Nuclear spin decoherence of neutral $^{31}$P donors in silicon: Effect of environmental $^{29}$Si nuclei

TL;DR

This study measures how $^{29}$Si nuclear spins cause decoherence of $^{31}$P nuclear spins in silicon, showing that lower $^{29}$Si concentration significantly prolongs coherence times, with electron spins providing additional protection.

Contribution

It provides the first quantitative measurement of $^{29}$Si-induced spectral diffusion effects on neutral donor nuclear spins in silicon across different isotopic concentrations.

Findings

Decoherence times range from 100 ms to 3 s depending on $^{29}$Si concentration.

Neutral donor electron spins suppress $^{29}$Si flip-flops, extending nuclear spin coherence.

Longer coherence times for neutral donors compared to ionized donors in natural silicon.

Abstract

Spectral diffusion arising from $^{29}$Si nuclear spin flip-flops, known to be a primary source of electron spin decoherence in silicon, is also predicted to limit the coherence times of neutral donor nuclear spins in silicon. Here, the impact of this mechanism on $^{31}$P nuclear spin coherence is measured as a function of $^{29}$Si concentration using X-band pulsed electron nuclear double resonance (ENDOR). The $^{31}$P nuclear spin echo decays show that decoherence is controlled by $^{29}$Si flip-flops resulting in both fast (exponential) and slow (non-exponential) spectral diffusion processes. The decay times span a range from 100 ms in crystals containing 50% $^{29}$Si to 3 s in crystals containing 1% $^{29}$Si. These nuclear spin echo decay times for neutral donors are orders of magnitude longer than those reported for ionized donors in natural silicon. The electron spin of the neutral donors `protects' the donor nuclear spins by suppressing $^{29}$Si flip-flops within a `frozen core', as a result of the detuning of the $^{29}$Si spins caused by their hyperfine coupling to the electron spin.