Phase-field microelasticity theory and micromagnetic simulations of domain structures in giant magnetostrictive materials

A computational model is proposed to predict the stability of magnetic domain structures and their temporal evolution in giant magnetostrictive materials by combining a micromagnetic model with the phase-field microelasticity theory of Khachaturyan. The model includes all the important energetic contributions, including the magnetocrystalline anisotropy energy, exchange energy, magnetostatic energy, external field energy, and elastic energy. While the elastic energy of an arbitrary magnetic domain structure is obtained analytically in Fourier space, the Landau–Liftshitz–Gilbert equation is solved using the efficient Gauss–Seidel projection method. Both Fe81.3Ga18.7 and Terfenol-D are considered as examples. The effects of elastic energy and magnetostatic energy on domain structures are studied. The magnetostriction and associated domain structure evolution under an applied field are modeled under different pre-stress conditions. It is shown that a compressive pre-stress can efficiently increase the overall magnetostrictive effect. The results are compared with existing experiment measurements and observations.