Anomalous spin Hall and inverse spin Hall effects in magnetic systems

The spin Hall effect is typically used to generate a spin current and is a key parameter for designing spintronic devices. Here, the authors theoretically demonstrate an anomalous spin Hall and inverse spin Hall effect and demonstrate how they can generate a spin current where the direction and polarisation does not occur perpendicular to the charge current. Spin current is a very important tensor quantity in spintronics. However, the well-known spin-Hall effect (SHE) can only generate a few of its components whose propagating and polarization directions are perpendicular with each other and to an applied charge current. It is highly desirable in applications to generate spin currents whose polarization can be in any possible direction. Here anomalous SHE and inverse spin-Hall effect (ISHE) in magnetic systems are predicted. Spin currents, whose polarisation and propagation are collinear or orthogonal with each other and along or perpendicular to the charge current, can be generated, depending on whether the applied charge current is along or perpendicular to the order parameter. In anomalous ISHEs, charge currents proportional to the order parameter can be along or perpendicular to the propagating or polarization directions of the spin current.