We derive the current-induced torque in metallic magnetic multilayers in the ballistic regime for the case that one of the ferromagnetic layers is acting as a full polarizer. We generalize previous results to the case when transmission and reflection amplitudes of one of the ferromagnets are different from zero or one and are complex. The obtained expressions are valid for the situation when the interfaces are sufficiently flat and when there are no scatterers in the metallic spacers. Particular attention is paid to multilayers containing a perpendicular polarizer whose magnetization is pointed along the current flow. We present analytical expressions for the spin torque that may serve as a theoretical upper bound for realistic structures.

• Received 18 December 2007

DOI:https://doi.org/10.1103/PhysRevB.77.174428