Optical Dynamic Nuclear Polarization of 13C Spins in Diamond at a Low Field with Multi-Tone Microwave Irradiation

Majority of dynamic nuclear polarization (DNP) experiments have been requiring helium cryogenics and strong magnetic fields for a high degree of nuclear polarization. In this work, we instead demonstrate an optical hyperpolarization of naturally abundant 13C nuclei in a diamond crystal at a low magnetic field and the room temperature. It exploits continuous laser irradiation for polarizing electronic spins of nitrogen vacancy centers and microwave irradiation for transferring the electronic polarization to 13C nuclear spins. We have studied the dependence of 13C polarization on laser and microwave powers. For the first time, a triplet structure corresponding to the 14N hyperfine splitting has been observed in the 13C polarization spectrum. By simultaneously exciting three microwave frequencies at the peaks of the triplet, we have achieved 13C bulk polarization of 0.113 %, leading to an enhancement of 90,000 over the thermal polarization at 17.6 mT. We believe that the multi-tone irradiation can be extended to further enhance the 13C polarization at a low magnetic field.

NV-based optical DNP can be performed without a cryogenic apparatus and in the presence of only tens of millitesla. Although the instrumentation may contain elevated magnetic fields, they are essential for the readout of induced nuclear polarizations. The magnetic field in the range of tens of millitesla is easily accessible, but not favorable for an efficient hyperpolarization. Both weak thermal nuclear polarization and short T 1 relaxation time [35] are disadvantageous. In addition, the positive and negative nuclear polarization spectra, being a part of solid-state DNP spectrum, are located in close proximity, separated by the order of nuclear resonance frequency [36]. Thus, the overlap of positive and negative nuclear polarizations often occurs and leads to a moderate net polarization. Nevertheless, the nuclear polarization spectrum, which reflects the weak 13 C Zeeman splitting, has not been observed in optical DNP studies of diamonds. If 13 C resonance frequency is less than 14 N hyperfine splitting (2.16 MHz) of NV electronic spin (Figure 1b), the nuclear polarization spectrum would be duplicated three times at intervals of 2.16 MHz. Such triplet structure has not been reported either. In the present study, we conduct NV-based optical DNP of bulk 13 C nuclear spins in diamond at a low field and the room temperature. This hyperpolarization method requires continuous laser and MW irradiations with optimized powers. The applied field for optical DNP is 17.6 mT, which corresponds to 13 C resonance frequency of approximately 0.2 MHz. After the hyperpolarization process, a diamond can be shuttled to a center of 6 T superconducting magnet for 13 C polarization readout by NMR spectrometer. In the 13 C nuclear polarization spectrum, we clearly observe the triplet structure revealing the 14 N hyperfine splitting. As anticipated, nitrogen nuclear spin does not participate in the polarization transfer process except for determining the resonance frequency of NV spins through the hyperfine interaction. Such independence can be utilized. Inspired by frequency comb [22], we apply triple microwave frequencies simultaneously and obtain a 13 C nuclear polarization of 0.113%, which is about 1.7 times as high as that with single MW frequency excitation.

Experimental Methods
HPHT-grown diamond crystal with natural abundance of 13 C nuclear spins is used in all measurements presented in this paper. NV centers, with a concentration of 1.25 ppm, are created in the diamond via electron irradiation and thermal annealing process.
We have developed a system which includes a low-field region (17.6 mT) for hyperpolarizing 13 C in diamonds by DNP, a high-field region (6 T) for all 13 C NMR readouts, and a rapid shuttling device for moving the diamond from one region to another in 2 s. From 13 C NMR signals at 6 T, enhancement factors and absolute polarization levels can be estimated. 13 C NMR acquisition and the timing controls are conducted with a commercial NMR console. (More detailed explanation in the Appendix C).

13 C Polarization Spectrum
The investigation of the 13 C polarization spectrum reveals us the triple structure ( Figure 2). Varying the frequency of MW irradiation for optical DNP allows us to record the 13 C NMR signal as represented by the blue lines. The green lines illustrate opticallydetected magnetic resonance (ODMR) lines of NV center, including the transitions of m s = 0 → m s = −1 ( Figure 2a) and m s = 0 → m s = +1 (Figure 2b). All these measurements are performed through NV centers of 111 orientation, which is parallel with the direction of magnetic field. Each data point is averaged by 10 measurements. After each NMR scan, a series of 90 pulses are applied to deplete residual 13 C polarization ensuring zero polarization for a next measurement. The triplet structures are clearly observed for both NV spin transitions. The 14 N (I = 1) nuclear spin of the NV center splits the NV spin levels each into three hyperfine sublevels with an energy splitting of 2.16 MHz, and this explains the triplet shown in Figure 2. Although ODMR does not exhibit the 14 N hyperfine splitting, it is clearly visible in the 13 C polarization spectra. Notably, the signs of the 13 C polarization are identical for both NV spin transitions. The results in Figure 2 are obtained at a magnetic field of 17.6 mT with a diamond containing natural abundance of 13 C nuclear spins. A similar measurement was performed in Ref. [19], where a magnetic field of 18 mT was applied. However, the 13 C polarization spectrum showed no triplet structure. Since a diamond of 10% enriched 13 C was used in Ref. [19], strong dipolar couplings between NV and proximate 13 C spins may dominate over the 14 N hyperfine interaction. In Ref. [25], a higher magnetic field of 473 mT was applied, corresponding to a 13 C resonance frequency of 5 MHz. In this case, the overlap of three spectra with a separation of 2.16 MHz could wipe the triplet structure, resulting in a single curve.

Optimal Microwave Power and Laser Power
An optimization of the MW power is important for improving 13 C polarization. Particularly at a low magnetic field, a strong MW excitation may not be a beneficial. As the separation between positive and negative peaks in the nuclear polarization spectrum is proportional to the nuclear Zeeman splitting [36], the strong MW that is on-resonant with one polarization can also induce the transition of the opposite polarization, which is off-resonant as illustrated in Figure 3a. Then, the opposite polarization will be imposed and eventually lead to a lower net nuclear polarization. Figure 3b shows the 13 C nuclear polarization as a function of MW power. The polarization rises initially but decays afterwards as the MW power increases. From the curve in Figure 3, we can determine the optimal MW power, which is near 10 W. The solid line is the fitted curve with two exponents for a guide to eyes. A similar result was reported in Ref. [19], where it was explained by a transition from selective regime to Λ regime when MW becomes stronger. An optimization of the laser power is also important for improving 13 C polarization. Figure 4a shows that the maximum 13 C polarization signal is obtained at a laser power density of 30 mW/mm 2 . After the maximum, the polarization gradually decreases as the laser power increases. Initially, we speculated that the 13 C polarization decrease is due to the rise of diamond's temperature. The temperature of the diamond crystal can be measured from the position of zero-field splitting. In the ODMR spectrum, the peak positions of the two transitions, m s = 0 → m s = −1 and m s = 0 → m s = +1, can be obtained. Then, their mean leads to the temperature with an aid of the conversion factor, dD dT ∼ = −74 kHz/K [37].
As shown in Figure 4b, the temperature rise is linearly proportional to the laser power density. At the optimal near 30 mW/mm 2 , the diamond's temperature is raised above 100 • C. Because the thermal 13 C polarization is inversely proportional to temperature, one may attribute the decrease in Figure 4a to the laser-induced heating shown in Figure 4b. However, that the laser-induced heating alone is an insufficient to explain the 13 C polarization decrease. It's because the NV electronic spin polarization becomes higher with increasing the laser power (or power density). Figure 4c shows the fluorescence intensity from NV centers in the diamond. It increases proportionally to the laser power density. In contrast to Ref. [38], the reduction of the fluorescence when laser power is over a certain level is not observed. This indicates the laser-induced non-radiative process in optical cycle [38] is not activated. Thus, the average polarization of NV centers in the diamond increases linearly within the range of the laser power we apply. The enhancement factor should be proportional to the average NV spin polarization (P NV ). 13 C polarization (P Hyper ) obtained by the optical DNP, then, is determined by the NV spin polarization (P NV ) times the 13 C thermal polarization (P Thermal ) as P Hyper ∝ P NV · P Thermal . Given a pump laser density σ Laser , P NV and P Thermal can be expressed as follows in which α and β are the slopes of the curves in Figure 4b,c, respectively. (c is a constant from Curie's law of nuclear para-magnetism.) The resulting curve of P Hyper is shown in Figure 4d, which is certainly inconsistent with the result in Figure 4a. This discrepancy may indicate the existence of an additional 13 C depolarization process in the diamond. Possibly, this depolarization process is thermally activated by the laser-induced heating. And we have measured the nuclear spin-lattice relaxation rate has almost no influence on the decrease of 13 C polarization (More details in the Supplementary file).

13 C Hyperpolarization by Multi-Tone MW Frequencies
Since multiple peaks are observed in the 13 C polarization spectrum (Figure 2), using several MW sources, we can further enhance the 13 C polarization by simultaneous MW irradiations of the frequencies corresponding to those peaks. To estimate the 13 C polarization obtained through the optical DNP, we compare the 13 C NMR signal with that of thermal polarization at 6 T (300 K). A measurement of 13 C thermal polarization, for the diamond, requires at least 4 days, for a better signal-to-noise ratio (SNR), with 400 averages and 20 min interval between each scan. 13 C hyperpolarization, with triple MW irradiation, is performed by DNP through −1 state of NV − in Figure 2a. The diamond is exposed to the pump laser beam with a power density of 25 mW/mm 2 and the MW field with a power of 11 W, for 120 s. Figure 5 shows results of the multiple MW irradiation. The number of MW frequencies are increased from one (f 1 ) to three (f 1 , f 2 , f 3 ). The three MW frequencies are indicated by the arrows in Figure 2a.

Conclusions
We have demonstrated the optical DNP results obtained with a diamond crystal of natural abundance of 13 C nuclei at room temperature and a low magnetic field of 17.6 mT. A triplet structure in 13 C nuclear polarization spectrum has been observed, in which the splitting of 2.16 MHz attributes to 14 N hyperfine interaction in NV centers. We have reached 0.113% of bulk 13 C nuclear spin polarization. The optimal values of laser power density and MW power have been characterized. In addition, multi-tone MW excitation has been adopted. Simultaneous irradiation of three MW frequencies, matched to the peak frequencies in the 13 C nuclear spectrum, results in an improvement of 1.7 times. The number of microwave frequencies in the multi-tone irradiation scheme could be extended to further enhance the 13 C polarization at a low magnetic field.

Conflicts of Interest:
The authors declare no conflict of interest.
Sample Availability: Samples of the compounds are not available from the authors.

Appendix A. Diamond Sample
All the experimental results are measured from one industrial diamond (ElementSix) having a weight of 42 mg. It is synthesized by the high-pressure high-temperature method, which is, then, electron irradiated at 1 MeV and annealed at about 800 • C. The diamond contains about 50 ppm of P 1 centers, 1.25 ppm of NV centers, and the natural abundance of 13 C. The spin concentrations in the diamond are estimated by performing electron spin resonance (ESR). The peak intensities in ESR spectra are compared to that from a diamond crystal having a known P 1 concentration. The diamond is 111 surface-oriented.

Appendix B. Estimation of 13 C Nuclear Polarization and Enhancement Factor
The hyperpolarization of 13 C in the diamond is conducted at B EM = 17.6 mT. The thermal polarization of the same diamond is obtained at B SM = 6 T. The thermal polarization (P Thermal ) is used for estimating the 13 C polarization (P Hyper ): where S Hyper is the integral of FT signal from a hyperpolarized 13 C nuclei in the diamond. S Thermal is the integral of FT signal measured from thermally polarized 13 C nuclei in the diamond. T R is the room temperature. The enhancement factor (ε) is about 90,000 over in situ thermal equilibrium polarization and can be estimated as follows: where T L is diamond's temperature under laser irradiation during DNP process (Figure 4b).

Appendix C. Experimental Setup
Our experimental setup is a sophisticated system capable of hyperpolarizing 13 C in diamonds using DNP method and reading out polarizations by NMR method. This section thoroughly describes the experimental setup ( Figure A1) and a purpose of each hardware. The magnetic field of a superconducting magnet (OXFORD) is used for all NMR readouts. It has a diameter of 70 cm and a height of 97 cm. The magnet produces a homogeneous magnetic field of about 6 T in its central region. There is a cylindrical cavity with a diameter of about 5.2 cm in the center of magnet through its entire height. A handmade saddle coil is installed inside the cavity in homogeneous region for detecting polarization signals from samples. The coil is connected to a NMR probe ( Figure A1), which is LC circuit made of parallel and serial connected variable capacitors. By manipulating the capacitors, we can match the impedance and set a required resonance frequency for the saddle coil (∼64.237 MHz for 13 C). The probe is subsequently connected to an activetranscoupler and to a commercial spectrometer LapNMR from Tecmag. The purpose of transcoupler is to manage switching between transmitted signals from the spectrometer and received NMR signals from the saddle coil. The spectrometer is controlled by TNMR software, which allows us to set all required parameters for generating proper RF signals and acquire NMR signals. Transmitted RF signals, from LapNMR, are increased by CPC 9T100M power amplifier. NMR signals, captured by the saddle coil, are increased by two +35 dB amplifiers from the NMR service.

Appendix C.2. MW Hardware
One of the aspects in successful hyperpolarization of 13 C in a diamond is the application of MW field with enough power. In our experiments, MW signals are produced by APSIN12G and amplified by Sungsan TS2458BBP0 with a maximum power output of 50 W. A handmade Helmholtz coil, with a diameter of 13 mm, is used to generate MW fields ( Figure A1). A circulator (PE83CR1004) with a 50 W termination is used to protect the amplifier from reflected MW power. The MW coil is installed inside of an electrical Helmholtz magnet ( Figure A1), which is powered by a high precision DC power supply (KEITHLEY 2280S-32-6). The electrical magnet is installed right below the superconducting magnet and used for optical DNP. It provides a decent homogeneity and an easy access to variable magnetic fields.

Appendix C.3. Optical Configuration
Our laser produces vertically polarized 532 nm green light with a maximum power output of 4 W and a beam diameter of 2 mm. The delivery of the laser light to diamonds is performed by two separated optical setups ( Figure A2). The left setup locates inside a shielding box, where we perform optical DNP on the diamonds. The box shields ambient magnetic fields. The right setup locates outside of the shielding box and includes three mirrors, an isolator and the laser itself. The isolator is used to protect from reflected lights and to increase the beam size to a diameter of 5 mm matching the diamond's size. The long pass filter is used to exclude lights except the red light emitting by the diamond. The lens, with focal length of 25.4 mm, guides the emitted fluorescence, from diamonds, to a photodetector with a diameter of about 2 mm.

Appendix D. Experimental Procedure
Before each DNP experiment, ODMR measurement is performed at a specific magnetic field. The diamond is irradiated with a wide range of MW sweep (up to 1.5 GHz) and with 532 nm laser light. An emitted red light from a diamond is then captured by a photodetector. A data from the detector can be seen on a computer using a Labview program, where we can define exact MW frequencies corresponding to the states and estimate a magnetic field.
All DNP experiments, in this work, are performed at the magnetic field of about 17.6 mT, aligned with the one of four NV center's orientations in diamond crystals. 13 C nuclear spins, in the diamond, are hyperpolarized for over 100 s with continuous MW and laser (532 nm) irradiations. After 13 C nuclei are hyperpolarized, the diamond is shuttled 80 cm within 2 s, by a high-precision motion controller Newport XPS-RL, into the superconducting magnet, where the polarization is detected by the saddle coil. Then, the 13 C NMR signal at the resonance frequency of 64.237 MHz is transmitted to LapNMR console. Single NMR acquisition takes 5 ms and then the diamond is sent back to the low-field region within 2 s for repetitions. For a better SNR, the hyperpolarized 13 C NMR signal is typically averaged 10 times. For multi-tone MW excitation, three MW frequencies are synthesized by three separate sources and then combined into the MW coil.