# Anomalous Hall effect and topological defects in antiferromagnetic Weyl semimetals: Mn$_3$Sn/Ge

## TL;DR

This paper explores the complex interplay between magnetic topological defects and electronic properties in antiferromagnetic Weyl semimetals Mn$_3$Sn and Mn$_3$Ge, revealing new phenomena and potential device applications.

## Contribution

It introduces a theoretical framework describing spin structures and dynamics, and links topological defects to electronic features like Fermi arcs and bound states in these materials.

## Key findings

- Presence of $ ext{Z}_6$ vortex lines and double-domain patterns.
- Electronic structure shows Fermi arcs at domain walls.
- Proposal of a device based on domain-dependent anomalous Hall effect.

## Abstract

We theoretically study the interplay between bulk Weyl electrons and magnetic topological defects, including magnetic domains, domain walls, and $\mathbb{Z}_6$ vortex lines, in the antiferromagnetic Weyl semimetals \mnsn\ and Mn$_3$Ge with negative vector chirality. We argue that these materials possess a hierarchy of energies scales which allows a description of the spin structure and spin dynamics using a XY model with $\mathbb{Z}_6$ anisotropy. We propose a dynamical equation of motion for the XY order parameter, which implies the presence of $\mathbb{Z}_6$ vortex lines, the double-domain pattern in the presence of magnetic fields, and the ability to control domains with current. We also introduce a minimal electronic model which allows efficient calculation of the electronic structure in the antiferromagnetic configuration, unveiling Fermi arcs at domain walls, and sharp quasi-bound states at $\mathbb{Z}_6$ vortices. Moreover, we have shown how these materials may allow electronic-based imaging of antiferromagnetic microstructure, and propose a possible device based on domain-dependent anomalous Hall effect.