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.