  We report on the study of the magnetic ratchet effect in AlGaN/GaN
heterostructures superimposed with lateral superlattice formed by dual-grating
gate structure. We demonstrate that irradiation of the superlattice with
terahertz beam results in the dc ratchet current, which shows giant
magneto-oscillations in the regime of Shubnikov de Haas oscillations. The
oscillations have the same period and are in phase with the resistivity
oscillations. Remarkably, their amplitude is greatly enhanced as compared to
the ratchet current at zero magnetic field, and the envelope of these
oscillations exhibits large beatings as a function of the magnetic field. We
demonstrate that the beatings are caused by the spin-orbit splitting of the
conduction band. We develop a theory which gives a good qualitative explanation
of all experimental observations and allows us to extract the spin-orbit
splitting constant \alpha_{\rm SO}= 7.5 \pm 1.5 meV \unicode{x212B}. We also
discuss how our results are modified by plasmonic effects and show that these
effects become more pronounced with decreasing the period of the gating gate
structures down to sub-microns.
