Decoherence of Neutral $^{31}$P Donor Nuclear Spins by $^{29}$Si

NMR data from degenerately doped Si:P has suggested that the coherence of $^{31}$P nuclear spins can be limited to a few ms in natural Si by spectral diffusion from $^{29}$Si [1]. Here we report measurements of the nuclear spin coherence of neutral isolated $^{31}$P donors in lightly-doped ($\sim $10$^{15}$ /cm$^{3})$ Si with $^{\mathrm{29}}$Si concentrations from 1\% to 50\%. Pulsed ENDOR at X-band microwave frequency and a magnetic field of 0.35 T was used to measure the nuclear spins. The light doping and measurement temperature of 1.7K ensured that neither electron spin flips nor flip-flops limited the nuclear T$_{2}$. We find that the resulting echo intensity decays are nonexponential, and the time to reach 1/e is inversely proportional to the $^{29}$Si density. The nuclear decoherence time for natural silicon is found to be approximately 1 second, about 2000 times longer than donor electron spins in natural Si.\\[4pt] [1] G.P. Carver et al., Phys. Rev. B 3, 4285 (1971).