Optimal control for a coupled spin-polarized current and magnetization system

This paper is devoted to an optimal control problem of a coupled spin drift-diffusion Landau-Lifshitz-Gilbert system describing the interplay of magnetization and spin accumulation in magnetic-nonmagnetic multilayer structures, where the control is given by the electric current density. A variational approach is used to prove the existence of an optimal control. The first-order necessary optimality system for the optimal solution is derived in one space-dimension via Lagrange multiplier method. Numerical examples are reported to validate the theoretical findings.