Giant Extrinsic Spin Hall Effect due to Rare-Earth Impurities

We investigate the extrinsic spin Hall effect in the electron gas model due to magnetic impurities, by focusing on Ce- and Yb-impurities. In the dilute limit, the skew scattering term dominates the side jump term. For Ce-impurities, the spin Hall angle $\alpha_{\rm SH}$ due to skew scattering is given by $-8\pi\sin\delta_2/7$, where $\delta_2 (\ll 1)$ is the phase shift for$d (l=2)$ partial wave. Since $\alpha_{\rm SH}$ reaches $O(10^{-1})$ if $\delta_2 \simge 0.03$, the spin Hall effect is anticipated to be considerable in metals with rare-earth impurities. The giant extrinsic SHE originates from the large orbital angular momentum, which is also significant for the intrinsic SHE.