Newton's second law in spin-orbit torque

TL;DR

This paper presents a new, intuitive spin force framework to describe spin-orbit torque in Rashba systems, linking magnetic energy transfer to conduction electrons and proposing an experimental test via anisotropic magnetoresistance.

Contribution

It introduces a simple spin force-based description of SOT in Rashba systems, connecting classical torque-force analogy with energy dissipation and experimental verification methods.

Findings

Damping-like SOT expressed as a cross product of effective radius and spin force

Magnetic energy transfer to conduction electrons causes Joule heating

Proposed experimental measurement via anisotropic magnetoresistance

Abstract

Spin-orbit torque (SOT) refers to the excitation of magnetization dynamics via spin-orbit coupling under the application of a charged current. In this work, we introduce a simple and intuitive description of the SOT in terms of spin force. In Rashba spin-orbit coupling system, the damping-like SOT can be expressed as ${\mathbf T}^\mathrm{so}={\mathbf R}_c\times {\mathbf F}^{{\mathrm {so}}}$, in analogy to the classical torque-force relation, where $R_c$ is the effective radius characterizing the Rashba splitting in the momentum space. As a consequence, the magnetic energy is transferred to the conduction electrons, which dissipates through Joule heating at a rate of $({\mathbf j}_e\cdot {\mathbf F}^{\mathrm {so}})$, with $j_e$ being the applied current. Finally, we propose an experimental verification of our findings via measurement of the anisotropic magnetoresistance effect.