Spin-transfer torques: Self-consistent solution of the spin-diffusion equation and the Landau-Lifshitz equation

We present a numerical scheme that allows for the self-consistent treatment of the Landau-Lifshitz equation and the spin-diffusion equation in one space dimension. The scheme is used to simulate magnetic precessions in ferromagnet/normal-metal multilayers that are traversed by strong currents and results are compared to recent experimental observations. The good qualitative and quantitative agreement shows that the diffusive exchange-torque model proposed by Zhang et al. [8] is a legitimate alternative to the ballistic interface-torque model commonly used to describe magnetization dynamics in spin valves.