  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.
