  The spin Hall effect (SHE) is normally discussed in terms of a spin current,
which is ill-defined in strongly spin-orbit-coupled systems because of spin
non-conservation. In this work we propose an alternative view of SHE phenomena
by relating them to a spin analog of charge polarization induced by an electric
field. The spin density polarization is most conveniently defined in
insulators, which can have a SHE if they break time-reversal symmetry, i.e. if
they are magnetic. The reciprocal of this SHE is a counterpart of the inverse
SHE (ISHE), and is manifested in magnetic insulators as a charge polarization
induced by a Zeeman field gradient. We use a modified Kane-Mele model to
illustrate the magnetic spin Hall effect, and to discuss its bulk-boundary
relationship.
