phase is lower than that of the I-phase because of the large magnetocrystalline anisotropy of the M-phase, while the relation reverses in high field region because of higher spontaneous magnetization in the M-phase. Considering that the magnetization of the M-phase depend on the field orientation, we can expect

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that field dependence of T0 should be influenced by the field orientation. In the present paper, we will examine the magnetic field dependence of the martensitic transformation temperature under various field orientation. Then, the result is discussed quantitatively based on the Clausius-Clapeyron equation.

Experimental Procedure An ingot of Ni2MnGa was prepared by arc-melting, and its single crystal was grown by a floating zone method. From the crystal, a specimen with a dimension of 3 mm x 1 mm x 0.2 mm was cut out. The longest edge was parallel to [001]P, where the index is given by the parent phase. Single variant state of the M- phase was achieved by applying magnetic field in the [001]P direction or by applying a compressive stress. The transformation temperature form the single variant of the martensite to the I-phase was determined by electrical resistance measurements. The reason for evaluating As instead of equilibrium temperature is the following: when the I-phase transforms to the M-phase thermally, we cannot avoid the formation of multi-variant state because the invariant plane (habit plane) requires the formation of multi-variant state; so we cannot evaluate martensitic transformation start temperature of a single variant state. In the measurements, magnetic field was applied in various directions: the angle between magnetization easy axis and magnetic field, θ, was 0, 45, 55 or 90 degree. These directions correspond to [001], [011], [111] and [100] of the M-phase in the pseudotetragonal structure. Electrical resistance of the specimen was measured by a direct current four probe method with a current of 100 mA passed along the longest direction.

Results and Discussion Figure 1 shows temperature dependence of electrical resistance of in the heating process under magnetic fields of 0, 0.8 and 5.6 MA/m, where the fields were applied in the magnetization easy axis (θ = 0 degree). The single variant state of the specimen was obtained beforehand by applying magnetic field of 3.2 MA/m in the martensite state followed by removing the field. We can obtain the single variant by this method because rearrangement of martensite variants occurs under a magnetic field in Ni2MnGa. In the heating process under zero magnetic field, the resistance starts to increase at 206 K (As). This increase is due to reverse transformation. The increase in resistance is also seen under magnetic field of 0.8 MA/m and 5.6 MA/m, but the As temperature under magnetic field is obviously higher than that under zero magnetic field. From these experiments, we have obtained magnetic field dependence of As. In Fig. 2(a) the change in As (∆T) thus obtained is shown with solid squares. It is obvious from Fig. 2(a) that As increases linearly with increasing magnetic field when the magnetic field is applied parallel to the magnetization easy axis. Incidentally, electrical resistance of Ni2MnGa usually decreases at As in association with the transformation from the M-phase to the I-phase. The increase in electrical resistance at As in the present experiment is due to the shape change associated with the reverse transformation from single variant M-phase to the I- phase. That is, the length of the specimen in the electrical current direction increases and the cross section decreases at As.

Electrical resistance (A.U.)

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As 5.6 MA/m As 0.8 MA/m

As

0 MA/m 180

190

200

210

220

Temperature, T / K

Transformation temperature change, ∆T / K

Figure 1 Temperature dependencies of electrical resistance in the heating process of Ni2MnGa under magnetic fields of 0, 0.8 and 5.6 MA/m applied in the direction parallel to the magnetization easy axis. Measurements were made in the heating process. The As temperature is indicated with an arrow.

4 (a) θ = 0 deg.

(b) θ = 45 deg. (c) θ = 55 deg. (d) θ = 90 deg.

2

0

-2

-4 0

2

4

0

2

4

0

2

4

0

2

4

Magnetic field, H / (MA/m) Figure 2 Magnetic field dependence of the change in reverse transformation start temperature ∆T of Ni2MnGa. The angle between the easy axis and magnetic field θ is (a) 0 degree, (b) 45 degree, (c) 55 degree and (d) 90 degree. Solid curves are calculated ∆T using the Clausius-Clapeyron-like equation.

We also measured field dependence of As by applying magnetic field in other directions, and the change in As (∆T) is plotted by solid marks as a function of field strength in Fig. 2. In the figure, θ is the angle between magnetization easy axis and field direction. When the field direction is not parallel to the easy axis (i.e., θ ≠ 0), As decreases with increasing magnetic field in the field region of lower than about 1 MA/m, and then increases linearly with increasing magnetic field. The

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decrease in As is obviously larger for larger θ. In the following, we will discuss quantitatively the result shown in Fig. 2 from the Clausius-Clapeyron equation. Since the temperature hysteresis of the martensitic transformation in Ni2MnGa is not large, the field dependence of As will be identical with the field dependence of equilibrium temperature. Thus, the field dependence of As should be given by the Clausius-Clapeyron equation, dT ∆M =− , dH ∆S

(1)

Magnetization, M / (µB/atom)

where ∆M is the difference in magnetization between the M-phase and the I-phase, and ∆S is the entropy change associated with the transformation. The value of ∆S was obtained previously by differential scanning calorimetry to be -95 J/mol[5]. We assumed that the influence of magnetic field on ∆S is negligible. The value of ∆M, however, depends strongly on the field strength and also field orientation because of the large magnetocrystalline anisotropy of Ni2MnGa.

1.0 (a) θ = 0 deg.

(d) θ = 90 deg.

(b) θ = 45 deg. (c) θ = 55 deg.

0.8 0.6 0.4 205K (M) 209K (I)

0.2 0.0

0

2

4

197K (M) 202K (I)

0

2

4

197K (M) 202K (I)

213K (M) 213K (I)

0

2

4

0

2

4

Magnetic field, H / (MA/m) Figure 3 Magnetization curves of the intermediate phase (I) and the martensite (M) with single variant state near reverse transformation start temperature (As). The angle between the magnetization easy axis and the field direction is (a) 0 degree, (b) 45 degree, (c) 55 degree and (d) 90 degree.

Thus we evaluated ∆M by measuring magnetization of both the martensite and intermediate phases near As, and the result is shown in Fig. 3. When the applied magnetic field is parallel to the easy axis, the magnetization of the martensite phase is always higher than that of the I-phase (∆M is positive) in the examined field region. On the other hand, when the magnetic field is not parallel to the easy axis, the magnetization of the martensite phase is lower than that of the I-phase (∆M is negative) in the low field region (below about 1 MA/m) and the relation reverses in the high field region (above about 1 MA/m). Comparing Fig. 3 with Fig. 2, we notice that dT/dH is negative when ∆M is negative and dT/dH is positive when ∆M is positive. This correlation can be easily understood from Eq. (1). By putting the value of ∆M obtained from Fig. 3 into Eq.(1) and

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integrating with H, we calculated magnetic field dependence of ∆T, which is shown by solid curves in Fig. 2. The calculated result is in good agreement with experimentally obtained result. Incidentally, in Fig. 3, the difference in the measured temperature between different orientations is due to the slight difference in composition of the specimen used for magnetization measurements. In addition, the difference in the measured temperature between the M-phase and the I-phase is due to the difficulty in obtaining single M-phase state and single I-phase state at the same temperature.

Conclusions Magnetic field dependence of reverse transformation temperature As in Ni2MnGa is strongly affected by the orientation of the crystal because of the large magnetocrystalline anisotropy of the martensite phase. When the magnetic field is applied parallel to the magnetization easy axis of the martensite phase, As increases monotonically with increasing magnetic field. On the other hand, when the magnetic field is applied in a direction not parallel to the easy axis, As decreases with increasing magnetic field in the low field region, and then it increasing on further increasing magnetic field. These field dependencies of As is quantitatively explained by the Clausius-Clapeyron equation.

Acknowledgement A part of this work is supported by the Ministry of Education, Culture, Sports, Science and Technology of Japan (MEXT): Grant-in Aid for Scientific Research (Kiban(B) 18360331), Priority Assistance for the Formation of Worldwide Renowned Centers of Research – The 21st Global COE Program (Project : Center of Excellence for Advanced Structural and Functional Materials Design).

References [1] L. Straka and O. Heczko: J. Appl. Phys. Vol. 93 (2003), p.8636. [2] N. Okamoto, T. Fukuda, T. Kakeshita and T. Takeuchi: Mater. Sci. Forum Vol. 512 (2006), p. 195 [3] K. Ullakko, J. K. Huang, C. Kanter, R. C. O'Handley and V. V. Kokorin: Appl. Phys. Lett. Vol. 69 (1996), p. 1966 [4] S. J. Murray, M. Marioni, P. G. Tello, S. M. Allen and R. C. O'Handley: J. Mag. Mag. Mater. Vol. 226-230 (2001), p. 945 [5] J-h. Kim, F. Inaba, T. Fukuda, T. Kakeshita: Acta Materialia Vol. 54 (2006) 493 [6] V. D. Sadovski, L. V. Smirov, Ye. A. Fokina, P. A. Malinen and I. P. Sorokin: Fiz. Met. Metalloved Vol. 27 (1967) p. 918 [7] T. Kakeshita, T. Saburi, K. Kindo and S. Endo: Phase Transformaitons, Vol. 79 (1999) p. 65

VI. Coupled Effects: Magnetoresistance and Magnetocaloric effects

Advanced Materials Research Vol. 52 (2008) pp 207-213 © (2008) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/AMR.52.207

Magneto-transport and magnetic properties of Ni-Mn-Ga S. Banik 1,a, R. Rawat1,b, P. K. Mukhopadhyay2,c, B. L. Ahuja3,d, Aparna Chakrabarti4,e, and S. R. Barman1,f 1

UGC-DAE Consortium for Scientific Research, Khandwa Road, Indore, 452017, Madhya Pradesh, India.

2

LCMP S. N. Bose National Centre for Basic Sciences, Kolkata, 700098, West Bengal, India. 3

Department of Physics, M. L. Sukhadia University, Udaipur 313001, India.

4

Raja Ramanna Centre for Advanced Technology, Indore, 452013, Madhya Pradesh, India. a

[email protected], [email protected], [email protected], [email protected], e [email protected], [email protected]

Keywords: Magnetic shape memory alloy, magnetoresistance, martensitic transition.

Abstract. We report a detailed investigation of the magneto-transport and magnetic properties of Mn excess Ni-Mn-Ga using the resistivity and magnetization measurements. Magnetoresistance (MR) has been measured in the ferromagnetic state for different compositions in the austenitic, premartensitic and martensitic phases. With Mn doping in Ni2-yMn1+yGa, a decrease in magnetization and MR has been found, since the doped Mn atoms in Ni position are in the antiferromagnetic configuration with the Mn atoms in Mn position. MR for the parent stoichiometric composition Ni2MnGa varies almost linearly with field in the austenitic and pre-martensitic phases, and shows a cusp-like shape in the martensitic phase. This has been explained by the changes in twin and domain structures in the martensitic phase. Hysteresis in the heating and cooling cycles is a characteristic of the first order nature of the martensitic phase transition.

Introduction The ferromagnetic Heusler alloy Ni-Mn-Ga had been of tremendous interest in past few years because of its property of shape memory effect. The shape memory effect added to ferromagnetism makes it a very important candidate for application in magnetically controlled actuators [1,2]. A large magnetic field induced strain of about 10% has been reported in these system that makes actuation much faster than conventional shape memory alloys [3,4]. The physical properties and transition temperatures of Ni-Mn-Ga are sensitive to composition [5,6]. With the variation of composition, the structural, thermal and magnetic properties of this Ni-Mn-Ga alloys have been studied extensively but its galvanomagnetic properties have received less attention. The behavior of magnetoresistance (MR) has been studied on the Ni-Mn-Ga thin films by different groups [7-10]. We have observed a 7.3% negative magnetoresistance in the bulk Ni2.35Mn0.66Ga [11]. In this paper, we study the effect of Mn doping on the magneto-transport properties of Ni2-yMn1+yGa. The Mn excess compositions are reported to have the higher magnetocrystalline anisotropy as compared to the Ni excess composition and hence these are expected to show a large magnetic field induced strain [12]. Moreover the theoretical calculations suggests that the additional Mn atoms favour antiferromagnetic alignment when Ni atoms are replaced by the Mn atoms [13,14].

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Experimental methods The polycrystalline ingot of Ni2-yMn1+yGa has been prepared by melting appropriate quantities of Ni, Mn and Ga (99.99% purity) in an arc furnace. The ingot is then annealed at 1100K for nine days for homogenization and subsequently quenched in ice water [6,12]. The composition has been determined by energy dispersive analysis of x-rays using a JEOL JSM 5600 electron microscope. It shows that the samples are homogeneous and the intended and actual compositions agree well, e.g. Ni2Mn1.05Ga0.95, Ni1.94Mn1.07Ga0.99, Ni1.75Mn1.25Ga for y= 0, 0.07 and 0.25 respectively. The x-ray diffraction pattern obtained for all the compositions at room temperature (RT) are in the austenitic phase and could be indexed as the cubic L21 structure. Resistivity and MR have been performed by using an indigenously built set up, as functions of temperature (5-300 K) and field (0-8 Tesla). MR measurements were carried out in longitudinal geometry and magnetic field is applied using a superconducting magnet from Oxford Instruments Inc., U.K. The MR is defined as ∆ρ/ρ0=(ρHρ0)/ρ0 where ρH is the resistivity in the presence of magnetic field H and ρ0 is the resistivity at zero field. The magnetization measurements as function of field and temperature have been performed in SQUID (MPMS XL5) and another vibrating sample magnetometer.

Results and discussions In Fig. 1 we show the room temperature magnetoresistance (MR) and magnetization (M) as a function of field with the increasing y in Ni2-yMn1+yGa. Both the MR and M decreases with increase in y. At 300 K all the samples are in the ferromagnetic state. It is well known that the Ni2MnGa is an ideal local moment ferromagnet where the magnetic moment is mainly localized on Mn ions (≈ 3.06 µB) and Ni atoms contribute small magnetic moment (≈ 0.21 µB) [15]. In the austenitic phase Ni2MnGa has a cubic L21 structure consists of four interpenetrating f.c.c. lattices where Ni atoms are at (0.25, 0.25, 0.25) and (0.75, 0.75, 0.75), while Mn and Ga are at (0.5, 0.5, 0.5) and (0, 0, 0),respectively. When excess Mn is doped in place of Ni in Ni2MnGa, it replaces Ni at the site (0.75, 0.75, 0.75). For example in Mn2NiGa, one Mn atom (MnII) will be at (0.5, 0.5, 0.5) site, while other Mn (MnI) will be at (0.75, 0.75, 0.75) site. Our zero temperature density functional theory calculations show that the antiferromagnetic orientation between MnI and MnII is energetically favoured [14].

Fig. 1: Isothermal magnetoresistance (MR) (a) and magnetization (M) (b) as a function of field for Ni2-yMn1+yGa at 300 K. The reason for such anti-parallel alignment of Mn spins is related to their direct nearest neighbour interaction. Hence, we conclude that the decrease in moments with the Mn doping decreases MR. Moreover, with the Mn doping the Curie temperature is reported to increase [12],

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which also cause the MR to decrease since the spin disorder scattering reduces as the Curie transition temperature moves away from the measurement temperature. In Fig. 2 we show the MR of Ni2MnGa in the austenitic (300K), pre-martensitic (235K) and the martensitic (150K) phases. At 300K, the sample is in the austenitic phase and shows a linear behavior, which can be well explained by the s-d scattering model for ferromagnets with different electron concentrations. In this model, the scattering of s conduction electrons by localized d spins is suppressed by the magnetic field resulting in a decrease in ρ [16]. The behavior of MR between austenitic and martensitic phases in the low field region is different. Hence, in the inset of Fig.2 we show the low field region below 1.5 T. In the martensitic phase, MR exhibits a cusp-like shape below 1.3 T. The austenitic phase has an L21 cubic structure which upon martensitic transition changes to a tetragonal structure. In the martensitic phase, twinning takes place with different twin

Fig. 2. Isothermal MR as a function of field for Ni2MnGa at austenitic (300 K), pre-martensitic (235 K) and martensitic (150 K) phases. Inset shows the MR behavior in low field region below 1.5 T. variants to reduce the strain. Although the magnetic moments are not considerably different, the magnetocrystalline anisotropy is large for the martensitic phase, whereas it is very small in the austenitic phase [17]. So, the magnetization saturates rapidly in the austenitic phase in contrast to the martensitic phase where the change is gradual [18]. Due to twinning and large magnetocrystalline anisotropy, the effect of magnetic field in the martensitic phase is more complicated resulting in twin-boundary motion and variant nucleation which results in the cusp like behavior at low field in the martensitic phase [18]. On the other hand, the pre-martensitic phase MR in the low field region is similar to the austenitic phase because it is essentially the austenitic phase with a micro-modulated structure and no twinning [19]. The MR at the highest measured field in the austenitic, pre-martensitic and the martensitic phases are 4.27%, 3.19% and 3.48% respectively. We find that in the pre-martensitic phase, the MR decreases and again it increases in the martensitic phase. Similar kind of behavior is also observed for y= 0.07 composition as shown in Fig. 3. For y= 0.07 at 300 K, 3.2% MR is obtained at the highest measured field. At 235 K where the sample is in the pre-martensitic phase, a decrease in MR has been observed at 8 T, which is about 1.6% and the MR variation with field is found quite different as compared to the austenitic phase. We observe an inflection point at 0.5 T up to which a substantial increase in MR is observed and above 0.5 T a gradual increase is observed: this may be related with the formation of the micromodulated structure in the pre-martensitic phase. At 150 K where the sample is very near to the martensitic phase the MR is about 1.9 % at 8 T, which is more than the MR in the premartensitic phase.

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Fig. 3. Magnetic field dependence of MR of Ni1.94Mn1.07Ga0.99 (y= 0.07) at different temperatures. To explain this behavior we show the magnetization as a function of temperature for y= 0 and 0.07 in Fig. 4. A small dip at 260 K and 245 K for y= 0 and 0.07, respectively, with no hysteresis in the heating and the cooling cycles is a characteristic of the pre-martensitic transition. Pre-martenstitic transition has been observed in different compositions of Ni2+xMn1-xGa [20-23]. It is a weakly first order transition from the cubic (austenitic) to a micromodulated phase due to the incomplete condensation of the TA2 phonon branch [20-22]. Besides phonon dispersions measurement by neutron scattering experiments [22], signature of pre-martensitic transition has been observed in ρ (as an upturn), magnetization and ac-susceptibility (as a dip) and calorimetric and ultrasonic studies [6, 20, 21, 23]. So from magnetization a small decrease in moments has been observed at pre-martensitic transition which causes the decrease in MR.

Fig. 4. Isothermal magnetization as a function of temperature for Ni2-yMn1+yGa, y= 0 and 0.07 at a low field of 10 Oesterd. In the martensitic phase, a sharp decrease in the magnetization is obtained in the cooling cycle at 210 K and 171 K for y= 0 and 0.07 respectively due to large magnetocrystalline anisotropy in the martensitic phase. The first order nature of the martensitic transition is evident from the hysteresis loop in the heating and cooling cycles.

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In Fig. 3, below 150 K where the sample is in the martensitic phase, we find that the inflection point is around 1.5 T and this does not change with further decrease in temperature. However, above 1.5 T, we find a change in the slope of MR with the temperature. This corresponds to the field at which magnetization tends to saturate. In order to confirm this, we also show the magnetization of y= 0.07 at different temperatures in Fig. 5. At and below 100 K, we find that the magnetization saturates around 1.5 T in the martensitic phase. Thus the decreasing trend in MR up to the saturation field is due to the formation of larger size twin variants that decreases scattering of electrons at twin boundaries. But as the temperature is increased, a decrease in the saturation magnetization is observed due to formation of the austenitic phase that has almost negligible magnetocrystalline anisotropy. For 150 K, 235 K and 300 K, we find the magnetization saturates around 1.2, 0.5 and 0.3 T respectively. At 2 T, the magnetization are found to be 0.18, 0.21, 0.23 and 0.24 emu for 300, 235, 150 and 100 K respectively. In the martensitic phase, below 100 K the magnetic moment does not change.

Fig. 5. Isothermal magnetization as a function of field for Ni1.94Mn1.07Ga0.99 (y= 0.07) at different temperatures.

Summary We have studied the effect of Mn doping on the magneto-transport and magnetic properties of Ni2-yMn1+yGa. Both MR and magnetization are found to decrease with increasing in y. The reason is that the doped Mn atom is in the antiferromagnetic configuration with the other Mn atoms, which causes the decrease in the total moment with increasing y. MR for Ni2MnGa varies almost linearly in the austenitic and pre-martensitic phases, and shows a cusp-like shape in the martensitic phase due to the changes in twin and domain structures in the martensitic phase. We also find that MR decreases in the pre-martensitic phase at the highest measured field for y= 0 and 0.07, due to decrease in moment in the pre-martensitic phase and is evident from the dip in the magnetization. We are grateful to P. Nordblad and A. Banerjee for the magnetization data. P. Chaddah, K. Horn, A. K. Raychaudhari and A. Gupta are thanked for constant encouragement and support. Financial support from Ramanna Research Grant and Max Planck Partner Group Project is acknowledged.

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References [1] M. A. Marioni, R. C. O’Handley and S. M. Allen: Appl. Phys. Lett. Vol. 83 (2003), p. 3966. [2] C. P. Henry, D. Bono, J. Feuchtwanger, S. M. Allen and R. C. O’Handley: J. Appl. Phys. Vol. 91 (2002), p. 7810. [3] S. J. Murray, M. Marioni, S. M. Allen, R. C. O Handley and T. A. Lograsso: Appl. Phys. Lett. Vol. 77 (2000), p. 886. [4] A. Sozinov, A. A. Likhachev, N. Lanska and K. Ullakko: Appl. Phys. Lett. Vol. 80 (2002), p. 1746. [5] A. N. Vasil'ev, A. D. Bozhko, V. V. Khovailo, I. E. Dikshtein, V. G. Shavrov, V. D. Buchelnikov, M. Matsumoto, S. Suzuki, T. Takagi and J. Tani: Phys. Rev. B Vol. 59 (1999), p. 1113. [6] S. Banik, A. Chakrabarti, U. Kumar, P. K. Mukhopadhyay, A. M. Awasthi, R. Ranjan, J. Schneider, B. L. Ahuja, and S. R. Barman: Phys. Rev. B Vol. 74 (2006), p. 085110; S. Banik, R. Ranjan, A. Chakrabarti, S. Bhardwaj, N. P. Lalla, A. M. Awasthi, V. Sathe, D. M. Phase, P. K. Mukhopadhyay, D. Pandey, and S. R. Barman: Phys. Rev. B Vol. 75 (2007), p. 104107. [7] V. O. Golub, A. Y. Vovk, L. Malkinski, C. J. O’Connor, Z. Wang and J. Tang: J. Appl. Phys. Vol. 96 (2004), p. 3865. [8] P. G. Tello, F. J. Castano, R. C. O’Handley, S. M. Allen, M. Esteve, F. Castano, A. Labarta and X. Batlle: J. Appl. Phys. Vol. 91 (2002), p. 8234. [9] M. S. Lund, J. W. Dong, J. Lu, X. Y. Dong, C. J. Palmstrom, and C. Leighton: Appl. Phys. Lett. Vol. 80 (2002), p. 4798. [10] A. Y. Vovk, L. Malkinski, V. O. Golub, C. O’Connor, Z. Wang and J. Tang: J. Appl. Phys. Vol 97 (2005), p. 100503. [11] C. Biswas, R. Rawat, and S. R. Barman: Appl. Phys. Lett. Vol. 86 (2005), p. 202508; S. Banik, R. Rawat, P. K. Mukhopadhyay, B. L. Ahuja, Aparna Chakrabarti, P. L. Paulose, S. Singh, A. K. Singh, D. Pandey, and S. R. Barman: submitted to Phys. Rev. B (2008). [12] G. D. Liu, J. L. Chen, Z. H. Liu, X. F. Dai, G. H. Wua, B. Zhang and X. X. Zhang: Appl. Phys. Lett. Vol. 87 (2005), p. 262504. [13] J. Enkovaara, O. Heczko, A. Ayuela, and R. M. Nieminen: Phys. Rev. B Vol. 67 (2003), p. 212405. [14] S. R. Barman, S. Banik, A. K. Shukla, C. Kamal and A. Chakrabarti: Europhys. Lett. Vol. 80 (2007), p. 57002; S. R. Barman and A. Chakrabarti: Phys. Rev. B (2008), in press. [15] A. Chakrabarti, C. Biswas, S. Banik, R. S. Dhaka, A. K. Shukla, and S. R. Barman: Phys. Rev. B Vol. 72 (2005), p. 073103; S. R. Baman, S. Banik and A. Chakrabarti: Phys. Rev. B Vol. 72 (2005), p. 184410. [16] M. Kataoka: Phys. Rev. B Vol. 63 (2001), p. 134435. [17] F. Albertini, L. Pareti, A. Paoluzi, L. Morellon, P. A. Algarabel, M. R. Ibarra, and L. Righi : Appl. Phys. Lett. Vol. 81 (2002), p. 4032. [18] F. Albertini, L. Morellon, P. A. Algarabel, M. R. Ibarra, L. Pareti, Z. Arnold and G. Calestani: J. Appl. Phys. Vol. 89 (2001), p. 5614; Q. Pan and R. D. James: J. Appl. Phys. Vol. 87 (2000), p. 4702. [19] L. Manosa, A. Planes, J. Zarestky, T. Lograsso, D. L. Schlagel and C. Stassis: Phys. Rev. B Vol. 64 (2001), p. 024305. [20] A. Planes, E. Obrado, A. Gonzalez-Comas, and L. Manosa : Phys. Rev. Lett. Vol. 79 (1997), p. 3926. [21] A. Gonzalez-Comas, E. Obrado, L. Manosa, A. Planes, V. A. Chernenko, B. J. Hattink, and A. Labarta: Phys. Rev. B Vol. 60 (1999), p. 7085.

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[22] U. Stuhr, P. Vorderwisch, V. V. Kokorin, P. -A. Lindgard: Phys. Rev. B Vol. 56 (1997), p. 14360. [23] V. V. Khovailo, T. Takagi, A. D. Bozhko, M. Matsumoto, J. Tani, and V. G. Shavrov: J. Phys.: Condens. Matter Vol. 13 (2001), p. 9655.

Advanced Materials Research Vol. 52 (2008) pp 215-220 © (2008) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/AMR.52.215

Magnetic Investigations on Ni-Mn-Sn Ferromagnetic Shape Memory Alloy 1

1

2

S. Chatterjee , S. Giri , S. K. De and S. Majumdar

1,a

1

Department of Solid State Physics, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700 032, INDIA

2

Department of Materials Science, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700 032, INDIA a

[email protected]

Keywords: Shape Memory Alloy; Martensitic Transformation; Magnetic Behavior.

Abstract. Ferromagnetic shape memory alloy of nominal composition Ni50Mn35Sn15 has been investigated by magnetic and transport measurements. Clear signature of first order martensitic transition is observed over a region around 180 K in resistivity, dc magnetization and ac susceptibility data. Field-cooled and zero-field-cooled magnetizations diverge below the martensitic transition, signifying magneto-thermal irreversibility originating from pinning by variants. The sample shows large negative magneto-resistance (-25% at 90 kOe) in the region of martensitic transition, which was found to be highly irreversible. A clear correspondence between magnetoresistance and dc magnetization is observed above the field of technical saturation. Introduction Among the Heusler derived Ferromagnetic Shape Memory Alloys (FSMAs), Ni-Mn-Ga based compositions have been under extensive investigations for their possible application as magnetic actuators [1]. Recently, Sutou et al. [2] have reported few new systems of alloys with general formula Ni50Mn50-yXy (X = Sn, Sb, In), which show magnetic shape memory related phenomena. The advantages of these alloys are that they do not contain toxic and expensive Gallium, and are found to be less brittle [3] than their Gallium counterparts. Ni50Mn50-yXy alloys orders ferromagnetically above room temperature and undergo martensitic transition (MT) from the cubic Heusler phase to a four layered orthorhombic structure. These alloys have been reported to show large magneto-resistance [4], magneto-striction [5], and inverse magneto-caloric effect [6] close to the MT. The large change in shape by an external magnetic field (H) and associated magnetic anomalies are related to the field induced reverse MT [7]. The magnetic shape change in these alloys is therefore different from the conventional materials, where variant rearrangement is primarily responsible for the observed shape memory effect. Since a fieldinduced transition is playing a major role, this phenomenon has been referred as meta-magnetic shape-memory effect [5] or magnetic super-elasticity [8]. The above scenario of the field induced transition across the highly metastable region of MT is not only important from technological point of view; it can also provide us essential insight related to the solid-solid magneto-structural transition. In order to understand the effect of a magnetic field on the electronic and magnetic properties of the system, we have carefully investigated the magnetization and magneto-resistance (MR) of the alloy with nominal composition Ni50Mn35Sn15. The present alloy has ferromagnetic transition temperature (TC) of 320 K, and it

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FIG.1 [a] Dc Magnetization versus temperature data recorded at 100 Oe for zero-field-cooled heating (ZFCH), field-cooled heating (FCH) and field cooling (FC) protocols. [b] and [c] depict dc magnetization data in FCH protocol in presence of 10 kOe of field in different temperature regions. The solid line are fit to the data (discussed in the text) Inset in [a] shows ac susceptibility plotted against temperature.

undergoes MT around 180 K. Our study reveals interesting changes in the magnetic and transport behavior across the magneto-structural instability.

Experimental Details The polycrystalline sample of composition Ni50Mn35Sn15 was prepared by argon arc melting the constituent metals. The sample was annealed at 900o C for 43 hours and then quenched into ice water. The room temperature powder x-ray diffraction pattern confirms that the material is a singlephase alloy with L21 Heusler structural having lattice parameter, a = 6.083 Å. The composition of the sample was also confirmed by energy dispersive x-ray spectroscopy. The magnetization was measured by Quantum Design SQUID magnetometer (MPMS 6, Ever-cool model). The resistivity (ρ) and the MR were measured using a commercial cryogen free high magnetic field system from Cryogenic Ltd., UK.

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FIG. 2 [a] Zero field resistivity as a function of temperature recorded for both heating and cooling runs (indicated by arrows). [b] Resistivity versus temperature data (heating only) recorded in zero and 90 kOe of applied field. [c] Magnetoresistance (MR = [ρ(H) - ρ(0)]/ ρ(0)) as a function of temperature (calculated from the data of [b]) for an applied field of 90 kOe .

Results Figure 1 (a) shows the dc magnetization (M) versus temperature (T) data measured for zero-field cooled heating (ZFCH), field-cooled heating (FCH) and field cooling (FC) sequences. The zerofield-cooled and field-cooled conditions were achieved by cooling the sample down to 10 K in zero field or in an applied field of 100 Oe respectively. The FC and FCH magnetizations show a clear anomaly around 180 K which is associated with large thermal hysteresis. The observed thermal hysteresis indicates a first order phase transition and it can be identified as the MT in the sample. The similar thermal hysteresis across the MT is also observed in the ac susceptibility (inset of figure 1 (a)) versus T data recorded between 77 and 360 K. The ferromagnetic Tc (= 320 K) is also clearly visible in the ac susceptibility data, where it rises sharply with decreasing T. Now coming back to the dc magnetization measurements, the FCH and ZFCH data starts to deviate from each other with decreasing T from just below the onset point of the MT. This indicates the development of thermo-magnetic irreversibility of the system. The separation between low field FCH and ZFCH susceptibilities near TC is observed even in a pure ferromagnet due to pinning of magnetic flux at the defect sites (say, grain boundaries) in presence of magneto-crystalline anisotropy. However, in the present case the separation occurs well below TC, and close to the MT. The martensite is developed with large number of structural variants, which can act as magnetic pinning centers. In addition, the martensite has stronger magneto-crystalline anisotropy than the austenite. The observed irreversibility in the FCH and ZFCH susceptibilities is related to the variant related magnetic pinning of the system. In the pure austenite and martensite (away from the MT), M was found to decrease with increasing T. This thermal demagnetization can provide us important information regarding the spin excitations in the system. In order to investigate the thermal demagnetization, we carefully measured M in the field cooled heating protocol for an applied field of 10 kOe. Cooling the sample

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in a field as high as 10 kOe helps to remove the domain related phenomena in the T dependence of M. Figure 1(b) shows M vs. T data recorded in the pure martensite phases (below 100 K), where a combination of T3/2 and T5/2 dependence of magnetization is observed: M =MM0 (1 - BT3/2 – CT5/2). Here MM0 is the saturation magnetization at absolute zero temperature, which was obtained by extrapolating the data to T = 0. Solid line in figure 1(b) represents the fit to the data with a combination of T3/2 and T5/2 terms. This kind of thermal demagnetization corresponds to the typical long wavelength spin wave excitation with dispersion relation, ћω = D2q2 + D4q4, where B is related to the spin wave stiffness constant as D2 = (2.612) 2/3 (gµB/MM0B) 2/3(kB/4π). By inserting the

FIG. 3 Magnetoresistance as a function of field recorded at 180 K for both increasing and decreasing field legs (indicated by arrows). The data were recorded after heating the sample from 10 K to 180 K in zero field condition.

values of B and MM0 from our fitting, we obtain D2 = 32 meV Å2. At high temperature, when the system is pure austenite, the thermal demagnetization behavior was found to be completely different. Here M2 was found to vary linearly with T2, which has been depicted in Fig. 1(c). Theoretical models based on the itinerant electron model predict that due to spin fluctuations, in the intermediate temperature below Tc, the thermal demagnetization follows approximately, M2 = MA02 (1-(T/Tc)2), where MA0 is the saturation magnetization at T = 0. By fitting our data to this relation, we obtain MA0= 98.2 emu/g and TC = 320 K. The Curie temperature matches well with the value obtained from ac susceptibility measurement. It is therefore clear that at low T, the sample show typical spin wave type thermal demagnetization, while at higher T (above MT), the behavior is dominated by spin fluctuations. Similar change in thermal demagnetization was observed in case of Ni2FeGa alloy [9]. The saturation magnetizations MM0 for the martensite is lower than that of MA0 for the austenite. This is in line with the lower magnetic moment observed in the martensite. The resistivity of the sample was measured at zero-field and in presence of magnetic field. Fig. 2 (a) shows the zero field ρ(T) behavior measured down to 77 K for both cooling and heating sequences. The clear signature of the MT is observed around 180 K, which is associated with thermal hysteresis in the temperature range 90-200 K. The signature of the ferromagnetic transition is also observed by a change in slope around 320 K. The resistivity shows marked change in presence of applied field, which has been depicted by the heating runs at H = 0 and 90 kOe in Fig 2(b). The MT is found to get shifted to lower temperature in presence of magnetic field, and the sample shows large negative MR. In the cooling run, the martensite develops between temperatures MS and MF, while austenite develops between AS and AF during heating. We observe shift of all these characteristics temperatures to lower values in an applied field. The martensitic start temperature, MS (the point where we see the minimum in the cooling ρ(T) ) changes from 178 to 159 K in H = 90 kOe. The MR in the present case is defined as MR = [ρ(H) - ρ(0)]/ ρ(0), and it has

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been plotted as a function of T in Fig. 2(c) for H = 90 kOe. The MR peaks around the MT with value as large as –25%, and it becomes negligible on both sides of the transition. This clearly indicates that the large negative MR is only observed around the MT, which is a metastable region with both austenite and martensite coexisting.

FIG. 4 Magnetoresistance is plotted as a function of dc magnetization, both recorded at 180 K. The solid line is a fit to the data (discussed in the text). The inset shows the dc magnetization versus field data recorded at 180 K for both increasing and decreasing field legs.

In order to shed light on the MR behavior we have measured ρ as a function of H at a constant temperature of 180 K, which is just inside the MT. The sample was first zero-field cooled to 10 K and then heated back and stabilized at 180 K for the isothermal MR measurements. In Fig (3), resultant MR versus H is plotted for maximum field of 80 kOe, for both increasing and decreasing fields. In line with the previous data, sample shows large negative MR for the field increasing leg; however, the MR was found to be highly irreversible with respect to the applied field. In the decreasing leg, the sample does not regain its zero field ρ even when the field is completely removed. In other words, the application and subsequent removal of H locks the sample in a state of lower ρ. Some more interesting points of the MR data are as follows: 1. There is a threshold field, beyond which the sample starts to show large negative MR (indicated by HC), and for the present sample it is about 1 kOe. 2. For the field-increasing leg, magnitude of MR increases almost linearly with H up to 45 kOe. Above this a change in slope is observed, and there is a tendency for saturation at higher fields. 3. The irreversible behavior of MR is only observed around the MT, and MR is small and reversible in the pure martensitic and austenitic phases (not shown here). 4. The return leg shows a change in ρ of about 3% when the field is changed from 80 to 0 kOe. The change is monotonous and shows a power law dependence of H. We have also measured magnetization as a function of H at 180 K, which is depicted in Fig.4 (inset). M vs. H curve also shows irreversibility with field-increasing virgin curve being steeper and lying below the field-decreasing leg. However, sample does not show any remnant magnetization. In Fig. 4, we have plotted MR against M, which has been obtained by using MR vs. H and M vs. H data both for the field-increasing virgin legs recorded at 180 K. MR is found to vary quasi-linearly beyond the technical saturation point of M and the best fit is obtained for MR = a +bM0.88 (a, b are fitting coefficients).

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Considering the fact that Ni-Mn-Sn alloys show reverse transformation under an applied magnetic field, the magneto-transport and magnetic anomaly can be assigned to the field induced structural transition. When we heat the sample from the lowest temperature (pure martensite) to a temperature (180 K) in the region of hysteresis, both austenite and martensite coexists here. The likely scenario for the large irreversible MR at this constant temperature is the field-induced transition [8], where a fraction of martensite transforms into austenite under an applied magnetic field. Since, austenite has lower resistivity than martensite, the observed MR is negative, i.e., H causes the lowering of resistivity. This irreversible nature of the MR versus H data related to the fact that the transformed martensitic fraction might not be recovered upon removal of the field. Probably large strain energy associated with the austenite to martensite transition prevents the system from recovering the transformed fraction of martensite. The field related irreversibility is also observed in the M vs. H data. In addition, above technical saturation of M, MR follows systematically with M, showing a sub-linear dependence (MR~ M0.88). In a ferromagnet, MR originating from suppression of spin disorder scattering varies quadratically with M. Present sub-linear variation of MR with M points that simple spin disorder model is not good enough, and this can be attributed to the field-induced transition in the material. It is clearly evident from the M versus T data that the austenite has higher magnetization than martensite. Therefore, when an applied filed changes the martensite austenite ratio, it gets reflected in M. Similarly, the resistivity difference between austenite and martensite is reflected in the MR behavior. The mutual correspondence between MR vs. H and M vs. H, therefore lies in the fact that both are related to the effect caused by the field induced transition. Summary Present investigations on the ferromagnetic shape memory alloy of nominal composition Ni50Mn35Sn15 identifies the first order martensitic transition, which is associated with a region of phase coexistence. The nature of the thermal demagnetization was found to be different above and below the transition. The sample shows large negative magneto-resistance in the martensitic transition region, which was found to be irreversible with respect to the applied magnetic field. Field induced structural transition is appeared to play key role towards the MR anomaly. References [1] J. Enkovaara et al., Mater. Sci. Eng. A 378, 52 (2004). [2] Y. Sutou et al., Appl. Phys. Lett. 85, 4358 (2004). [3] P. J. Brown et al., J. Phys.: Condens. Matter 18, 2249 (2006). [4] Z. H. et al., Appl. Phys. Lett. 86, 182507 (2005). [5] R. Kainuma et al., Nature 439, 957 (2006). [6] T. Krenke et al., Nat. Mater. 4, 450 (2005). [7] K. Koyama et al., Appl. Phys. Lett. 88, 132505 (2006). [8] T. Krenke et al., Phys. Rev. B 75, 104414 (2007). [9] Z. H. Liu et al., Phys. Rev. B 69, 134415 (2004).

Advanced Materials Research Vol. 52 (2008) pp 221-228 © (2008) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/AMR.52.221

Magnetocaloric and Shape-Memory Properties in Magnetic Heusler Alloys Antoni Planes1 , Llu´ıs Ma˜ nosa1 , Xavier Moya1 , Jordi Marcos2 , Mehmet Acet3 , Thorsten Krenke3 , Seda Aksoy3 , Eberhard F. Wassermann3 1 Departament

d’Estructura i Constituents de la Mat`eria. Facultat de F´ısica. Universitat de Barcelona. Diagonal 647, 08028 Barcelona, Catalonia 2 CELLS-Alba, Campus Universitat Aut` onoma de Barcelona, Bellaterrra, Barcelona. Catalonia 3 Experimentalphysik, Universit¨ at Duisburg-Essen, D-47048 Duisburg, Germany

Keywords: Magnetocaloric effect, shape-memory alloys, ferromagnetism, Heusler alloys.

Abstract. In this paper, we discuss the magnetocaloric behavior of Ni-Mn-based Heusler alloys in relation to their shape-memory and superelastic properties. We show that the magnetocaloric effect in these materials originates from two different contributions: (i) the coupling that is related to a strong uniaxial magnetic anisotropy and takes place at the length scale of martensite variants and magnetic domains (extrinsic effect), and (ii) the intrinsic microscopic magnetostructural coupling. The first contribution is intimately related to the magnetically induced rearrangement of martensite variants (magnetic shape-memory) and controls the magnetocaloric effect at small applied fields, while the latter is dominant at higher fields and is essentially related to the possibility of magnetically inducing the martensitic transition (magnetic superelasticity). The possibility of inverse magnetocaloric effect associated with these two contributions is also considered. Introduction The magnetocaloric effect is defined as the adiabatic change of temperature or the isothermal change of entropy taking place in a magnetic material as a consequence of the application or the removal of a magnetic field [1]. This is an old subject that has revived both basic and applied interest after the discovery of the giant magnetocaloric effect in a number of materials undergoing magnetostructural transitions. From a practical viewpoint, the development of materials displaying large magnetocaloric effect is of great interest for refrigeration applications. From the basic point of view, the interest lies in the fact that the giant effect is directly related to the existence of a first-order phase transition involving a strong interplay between structure and magnetism [2]. Promising candidates to show interesting magnetocaloric properties are Heusler magnetic shape-memory alloys. These materials undergo a martensitic transition with associated shapememory properties. Ni-Mn-Ga with composition close to the 2-1-1 stoichiometric composition is the prototypical and first discovered magnetic shape-memory alloy [3]. In relation to the martensitic transition, Heusler shape-memory alloys show giant magnetostriction which is related to either a field-induced reorientation of martensitic domains (or variants) or to a magnetic superelasticity which originates from the possibility of inducing the transition by means of a magnetic field. Associated with this martensitic transition, these materials also display magnetocaloric properties. Interestingly, they show either conventional or inverse magnetocaloric

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2 effects depending on the specific composition, and in some cases, on the strength of the applied magnetic field. This behaviour is a direct consequence of the coupling between magnetic and structural degrees of freedom. In this paper, we discuss the magnetocaloric effect exhibited by Ni-Mn-based magnetic shape-memory alloys. The paper is organized as follows: The thermodynamics of the magnetocaloric effect associated with first-order magnetostructural transitions is presented in the next section. In the following two sections, results for Ni-Mn-Ga, Ni-Mn-Sn and Ni-Mn-In alloys are presented and discussed. Finally, we conclude and summarize. Thermodynamics In what follows, we will quantify the magnetocaloric effect by means of the isothermal entropy change which results from the application of a magnetic field H. This field-induced entropy change is usually obtained from magnetization measurements. It is given by, ∆S(T, H) =

! Z HÃ ∂M 0

∂T

dH ,

(1)

H

where the Maxwell relation (∂S/∂H)T = (∂M/∂T )H has been taken into account. In this paper, we focus on the contribution to this entropy change arising from a first-order magnetostructural transition, and we therefore do not take the temperature dependence of the magnetization outside the transition region into consideration. We thus assume that the general dependence of the magnetization in the vicinity of the magnetostructural transition is of the general type, "

#

T − Tt (H) M (H, T ) = M0 + ∆M (H)F , ∆T (H)

(2)

where M0 is assumed to be constant, which means that any contribution from outside the transition region has been subtracted. F is an arbitrary continuous function (not necessarily analytical) which varies from 0 to 1 within the range ∆T (H). In general, due to the existence of hysteresis, this range is different for the forward transition on cooling and for the reverse transition on heating. Our discussion will apply to one of these transitions. Tt is an estimate of the corresponding transition temperature. For an ideal firstorder transition taking place in strict equilibrium, no hysteresis occurs and ∆T → 0. Therefore, lim F = h(T − Tt ) ,

∆T →0

(3)

where h is a Heaviside step function (which describes the discontinuity in the magnetization). Assuming that ∆M is independent of H, the following expression is then easily obtained: ∆S =

(

− ∆M α 0

for T ∈ [Tt (0), Tt (H)] . for T ∈ / [Tt (0), Tt (H)]

(4)

In the previous expression α ≡ dTt /dH = −∆M/∆St , where the Clausius–Clapeyron equation has been taken into account. Thus, we conclude that in this case, the field-induced entropy change coincides with the transition entropy change ∆St . Note that Tt (H) − Tt (0) [= ∆Tt = −(∆M/∆St )H] is the shift of the transition temperature induced by the field H. Interestingly, when α > 0, the magnetocaloric effect is conventional, while it is inverse when α < 0. This last situation can occur, for instance, when the magnetization of the low-temperature phase is lower than the magnetization of the high temperature phase [4].

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Table 1: Data corresponding to the analyzed Ni-Mn-Ga alloys: bibliographic reference, atomic composition, valence electron concentration (e/a) and transition temperatures (TM and Tc ). Alloyb 1 2 3 4 5 b

Ref. [5] [6] [7] [8] [8]

at.% Ni

at.% Mn

at.% Ga

49.5 51.5 52.6 55.1 56.2

25.4 22.7 23.1 19.2 18.2

25.1 25.8 24.3 25.6 25.6

e/a TM (K) 7.48 180 7.51 197 7.61 297 7.63 310 7.66 361

Tc (K) Tc − TM (K) 381 201 351 154 345 48 335 25 361 ∼0

Alloys 1 and 3 are single crystals; the others are polycrystals.

In the general case, when the transition spreads over a certain temperature range, it is convenient to define an average field-induced entropy change for each (maximum) applied field H as, Z 1 h∆S(H)i = ∆S(T, H) dT , ∆T (H) ∆T

(5)

where ∆T (H) is an effective temperature range which takes into account the shift of the transition induced by the magnetic field. The following expression can then be obtained: 1 ZH h∆S(H)i = ∆M (H) dH , ∆T 0

(6)

which indicates that in the vicinity of a magnetostructural transition, the magnetocaloric effect is essentially controlled by the behavior of the change of magnetization at the transition. Experimental results: Ni-Mn-Ga alloys In Fig. 1, we present magnetization data as a function of temperature for given values of the magnetic field for Ni-Mn-Ga alloys of selected compositions (see Table 1). Data have been extracted from published isothermal magnetization curves, [M (H)]T , measured following a sequence of increasing temperatures. In all cases, magnetization displays a significant abrupt change, ∆M (H), at the martensitic transition. The dependence of ∆M (H) on the applied field is shown in Fig. 2. For the studied alloys, ∆M is negative for small fields showing a minimum at Hm . For larger fields, it increases reaching a positive saturation value ∆Msat for fields larger than Hs (defined as the field which characterizes the exponential increase towards the saturation value). This saturation value determines the difference of magnetic moments between martensite and parent phases. This peculiar behaviour can be understood by taking into account that when cooled down (without applied mechanical stress and without applied magnetic field) through the martensitic transition, Ni-Mn-Ga shape-memory alloys develop a complex heterogeneous mesostructure made up of regions consisting of parallel stripes of twin-related variants. Magnetic domains are formed within each variant in such a way that the magnetization alternates between two opposite values along the corresponding easy axis. Application of a magnetic field gives rise to a rearrangement of these twin-related variants. This mechanism, which is at the origin of the magnetic shape-memory effect [9], enables a reduction of the Zeeman energy when a rotation

224

Ferromagnetic Shape Memory Alloys

4

6

alloy 1

4 2

emu/mo l) 3

4 kOe

50 0Oe

6 kOe

750Oe

10kOe

1 kOe

20kOe

2 kOe

40kOe 50kOe

0 170

175

180

6

185

alloy 2

alloy 3

6

4

4

2

2

0 190

M

(1 0

250Oe

195

200

6

205 295

300

305

alloy 4

0 310

alloy 5

6

4

4

2

2

0

305

310

315

355

T (K)

360

365

0 370

∆M (103 emu/mol)

Fig. 1: Magnetization curves as a function of temperature, M (T ), through the martensitic transition corresponding to the set of Ni-Mn-Ga alloys analysed in this work. In all cases, the original isothermal magnetization curves [M (H)]T were measured in a sequence of increasing temperatures (reverse transition).

2.0 1.0 0 Alloy Alloy Alloy Alloy Alloy

-1.0

(a)

-2.0 0

2

4

6

0

10

20

30

1 2 3 4 5

40

(b) 50

H (kOe) Fig. 2: Magnetic field dependence of the magnetization change associated with the martensitic transition, ∆M (H), corresponding to the five Ni-Mn-Ga alloys analysed in this work. (a) Detail of the low applied magnetic field region. (b) Whole range of applied magnetic fields (up to 50 kOe).

Advanced Materials Research Vol. 52

225

〈∆S〉

(J/K mol)

0.2

(a)

0.1 0 -0.1 -0.2

〈∆S〉 (10-2 J/K mol)

5 6

(b)

4 2 0 -2 -4 0

1

2

3

4

5

6

H (kOe)

-0.3 -0.4 0

10

20

30

H (kOe)

40

50

Alloy Alloy Alloy Alloy Alloy

1 2 3 4 5

Fig. 3: (a) Average field-induced entropy change, h∆Si, as a function of the applied magnetic field for the set of Ni-Mn-Ga alloys studied in this work. The symbols correspond to experimental data (calculated from the data in Fig. 1). Continuous lines are fits to a model for the average field induced entropy change proposed in [12]. (b) Detail corresponding to the low magnetic field region. of crystal axes is preferred to a rotation of magnetic moments. The basic ingredients for this mechanism to be dominant are both a high magnetic uniaxial anisotropy of the martensitic phase and a high mobility of the twin-boundaries. Within this picture, the decrease of magnetization at the transition is explained by the corresponding increase of magnetic anisotropy [10]. In contrast, for high enough fields, the increase of the magnetization change simply reflects the fact that the magnetic moment of the martensite is larger than the magnetic moment of the cubic phase. The dominant mechanism at low field can be interpreted as an extrinsic magnetostructural coupling taking place at the length scale of the martensitic variant. By contrast, at high fields, the behaviour is dominated by the intrinsic magnetostructural interplay, which occurs at a microscopic scale and is related to the possibility of inducing the martensitic transition by means of a magnetic field. It is interesting to note that the range of fields where ∆M is negative (quantified by the field Hm ) and its minimum value are reduced as the composition moves away from the 21-1 stoichimetric composition in such a way that the martensitic transition temperature TM approaches the Curie temperature TC (i.e., by increasing the electron concentration e/a). This is consistent with the corresponding decrease of the uniaxial magnetic anisotropy (measured as the first order anisotropy constant, A) of the martensitic phase which shows a roughly linear dependence on the temperature difference TA − TM [11]. Thus, as e/a increases, the magnetostructural interplay at the microscopic scale becomes dominant and lower fields are needed to induce the magnetostructural transition. Once the behaviour of ∆M (H) has been analysed, we can proceed with the calculation and study of the magnetic field induced entropy change. From the magnetization data in Fig. 1, and by using Eqs. (1) and (5), the associated average field induced entropy change, h∆S(H)i, is obtained. The derivatives and integrals involved in the calculations have been performed numerically. The effective temperature range of the transition, ∆T (H), has been estimated as the width of the peak in the corresponding [∆S(T )]H curves. In Fig. 3, we show the obtained h∆S(H)i curves for the whole set of studied Ni-Mn-Ga alloys. In all cases, the observed

226

Ferromagnetic Shape Memory Alloys

∆M (103 emu/mol)

6 0

(b)

(a) -1 -2 -3 -4 0

10

20

30

H (kOe)

40

50

0

10

20

30

40

50

H (kOe)

Fig. 4: Magnetization change as a function of H for (a) Ni50 Mn35 Sn15 and (b) Ni50 Mn34 In16 . behaviour is very similar: the entropy change first increases with H, then reaches a positive maximum, and, finally, it decreases linearly for high fields. Except for alloys 1 and 2, the initial increase of h∆Si is very weak and is not even observed for sample 5 (for which TM ∼ TC ). Taking into account eq. (6), the initial increase of h∆S(H)i is likely to be related to the decrease of ∆M (H) observed at low applied fields and, therefore, is a consequence of the extrinsic magnetostructural interplay driven by the magnetic anisotropy. At high fields, h∆S(H)i decreases linearly with increasing field. Actually, this is the behaviour expected to be determined by the intrinsic microscopic magnetostructural interplay. Experimental results: Ni-Mn-Sn and Ni-Mn-In alloys Besides Ni-Mn-Ga, martensitic transformations have been reported in other ferromagnetic Heusler alloys. Within the Ni-Mn-based family, Ni-Mn-Sn and Ni-Mn-In are especially interesting. These alloys show a martensitic transition in the composition region 2-(2 − 4x)-4x, with x < 0.25 (Mn-rich region) far from stoichiometry. The interesting compositions range is a narrow interval close to e/a ≃ 8 where, on cooling, these systems first become ferromagnetic and on further cooling undergo a martensitic transition [13]. As in the case of Ni-Mn-Ga, from magnetization curves, we have obtained the change of magnetization at the transition as a function of the applied magnetic field. Results for Ni-MnSn and Ni-Mn-In are shown in Figs. 4 a) and b) respectively. In these two systems ∆M initially decreases with increasing field, and a negative saturation value is reached. This behaviour is essentially different from that described for the Ni-Mn-Ga alloy family reported in the preceding section. The monotonous decrease reflects the low magnetic anisotropy of the martensitic phase in these systems [14]. More interesting is the fact that the magnetic moment of the martensitic phase is smaller than the magnetic moment of the cubic phase. This can be ascribed to the fact that in these Heusler alloys, the magnetic moments are localized mainly on the Mn atoms and the exchange interaction strongly depends on the Mn-Mn distance. In systems with excess of Mn atoms (with respect to the 2-1-1 stoichiometry), it has been argued [15] that nearestneighbours Mn-Mn pairs exist that become antiferromagnetically coupled in the martensitic phase due to the change of lattice parameter at the magnetostructural transition (giving rise to a volume reduction). Thus, in spite that atomic magnetic moments remain unchanged, this leads to a decrease of the whole magnetic moment of the system[16]. The field induced entropy change is shown in Fig. 5. Consistent with the behaviour of ∆M , an inverse magnetocaloric effect is obtained which increases linearly with the applied

Advanced Materials Research Vol. 52

227 7

〈∆S〉

(J/K mol)

0.4 Ni50Mn35Sn15 Ni50Mn34In16

0.3 0.2 0.1 0 0

10

20

30

40

50

H (kOe) Fig. 5: Average field induced entropy change as a function of the field H for Ni50 Mn35 Sn15 and Ni50 Mn34 In16 . magnetic field. This behaviour is controlled by the microscopic coupling mechanism associated with the reduction of the magnetic moment at the magnetostructural transition. Interestingly, this mechanism enables that the reverse martensitic transition can be induced by means of an applied field (the change of transition temperature with the applied magnetic field is particularly strong in the case of the Ni-Mn-In alloy for which |∆M | is large). This is at the origin of the magnetic superelastic behaviour displayed by these alloys [17]. In contrast, as the magnetic anisotropy is low, field induced reorientation of martensitic variants is not operative in these systems.

Summary In this work, we have developed a general thermodynamic framework for the study of the magnetocaloric effect associated with magnetostructural transitions. The main result is that the magnetocaloric effect is intimately related to the dependence on the magnetic field of the magnetization change associated with the transition. We have first analyzed experimental data for composition related Ni-Mn-Ga ferromagnetic shape-memory alloys. Results show that the magnetocaloric effect in these materials is determined by two contributions. The first contribution, dominant at low magnetic fields, arises from magnetostructural coupling at the length scale of the martensitic twin variants. This term is enhanced by a large (uniaxial) magnetic anisotropy of the martensitic phase. The second contribution is the one expected in magnetostructural transitions and is associated with the coupling between structure and magnetism at the microscopic level. This gives rise to the change of the transition temperature when a magnetic field is applied. In Ni-Mn-Sn and Ni-Mn-In the inverse magnetocaloric effect is controlled by the magnetostructural interplay at the microscopic level associated with the tendency of the excess of Mn atoms to introduce antiferromagnetic coupling caused by the change in the Mn-Mn distances as the lower symmetry martensitic phase gains stability.

228

Ferromagnetic Shape Memory Alloys

8 Acknowledgements This work has received financial support from CICyT (Spain), project MAT2007-61200, DURSI (Catalonia), Project No. 2005SGR00969 and Deutsche Forschungsgemeinschaft (No. SPP1239). References [1] A.M. Tishin, in Handbook of magnetic materials, vol. 12, ed. by K.H.J. Buschow, Elsevier Science, Amsterdam, 1999, pp. 395–524. [2] V.K. Pecharsky and K.A. Gschneidner, in Interplay of Magnetism and Structure in Functional Materials, ed. by A. Planes, Ll. Ma˜ nosa and A. Saxena, Springer-Verlag, Heidelberg 2005, pp. 199– 222, and references therein. [3] O. S¨oderberg, A. Sozinov, Y. Ge, S.-P. Hannula, and V. K. Lindroos, in Handbook of Magnetic Materials, vol. 6, ed. by K.H.J. Buschow, Elsevier Science, Amsterdam (2006), pp. 1–39, and references therein. [4] In general an inverse magnetocaloric effect is expected to occur in those regions of the space of thermodynamic variables where (∂M/∂T )H < 0. See, T. Krenke, M. Acet, E.F. Wassermann, X. Moya, Ll. Ma˜ nosa, and A. Planes, Nature Mater. 4, 450 (2005). [5] J. Marcos, A. Planes, Ll. Ma˜ nosa, F. Casanova, X. Batlle, A. Labarta, and B. Mart´ınez, Phys. Rev. B 66, 224413 (2002). [6] F. Hu, B. Shen, and J. Sun, Appl. Phys. Lett. 76, 3460 (2000). [7] F. Hu, B. Shen, and G. Wu, Phys. Rev. B 64, 132412 (2001). [8] L. Paretti, M. Solzi, F. Albertini, and A. Paulozi, Eur. Phys. J. B 32, 303 (2003). [9] R.C. O’Handley, J. Appl. Phys. 83, 3263 (1998). [10] Note that the cubic phase is almost magnetically isotropic. [11] F. Albertini, L. Pareti, A. Paoluzi, L. Morellon, P.A. Algarabel, M.R. Ibarra, and L. Righi, Appl. Phys. Lett. 81, 4032 (2002). [12] J. Marcos, Ll. Ma˜ nosa, A. Planes, F. Casanova, X. Batlle, and A. Labarta, Phys. Rev. B 68,094401 (2003). [13] X. Moya, Ll. Ma˜ nosa, A. Planes, T. Krenke, M. Acet, E.F. Wassermann, Mater. Sci. Engng. A 438-440 911 (2006). [14] S. Aksoy, T. Krenke, M. Acet, E.F. Wassermann X. Moya, Ll. Ma˜ nosa, and A. Planes, Appl. Phys. Lett. 91, 251915 (2007). [15] J. Enkovaara, O. Heczko, A. Ayuela, and R. M. Nieminen, Phys. Rev. B 67, 212405 (2003). [16] P.J. Brown, A.P. Gandy, K. Ishida, R. Kainuma, T. Kanomata, K.-U. Neumann, K. Oikawa, B. Ouladdiaf and K.R.A. Ziebeck, J. Phys. Condens. Matter 18, 2249 (2006). [17] T. Krenke, E. Duman, M. Acet, E.F. Wassermann, X. Moya, Ll. Ma˜ nosa, A. Planes, E. Suard, and B. Ouladdiaf, Phys Rev. B 75, 104414 (2007).

Keywords Index A Acoustic Attenuation Actuator Aging Annealing

87 121 47 57

B Band Structure Calculations

145, 181

C Compton Scattering Copper Based Shape Memory Alloy Crystal Structure Curie Temperature

181 135 63 57, 95, 103

D Density Function Theory (DFT) Density of States (DOS) Differential Scanning Calorimetry (DSC) Double Arrhenius Kinetics

165 165 69

M Magnetic Behaviour Magnetic Compton Scattering Magnetic Domain Structures Magnetic Field Induced Strain (MFIS) Magnetic Force Microscopy (MFM) Magnetic Material Magnetic Shape Memory Alloy (MSMA) Magnetic Shape Memory Material Magnetisation Magnetocaloric Effect Magnetoelastic Mechanism Magnetoresistivity MR Martensite Martensite Transformation Martensitic Phase Transition Martensitic Temperature Martensitic Transformation (MT)

69 Martensitic Transition

E Elastic Constant Electronic Structure EXAFS

135 145, 181 175

F Ferromagnetic Shape Memory Alloys (FSMAs) Ferromagnetic Shape Memory Effect Ferromagnetism Field-Induced Transformation

35, 47, 77, 129, 199 3 189, 221 189

189, 221

I Intermartensitic Transformation Internal Friction Itinerant-Electron Magnetism

115 121 109, 207 87 17, 35, 77, 199 221 3 77, 207 155, 199 57 77 121 3, 17, 63, 95, 103, 175, 215 69, 109, 165, 207 17 63

N Ni2MnGa NiMnGa Alloy NiMnGa/Si(100) Thin Film Composite

115, 155 3, 29, 57 35

O Ordering

47

S

H Heusler Alloy

Melt Spun Ribbons Microstructure

215 145 35 29

47 129 77

Shape Memory Alloy Actuator Smart Composite Sound Velocity Stress Relaxation

17, 115, 145, 155, 181, 189, 215, 221 87 129 129

230

Ferromagnetic Shape Memory Alloys

T Textured Polycrystal Thermal Expansion Total Energy Twin Rearrangement

29 135 165 3

V Variants

199

X X-Ray Diffraction (XRD) XAFS XANES

95, 103, 109 155 175

Authors Index A Abhyankar, A.C. Acet, M. Ahmed, G. Ahuja, B.L. Aksoy, S. Awasthi, A.M.

77 189, 221 181 145, 181, 207 189, 221 69, 109, 175

Barandiarán, J.M. Barman, S.R. Besseghini, S. Bhardwaj, S. Bhobe, P.A.

69, 109, 115, 175, 181, 207 35 69, 109, 115, 165, 175, 207 35 69 155

47 165, 207 215 3, 35 121

D De, S.K. D'Santhoshini, B.A. Dubey, A.

215 77 175

87 199

G Gaitzsch, U. Gambardella, A. Ganesan, V. Giri, S. Gopalan, R.

29 35 115 215 57

H Heda, N.L.

J Jain, D.

Kakeshita, T. Kanth, R.B. Kaul, S.N. Krenke, T.

115

199 129 77, 129 189, 221

L López Antón, R.

Mahendran, M. Majumdar, S. Mañosa, L. Marcos, J. Menon, C.S. Mitra, A. Moya, X. Mukhopadhyay, P.K. Müllner, P.

35

181

87, 121 215 189, 221 221 135 17 189, 221 109, 129, 207 35

N Nath, R. Nigam, A.K.

F Feuchtwanger, J. Fukuda, T.

181

M

C Cesari, E. Chakrabarti, A. Chatterjee, S. Chernenko, V.A. Chokkalingam, R.

Itou, M.

K

B Banik, S.

I

115 77

O O'Handley, R.C. Ohtsuka, M. Olivi, L.

87 35 175

P Panda, A.K. Planes, A. Pons, J. Potharay Kuruvilla, S. Pötschke, M.

17 189, 221 47 135 29

232 Priolkar, K.R. Pushpanathan, K.

Ferromagnetic Shape Memory Alloys 155 121

R Rathor, A. Rawat, R. Roth, S.

181 207 29

S Sakurai, Y. Sarma, S. Sarode, P.R. Sathe, V.G. Schultz, L. Seguí, C. Senthur Pandi, R. Sharath Chandra, L.S. Sharma, B.K. Sharma, V. Singh, R.K. Srinivasan, A.

145, 181 63, 95, 103 155 175 29 47 121 115 181 145, 181 57 63, 95, 103

W Wassermann, E.F.

189, 221