We study the high power ferromagnetic resonance of perpendicularly magnetized BiYIG nanodisks where the uniaxial anisotropy almost compensates for the shape anisotropy. We observe a strong saturation of the averaged magnetization upon moderately increasing the amplitude of the rf field and a broadening of the ferromagnetic resonance line toward lower and higher magnetic fields. Full micromagnetic simulations reveal that a self-modulation of the dynamic magnetization is responsible for this behavior. To get more insight into this unstable dynamics, we analyze it in terms of normal modes. The number of modes involved is found to rapidly increase above the critical threshold. Still, a normal mode model taking into account only a few of them and their mutual nonlinear couplings allows us to reproduce the observed phenomenon. The normal mode analysis and micromagnetic simulations also predict a Suhl-like instability at a larger excitation power, when it is slowly increased from low values, and bistability. Using two-tone spectroscopy, we directly measure the self-modulation spectrum and provide experimental evidence of bistable dynamics. These findings open some perspectives on using high dimensional dynamics in magnetic nanostructures for unconventional information processing.

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• Magnetization dynamics
• Spin waves
• Dynamical systems
• Nanodisks