Real-space phase field investigation of evolving magnetic domains and twin structures in a ferromagnetic shape memory alloy

A real-space phase field model combining Landau–Lifshitz–Gilbert equationand time-dependent Ginzburg–Landau equation is developed to investigate the evolution of ferromagnetic domains and martensitic twin structures in aferromagnetic shape memory alloy at different lengthscales. Both domain and twin structures are obtained by simultaneously solving for minimization of magnetic, elastic, and magnetoelastic coupling energy terms via a nonlinear finite element method. The model is applied to simulate magneto-structural evolution within a nanoparticle and a bulk single-crystal of the alloy Ni2MnGa, which are subjected to mechanical strains. It is shown that a nanoparticlecontains magnetic vortex structures within a single twin variant, whereas for a bulk crystal both 90° and 180° domain structures are present within multiple twin variants.