Modeling Torques in Systems With Spin-Orbit Coupling

We generalize the description of transport in ferromagnetic systems using a coupled spin and charge drift-diffusion approach to account for the spin-orbit torques acting on the magnetization. We consider both bulk and interfacial spin-orbit coupling and treat the transverse spin transport in the bulk of ferromagnets. We compare our approach with the typical assumption that the transverse spin currents are instantaneously absorbed in the ferromagnet. Furthermore, we investigate the effects of a strong interfacial Rashba spin-orbit coupling on the thickness and angular dependence of the torques, and we demonstrate its importance in capturing the behavior reported by experiments in the literature.