Spin-orbit coupled transport and spin torque in a ferromagnetic heterostructure

TL;DR

This paper develops a theoretical framework using coupled diffusion equations to analyze spin-orbit torques in ferromagnetic heterostructures, matching experimental symmetry and angular dependence, and incorporating dynamic effects.

Contribution

It introduces a set of coupled diffusion equations to describe spin dynamics and spin-orbit torques in ferromagnetic heterostructures, accounting for various effects and experimental observations.

Findings

Characterized out-of-plane and in-plane spin torque components.

Matched symmetry and angular dependence with experimental data.

Generalized diffusion equations to include dynamic effects like spin pumping.

Abstract

Ferromagnetic heterostructures provide an ideal platform to explore the nature of spin-orbit torques arising from the interplay mediated by itinerant electrons between a Rashba-type spin-orbit coupling and a ferromagnetic exchange interaction. For such a prototypic system, we develop a set of coupled diffusion equations to describe the diffusive spin dynamics and spin-orbit torques. We characterize the spin torque and its two prominent--out-of-plane and in-plane--components for a wide range of relative strength between the Rashba coupling and ferromagnetic exchange. The symmetry and angular dependence of the spin torque emerging from our simple Rashba model is in an agreement with experiments. The spin diffusion equation can be generalized to incorporate dynamic effect such as spin pumping and magnetic damping.