Fate of Topological Dirac Magnons in van der Waals Ferromagnets at Finite Temperature

Dirac magnons, the bosonic counterparts of Dirac fermions in graphene, provide a versatile platform to explore symmetry-protected band crossings and quantum geometry in magnetic insulators while promising high-velocity, low-dissipation spin transport for next-generation magnonic technologies. However, their stability under realistic, finite-temperature conditions remains an open question. Here, we develop a microscopic theory of thermal magnon-magnon interactions in van der Waals honeycomb ferromagnets, focusing on both gapless and gapped Dirac magnons. Using nonlinear spin-wave theory with magnon self-energy corrections and a T-matrix resummation that captures two-magnon bound states, we quantitatively reproduce temperature- and momentum-dependent energy shifts and linewidths observed experimentally in the gapless Dirac magnon material CrBr₃, even near the Curie temperature. Our approach provides a consistent interpretation of theoretical predictions and experiment shedding light on the role of bound states in enhancing magnon damping at low temperatures. For gapped Dirac magnon materials such as CrI₃, CrSiTe₃, and CrGeTe₃, we find a thermally induced reduction of the topological magnon gap, while no indication of thermally driven topological phase transitions is observed within the considered parameter range. Classical atomistic spin-dynamics simulations corroborate the gap’s robustness up to the Curie temperature. Furthermore, we establish a practical criterion for observing topological gaps by determining the minimum ratio of Dzyaloshinskii-Moriya interaction to Heisenberg exchange required to overcome thermal broadening throughout the ordered phase, typically around 5%. Taken together, our results elucidate the interplay between thermal many-body effects and topology in low-dimensional magnetic systems and provide a controlled framework for the interpretation of spectroscopic measurements.