Band tuning with magnon amplification and interaction in honeycomb ferromagnets with Dzyaloshinskii–Moriya interaction*

In this work, we study the magnon-magnon interaction effect in typical honeycomb ferromagnets consisting of stacked van der Waals honeycomb layers, e.g., Chromium trihalides CrX3 compounds (X= F, Cl, Br and I), that display two magnon modes (Dirac magnon). Using the Green function formulism in the presence of Dzyaloshinskii–Moriya interaction, we obtain a spinor Dyson equation up to second-order approximation by the cluster expansion method,  showing prominent renormalizations of the single-particle spectrum. Furthermore, we propose a tunable renormalization effect using a parametric magnon amplification scheme. By altering the magnon population at different k spaces, the resulting renormalization effect not only reshapes the band structure, but also modifies the Berry curvature distribution. Our work demonstrates the interplay between band geometry, interactions and the external light field in the bosonic system and can potentially lead to new applications in magnon-based spintronic devices.