Newton's second law in spin-orbit torque

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.