Theoretical study of the dynamics of magnetization on the topological surface

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 $\ensuremath{\alpha}$ are related to the two-dimensional diagonal conductivity ${\ensuremath{\sigma}}_{xx}$ of the Dirac fermion, while the Berry phase of the ferromagnetic moment to the Hall conductivity ${\ensuremath{\sigma}}_{xy}$. The spin-transfer torque and the so-called $\ensuremath{\beta}$ terms are shown to be negligibly small. Anomalous behaviors in various phenomena including the ferromagnetic resonance are predicted in terms of this LLG equation.