Current-induced magnetization reversal on the surface of a topological insulator

We study the dynamics of magnetization coupled to the surface Dirac fermions of a three-dimensional topological insulator. By solving the Landau-Lifshitz-Gilbert equation in the presence of a charge current, we find current-induced magnetization dynamics and discuss the possibility of magnetization reversal. The torque from the current injection depends on the transmission probability through the ferromagnet and shows nontrivial dependence on the exchange coupling. The magnetization dynamics is a direct manifestation of the inverse spin-galvanic effect and hence another ferromagnet is unnecessary to induce spin-transfer torque in contrast to the conventional setup.

Figure 1

Schematic of the model. By injecting charge current on the surface, one can induce magnetization dynamics in the ferromagnet deposited on top of a topological insulator.

Figure 2

Time evolution of the magnetization vector with $h/E=0.1$, $\overline{V}=1$, $k_{F}L=100$, and ${\alpha }_G=0.1$. Solid line, $\Omega /{\omega }_F=0.1$; dotted line, $\Omega /{\omega }_F=10$.

Figure 3

Time evolution of the magnetization vector for weaker damping with ${\alpha }_G=0.01$, $h/E=0.1$, $k_{F}L=100$, and $\Omega /{\omega }_F=10$. Solid line, $\overline{V}=100$; dotted line $\overline{V}=1$.

Figure 4

Time evolution of $n_x$ for ${\alpha }_G=0.1$, $\overline{V}=1$, and $\Omega /{\omega }_F=1$ with $k_{F}L=100$ and various $h/E$ (top) and with $h/E=0.9$ and various $k_{F}L$ (bottom).