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 ${\mathrm{Mn}}_3\mathrm{Sn}$ and ${\mathrm{Mn}}_3\mathrm{Ge}$ with negative vector chirality. We argue that these materials possess a hierarchy of energy scales, which allows a description of the spin structure and spin dynamics using an $XY$ 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 that allows efficient calculation of the electronic structure in the antiferromagnetic configuration, unveiling Fermi arcs at domain walls, and sharp quasibound 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 the domain-dependent anomalous Hall effect.

• Received 12 May 2017

DOI:https://doi.org/10.1103/PhysRevLett.119.087202