Dirac electrons and domain walls: a realization in junctions of ferromagnets and topological insulators

TL;DR

This paper explores how Dirac electrons at the interface of ferromagnets and topological insulators influence domain wall dynamics, revealing mechanisms that stabilize wall motion and prevent early breakdown.

Contribution

It introduces a model of Dirac electrons coupled to magnetic domain walls in topological insulator systems, highlighting the role of edge currents and quantum fluctuations in domain wall behavior.

Findings

Edge electronic currents compete with anisotropy energy in domain walls.

Quantum fluctuations induce in-plane anisotropy stabilizing the wall angle.

Weak intrinsic anisotropies allow for stable domain wall motion without early Walker breakdown.

Abstract

We study a system of Dirac electrons with finite density of charge carriers coupled to an external electromagnetic field in two spatial dimensions, with a domain wall (DW) mass term. The interface between a thin-film ferromagnet and a three-dimensional topological insulator provides a condensed-matter realization of this model, when an out-of-plane domain wall magnetization is coupled to the TI surface states. We show how, for films with very weak intrinsic in-plane anisotropies, the torque generated by the edge electronic current flowing along the DW competes with an effective in-plane anisotropy energy, induced by quantum fluctuations of the chiral electrons bound to the wall, in a mission to drive the internal angle of the DW from a Bloch configuration towards a N\'eel configuration. Both the edge current and the induced anisotropy contribute to stabilize the internal angle, so that for weak intrinsic in-plane anisotropies DW motion is still possible without suffering from an extremely early Walker breakdown.