Non-collinear Antiferromagnets and the Anomalous Hall Effect

Understand

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.