Dimension transcendence and anomalous charge transport in magnets with moving multiple-$Q$ spin textures

TL;DR

This paper reveals that the motion of multiple-Q spin textures in magnets induces high-dimensional topological effects in electronic states, leading to anomalous charge transport and nonlinear responses linked to Chern numbers.

Contribution

It introduces a higher-dimensional momentum space framework incorporating phason modes to accurately describe electronic dynamics in moving spin textures, unveiling topological charge transport phenomena.

Findings

Electronic states exhibit non-trivial topology characterized by Chern numbers.

Motion of spin textures induces anomalous electric charge transport.

Deforming spin textures can generate nonlinear responses related to the second Chern number.

Abstract

Multiple-$Q$ spin textures, such as magnetic bubble and skyrmion lattices, can be driven into motion by external stimuli. The motion of spin textures affects the electronic states. Here we show that to describe correctly the electronic dynamics, the momentum space needs to be transcended to higher dimensions by including the ancillary dimensions associated with phason modes of the translational motion of the spin textures. The electronic states have non-trivial topology characterized by the first and second Chern numbers in the high dimensional hybrid momentum space. This gives rise to an anomalous electric charge transport due to the motion of spin textures. By deforming the spin textures, a nonlinear response associated with the second Chern number can be induced. The charge transport is derived from the semi-classical equation of motion of electrons that depends on the Berry curvature in the hybrid momentum space. Our results suggest that the motion of multiple-$Q$ spin textures has significant effects on the electronic dynamics and provides a new platform to explore high dimensional topological physics.