Self-induced spin-orbit torques in metallic ferromagnets

TL;DR

This paper develops a phenomenological model for self-induced spin-orbit torques in metallic ferromagnets, incorporating charge-spin diffusion and boundary effects, and explains experimental observations of current-dependent ferromagnetic resonance linewidths.

Contribution

It introduces a comprehensive diffusion-based theory accounting for boundary spin relaxation and anomalous Hall effects in metallic ferromagnets, advancing understanding of self-induced spin-orbit torques.

Findings

The model explains current-dependent linewidth in ferromagnetic resonance.

It captures the angular dependence of spin-torque effects.

Comparison with experiments shows the model's relevance.

Abstract

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.