Dynamics of curved domain walls in hexagonal magnetostrictive materials with nonlinear dissipation and Rashba effects

Abstract

This study presents an analytical investigation of the dynamics of curved domain walls in a bilayer magnetostrictive–piezoelectric heterostructure, using the extended Landau–Lifshitz–Gilbert equation. The system comprises a thin magnetostrictive layer perfectly bonded to the upper surface of a thick piezoelectric layer. We consider a transversely isotropic hexagonal class of magnetostrictive materials that exhibit structural inversion asymmetry. Our analysis accounts for the coupled effects of external magnetic fields, spin-polarized electric currents, magnetoelastic interactions, magnetocrystalline anisotropy, Rashba spin–orbit fields, and nonlinear viscous-dry friction dissipation mechanisms. Employing the reductive perturbation technique, we derive explicit analytical expressions for key dynamic parameters, such as the velocity, mobility, threshold, and breakdown conditions of the domain wall motion in the steady state. Our results reveal the intricate interplay between mean curvature, Rashba field, magnetoelastic coupling, and nonlinear dissipation, which collectively govern the propagation of domain walls in the magnetostrictive layer. Further, we numerically illustrate the analytical results obtained for curved domain walls on constant-curvature surfaces, such as planes, spheres, and cylinders. The results derived here demonstrate good qualitative alignment with recent studies.