  We investigate the intrinsic spin dynamics of electrons bound to Al
impurities in bulk ZnO by optical spin noise spectroscopy. Spin noise
spectroscopy enables us to investigate the longitudinal and transverse spin
relaxation time with respect to nuclear and external magnetic fields in a
single spectrum. On one hand, the spin dynamic is dominated by the intrinsic
hyperfine interaction with the nuclear spins of the naturally occurring
$^{67}$Zn isotope. We measure a typical spin dephasing time of 23 ns in
agreement with the expected theoretical values. On the other hand, we measure a
third, very high spin dephasing rate which is attributed to a high defect
density of the investigated ZnO material. Measurements of the spin dynamics
under the influence of transverse as well as longitudinal external magnetic
fields unambiguously reveal the intriguing connections of the electron spin
with its nuclear and structural environment.
