Electron-spin phase relaxation of phosphorus donors in nuclear-spin-enriched silicon

We report a pulsed electron paramagnetic resonance study of the phase relaxation of electron spins bound to phosphorus donors in isotopically purified ${}^{29}\mathrm{Si}$ and natural abundance Si $\left({}^{\text{nat}}\mathrm{Si}\right)$ single crystals measured at $8\mathrm{K}$. The two-pulse echo decay curves for both samples show quadratic dependence on time, and the electron phase relaxation time $T_M$ for ${}^{29}\mathrm{Si}$ is about an order of magnitude shorter than that for ${}^{\text{nat}}\mathrm{Si}$. The orientation dependence of $T_M$ demonstrates that the phase relaxation is caused by spectral diffusion due to flip-flops of the host nuclear spins. The electron spin echo envelope modulation effects in ${}^{29}\mathrm{Si}$ are analyzed in the frequency domain.