Anomalous spin Hall and inverse spin Hall effects in magnetic systems

We predict anomalous spin-Hall effects (SHEs) and anomalous inverse SHEs in magnetic systems. A spin current with propagation and polarization collinear can be generated by a charge current along the order parameter. Spin currents polarized along the order parameter (the charge current) and propagating along the charge current (the order parameter) are generated by the charge current perpendicular to the order parameter. In anomalous inverse SHEs, the charge current, due to a spin current with propagation and polarization collinear, is proportional and is along the projection of order parameter in the plane perpendicular to the spin current. For an applied spin current with mutually perpendicular propagation and polarization directions, a charge current along the spin current propagation direction is generated if the order parameter is collinear with the polarization of the spin current. Also, a charge current along the polarization of spin current is generated if the order parameter is collinear with the propagation direction of the spin current.