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