The influence of spin-diffusion effects on current driven domain-wall motion

Micromagnetic studies of current driven domain-wall motion nowadays usually employ a local spin-transfer torque model by Zhang and Li. In this model the right-hand side of the Landau-Lifshitz-Gilbert equation is extended by two torque terms referred to as adiabatic and nonadiabatic spin torque . The prefactor of the nonadiabatic term β describes the degree of nonadiabacity . Both the adiabatic and the nonadiabatic term depend on the local magnetization and its spatial derivatives only . Hence the model does not describe any nonlocal effects caused by spin diffusion . We implement a three-dimensional spin-diffusion model that accounts for spin accumulation and compare our simulation results with results obtained from the model by Zhang and Li . For the static case we investigate a vortex structure in a magnetic thin film with the material parameters of Permalloy. We compute the torque for an in-plane current as predicted by the diffusion model and reconstruct the degree of nonadiabacity β by projecting the torque onto the adiabatic and nonadiabatic torque terms of the Zhang and Li model respectively . As shown in Fig . 1(b) this results in a spatially varying β . This contradicts the model of the model of Zhang and Li that assumes β to be constant.