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Abstract

We study the effects of magnon-magnon interactions in the two-dimensional van der Waals ferromagnet CrBr$_3$ focusing on its honeycomb lattice structure. Motivated by earlier theoretical predictions of temperature-induced spectral shifts and van Hove singularities in the magnon dispersion~[S. S. Pershoguba \textit{et al}., Dirac Magnons in Honeycomb Ferromagnets, \href{https://journals.aps.org/prx/abstract/10.1103/PhysRevX.8.011010}{Phys. Rev. X {\textbf{8}}, 011010 (2018)}], we go beyond the commonly used thermal magnon approximation by applying second-order perturbation theory in a fully numerical framework. Our analysis uncovers significant deviations from previous analysis: in particular, the predicted singularities are absent, consistent with recent inelastic neutron scattering measurements~[S. E. Nikitin \textit{et al}., Thermal Evolution of Dirac Magnons in the Honeycomb Ferromagnet CrBr$_3$, \href{https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.129.127201}{Phys. Rev. Lett. {\textbf{129}}, 127201 (2022)}]. Moreover, we find that the temperature dependence of the renormalized magnon spectrum exhibits a distinct $T^3$ behavior for the optical magnon branch, while retaining $T^2$ behavior for the acoustic or down magnon band. This feature sheds new light on the collective dynamics of Dirac magnons and their interactions. We further compare the honeycomb case with a triangular Bravais lattice, relevant for ferromagnetic monolayer MnBi$_2$Te$_4$, and show that both systems lack singular features while displaying quite distinct thermal trends.