Interacting Floquet topological magnons in laser-irradiated Heisenberg honeycomb ferromagnets

Upon irradiation with high-frequency circularly polarized light, the Heisenberg spin system on a honeycomb lattice develops a next-nearest neighbor Dzyaloshinskii-Moriya interaction (DMI) term, transforming it into a magnonic Floquet topological insulator with intriguing physical properties. In this context, we investigate the many-body interaction effects of Floquet magnons in a laser-irradiated Heisenberg honeycomb ferromagnet featuring DMI under circularly polarized off-resonant light illumination. Our analysis employs the magnon Floquet-Bloch theory and Green's function method. We demonstrate that quantum ferromagnet systems driven periodically by lasers exhibit temperature-driven topological phase transitions due to Floquet magnon-magnon interactions, transitions that are absent when such interactions are neglected. Furthermore, we observe that the critical temperature necessary for reversing the sign of the topological phase gradually increases with elevated light intensity. This study introduces a novel approach to constructing Floquet topological phases in periodically driven quantum magnet systems.