Non-collinear antiferromagnets and the anomalous Hall effect

¹ Institut für Festkörperphysik, Technische Universität Darmstadt - D-64289 Darmstadt, Germany
² Max Planck Institute for Chemical Physics of Solids - D-01187 Dresden, Germany

Received: 10 November 2014
Accepted: 2 December 2014

Abstract

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 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 . The non-planar configuration allows a quantitative evaluation of the topological Hall effect that is seen to determine this value of 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 .