Interacting topological magnons in the Kitaev-Heisenberg honeycomb ferromagnets with Dzyaloshinskii-Moriya interaction

This theoretical work is devoted to investigating the magnon-magnon interaction effect in a two-dimensional Heisenberg-Kitaev honeycomb ferromagnet with Dzyaloshinskii-Moriya interaction (DMI). Based on the first-order Green function formalism, we calculate the thermal-fluctuation-induced temperature-dependent self-energy corrections of magnons. Our calculations reveal that the critical temperature for temperature-induced topological phase transitions monotonically approaches the Curie temperature with increasing DMI strength. Furthermore, it is shown that the critical temperature for topological phase transitions is correlated with Dzyaloshinskii-Moriya interaction and magnetic field strength.