The chiral Hall effect of magnetic skyrmions from a cyclic cohomology approach

TL;DR

This paper reveals a novel chiral Hall effect in magnetic textures, emerging from noncommutative geometry, which differs from known effects and impacts the understanding of electrical transport in skyrmions.

Contribution

It introduces a new chiral Hall effect arising from magnetization gradients, interpreted via noncommutative geometry, distinct from traditional topological and emergent magnetic field effects.

Findings

The effect appears at linear order in magnetization gradients.

It occurs in one-dimensional magnetic textures like domain walls.

It requires reinterpretation of experimental data on magnetic skyrmions.

Abstract

We demonstrate the emergence of an anomalous Hall effect in chiral magnetic textures which is neither proportional to the net magnetization nor to the well-known emergent magnetic field that is responsible for the topological Hall effect. Instead, it appears already at linear order in the gradients of the magnetization texture and exists for one-dimensional magnetic textures such as domain walls and spin spirals. It receives a natural interpretation in the language of Alain Connes' noncommutative geometry. We show that this chiral Hall effect resembles the familiar topological Hall effect in essential properties while its phenomenology is distinctly different. Our findings make the re-interpretation of experimental data necessary, and offer an exciting twist in engineering the electrical transport through magnetic skyrmions.