Self-consistent renormalized spin-wave theory of magnetic and topological transitions in two-dimensional honeycomb ferromagnets

We investigate finite-temperature magnetic and topological phase transitions in two-dimensional honeycomb ferromagnets using an extended self-consistent renormalized spin-wave theory (SRSWT) that incorporates higher-order corrections from the Holstein--Primakoff expansion. Focusing on the combined effects of single-ion anisotropy, Zeeman field, next-nearest-neighbor (NNN) exchange, and Dzyaloshinskii--Moriya interaction, we analyze how these parameters influence the magnetization curves and magnon spectra. This work serves two main goals. First, we critically examine the limitations of SRSWT, showing that in the absence of external or interaction tuning, the theory tends to overestimate magnon self-energy corrections, often predicting first-order magnetic transitions with multivalued magnetization and metastable solution branches (i.e., self-consistent but thermodynamically unstable states). Second, we demonstrate that topological transitions -- signaled by magnon gap closings at the Dirac points -- can be tuned to occur below the magnetic transition temperature and within the thermodynamically stable regime. In particular, we identify two practical tuning strategies: applying an external Zeeman field of appropriate sign depending on the anisotropy strength, and introducing a small antiferromagnetic NNN exchange coupling. These findings not only clarify the predictive scope and limitations of SRSWT but also provide experimentally relevant guidance for realizing thermally driven topological transitions in two-dimensional honeycomb magnetic insulators.