Angular dependence of spin-orbit spin transfer torques

TL;DR

This paper investigates how spin-orbit spin transfer torques depend on magnetization direction in ferromagnet/heavy metal bilayers, revealing complex angular behaviors influenced by Rashba spin-orbit coupling and exchange interactions, aligning with experimental data.

Contribution

It provides a detailed theoretical analysis of the angular dependence of spin-orbit torques, highlighting the roles of Fermi surface distortion and Fermi sea contributions in different coupling regimes.

Findings

Field-like torque shows nontrivial angular dependence related to Fermi surface distortion.

Damping-like torque's angular dependence arises from combined Fermi surface and sea effects.

Results align with experimental observations of magnetization dynamics.

Abstract

In ferromagnet/heavy metal bilayers, an in-plane current gives rise to spin-orbit spin transfer torque which is usually decomposed into field-like and damping-like torques. For two-dimensional free-electron and tight-binding models with Rashba spin-orbit coupling, the field-like torque acquires nontrivial dependence on the magnetization direction when the Rashba spin-orbit coupling becomes comparable to the exchange interaction. This nontrivial angular dependence of the field-like torque is related to the Fermi surface distortion, determined by the ratio of the Rashba spin-orbit coupling to the exchange interaction. On the other hand, the damping-like torque acquires nontrivial angular dependence when the Rashba spin-orbit coupling is comparable to or stronger than the exchange interaction. It is related to the combined effects of the Fermi surface distortion and the Fermi sea contribution. The angular dependence is consistent with experimental observations and can be important to understand magnetization dynamics induced by spin-orbit spin transfer torques