  Germanium is a widely used material for electronic and optoelectronic devices
and recently it has become an important material for spintronics and quantum
computing applications. Donor spins in silicon have been shown to support very
long coherence times ($T_{2}$) when the host material is isotopically enriched
to remove any magnetic nuclei. Germanium also has non-magnetic isotopes so it
is expected to support long $T_{2}$s while offering some new properties.
Compared to Si, Ge has a strong spin-orbit coupling, large electron
wavefunction, high mobility, and highly anisotropic conduction band valleys
which will all give rise to new physics. In this Letter, the first pulsed
electron spin resonance (ESR) measurements of $T_{2}$ and the spin-lattice
relaxation ($T_1$) times for $^{75}$As and $^{31}$P donors in natural and
isotopically enriched germanium are presented. We compare samples with various
levels of isotopic enrichment and find that spectral diffusion due to $^{73}$Ge
nuclear spins limits the coherence in samples with significant amounts of
$^{73}$Ge. For the most highly enriched samples, we find that $T_1$ limits
$T_2$ to $T_2 = 2T_1$. We report an anisotropy in $T_1$ and the ensemble
linewidths for magnetic fields oriented along different crystal axes but do not
resolve any angular dependence to the spectral-diffusion-limited $T_2$ in
samples with $^{73}$Ge.
