Geometric Dynamics of Magnetization: Electronic Contribution

TL;DR

This paper develops a semiclassical theory describing how electric fields influence magnetization dynamics through electronic effects, clarifying the roles of Berry curvature, effective magnetic fields, and damping, with applications to topological insulator interfaces.

Contribution

It introduces a comprehensive semiclassical framework for magnetization-electron coupling, including effects of electric fields on spin-orbit torques and magnetization stability.

Findings

Electric fields modify Berry curvature and damping in magnetization dynamics.

Predicted anisotropic gyromagnetic ratio in ferromagnet-topological-insulator interfaces.

Demonstrated the formalism's applicability to other order parameters in solids.

Abstract

To give a general description of the influences of electric fields or currents on magnetization dynamics, we developed a semiclassical theory for the magnetization implicitly coupled to electronic degrees of freedom. In the absence of electric fields the Bloch electron Hamiltonian changes the Berry curvature, the effective magnetic field, and the damping in the dynamical equation of the magnetization, which we classify into intrinsic and extrinsic effects. Static electric fields modify these as first-order perturbations, using which we were able to give a physically clear interpretation of the current-induced spin-orbit torques. We used a toy model mimicking a ferromagnet-topological-insulator interface to illustrate the various effects, and predicted an anisotropic gyromagnetic ratio and the dynamical stability for an in-plane magnetization. Our formalism can also be applied to the slow dynamics of other order parameters in crystalline solids.