Unconventional spin Hall effects in nonmagnetic solids

Direct and inverse spin Hall effects lie at the heart of novel applications that utilize spins of electrons as information carriers, allowing the generation of spin currents and detecting them via the electric voltage. In the standard arrangement, an 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 an unconventional spin Hall effect can be induced by controllable breaking of the crystal symmetries by an external electric field, which opens a perspective for the 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.