Dynamics of magnetization on the topological surface

TL;DR

This paper theoretically analyzes the magnetization dynamics on the surface of a topological insulator, deriving a modified LLG equation that links electronic conductivity to magnetic behavior and predicts novel phenomena.

Contribution

It derives a new form of the LLG equation for topological insulator surfaces, connecting conductivity, Berry phase, and magnetization dynamics, with predictions of anomalous effects.

Findings

Inverse spin-Galvanic effect related to conductivity

Berry phase linked to Hall conductivity

Predicted anomalous ferromagnetic resonance behaviors

Abstract

We investigate theoretically the dynamics of magnetization coupled to the surface Dirac fermions of a three dimensional topological insulator, by deriving the Landau-Lifshitz-Gilbert (LLG) equation in the presence of charge current. Both the inverse spin-Galvanic effect and the Gilbert damping coefficient $\alpha$ are related to the two-dimensional diagonal conductivity $\sigma_{xx}$ of the Dirac fermion, while the Berry phase of the ferromagnetic moment to the Hall conductivity $\sigma_{xy}$. The spin transfer torque and the so-called $\beta$-terms are shown to be negligibly small. Anomalous behaviors in various phenomena including the ferromagnetic resonance are predicted in terms of this LLG equation.