Self-induced spin-orbit torques in metallic ferromagnets

Abstract

Herein we present a phenomenological theory of spin-orbit torques in a metallic ferromagnet with spin-relaxing boundaries. The model is rooted in the coupled diffusion of charge and spin in the bulk of the ferromagnet, where we account for the anomalous Hall effects as well as the anisotropic magnetoresistance in the corresponding constitutive relations for both charge and spin sectors. The diffusion equations are supplemented with suitable boundary conditions reflecting the spin-sink capacity of the environment. In inversion-asymmetric heterostructures, the uncompensated spin accumulation exerts a dissipative torque on the order parameter, giving rise to a current-dependent linewidth in the ferromagnetic resonance with a characteristic angular dependence. We compare our model to recent spin-torque ferromagnetic resonance measurements, illustrating how rich self-induced spin-torque phenomenology can arise even in simple magnetic structures.