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.

自旋霍尔（SH）效应，即电流沿横向转换为自旋电流，依赖于相对论自旋轨道耦合（SOC）。在这里，我们开发了关于磁性金属中 SH 效应机制的微观理论，其中巡回电子通过 Hund 交换相互作用和 SOC 与局域磁矩耦合。反铁磁金属和铁磁金属都被考虑。结果表明，当接近两种情况的磁转变温度时，自旋波动可以显着增强SH电导率。对于反铁磁金属，纯SH效应出现在整个温度范围内，而对于铁磁金属，纯SH效应预计在转变温度以下被反常霍尔效应取代。我们讨论了可能的实验实现以及当反铁磁转变温度调谐为零温度时量子临界性的影响。