First-principles calculation of spin-orbit torque in a Co/Pt bilayer

TL;DR

This study uses first-principles calculations to analyze the angular dependence of spin-orbit torque in a disordered Co/Pt bilayer, revealing new torque components and their dependence on disorder.

Contribution

It introduces a first-principles non-equilibrium Green's function approach with supercell averaging to study spin-orbit torque in disordered bilayers, identifying a new planar Hall-like torque component.

Findings

The odd torque includes a sizeable planar Hall-like term.

Dampinglike and planar Hall-like torques are weakly dependent on disorder.

Fieldlike torque decreases with increasing disorder.

Abstract

The angular dependence of spin-orbit torque in a disordered Co/Pt bilayer is calculated using a first-principles non-equilibrium Green's function formalism with an explicit supercell averaging over Anderson disorder. In addition to the usual dampinglike and fieldlike terms, the odd torque contains a sizeable planar Hall-like term $(\mathbf{m\cdot E})\mathbf{m}\times(\mathbf{z}\times\mathbf{m})$ whose contribution to current-induced damping is consistent with experimental observations. The dampinglike and planar Hall-like torquances depend weakly on disorder strength, while the fieldlike torquance declines with increasing disorder. The torques that contribute to damping are almost entirely due to spin-orbit coupling on the Pt atoms, but the fieldlike torque does not require it.