Model for strain and magnetization in magnetic shape-memory alloys

TLDR

Large magnetic‑field‑induced strains in Ni₂MnGa and related magnetic shape‑memory alloys arise from twin‑boundary motion rather than magnetostriction, and the strain–magnetization dependence is largely linear below saturation. The authors propose a simple phenomenological model to describe the magnetization process and field‑induced strain via twin‑boundary and phase‑boundary motion in both strong and weak anisotropy regimes. The model expresses field dependence of magnetization and strain through an effective stiffness constant, transformation strain, and magnetic anisotropy, using reduced field parameters he = MsH/Ce02 and ha = MsH/2Ku. The model reproduces the nearly linear strain–magnetization relationship, explains magnetization remanence and the nonlinear field dependence near saturation, and indicates that low‑field curvature may stem from additional variants with distributed susceptibilities.

Abstract

The large magnetic-field-induced strains observed in martensitic phases based on Ni2MnGa and in other magnetic shape memory alloys are believed to arise from a process of twin-boundary motion rather than magnetostriction. The dependence of strain on magnetization, e(M), generally shows a large component that is linear (rather than quadratic) in M below saturation (quadratic dependence being typical of magnetostrictive strain). A simple phenomenological model for the magnetization process and field-induced strain by twin-boundary and phase-boundary motion is proposed for both the strong and weak anisotropy cases. The model is shown to account for the nearly linear dependence of strain on magnetization in the martensitic phases of these materials. It shows the field dependence of the magnetization and strain to be functions of an effective stiffness constant, C, the transformation strain, e0, and the magnetic anisotropy of the martensitic phase, Ku, through two reduced field parameters, he=MsH/Ce02 and ha=MsH/2Ku. The model also accounts for the magnetization remanence and the nonlinear field dependence closer to saturation (which produces little strain). The curvature observed in e(H) at very low fields is not described by this two-variant model and may be related to the fact that more variants exist which respond to the field with a distribution of susceptibilities.