  Spin Hall effect for excitons in alkali halides and in Cu_2O is investigated
theoretically. In both systems, the spin Hall effect results from the Berry
curvature in k space, which becomes nonzero due to lifting of degeneracies of
the exciton states by exchange coupling. The trajectory of the excitons can be
directly seen as spatial dependence of the circularly polarized light emitted
from the excitons. It enables us to observe the spin Hall effect directly in
the real-space time.
