Nonlinear mode crossing and spontaneous frequency comb generation in driven magnetic nanodisks

Abstract

Nonlinear magnetization dynamics in confined nanostructures provide a rich platform for fundamental studies and advanced spintronic applications. Here, we investigate the driven dynamics of a perpendicularly magnetized permalloy nanodisk using high-resolution micromagnetic simulations. In the linear regime, geometric confinement quantizes the uniform precession into discrete radial standing spin-wave (SSW) modes. As the excitation amplitude increases, the fundamental Kittel mode exhibits a pronounced nonlinear frequency shift relative to the higher-order SSW modes, ultimately leading to a critical mode crossing associated with nonlinear resonance overlap and the breakdown of modal orthogonality. Time-domain analysis reveals that strong mode hybridization governs the ensuing dynamics, giving rise to amplitude beating and delayed switching mediated by nonlinear bistability. In the frequency domain, phase-coherent, equidistant magnetic frequency combs emerge near the mode-crossing point, which we attribute to multimagnon scattering processes. At still higher drive amplitudes, these frequency combs are followed by a collapse of the modal structure. These results elucidate the role of nonlinear mode interactions in confined magnetic systems and establish magnetic nanodisks as highly tunable platforms for integrated microwave signal processing and precision metrology.