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

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.