‘Spin–spin’ Hall effect in two dimensional electron systems with spin–orbit interaction

Abstract

We calculate spin-Hall conductivities in two dimensional electron systems with Rashbaspin–orbit interaction. The salient feature is that, apart from the usual spin-Hall conductivityσxyz, which corresponds to the induction of out-of-plane spin current due to the application oftransverse charge current, there is a novel spin-Hall conductivity , which arises due to the induction of transverse spin-polarized current in the transversedirection by the application of in-plane spin-polarized current. This phenomenon, which wecall the ‘spin–spin’ Hall effect, is a spin analogue of the conventional Hall effect, but withno magnetic field. This contribution may be understood through the spin-diffusiveequation.