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We demonstrate that the strongly nonlinear regime of the magnetic dynamicsdriven high harmonic generation (HHG) can be captured through an adiabatictreatment. Within this approximation, the instantaneous energy levels reveal ahighly nonlinear term that mirrors the high-frequency excitations present innon-equilibrium transport quantities. Therefore, we find that the revelation ofnonlinear dynamics in the instantaneous energy levels offers a simplifiedunderstanding of HHG in magnetic systems. Additionally, leveraging the highlynonlinear nature of these instantaneous bands, we predict the emergence oftunable integer and fractional high harmonics in the presence of atime-modulated spin-orbit interaction. Our findings initiate tantalizingprospects for harnessing HHG in condensed matter systems.

Magnetic dynamics driven integer and fractional high harmonic generation arising from highly nonlinear instantaneous energy levels