Domain wall motion in junctions of thin-film magnets and topological insulators

We derive the equations of motionof a domain wall in a thin-film magnet coupled to the surface states of a topological insulator, in the presence of both an electric field along the domain wall and a magnetic field perpendicular to the junction. We show how the electric field acts as a chirality stabilizer holding off the appearance of Walker breakdown and enhancing the terminal velocity of the wall. We also propose a mechanism to reverse the domain wall chirality in a controllable manner, by tuning the chiral current flowing through the wall. An input from a weak perpendicular magnetic field is required in order to break the reflection symmetry that protects the degeneracy of the chirality vacuum.