Sign Changes of Intrinsic Spin Hall Effect in Semiconductors and Simple Metals: First-Principles Calculations

First-principles calculations are applied to study spin Hall effect in semiconductors and simple metals. We found that intrinsic spin Hall conductivity (ISHC) in realistic materials shows rich sign changes, which may be used to distinguish the effect from the extrinsic one. The calculated ISHC in n-doped GaAs can be well compared with experiment, and it differs from the sign obtained from the extrinsic effect. On the other hand, the ISHC in W and Au, which shows opposite sign, respectively, is robust and not sensitive to the disorder.