Long-range spin jump diffusion revealed by dynamic light scattering

Spatiotemporal spin noise spectroscopy is combined with dynamic light scattering in order to reach spatial resolutions down $\ensuremath{\sim}\ensuremath{\lambda}/10$. Applied a system of localized electron spins, an insulating n-doped CdTe layer, this allows us reveal long jump distances $\ensuremath{\ell}\ensuremath{\sim}2.7\phantom{\rule{4.pt}{0ex}}\ensuremath{\mu}\mathrm{m}$. Spin spectra at large wave vectors $q$ ($q\ensuremath{\ell}\ensuremath{\gg}1$) provide snapshot the dynamics before (therefore not affected by motion), while smaller $q$, motion sets in. This unravel contributions spin-orbit and hyperfine fields relaxation determine self-consistently all parameters relevant dynamics. We propose phenomenological equation inspired studies atomic diffusion neutron scattering, which includes mechanisms effect time flight fluctuation across laser spot. modeling reproduces experimental results.