Theoretical study of the dynamics of magnetization on the topological surface

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.

Figure 1

(Color online) (a) Illustration of the Dirac dispersion on top of TI. The Fermi level ${\epsilon }_F$ is far above the surface gap opened by magnetization in the ferromagnetic layer. (b) Sketch of FMR experiment in the soft magnetic layer. The substrate in the figure is TI, which is capped by a layer of soft ferromagnet. The magnetization precesses around the external magnetic field ${\mathit{H}}_{\text{eff}}$.