  We present spin noise (SN) measurements on an ensemble of donor-bound
electrons in ultrapure GaAs:Si covering temporal dynamics over six orders of
magnitude from milliseconds to nanoseconds. The SN spectra detected at the
donor-bound exciton transition show the multifaceted dynamical regime of the
ubiquitous mutual electron and nuclear spin interaction typical for III-V based
semiconductor systems. The experiment distinctly reveals the finite
Overhauser-shift of an electron spin precession at zero external magnetic field
and a second contribution around zero frequency stemming from the electron spin
components parallel to the nuclear spin fluctuations. Moreover, at very low
frequencies features related with time-dependent nuclear spin fluctuations are
clearly resolved making it possible to study the intricate nuclear spin
dynamics at zero and low magnetic fields. The findings are in agreement with
the developed model of electron and nuclear SN.
