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

TL;DR

This study measures electron spin coherence times of donor spins in germanium, revealing how isotopic composition and magnetic field orientation influence quantum coherence, with implications for spintronics and quantum computing.

Contribution

First pulsed ESR measurements of T2 and T1 times for donors in germanium, analyzing effects of isotopic enrichment and magnetic field orientation on spin coherence.

Findings

Spectral diffusion limits coherence in samples with natural isotopic composition.

T1 times constrain T2 to approximately twice T1 in highly enriched samples.

Anisotropy observed in T1 and linewidths depending on magnetic field orientation.

Abstract

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.