Spin noise of localized electrons: Interplay of hopping and hyperfine interaction

TL;DR

This paper develops a theory for spin noise in localized electrons considering hyperfine interactions and hopping, deriving an analytical spectrum and analyzing how hopping rate influences the noise characteristics.

Contribution

It introduces an analytical model for spin noise spectrum of localized electrons incorporating both hyperfine interaction and hopping effects, covering arbitrary parameter regimes.

Findings

Hopping rate significantly alters the spin noise spectrum.

Analytical expression derived for arbitrary relation between precession frequency and hopping rate.

External magnetic field effects are briefly discussed.

Abstract

The theory of spin fluctuations is developed for an ensemble of localized electrons taking into account both hyperfine interaction of electron and nuclear spins and electron hopping between the sites. The analytical expression for the spin noise spectrum is derived for arbitrary relation between the electron spin precession frequency in the field of the nuclear fluctuation and the hopping rate. An increase in the hopping rate results in the drastic change of the spin noise spectrum. The effect of an external magnetic field is briefly addressed.