Spin noise of conduction electrons inn-type bulk GaAs

We report a comprehensive study of stochastic electron spin fluctuations---spin noise---in lightly doped (n-type) bulk GaAs, which are measured using sensitive optical magnetometry based on off-resonant Faraday rotation. Frequency spectra of electron spin noise are studied as a function of electron density, magnetic field, temperature, probe-laser wavelength and intensity, and interaction volume. Electron spin lifetimes τₛ are inferred from the width of the spin noise spectra and are compared to direct measurements of τₛ using conventional Hanle-effect methods. Both methods reveal a strong and similar dependence of τₛ on the wavelength and intensity of the probe laser, highlighting the undesired influence of sub-bandgap absorption effects on the nominally ``nonperturbative'' spin noise measurements. As a function of temperature, the spin noise power increases approximately linearly from 1.5 to 30 K, as expected for degenerate electrons obeying Fermi-Dirac statistics, but with an additional zero-temperature offset. Finally, as the cross-sectional area of the probe laser shrinks and fewer electrons are probed, the measured Faraday rotation fluctuations due to electron spin noise are shown to increase, as expected.