Spatiotemporal electronic spin fluctuations in random nuclear fields in n-CdTe

Abstract: We report on the dynamics of electron spins in n-doped CdTe layers that differs significantly from the expected response derived from the studies dedicated to electron spin relaxation in n-GaAs. At zero magnetic field, the electron spin noise spectra exhibit a two-peak structure - a zero-frequency line and a satellite - that we attribute to the electron spin precession in a frozen random nuclear spin distribution. This implies a surprisingly long electron spin correlation time whatever the doping level, even above the Mott transition. Using spatiotemporal spin noise spectroscopy, we demonstrate that the observation of a satellite in the spin noise spectra and a fast spin diffusion are mutually exclusive. This is consistent with a shortening of the electron spin correlation time due to hopping between donors. We interpret our data via a model assuming that the low temperature spin relaxation is due to hopping between donors in presence of hyperfine and anisotropic exchange interactions. Most of our results can be interpreted in this framework. First, a transition from inhomogeneous to homogeneous broadening of the spin noise peaks and the disappearance of the satellite are observed when the hopping rate becomes larger than the Larmor period induced by the local nuclear fields. In the regime of homogeneous broadening the ratio between the spin diffusion constant and the spin relaxation rate has a value in good agreement with the Dresselhaus constant. In the regime of inhomogeneous broadening, most of the samples exhibit a broadening consistent with the distribution of local nuclear fields. We obtain a new estimate of the hyperfine constants in CdTe and a value of 0.10 Tesla for the maximum nuclear field. Finally, our study also reveals a puzzle as our samples behave as if the active donor concentration was reduced by several orders of magnitudes with respect to the nominal values.