Spin-Motive Forces and Current-Induced Torques in Ferromagnets

TL;DR

This paper develops a comprehensive phenomenological framework for understanding the reciprocal relationship between spin-motive forces and current-induced torques in ferromagnets, applicable across various spin-orbit coupling strengths.

Contribution

It introduces a systematic formalism that derives all possible torque and charge-pumping terms consistent with symmetry, unifying the understanding of these processes in ferromagnets.

Findings

Formalism valid for any spin-orbit coupling strength.

Connects charge pumping and torques via Onsager reciprocal relations.

Applied to isotropic and $C_{2v}$ ferromagnets, illustrating the framework's versatility.

Abstract

In metallic ferromagnets, the spin-transfer torque and spin-motive force are known to exhibit a reciprocal relationship. Recent experiments on ferromagnets with strong spin-orbit coupling have revealed a rich complexity in the interaction between itinerant charge carriers and magnetization, but a full understanding of this coupled dynamics is lacking. Here, we develop a general phenomenology of the two reciprocal processes of charge pumping by spin-motive forces and current-driven magnetization dynamics. The formalism is valid for spin-orbit coupling of any strength and presents a systematic scheme for deriving all possible torque and charge-pumping terms that obey the symmetry requirements imposed by the point group of the system. We demonstrate how the different charge pumping and torque contributions are connected via the Onsager reciprocal relations. The formalism is applied to two important classes of systems: isotropic ferromagnets with non-uniform magnetization and homogeneous ferromagnets described by the point group $C_{2v}$.