Spin Anisotropy and Quantum Hall Effect in the Kagome Lattice - Chiral Spin State based on a Ferromagnet-

TL;DR

This paper theoretically investigates a ferromagnetic Kagome lattice with spin anisotropies, revealing a chiral spin state that exhibits quantized Hall conductance without an external magnetic field, relevant to anomalous Hall effects in certain ferromagnets.

Contribution

It introduces a realistic chiral spin state on the Kagome lattice driven by spin anisotropy and Berry phase effects, expanding understanding of quantum Hall phenomena in ferromagnetic systems.

Findings

Berry phase induces band gap and quantized Hall conductance

Chiral spin state realized without external magnetic field

Implications for anomalous Hall effect in pyrochlore ferromagnets

Abstract

A ferromagnet with spin anisotropies on the 2D Kagome lattice is theoretically studied. This is a typical example of the flat-band ferromagnet. The Berry phase induced by the tilting of the spins opens the band gap and quantized Hall conductance \sigma_{xy}=\pm e^2/h is realized without external magnetic field. This is the most realistic chiral spin state based on the ferromagnetism. We also discuss the implication of our results to anomalous Hall effect observed in the metallic pyrochlore ferromagnets R_2Mo_2O_7(R=Nd, Sm, Gd).