Non-collinear Antiferromagnets and the Anomalous Hall Effect

TL;DR

This paper theoretically investigates the anomalous Hall effect in non-collinear antiferromagnets Mn₃Ge and Mn₃Sn, revealing how magnetic configurations influence Hall conductivity and its topological origins.

Contribution

It provides a detailed theoretical analysis of how planar and non-planar magnetic configurations affect the anomalous Hall conductivity in Mn₃Ge and Mn₃Sn, linking it to Weyl points and topological effects.

Findings

Planar configurations in Mn₃Ge could yield ~900 S/cm AHC.

Non-planar Mn₃Ge configuration results in ~100 S/cm AHC.

Planar configurations in Mn₃Sn could produce up to 250 S/cm AHC.

Abstract

The anomalous Hall effect is investigated theoretically by means of density functional calculations for the non-collinear antiferromagnetic order of the hexagonal compounds Mn$_3$Ge and Mn$_3$Sn using various planar triangular magnetic configurations as well as unexpected non-planar configurations. The former give rise to anomalous Hall conductivities (AHC) that are found to be extremely anisotropic. For the planar cases the AHC is connected with Weyl-points in the energy-band structure, which are described in detail. If this case were observable in Mn$_3$Ge, a large AHC of about 900 S/cm should be expected. However, in Mn$_3$Ge it is the non-planar configuration that is energetically favored, in which case it gives rise to an AHC of 100 S/cm. The non-planar configuration allows a quantitative evaluation of the topological Hall effect that is seen to determine this value of the conductivity to a large extent. For Mn$_3$Sn it is the planar configurations that are predicted to be observable. In this case the AHC can be as large as 250 S/cm.