Magnetic spin and orbital Hall effects in centrosymmetric ferromagnets

The magnetic spin Hall effect (MSHE) and magnetic orbital Hall effect (MOHE) are the magnetization-dependent counterparts of the conventional spin Hall and orbital Hall effects, respectively. Here, we theoretically investigate their underlying mechanisms in centrosymmetric ferromagnets and find a fundamental difference between them. In particular, the orbital multipole (i.e., orbital angular position) plays a central role in the MOHE, with no analogue in the MSHE. This distinction is reflected in two key features: (i) while the magnetic spin Hall conductivity remains identical in magnitude for electric fields applied both parallel and perpendicular to the magnetization, the magnetic orbital Hall conductivity differs significantly between these cases; (ii) the dominant k points responsible for the MSHE and MOHE differ in the spin and orbital characters of the corresponding nearly degenerate bands. These results clarify the distinct physical origins of the MSHE and MOHE in centrosymmetric ferromagnets, providing fundamental insights into angular momentum transport and guidelines for spin-orbitronic applications. The authors investigate magnetic spin and orbital Hall effects in centrosymmetric ferromagnets. The results show that the two effects have fundamentally different mechanisms, which manifest in two distinguishing features.