  The spin Hall (SH) effect, the conversion of the electric current to the spin
current along the transverse direction, relies on the relativistic spin-orbit
coupling (SOC). Here, we develop a microscopic theory on the mechanisms of the
SH effect in magnetic metals, where itinerant electrons are coupled with
localized magnetic moments via the Hund exchange interaction and the SOC. Both
antiferromagnetic metals and ferromagnetic metals are considered. It is shown
that the SH conductivity can be significantly enhanced by the spin fluctuation
when approaching the magnetic transition temperature of both cases. For
antiferromagnetic metals, the pure SH effect appears in the entire temperature
range, while for ferromagnetic metals, the pure SH effect is expected to be
replaced by the anomalous Hall effect below the transition temperature. We
discuss possible experimental realizations and the effect of the quantum
criticality when the antiferromagnetic transition temperature is tuned to zero
temperature.
