Spin Hall current and spin-transfer torque in ferromagnetic metal

Abstract

We theoretically examine the spin-transfer torque in the presence of spin-orbit interaction (SOI) at impurities in a ferromagnetic metal on the basis of linear response theory. We obtained, in addition to the usual spin-transfer torque, a new contributioin ∼ jSH·∇n in the first order in SOI, where jSH is the spin Hall current driven by an external electric field. This is a reaction to inverse spin Hall effect driven by spin motive force in a ferromagnet. © 2010 IOP Publishing Ltd.