Self-induced Floquet magnons in magnetic vortices

Driving condensed matter systems with periodic electromagnetic fields can result in exotic states not found in equilibrium. Termed Floquet engineering, such periodic driving applied to electronic systems can induce topological band structures and control spin interactions. In this study, we present a class of Floquet states in a magnetic vortex that arise from nonlinear interactions between the vortex core and microwave magnons. Floquet bands emerge through the periodic oscillation of the core, which can be initiated by either driving the core directly or pumping azimuthal magnon modes. For the latter, the azimuthal modes induce core gyration through nonlinear interactions, which in turn renormalizes the magnon band structure. This represents a self-induced mechanism for Floquet band engineering and opens avenues to study and control nonlinear magnon dynamics.