Scaling Laws of Magnetically Driven High-order Harmonic Generation in Spin-Orbit Coupled Systems

Abstract

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 $\omega^{-3}$ with the driving frequency $\omega$--our time-dependent quantum transport simulations reveal a qualitatively distinct scaling law for magnetically driven HHG in the presence of Rashba spin-orbit interaction: the harmonic cutoff $n_{\mathrm{max}}$ scales as $\omega^{-1}$. 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 $\theta$ serves as a crucial control parameter. Increasing $\theta$ 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.