Surface spin-transfer torque and spin-injection effective field in ferromagnetic junctions: Unified theory

Abstract

We consider theoretically a current flowing perpendicular to interfaces of a spin-valve type ferromagnetic metallic junction. For the first time an effective approach is investigated to calculate a simultaneous action of the two current effects, namely, the nonequilibrium longitudinal spin injection and the transversal spin-transfer surface torque. Dispersion relation for fluctuations is derived and solved. Nonlinear problem is solved about steady state arising due to instability for a thick enough free layer.Comment: 9 page