Intrinsic anomalous spin Hall effect

Charge-spin interconversion in magnetic materials is investigated by using the first-principles calculations. In addition to the conventional spin Hall effect (SHE) that requires mutual orthogonality of the charge current, spin-flow direction, and spin polarization, the recently proposed anomalous SHE (ASHE) is confirmed in Mn₂Au and WTe₂. The interaction of the order parameter with conduction electrons leads to sizeable non-zero spin Berry curvatures that give rise to anomalous spin Hall conductivity (ASHC). Our calculations show that the ASHE is intrinsic and originates from the order-parameter-controlled spin-orbit interaction, which generates an extra anomalous effective field. A useful relationship among the order parameter, the spin Berry curvature, and the ASHC is revealed. Our findings provide a new avenue for generating and detecting arbitrary types of spin currents.