Non-collinear antiferromagnets and the anomalous Hall effect

The anomalous Hall effect is investigated theoretically by employing density functional calculations for the non-collinear antiferromagnetic order of the hexagonal compounds Mn3Ge and Mn3Sn 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. If this case were observable in Mn3Ge, a large AHC of about $\sigma_{zx}\approx 900\ (\Omega \text{cm})^{-1}$ should be expected. However, in Mn3Ge it is the non-planar configuration that is energetically favored, in which case it gives rise to an AHC of $\sigma_{xy}\approx 100\ (\Omega \text{cm})^{-1}$ . The non-planar configuration allows a quantitative evaluation of the topological Hall effect that is seen to determine this value of $\sigma_{xy}$ to a large extent. For Mn3Sn it is the planar configurations that are predicted to be observable. In this case the AHC can be as large as $\sigma_{yz}\approx250\ (\Omega \text{cm})^{-1}$