Simulation of spin transport and magnetization dynamics in FNF structures within a drift-diffusion model

We present a self-consistent simulation of the magnetization dynamics and the spin dynamics in ferromagnetic/normal/ferromagnetic (FNF) heterostructures. We use a spin drift-diffusion equation (SDDE) and the Landau-Lifshitz-Gilbert equation (LLGE) to compute the coupled dynamic of both conduction (spin-) carriers and localized magnetic moments. Deriving a complete analytic solution of the stationary SDDE we develop a fast and robust method to compute the spin-torque in the LLGE. Optimal control theory is used to compute time-dependent electric current profiles to switch the magnetization in specified time. Uniqueness of the optimal solution is discussed.