Efficient Dynamic Polarization of Phosphorus Nuclei in Silicon in Strong Magnetic Fields and Low Temperatures

We demonstrate that the dynamic nuclear polarization (DNP) of phosphorus donors in silicon can be very effective in a magnetic field of 4.6 T and at temperatures below 1 K. The DNP occurs due to the Overhauser effect following a cross relaxation via the forbidden flip-flop or flip-flip transitions. Nuclear polarization values $P>0.98$ were reached after 20 min of pumping with 0.4 $\mu$W of microwave power. We evaluated that the ratio of hyperfine state populations increased by three orders of magnitude after 2 hours of pumping, and an extremely pure nuclear spin system containing $<10^{-11}$ of the other spin state can be created. An inverted DNP has been obtained by pumping the low field ESR line of P followed by the flip-flip cross relaxation. This transition has much smaller relaxation rate and required substantially longer pumping times. We found that the nuclear polarization dynamics deviates substantially from a simple exponential function. The evolution of the polarization is characterized by two time constants $T^{'}_{ac}\approx$15 s in the beginning, and $T^{"}_{ac}\approx$1100 s for long pumping time. Temperature dependence of the nuclear relaxation rate of $^{31}$P was studied down to 0.75 K, below which the relaxation time became too long to be measured. The nuclear polarization followed a bi-exponential time dependence during relaxation. We suggest that the non-exponential behavior of DNP dynamics and the subsequent relaxation is mediated by the nuclei of $^{29}$Si surrounding $^{31}$P donors, which affect the transition probabilities of the forbidden cross-relaxation processes.