Spin torques due to various linear spin-orbit coupling in semiconductor and graphene systems in the adiabatic limit

Abstract

We use the gauge formalism to investigate the current-induced spin dynamics in ferromagnetic media with spatially varying local magnetization, which is coupled to various material systems exhibiting linear spin-orbit coupling (SOC) effects, such as semiconductor and graphene materials. We perform a gauge transformation to the system, and obtain a gauge field (vector potential) in the adiabatic limit, i.e., strong coupling between the spin of the conduction electrons to the magnetization. The gauge field interacts with the applied current, resulting in a current-driven effective magnetic field and the corresponding spin torque acting on the magnetization of the FM media. We find that the current-driven spin orbit torque in various linear SOC systems and graphene systems can be described by a unified way. We propose a generalized Landau-Lifshitz-Gilbert (LLG) equation which includes this effective field term.