Anomalous Hall Effect due to the spin chirality in the Kagom\'{e} lattice

TL;DR

This paper investigates how the anomalous Hall effect arises from spin chirality in a kagome lattice, revealing topological transitions and quantized conductivities without spin-orbit coupling.

Contribution

It introduces a model showing the anomalous Hall effect driven by spin chirality in a kagome lattice, highlighting topological transitions and quantized conductivities.

Findings

Transverse conductivity can be non-zero without spin-orbit coupling.

Topological transitions change band Chern numbers.

Hall conductivity can be quantized or non-monotonic depending on parameters.

Abstract

We consider a model for a two dimensional electron gas moving on a kagom\'{e} lattice and locally coupled to a chiral magnetic texture. We show that the transverse conductivity $\sigma\_{xy}$ does not vanish even if spin-orbit coupling is not present and it may exhibit unusual behavior. Model parameters are the chirality, the number of conduction electrons and the amplitude of the local coupling. Upon varying these parameters, a topological transition characterized by change of the band Chern numbers occur. As a consequence, $\sigma\_{xy}$ can be quantized, proportional to the chirality or have a non monotonic behavior upon varying these parameters.