Momentum-space and real-space Berry curvatures in Mn$_{3}$Sn

TL;DR

This paper investigates the Berry curvature in Mn₃Sn, linking momentum-space Weyl nodes and real-space spin textures to the anomalous Hall effect, revealing the role of domain walls and non-coplanar spins.

Contribution

It provides a detailed analysis of the Berry curvature's dependence on magnetic field and spin texture, highlighting the topological Hall effect in Mn₃Sn.

Findings

Berry curvature orientation is set by spin texture with no in-plane anisotropy.

Multidomain regime is limited to a narrow magnetic field window.

Topological Hall effect indicates non-coplanar spins and real-space Berry curvature in domain walls.

Abstract

Mn$_{3}$X (X= Sn, Ge) are noncollinear antiferromagnets hosting a large anomalous Hall effect (AHE). Weyl nodes in the electronic dispersions are believed to cause this AHE, but their locus in the momentum space is yet to be pinned down. We present a detailed study of the Hall conductivity tensor and magnetization in Mn$_{3}$Sn crystals and find that in the presence of a moderate magnetic field, spin texture sets the orientation of the $k$-space Berry curvature with no detectable in-plane anisotropy due to the $Z_6$ symmetry of the underlying lattice. We quantify the energy cost of domain nucleation and show that the multidomain regime is restricted to a narrow field window. Comparing the field dependence of AHE and magnetization, we find that there is a distinct component in the AHE which does not scale with magnetization when the domain walls are erected. This so-called `topological' Hall effect provides indirect evidence for a non-coplanar spin components and real-space Berry curvature in domain walls.