Magnetic Topological Kagome Systems

TL;DR

This paper models the magnetic and topological properties of Co$_3$Sn$_2$S$_2$, revealing a transition between quantum anomalous Hall and quantum spin Hall phases driven by electron occupancy and magnetic fluctuations.

Contribution

It introduces a spin-1/2 model coupled with conduction electrons to explain topological phases in Co$_3$Sn$_2$S$_2$, including effects of temperature-induced magnetic fluctuations.

Findings

Identified a topological transition from QAH to QSH phase at 2/3 occupancy.

Showed QAH phase becomes metallic with slight occupancy changes.

Demonstrated smooth Hall conductivity evolution with magnetic fluctuations.

Abstract

The recently discovered material Co$_3$Sn$_2$S$_2$ shows an impressive behavior of the quantum anomalous Hall (QAH) conductivity driven by the interplay between ferromagnetism in the $z$ direction and antiferromagnetism in the $xy$ plane. Motivated by these facts, first we build and study a spin-1/2 model to describe the magnetism of Co-atoms on the Kagome planes. Then, we include conduction electrons which are coupled to the spins-1/2 through a strong Hund's coupling. The spin-orbit coupling results in topological low-energy bands. For 2/3 on-site occupancy, we find a topological transition from a QAH ferromagnetic insulating phase with Chern number one to a quantum spin Hall (QSH) antiferromagnetic phase. The QAH phase is metallic when slightly changing the on-site occupancy. To account for temperature effects, we include fluctuations in the direction of the Hund's coupling. We show how the Hall conductivity can now smoothly evolve when spins develop a $120^o$ antiferromagnetism in the $xy$ plane and can synchronize with the ferromagnetic fraction.