Mean-Field Dynamics of the Spin–Magnetization Coupling in Ferromagnetic Materials: Application to Current-Driven Domain Wall Motions

In this paper, we present a mean-field model of the spin-magnetization coupling in ferromagnetic materials. The model includes non-isotropic diffusion for spin dynamics, which is crucial in capturing strong spin-magnetization coupling. The derivation is based on a moment closure of the quantum spinor dynamics coupled to magnetization dynamics via the Landau-Lifchitz-Gilbert equation and the spin-transfer torque. The method is general and systematic, and can be used to study spin-orbit coupling as well. The form of the non-isotropic diffusion is generic, i.e., independent of the closure assumptions. Fully 3-D numerical simulation is implemented and applied to predict current-driven domain wall motions. It shows a non-linear dependence of the wall speed on the current density, which agrees with the experiments.