Anomalous Hall Effect and Topological Defects in Antiferromagnetic Weyl Semimetals: Mn_{3}Sn/Ge

We theoretically study the interplay between bulk Weyl electrons and magnetic topological defects, including magnetic domains, domain walls, and Z_{6} vortex lines, in the antiferromagnetic Weyl semimetals Mn_{3}Sn and Mn_{3}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 Z_{6} anisotropy. We propose a dynamical equation of motion for the XY order parameter, which implies the presence of 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 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.