Spin Chirality Fluctuation and Anomalous Hall Effect in Itinerant Ferromagnets

TL;DR

This paper theoretically investigates how spin chirality fluctuations can induce the anomalous Hall effect in itinerant ferromagnets without relying on spin-orbit coupling, highlighting a structure-dependent mechanism.

Contribution

It introduces a mechanism for the anomalous Hall effect driven by spin chirality fluctuations in a Kondo lattice model without spin-orbit interaction, supported by estimates for Nd₂Mo₂O₇.

Findings

Finite anomalous Hall conductivity (~10 Ohm^{-1}cm^{-1}) in Nd₂Mo₂O₇

High resistivity (~10^{-4} to 10^{-3} Ohm·cm) consistent with experiments

Condition identified for chirality-fluctuation driven anomalous Hall effect

Abstract

The anomalous Hall effect due to the spin chirality order and fluctuation is studied theoretically in a Kondo lattice model without the relativistic spin-orbit interaction. Even without the correlations of the localized spins, $\sigma_{xy}$ can emerge depending on the lattice structure and the spin anisotropy. We reveal the condition for this chirality-fluctuation driven mechanism for $\sigma_{xy}$. Our semiquantitative estimates for a pyrochlore oxide Nd$_2$Mo$_2$O$_7$ give a finite $\sigma_{xy} \sim 10 \Ohm^{-1} \cm^{-1}$ together with a high resistivity $\rho_{xx} \sim 10^{-4}-10^{-3} \Ohm \cm$, in agreement with experiments.