Submillisecond Hyperpolarization of Nuclear Spins in Silicon

In this Letter, we devise a fast and effective nuclear spin hyperpolarization scheme, which is, in principle, magnetic field independent. We use this scheme to experimentally demonstrate polarizations of up to 66% for phosphorus donor nuclear spins in bulk silicon, which are created within less than $100\mu \mathrm{s}$ in a magnetic field of 0.35 T at a temperature of 5 K. The polarization scheme is based on a spin-dependent recombination process via weakly coupled spin pairs, for which the recombination time constant strongly depends on the relative orientation of the two spins. We further use this scheme to measure the nuclear spin relaxation time and find a value of $\sim 100\mathrm{ms}$ under illumination, in good agreement with the value calculated for nuclear spin flips induced by repeated ionization and deionization processes.

Figure 1

Pulse sequence for the hyperpolarization of ${}^{31}\mathrm{P}$ nuclear spins (upper part) and the corresponding time evolution of the spin state populations (lower part) for nuclear spins with $I=1/2$ (green arrow, $n$) hyperfine coupled to electron spins with $S=1/2$ (blue arrow, $e_1$). The electron spins form weakly coupled spin pairs with electron spins $e_2$ in spatial proximity (red arrows). Only the four states with one orientation (spin-up) of $e_2$ are shown here. A similar line of arguments can be applied to the four states with $e_2$ in the spin-down state. The two states at the bottom denote the nuclear spin states of the ${}^{31}{\mathrm{P}}^{+}$. See text for details.

Figure 2

(a) EDMR spectroscopy of the ${}^{31}\mathrm{P}$ and SL1 electron spin transitions. Four additional peaks related to the SL1 are observed outside the magnetic field range shown here. (b), (c) Spectroscopy of the nuclear spin transitions of the ionized ${}^{31}{\mathrm{P}}^{+}$ and the neutral ${}^{31}{\mathrm{P}}^0$ (open circles). Resonance frequencies and peak widths are extracted from Lorentzian fits (red lines). For comparison, the spectroscopy of ${}^{31}{\mathrm{P}}^0$ nuclear spins near the $\mathrm{Si}/{\mathrm{SiO}}_2$ interface is shown as well (dashed green line, data taken from [27]).

Figure 3

(a) Pulse sequence for the hyperpolarization of ${}^{31}\mathrm{P}$ nuclear spins. The resulting polarization is detected using a spin echo after new spin pairs have been generated by a $500\mu \mathrm{s}$ long LED pulse with an intensity of $I_{\mathrm{LED}}=20\mathrm{mW}/{\mathrm{cm}}^2$. The time interval ${\tau }_{\mathrm{ap}}=1.8\mu \mathrm{s}\ll T_{\text{wait}}=20\mu \mathrm{s}\ll {\tau }_p=260\mu \mathrm{s}$ between the mw inversion pulse and the rf pulse is chosen to ensure that all antiparallel spin pairs have recombined, while the time interval of $20\mu \mathrm{s}$ between switching off the LED and the first mw pulse is chosen much longer than the fall time of the LED pulse. (b) Detection spin echoes with a resonant ($f_{\text{rf}}=6.036\mathrm{MHz}$) and an off-resonant rf pulse ($f_{\text{rf}}=7.036\mathrm{MHz}$) with the mw inversion pulse and the detection echo resonantly exciting the high-field ${}^{31}\mathrm{P}$ hyperfine transition [cf. Fig. 2] resulting in a single shot nuclear spin polarization of $p=60\%$. (c) Spin echo similar to (b), but with the detection echo on the high-field hyperfine transition and the inversion pulse on the low-field hyperfine transition resulting in $p=66\%$. (d) Detection spin echoes with resonant rf pulses on the ${}^{31}{\mathrm{P}}^0$ nuclear spin transitions (52.38 and 65.15 MHz) and without rf pulse with polarizations of 18% and 22%, respectively. (e) Exciting both ${}^{31}{\mathrm{P}}^0$ nuclear spin transitions, a polarization of 33% is achieved.

Figure 4

(a) Pulse sequence to measure the ${}^{31}\mathrm{P}$ nuclear spin relaxation time $T_{1}n$ for different illumination intensities $I_{\mathrm{LED}}$. (b) Polarization as a function of the optical excitation pulse length $T_{\mathrm{LED}}$ for different illumination intensities on a log-log scale (open symbols). For comparison, the data without a light pulse are shown as well (full diamonds). The nuclear spin relaxation time $T_{1n}$ as shown in (c) is determined by single exponential fits (solid lines) of the data in (b). The $I_{\mathrm{LED}}^{-1}$ dependence (dashed line) is a guide for the eye.