Renormalization of gapped magnon excitation in monolayer MnBi2Te4 by magnon-magnon interaction

We develop a self-consistent renormalized spin-wave theory for two-dimensional ferromagnetic ${\mathrm{MnBi}}_{2}{\mathrm{Te}}_{4}$ monolayer and study the magnon spectrum including the magnon-magnon interaction at finite temperatures. We consider the spin Hamiltonian containing the Heisenberg term, exchange anisotropy, and crystal field effect, with the parameters obtained from both first-principles calculations and recent experimental measurements. We demonstrate that exchange anisotropy and single-ion anisotropy are both important to describe the monolayer ${\mathrm{MnBi}}_{2}{\mathrm{Te}}_{4}$. A significant renormalization of the magnon spectrum is found to be momentum dependent, especially near the high-symmetry points, which confirms the effects of magnon-magnon interactions as the temperature approaches the Curie temperature. We also observe a notable increase in both the Curie temperature and magnetic anisotropy under the magnetic fields. Due to the suppression of spin fluctuations by the magnetic field, the energy gaps increase significantly as the magnetic fields increase. Our results agree well with recent experiments and deepen our understanding about the magnetic property of two-dimensional magnets.