Nonvanishing spin Hall currents in the presence of magnetic impurities

The intrinsic spin Hall conductivity in a two dimensional electron gas with Rashba spin-orbit coupling is evaluated by taking account of anisotropic coupling between magnetic impurities and itinerant electrons. In our calculation Kubo’s linear response formalism is employed and the vertex correction is considered. In the semiclassical limit $\mu \gg 1\mathrm{/}\tau$, a non-vanishing spin Hall conductivity ${\sigma }_{sH}^{}$ is found to depend on the momentum relaxation time $\tau$, spin-orbit splitting $\mathrm{\Delta }$ and the anisotropic coefficient of interaction between itinerant electrons and magnetic impurities. The clean limit of ${\sigma }_{sH}^{}$ is in the region of $e/8\pi \sim e/6\pi$, depending on the anisotropic coefficient.