  Recent experiments demonstrate that antiferromagnets exhibit the spin Hall
effect. We study a tight-binding model of an antiferromagnet on a square
lattice with Rashba spin-orbit coupling and disorder. By exact diagonalization
of a finite system connected to reservoirs within the
Landauer-B$\ddot{\text{u}}$ttiker formalism, we compute the transverse spin
Hall current in response to a longitudinal voltage difference. Surprisingly,
the spin Hall conductance can be considerably larger in antiferromagnets than
in normal metals. We compare our results to the Berry-phase-induced spin Hall
effect governed by the intrinsic contribution in the Kubo formula. The
Berry-phase-induced intrinsic spin Hall conductivity in bulk systems shows the
opposite behavior: large exchange couplings in AFs drastically reduce the spin
Hall current.
