Electron spin coherence of shallow donors in natural and isotopically enriched germanium

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.