Spin-orbit torques from interfacial spin-orbit coupling for various interfaces

TL;DR

This paper develops a perturbative formalism to analytically compute spin-orbit torques in various magnetic multilayer interfaces, accounting for different magnetic and material configurations, and predicts a dampinglike torque component distinct from intrinsic effects.

Contribution

It introduces a compact analytic approach to calculate spin-orbit torques across diverse interfaces using scattering coefficients, encompassing effects like proximity magnetism and layer insertion.

Findings

Predicts a dampinglike spin-orbit torque component separate from intrinsic contributions.

Provides formulas for in-plane current induced by perpendicular bias.

Applicable to multiple interface types including topological insulators and magnetic bilayers.

Abstract

We use a perturbative approach to study the effects of interfacial spin-orbit coupling in magnetic multilayers by treating the two-dimensional Rashba model in a fully three-dimensional description of electron transport near an interface. This formalism provides a compact analytic expression for current-induced spin-orbit torques in terms of unperturbed scattering coefficients, allowing computation of spin-orbit torques for various contexts, by simply substituting scattering coefficients into the formulas. It applies to calculations of spin-orbit torques for magnetic bilayers with bulk magnetism, those with interface magnetism, a normal metal/ferromagnetic insulator junction, and a topological insulator/ferromagnet junction. It predicts a dampinglike component of spin-orbit torque that is distinct from any intrinsic contribution or those that arise from particular spin relaxation mechanisms. We discuss the effects of proximity-induced magnetism and insertion of an additional layer and provide formulas for in-plane current, which is induced by a perpendicular bias, anisotropic magnetoresistance, and spin memory loss in the same formalism.