Inverse Spin-Galvanic Effect in the Interface between a Topological Insulator and a Ferromagnet

When a ferromagnet is deposited on the surface of a topological insulator the topologically protected surface state develops a gap and becomes a two-dimensional quantum Hall liquid. We demonstrate that the Hall current in such a liquid, induced by an external electric field, can have a dramatic effect on the magnetization dynamics of the ferromagnet by changing the effective anisotropy field. This change is dissipationless and may be substantial even in weakly spin-orbit coupled ferromagnets. We study the possibility of dissipationless current-induced magnetization reversal in monolayer-thin, insulating ferromagnets with a soft perpendicular anisotropy and discuss possible applications of this effect.

Figure 1

Corbino-disk-shaped TI coated with an ultrathin ferromagnet. (a) Top view: In the absence of electric fields, the magnetization of the ferromagnet points outside the page (dotted circles). When a voltage difference is applied between the inner and outer circles, a dissipationless Hall current flows at the interface between the two materials (solid arrows). This current magnetizes the surface states of the TI (inverse spin-galvanic effect) along the radial direction (dashed arrows), thus exerting a spin torque on the magnetization of the ferromagnet. (b) Cross sectional view: The shaded region is the TI, whereas the unshaded region is the ferromagnetic film. ${\mathbf{H}}_{\mathrm{FM}}$ is the anisotropy field in electric equilibrium. ${\mathbf{H}}_{\mathrm{CS},1}$ is a topological magnetic field proportional to (and parallel to) the applied electric field.

Figure 2

Feynman diagrams for (a) the electric-field-induced magnetization (inverse spin-galvanic effect), (b) the $xy$ component of the spin-spin response function, (c) the $xy$ component of the spin-spin response function in the presence of an electric current (it yields the adiabatic spin transfer torque ${\mathbf{v}}_s·\nabla \widehat{\Omega }$). The solid straight lines are propagators for massive Dirac quasiparticles (quasiholes). The solid wavy lines are magnons that couple to the spin operator, and the dashed straight lines are photons that couple to the velocity operator.