Spin force and intrinsic spin Hall effect in spintronics systems

We investigate the spin Hall effect (SHE) in a wide class of spin-orbit coupling systems by using spin force picture. We derive the general relation equation between spin force and spin current and show that the longitudinal force component can induce a spin Hall current, from which we reproduce the spin Hall conductivity obtained previously using Kubos formula. This simple spin force picture gives a clear and intuitive explanation for SHE.