Reorientation of Ni-Mn-Ga martensite in rotating magnetic field

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1 Available online at Physics Procedia 1 (1) Physics Procedia (1) 3rd International Symposium on Shape Memory Materials for Smart Syste Reorientation of Ni-Mn-Ga martensite in rotating magnetic field C.P. Sasso a, V.A. L vov b*, V.A. Chernenko c,d, J.M. Barandiaran c, M. Pasquale a a Istituto Nazionale di Ricerca Metrologica, Strada delle Cacce 91, Torino 1135, Italy b Institute of Magnetism, Vernadsky Str. 36-b, Kyiv 314, Ukraine c Universidad del País Vasco, Dpto. Electricidad y Electronica, P.O. Box 644, Bilbao 488 d Ikerbasque, Basque Foundation for Science, Bilbao 4811, Spain Abstract Reorientation of martensitic variants in e Ni 5. Mn 4.4 Ga 3.6 single crystalline disk under magnetic field rotating in e disk plane has been studied. The reorientation proved to be possible in e fields exceeding 13 kam 1 and started when e angle between e magnetic moment of e reorienting martensite variant and e crystallographic direction reached 56. The eoretical analysis of experimental results pointed to e comparatively low value of magnetocrystalline anisotropy constant (5 kjm 3 ) and e possibility of e reversible reorientation of martensitic variants under e co-operative action of e external magnetic field and internal magnetostatic field of e specimen. PACS: c Cc; Published 75.3.Gw; by Elsevier q Ltd Open access under CC BY-NC-ND license. Keywords: Ni Mn Ga; rotating magnetic field; twins; anisotropy constant; martensite reorientation; strain reversibility 1. INTRODUCTION As it is known [1], e large values (5%) of e magnetic-field-induced-strain (MFIS) are observed in Ni Mn Ga shape-memory alloys. The giant MFIS is caused by e magnetically induced twinning/detwinning of e martensitic phase. The twinning/detwinning process is triggered by e ordinary magnetostriction and is promoted by e softening of crystal lattice in e temperature range of e martensitic phase transformation [,3]. It is commonly recognized at e magnetic field influence on e twinned martensite is equivalent to e influence of e axial mechanical stress [4 6]. The magnetostress at is induced by e field applied in e 1 crystallographic directions was measured and evaluated eoretically by different auors (see [5,6] and references erein). At e same time, e stressing of a Ni Mn Ga single crystal by a rotating magnetic field may be considered a useful tool for e study of e mechanical performance of magnetically activated shape memory elements [7 9]. However, e measurement of magnetostress in a rotating magnetic field has not been carried out yet. In e present article, experimental data indicating e effect of a rotating magnetic field H on e twin structure of ferromagnetic Ni Mn Ga martensite are presented. The magnetostress values are evaluated eoretically for different orientations of e magnetic field. A magnetostress function computed from magnetoelastic model [3] is * Corresponding auor. Tel.: address: victorlvov@univ.kiev.ua c 1 Published by Elsevier Ltd Open access under CC BY-NC-ND license. doi:1.116/j.phpro

2 15 C.P. Sasso et al. / Physics Procedia 1 (1) Auor name / Physics Procedia (1) compared wi e function derived in Ref. [9] from e microscopic model [1]. The universal (applicable to e arbitrarily oriented magnetic field) criterion of e start of martensite reorientation is derived and applied to e results of magnetic measurements, which indicate e reorientation process. The possibility of martensite reorientation in an alloy wi reduced magnetic anisotropy is disclosed. The possibility of a reversible transformation of e twin structure in a variable magnetic field applied normally to e plane of e disk-shaped Ni Mn Ga single crystal is also discussed.. EXPERIMENT The experiments have been carried out using an oriented Ni 5. Mn 4.4 Ga 3.6 disk-shaped sample of 5-mm diameter and 1.5-mm ickness. The crystal was oriented to present e and crystallographic directions in e disk plane and e [1] direction out of plane. The magnetization measurements have been carried out by a twodimensional vibrating sample magnetometer. Before each magnetic measurement, a quasi-single-variant state was prepared by a proper mechanical training of e specimen. At e beginning of e magnetic measurements, e easy magnetic axis of e dominant martensitic variant ( direction) was aligned wi e direction of e constant magnetic field. The specimen was en rotated as it is shown in FIG. 1 (a) and e direction of e unit magnetic vector m [1 ] of e dominant variant was determined from e values of e components of e magnetic moment longitudinal and transversal to e field. The magnetostress increased in e course of is experiment due to e deviation of e magnetic vector from e axis. The jump-like reorientation of e magnetic moment m m was registered at a certain stress value. [ The experimental reshold values of e angle 1 ] between e and m directions are shown in FIG. 1 (b) for a series of magnetic field values. The appropriate values of e angle between e and magnetic field directions are also shown in e figure. m H (a) m x y FIG. 1. Schematic of e top-view of disk-shaped specimen wi e crystal axes, magnetic vectors of variants and magnetic field direction in e moment of e start of martensite reorientation; e curved arrows show e rotation directions of axis and magnetic vector jump, (a). Experimental (symbols) and eoretical (lines) dependencies of e reshold angles determined for e different values of magnetic field, (b). The experiment shows at e magnetically induced martensite reorientation is possible only if e magnetic 1 field exceeds e value H start 13 kam. For is minimal field, e reshold angles are 56 and. The former angle is weakly dependent on e magnetic field THEORY Let e twin structure of e martensite be formed by alternating x- and y-variants of tetragonal crystal lattice wi e principal axes (c-axes) of neighboring variants aligned wi e and crystallographic directions,

3 C.P. Sasso et al. / Physics Procedia 1 (1) Auor name / Physics Procedia (1) [ which are e equilibrium directions for e unit magnetic vectors of e variants m ( H ) and m 1] ( H). If e coordinate axes are parallel to ese directions, e transformation of e twin structure is caused by e difference of diagonal stress components ( H) xx ( H) yy( H), which breaks e physical equivalence of martensite variants and induces e twin boundary motion. A magnetically induced stress (H) arises due to e rotation of e magnetic vectors under e magnetic field. A magnetic field applied parallel to e or direction rotates e magnetic vector of one martensite variant only, and so, e average stress value is equal to ( H ) / eq ( H ) (for more details see Ref. [6]). The generalization of is formula to e case of an arbitrarily directed field is 1 ( H) [ ( H) ( H)], (1) where ( H) and ( H) are e stresses induced in e x- and y-variants wi c x and c y, respectively, where each stress represents e aforementioned components difference. The stress of Eq. (1) depends on e values of e dimensionless magnetoelastic constant, magnetization M and angles [ 1] [1 (H) and ] (H) between e x-axis and e unit magnetic vectors of e x- and y-variants as follows: ( H) 6M cos[ ( H )] cos[ ()], () where (H) is equal to ( H) for x-variant and to ( H) for y-variant [,6]. The functions ( H) and ( H) can be obtained by minimization of e magnetic energy F K m M ( m Dm) mhm, (3) u x where K u is e uniaxial anisotropy constant, and D is a demagnetization matrix. The "easy magnetic axes" of e variants of e modulated tetragonal Ni Mn Ga martensite are aligned wi e 1 crystallographic directions, e anisotropy constant Ku is positive, and so, e upper sign "+" in e Eq. (3) corresponds to e y-variant whereas e bottom sign " " is inherent to e x-variant. In is case m () x and m () y, as it was stipulated above. If e magnetic field is applied in e plane of e disc-shaped specimen, e equilibrium directions of e magnetic vectors can be found from e condition F /, which results in e equation sin hsin( ), (4) where h H / denotes a dimensionless field, and H K M is e magnetic anisotropy field. H A A u / The Eqs. () and (4) enable e computation of e equivalent stress value as a function of e angle between e magnetic field and e direction, depicted in FIG. (a). The equivalent stress functions computed for different magnetic field values are shown in FIG. (b). The computations were carried out using e magnetoelastic constant 3 typical of e Ni Mn Ga martensites wi c / a 1 [,6] and e magnetization value M.5 T. The stress function computed here is qualitatively different from e function, which was derived in Ref. [9] from e microscopic model [1]: i) The microscopic model predicts e linear stress field dependence in e limiting case of low magnetic fields, while e initial fragments of e curves presented in FIG. (b) are not linear.

4 15 C.P. Sasso et al. / Physics Procedia 1 (1) Auor name / Physics Procedia (1) ii) According to microscopic model e stress value saturates at e certain value of rotating magnetic field, while e FIG. (b) shows at saturation takes place only if e field is aligned wi e crystallographic axis. The equivalent stress value is positive when 45 (i. e. e magnetic field direction is close to ) and negative oerwise. The positive stress stabilizes e y-variant of martensite wi c / a 1 while e negative stress stabilizes e x-variant. The magnetic field applied in e [11] direction ( 45 ) does not transform e x-y twin structure, because e equivalent stress value is equal to zero in is case. FIG.. Magnetostress as a function of magnetic field direction, (a), and magnetic field value, (b). The magnetic field is parallel to when and aligned wi when /. In ese cases e value h 1 corresponds to e magnetic saturation, and erefore, e fields h 1, h, and h 4 induce e same magnetostress max 3.5 MPa, which is close to e values reported previously for e tetragonal Ni Mn Ga martensites wi c / a 1 [5,6]. In a tilted magnetic field, e magnetic saturation state is not attainable and e magnetostress smooly grows (in e increasing field) even when h 1. The martensite reorientation starts when e axial stress reaches e reshold value, i. e. at e condition ( H). (5) Using e Eq. (4), e eoretical value of e rotation angle can be fitted to e experimental magnitude of 56 by e appropriate choice of e parameter h H startm / Ku wiout any reference to e reshold stress. Physically, it means at e direction of magnetic vector is prescribed by e competition between e external magnetic field and e magnetic anisotropy field. The best fit was observed for a magnetic anisotropy constant of 3 Ku 5 kjm. Furermore, e reshold stress value was obtained from e condition (Hstart ) and proved to be equal to.3 MPa. Finally, e dependencies of e reshold angles on e external magnetic field shown in FIG. 1 (b) were computed from e Eqs. (4) and (5) indicating a reasonable agreement wi experimental data. 4. DISCUSSION AND CONCLUSION Experiments wi a Ni 5. Mn 4.4 Ga 3.6 single crystal in rotating magnetic fields were carried out and e jump-like reorientation of e magnetic moment of e quasi-single-variant martensite was indicated by a two-dimensional vibrating sample magnetometer when e rotation angle reached a reshold value. This physical effect indicates e transformation of a dominant martensite variant into a twin-related one. The eoretical treatment of e

5 C.P. Sasso et al. / Physics Procedia 1 (1) Auor name / Physics Procedia ( 1) experimental results showed at a magnetostress (H). 3 MPa was induced in e Ni Mn Ga single crystal wi 3 a reduced constant of magnetocrystalline anisotropy K u 5 kjm, which is noticeably smaller an e values previously reported for e bulk specimens [1,11]. It is wor noting at is constant is close to e constants evaluated for e Ni Mn Ga fil by a ferromagnetic resonance meod [1,13]. According to Eq. (1), e magnetostatic field of e disk-shaped specimen is ex pressed as H ( Dzz Dxx ) M. The demagnetization matrix elements of e ferromagnetic ellipsoid wi e axes A B C can approximate ose of e disk. For e specimen studied above, a ratio of A / C 3 is acceptable. In is case e routine calculation 3 results in e value of H 7 kam 1. The magnetocrystalline anisotropy constant of 5 kjm corresponds to 1 e magnetic anisotropy field H 16 kam A at is considerably smaller en e estimated magnetostatic field. It points to e possibility for e observation of large reversible deformation of e specimen in e magnetic field applied normally to its plane (i. e. along e [1] crystallographic direction and e reference axis z). To is end, e state wi dominating x-variant and residual z-variant must be induced by e proper mechanical or magnetic treatment of e disc. In e absence of any external magnetic field, e magnetic moments of bo variants would tend to lie in e disk plane. The external magnetic field H z H H A is sufficiently strong to be able to orient e magnetic vectors of all variants normally to e disk plane and to induce a magnetostress of about of 3 MPa, which, in turn, could elevate e volume fraction of e z-variant. The removal of e external magnetic field would be accompanied by e magnetic vectors rotation toward e disk plane, whereby leading to recovery of e initial martensitic state. Such magnetostatically-stimulated-strain-recovery of Ni-Mn-Ga martensite is also anticipated for in wires. More experimental work is needed to confirm ese expectations. Acknowledgements The financial support from e Department of Education, Basque Government (Project No. IT-347-7) and e Spanish Ministry of Education and Science (Project No. MAT8 654-C4-) is acknowledged. References [1] R. C. O Handley and S. M. Allen, in Encyclopedia of Smart Materials, edited by M. Schwartz. Wiley, New York,. [] V. A. Chernenko and V. A. Lvov, in Advances in Shape Memory Materials. Ferromagnetic shape memory alloys, edited by V. A. Chernenko, Mat. Sci. Forum, Vol. 583, TTP, Switzerland, 8. [3] V. A Chernenko, V. A. L vov, and E.Cesari, J.Magn.Magn.Mat (1999) 859. [4] A.A. Likhachev and K. Ullakko, Phys. Lett. A 75 () 14. [5] L. Straka and O. Heczko, IEEE Trans. Mag. 39 (3) 34. [6] V. A. Chernenko, V. A. L vov, P. Müllner, G.Kostorz, and T. Takagi, Phys. Rev. B 69 (4) [7] M.Pasquale, C. P. Sasso, G. Bertotti, V. L vov, V. Chernenko, and A. De Simone, J. Appl.Phys. 93 (3) [8] P. Müllner, V.A. Chernenko, and G. Kostorz, J.Magn. Magn.Mat. 67, 35 (3). [9] P. Müllner, V. A. Chernenko, M. Wollgarten, and G. Kostorz, J.Appl. Phys. 9 () 678. [1] S. J. Murray, M. Marioni, S. M. Allen, R. C. O Handley, and T. A. Lograsso, Appl. Phys. Lett. 77 () 886. [11] R. Tickle and R. D. James, J. Magn. Magn. Mater. 195 (1999) 67. [1] J. Dubowik, Y. V. Kudryavtsev, and Y. P. Lee, J. Appl. Phys., 95 (4) 91. [13] V. Golub, K. M. Reddy, V.Chernenko, P. Müllner, A. Punnoose, and M.Ohtsuka, J. Appl. Phys. 15 (9) 7A94.