Topological magnon materials hold great promise for spintronics applications, particularly through their potential for back-scattering-free edge currents. In this work, we explore many-body interaction effects at finite temperatures in van der Waals honeycomb ferromagnets using an interacting spin-wave theory approach, which incorporates resummed Feynman diagrams. Our study reveals that interactions between magnons and bimagnon-bound states can play a crucial role in the energy shifts and broadening of magnon bands in CrBr3, offering new insights beyond previous analyses that emphasized the van-Hove singularity. Additionally, we clarify the nature of the thermally induced topological transition in CrI3, related to the Chern-insulating gap, by showing that earlier predictions were based on approximations that can now be improved. These findings contribute to a deeper understanding of many-body interactions in topological magnon systems and open pathways for more precise quantitative analyses in this exciting field.

Altermagnet is a new class of nonrelativistic collinear magnets with even-parity spin splittings. Using kinematic analysis, nonlinear spin-wave perturbation theory, and density-matrix renormalization group+matrix product operator-based time evolutions, we show that the spin-split upper branch of magnons in altermagets is generically unstable. This work establishes the trichotomy of magnon stability in nonrelativistic collinear magnets and illuminates possibilities of unique quantum dynamics in altermagnets.