Magnetic dynamics driven integer and fractional high harmonic generation arisingfrom highly nonlinear instantaneous energy levels.

We demonstrate that the strongly nonlinear regime of the magnetic dynamics driven high har- monic generation (HHG) can be captured through an adiabatic treatment. The corresponding instantaneous energy dispersion reveals a highly nonlinear term that mirrors the high-frequency excitations underlying the non-equilibrium transport quantities. We stress out that the instan- taneous energy levels dynamics carry much information on HHG and thereby provide a simplified understanding of the effect. Further, we exploit the present approach to predict the emergence of tunable integer and fractional high harmonics in the presence of a time-modulated spin-orbit inter- action. Finally, we apply the approach to the case of the light driven HHG to figure out differently emerging non-linearities. Our findings initiate a new direction for harnessing HHG in both laser and precession driven ultrafast carrier dynamics.