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

Abstract

Mn_{3}3X (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}3Sn crystals and find that in the presence of a moderate magnetic field, spin texture sets the orientation of the kk-space Berry curvature with no detectable in-plane anisotropy due to the Z_6Z6 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.