Extrinsic Spin Hall Effect Due to Transition-Metal Impurities

We investigate the extrinsic spin Hall effect in the electron gas model due to transition-metal impurities based on the single-impurity Anderson model with orbital degrees of freedom. Both the skew scattering and side jump mechanisms are analyzed in a unified way, and the significant role of orbital degrees of freedom are clarified. The obtained spin Hall conductivities are in proportion to the spin-orbit polarization at the Fermi level < l . s >(mu) as is the case with the intrinsic spin Hall effect: skew scattering term sigma(ss)(SH) proportional to < l . s)(mu)delta(1)sigma(xx,) and side jump term sigma(Sj)(SH) proportional to < l . s >(mu), where delta(1) is the phase shift for p (l = 1) partial wave. Furthermore, the present study indicates the existence of a nontrivial close relationship between the intrinsic term sigma(int)(SH) and the extrinsic side jump term sigma(Sj)(SH).