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We present an experimental investigation of radial spin-wave modes inmagnetic nano-disks with a vortex ground state. The spin-wave amplitude wasmeasured using a frequency-resolved magneto optical network analyzer, allowingfor high-resolution resonance curves to be recorded. It was found that withincreasing excitation amplitude up to about 10 mT, the lowest-order modebehaves strongly non-linearly as the mode frequency redshifts and the resonancepeak strongly deforms. This behavior was quantitatively reproduced bymicromagnetic simulations. At higher excitation the spinwaves are transformedinto a soliton by self-focusing, and collapse onto the vortex core, dispersingthe energy in short-wavelength spinwaves. Additionally, this process can leadto switching of the vortex polarization through the injection of a Bloch point.

Non-linear radial spinwave modes in thin magnetic disks