Chirality driven anomalous Hall effect in weak coupling regime

TL;DR

This paper investigates how non-trivial spin chirality induces an anomalous Hall effect in a weak coupling regime, highlighting a mechanism independent of spin-orbit interaction and relevant in mesoscopic spin glasses.

Contribution

It demonstrates that spin chirality can drive an anomalous Hall effect in the weak coupling limit, providing a new perspective beyond conventional spin-orbit mechanisms.

Findings

Chirality induces a local Hall current independent of spin-orbit coupling.

The effect is significant in systems with finite uniform chirality.

Chirality-induced Hall effect expected below spin-glass transition temperature.

Abstract

Anomalous Hall effect arising from non-trivial spin configuration (chirality) is studied based on the $s$-$d$ model. Considering a weak coupling case, the interaction is treated perturbatively. Scattering by normal impurities is included. Chirality is shown to drive locally Hall current and leads to overall Hall effect if there is a finite uniform chirality. This contribution is independent of the conventional spin-orbit contribution and shows distinct low temperature behavior. In mesoscopic spin glasses, chirality-induced anomalous Hall effect is expected below the spin-glass transition temperature. Measurement of Hall coefficient would be useful in experimentally confirming the chirality ordering.