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The Ni-Mn-Ga ferromagnetic shape memory alloys have exceptional magneto-deformational properties, such as giant magnetic field induced strain (MFIS) in martensitic phase [1]. This effect originates in the high mobility of twin boundaries combined with large magneto-crystalline anisotropy [1,2]. MFIS allows use of the alloy in applications such as micro-sensors and actuators [3] or as low-frequency energy harvesters [4]. The L21 structure of austenite can transform into several martensitic structures. Final structure is affected by composition e.g., increasing content of Mn. In near-stoichiometric compositions, modulated five-layered (10M) or seven-layered (14M) structures are stable. The non-modulated (NM) martensite is stabilized in compositions far from stoichiometry [5]. Only modulated martensitic structures exhibit significant MFIS [6].
We performed ab initio calculations to reveal the effect of increasing concentration of excess Mn and magnetic ordering on generalized planar fault energy (GPFE) curves, exactly on formation and propagation of twin boundaries. An influence of local arrangement of excess Mn in Ga sublattice has been considered as well. The spin-polarized DFT method implemented in the Vienna Ab Initio Simulation Package (VASP) [7] was used. The electron-ion interaction was described by the projector augmented-waves method [8, 9]. All compositions were modelled by monoclinic supercells with 32 or 64 atoms, where single or two Mn atoms replaced Ga atoms to describe off-stoichiometric compositions. Such model leads to two different local arrangements: one with excess Mn atom defect-free part of the supercell and second with excess Mn atom in planar fault. For each arrangement, both ferromagnetic and antiferromagnetic orientation magnetic moments at Mn-excess atoms were considered.
Our results show rising energy barriers for twin nucleation and propagation with increasing content of Mn with antiparallel magnetic orientation. It implies more difficult twin formation and growth in compositions far from stoichiometry. This effect is even more enhanced if excess Mn atom in Ga sublattice is located exactly in the planar fault. On the other hand, ferromagnetic ordering decreases barriers on the GPFE curves, but also is thermodynamically unstable because it exhibits significantly higher total energy than antiferromagnetic ordering along whole GPFE curve.
References
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[5] N. Lanska et al., J. Appl. Phys. 95 (2004) 8074.
[6] V. A. Chernenko, M. Chmielus and P. Müllner, Appl. Phys. Lett. 95 (2009) 104103.
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[8] G. Kresse and J. Furthmüller, Comput. Mater. Sci. 6 (1996) 15.
[9] P. E. Blöchl, Phys. Rev. B, 50 (1994) 17953.
