Macroscopic description of spin transfer torque

A macroscopic description of the current-induced torque due to spin transfer has been developed for layered systems consisting of ferromagnetic films, separated by nonmagnetic layers. The description is based on the classical spin diffusion equations for the distribution functions used in the theory of current-perpendicular-to-plane giant magnetoresistance (CPP-GMR), and the relevant boundary conditions for the longitudinal and transverse components of the spin current and spin accumulation. The torque is expressed as a function of the usual parameters derived from CPP-GMR experiments and two additional parameters involved in the transverse boundary conditions. The model describes qualitatively the normal and inverse switching phenomena studied in recent experiments. We also discuss a structure for which the spin torque disappears at a noncollinear magnetic configuration.