Classical description of current-induced spin-transfer torque in multilayer structures

Abstract

We develop a classical description of the current-induced torque due to spin transfer in a layered system consisting of two ferromagnetic films separated by a nonmagnetic layer. The description is based on the classical equations for time-space evolution of the macroscopic magnetization. It is assumed that the perpendicular component of the nonequilibrium magnetization relaxes very fast in ferromagnetic films. Such a fast relaxation is due to a strong exchange field. Accordingly, the perpendicular component is totally absorbed at the interfaces giving rise to the torque. The longitudinal component, on the other hand, decays on a much longer distance defined by the spin diffusion length.