  Direct and inverse spin Hall effects lie at the heart of novel applications
that utilize spins of electrons as information carriers, allowing generation of
spin currents and detecting them via the electric voltage. In the standard
arrangement, applied electric field induces transverse spin current with
perpendicular spin polarization. Although conventional spin Hall effects are
commonly used in spin-orbit torques or spin Hall magnetoresistance experiments,
the possibilities to configure electronic devices according to specific needs
are quite limited. Here, we investigate unconventional spin Hall effects that
have the same origin as conventional ones, but manifest only in low-symmetry
crystals where spin polarization, spin current and charge current are not
enforced to be orthogonal. Based on the symmetry analysis for all 230 space
groups, we have identified crystal structures that could exhibit unusual
configurations of charge-to-spin conversion. The most relevant geometries have
been explored in more detail; in particular, we have analyzed the collinear
components yielding transverse charge and spin current with spin polarization
parallel to one of them, as well as the longitudinal ones, where charge and
spin currents are parallel. In addition, we have demonstrated that
unconventional spin Hall effect can be induced by controllable breaking the
crystal symmetries by an external electric field, which opens a perspective for
external tuning of spin injection and detection by electric fields. The results
have been confirmed by density functional theory calculations performed for
various materials relevant for spintronics. We are convinced that our findings
will stimulate further computational and experimental studies of unconventional
spin Hall effects.
