Time-evolution of spin-orbit torque and magnetization in Rashba ferromagnet from multiscale time-dependent-quantum-transport/classical-micromagnetics formalism

Spin-orbit torque originates in a ferromagnetic material when the nonequilibrium electronic spin density emerging due to spin-orbit coupling is noncollinear to the local magnetization. In this work, we investigate the time-evolution of spin-orbit torque in a Rashba ferromagnet using a recently developed quantum-classical hybrid framework where quantum electrons described by time-dependent nonequilibrium Green functions (TDNEGF) are self consistently coupled to local magnetization dynamics described by classical-micromagnetics using the Landau-Lifshitz-Gilbert (LLG) equation. It has been previously shown that such a self-consistent TDNEGF+LLG framework microscopically generates a spatially inhomogeneous and time-dependent dynamical Gilbert damping [1] through a memory kernel, contrary to conventional micromagnetics where a static Gilbert damping parameter is introduced phenomenologically. Here, we explore the influence of Rashba spin-orbit coupling on the resulting time-dependent spin-orbit torque, magnetization dynamics and dynamical Gilbert damping parameter in our TDNEGF+LLG framework which is further compared to the Gilbert damping parameter and magnetization dynamics evaluated using the scattering matrix theory.

[1] U.Bajpai and B.K.Nikolic, Phys. Rev. B 99, 134409 (2019).