Scaling laws of magnetically driven high-order harmonic generation in spin–orbit coupled systems

We investigate the scaling behavior of high harmonic generation (HHG) driven by magnetic dynamics in spin-orbit coupled systems. In contrast to optically driven HHG-where the harmonic cutoff scales as<i>ω</i>^-3with the driving frequency<i>ω</i>-our time-dependent quantum transport simulations reveal a qualitatively distinct scaling law for magnetically driven HHG in the presence of spin-orbit interaction: the harmonic cutoff<i>n</i>_maxscales as<i>ω</i>^-1. This fundamental difference arises from distinct excitation mechanisms-namely, spin-flip transitions driven by vectorial magnetic precession, as opposed to scalar electric fields. Furthermore, we demonstrate that the precession cone angle<i>θ</i>serves as a crucial control parameter. Increasing<i>θ</i>broadens the harmonic bandwidth, with peak emission achieved for nearly in-plane magnetic dynamics. Our findings establish magnetically driven HHG as a robust and tunable mechanism for nonlinear spin transport, governed by unique scaling laws with potential applications in ultrafast spintronic technologies.