The anomalous Hall conductivity due to the vector spin chirality

TL;DR

This paper theoretically investigates how vector spin chirality in the $s$-$d$ model induces a local anomalous Hall effect when electron spin polarization exists, highlighting the role of spin current rotation.

Contribution

It demonstrates that vector spin chirality causes a local Hall effect in the $s$-$d$ model, with the global effect vanishing under homogeneous transport conditions.

Findings

Vector spin chirality induces local Hall effect with spin polarization.

Global Hall effect cancels out in homogeneous electron transport.

Anomalous Hall effect linked to rotational spin current component.

Abstract

We study theoretically the anomalous Hall effect due to the vector spin chirality carried by the local spins in the $s$-$d$ model. We will show that the vector spin chirality indeed induces local Hall effect in the presence of the electron spin polarization, while the global Hall effect vanishes if electron transport is homogeneous. This anomalous Hall effect can be interpreted in terms of the rotational component of the spin current associated with the vector chirality.