# Topology analysis for anomalous Hall effect in the non-collinear antiferromagnetic states of Mn$_3\mathit{A}$N ($A$ = Ni, Cu, Zn, Ga, Ge, Pd, In, Sn, Ir, Pt)

## TL;DR

This study uses first-principles calculations to analyze the topological electronic structures in non-collinear antiferromagnetic manganese nitrides, revealing how Berry curvature influences the anomalous Hall effect.

## Contribution

It predicts stable non-collinear antiferromagnetic structures and analyzes their topological features contributing to the anomalous Hall effect using Wannier models.

## Key findings

- Small Berry curvature from spin-orbit coupling dominates the Hall conductivity.
- Divergent Berry curvature at Weyl points has limited impact on Hall conductivity.
- Topological features are spread around the Fermi surface, not localized at Weyl points.

## Abstract

We investigate topological features of electronic structures which produce large anomalous Hall effect in the non-collinear antiferromagnetic metallic states of anti-perovskite manganese nitrides by first-principles calculations. We first predict the stable magnetic structures of these compounds to be non-collinear antiferromagnetic structures characterized by either $T_{1g}$ or $T_{2g}$ irreducible representation by evaluating the total energy for all of the magnetic structures classified according to the symmetry and multipole moments. The topology analysis is next performed for the Wannier tight-binding models obtained from the first-principles band structures. Our results reveal the small Berry curvature induced through the coupling between occupied and unoccupied states with the spin-orbit coupling, which is widely spread around the Fermi surface in the Brillouin zone, dominantly contributes after the $k$-space integration to the anomalous Hall conductivity, while the local divergent Berry curvature around Weyl points has a rather small contribution to the anomalous Hall conductivity.