Diffusive spin dynamics in ferromagnetic thin films with a Rashba interaction

In a ferromagnetic metal layer, the coupled charge and spin diffusion equations are obtained in the presence of both Rashba spin-orbit interaction and magnetism. The mis-alignment between the magnetization and the non-equilibrium spin density induced by the Rashba field gives rise to Rashba spin torque acting on the ferromagnetic order parameter. In a general form, we find that the Rashba torque consists of both in-plane and out-of-plane components, ie bm{T}=T_bothat{bm{y}}times{hat{bm m}}+T_parallel{hat{bm m}}times\({hat{bm y}}times{hat{bm m}}\). Numerical simulations on a two dimensional nano-wire discuss the impact of diffusion on the Rashba torque, which reveals a large enhancement to the ratio T_parallel/T_bot for thin wires. Our theory provides an explanation to the mechanism that drives the magnetization switching in a single ferromagnet as observed in the recent experiments.