Optimal control of magnetization dynamics in ferromagnetic heterostructures by spin--polarized currents

We study the switching-process of the magnetization in a ferromagnetic-normal-metal multilayer system by a spin polarized electrical current via the spin transfer torque. We use a spin drift-diffusion equation (SDDE) and the Landau-Lifshitz-Gilbert equation (LLGE) to capture the coupled dynamics of the spin density and the magnetization dynamic of the heterostructure. Deriving a fully analytic solution of the stationary SDDE we obtain an accurate, robust, and fast self-consistent model for the spin-distribution and spin transfer torque inside general ferromagnetic/normal metal heterostructures. Using optimal control theory we explore the switching and back-switching process of the analyzer magnetization in a seven-layer system. Starting from a Gaussian, we identify a unified current pulse profile which accomplishes both processes within a specified switching time.