Topological phase transition driven by magnetic field and topological Hall effect in an antiferromagnetic skyrmion lattice

TL;DR

This paper investigates how magnetic fields induce topological phase transitions in antiferromagnetic skyrmion lattices, leading to the emergence of the topological Hall effect and associated edge states, with detailed analysis of electronic properties.

Contribution

It demonstrates the occurrence of topological phase transitions driven by magnetic fields in AF-SkX, revealing the emergence of THE and edge states through Chern number and Berry curvature calculations.

Findings

Topologically non-trivial phases appear at specific fillings under strong Hund coupling.

External magnetic fields can induce a transition from insulator to a THE phase.

The transition involves bulk-gap closing and reopening, with the appearance of helical edge states.

Abstract

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 and the orbital magnetization of electrons moving in the AF-SkX texture.