  The interplay of spin-orbit coupling (SOC) and magnetism gives rise to a
plethora of charge-to-spin conversion phenomena that harbor great potential for
spintronics applications. In addition to the spin Hall effect, magnets may
exhibit a magnetic spin Hall effect (MSHE), as was recently discovered [Kimata
\textit{et al.}, Nature \textbf{565}, 627-630 (2019)]. To date, the MSHE is
still awaiting its intuitive explanation. Here we relate the MSHE to the
vorticity of spin currents in the Fermi sea, which explains pictorially the
origin of the MSHE. For all magnetic Laue groups that allow for nonzero spin
current vorticities the related tensor elements of the MSH conductivity are
given. Minimal requirements for the occurrence of a MSHE are compatibility with
either a magnetization or a magnetic toroidal quadrupole. This finding implies
in particular that the MSHE is expected in all ferromagnets with sufficiently
large SOC. To substantiate our symmetry analysis, we present various models, in
particular a two-dimensional magnetized Rashba electron gas, that corroborate
an interpretation by means of spin current vortices. Considering thermally
induced spin transport and the magnetic spin Nernst effect in magnetic
insulators, which are brought about by magnons, our findings for electron
transport can be carried over to the realm of spincaloritronics, heat-to-spin
conversion, and energy harvesting.
