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 $\sim { \bm j}_{ \rm SH}^{ \phantom{ \dagger}} \cdot \nabla { \bm n}$ in the first order in SOI, where ${ \bm j}_{ \rm SH}^{ \phantom{ \dagger}}$ 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.
Categories: cond-mat.mes-hall