Dynamically driven orbital magnetization beyond the adiabatic limit

Recently it has been shown that the adiabatic evolution of a periodically driven system can induce an orbital magnetization that is proportional to the driving frequency. Examples of driving include coherent chiral phonons and magnetization rotation. In this work, we numerically study the dynamically driven orbital magnetization of a toy model beyond the adiabatic limit. When the driving frequency is much lower than the band gap, our result agrees with previous theories in the adiabatic limit. In the high-frequency regime, it converges to the analytical result obtained from the high-frequency expansion. We also comment on the differences between the orbital magnetization driven by light and general driving mechanisms.