Abstract
This work is devoted to studying the magnon–magnon interaction effect in a two-dimensional checkerboard ferromagnet with the Dzyaloshinskii–Moriya interaction. Using a first-order Green function method, we analyze the influence of magnon–magnon interaction on the magnon band topology. We find that Chern numbers of two renormalized magnon bands are different above and below the critical temperature, which means that the magnon band gap-closing phenomenon is an indicator for one topological phase transition of the checkerboard ferromagnet. Our results show that the checkerboard ferromagnet possesses two topological phases, and its topological phase can be controlled either via the temperature or the applied magnetic field due to magnon–magnon interactions. Interestingly, it is found that the topological phase transition can occur twice with the increase in the temperature, which is different from the results of the honeycomb ferromagnet.
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