Magnetic-field-driven topological phase transition and topological Hall effect in AF-skyrmion lattice.

The topological Hall effect (THE), given by a composite of electric and topologically non-trivial spin texture is commonly observed in magnetic skyrmion crystals. Here we present a study of the THE of electrons coupled to antiferromagnetic Skyrmion lattices (AF-SkX). We show that, in the strong Hund coupling limit, topologically non-trivial phases emerge at specific fillings. Interestingly, at low filling an external field controlling the magnetic texture, drives the system from a conventional insulator phase to a phase exhibiting THE. Such behavior suggests the occurrence of a topological transition which is confirmed by a closing of the bulk-gap that is followed by its reopening, appearing simultaneously with a single pair of helical edge states. This transition is further verified by the calculation of the the Chern numbers and Berry curvature. We also compute a variety of observables in order to quantify the THE, namely: Hall conductivity (HC) and the orbital magnetization (OM) of electrons moving in the AF-SkX texture.