Topological Phase Transitions of Dirac Magnons in Honeycomb Ferromagnets

TL;DR

This paper investigates temperature-driven topological phase transitions in honeycomb ferromagnets with Dzyaloshinskii-Moriya interaction, revealing gap-closing at Dirac points and sign reversal in thermal Hall conductivity as signatures of topological changes.

Contribution

It demonstrates that magnonic topological phases in honeycomb ferromagnets can be tuned by temperature or magnetic field, showing a novel mechanism for topological phase transitions driven by magnon interactions.

Findings

Magnon energy gap closes and reopens at a critical temperature.

Chern numbers differ above and below the critical temperature.

Thermal Hall conductivity changes sign at the transition.

Abstract

The study of the magnonic thermal Hall effect in magnets with Dzyaloshinskii-Moriya interaction (DMI) has recently drawn attention because of the underlying topology. Topological phase transitions may arise when there exist two or more distinct topological phases, and they are often revealed by a gap-closing phenomenon. In this work, we consider the magnons in honeycomb ferromagnets described by a Heisenberg Hamiltonian containing both an out-of-plane DMI and a Zeeman interaction. We demonstrate that the magnonic system exhibits temperature (or magnetic field) driven topological phase transitions due to magnon-magnon interactions. Specifically, when the temperature increases, the magnonic energy gap at Dirac points closes and reopens at a critical temperature, $T_c$. By showing that the Chern numbers of the magnonic bands are distinct above and below $T_c$, we confirm that the gap-closing phenomenon is indeed a signature for the topological phase transitions. Furthermore, our analysis indicates that the thermal Hall conductivity in the magnonic system exhibits a sign reversal at $T_c$, which can serve as an experimental probe of its topological nature. Our theory predicts that in $\rm{CrI_3}$ such a phenomenon exists and is experimentally accessible.