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\title{\hspace{5cm} SUPPLEMENTARY
	\newline {Achieving 5\% $^{13}$C nuclear spin hyperpolarization in high-purity diamond at room temperature and low magnetic field}}

\author[1]{Vladimir V. Kavtanyuk}
\author[2,3]{Changjae Lee}
\author[3,*]{Keunhong Jeong}
\author[1,4,*]{Jeong Hyun Shim}
\affil[1]{Quantum Magnetic Sensing Group, Korea Research Institute of Standards and Science, Daejeon 34113, Republic of Korea}
\affil[2]{School of Biomedical Engineering, Korea University, Seoul 02842, Republic of Korea}
\affil[3]{Department of Chemistry, Korea Military Academy, Seoul 01805, Republic of Korea}
\affil[4]{Department of Applied Measurement, University of Science and Technology, Daejeon 34113, Republic of Korea}
\affil[*]{jhshim@kriss.re.kr, doas1mind@kma.ac.kr}

\begin{abstract}
Optically polarizable nitrogen-vacancy (NV) centers in diamond enable hyperpolarization of $^{13}$C nuclear spins at a low magnetic field and room temperature. However, it remains a challenge to achieve a high level of polarization, comparable to that of conventional dynamic nuclear polarization. In this paper, we demonstrate that a $^{13}$C polarization of 5\% can be attained at less than 10 mT, equivalent to an enhancement ratio of over $7 \times 10^6$. We used a high-purity diamond with an initial nitrogen concentration below 1 ppm, resulting in a storage time exceeding 100 minutes. Aligning the magnetic field along [100] increased the number of NV spins involved in polarization transfer by a factor of four. For this field orientation, a comprehensive optimization of the field intensity and microwave (MW) frequency-sweep parameters has been performed. The optimum MW sweep width suggests that polarization transfer occurs primarily to the bulk $^{13}$C spins through the integrated solid effect, followed by nuclear spin diffusion.
\end{abstract}

	\date{\today}
	
	
\begin{document}
	

	
	\maketitle
	
	\section{$\langle 100 \rangle$ and $\langle 111 \rangle$ diamond orientations}
	
	The current DNP method, which hinges on MW sweeping, is predominantly applied to diamond powders characterized by random NV$^-$ orientations. In contrast, our study employs this technique for $\langle 100 \rangle$ surface-oriented diamonds polarizing NV$^-$ in the four orientations of diamond's lattice. When multiple orientations are present, an optimal magnetic field emerges for polarizing $^{13}$C. A comparison of $^{13}$C polarization patterns between the single aligned $\langle 111 \rangle$ and four $\langle 100 \rangle$ diamond orientations is depicted in Figure~\ref{100vs111}. For the aligned $\langle 111 \rangle$ orientation, the observed linear dependence aligns with expectations. Notably, for the $\langle 100 \rangle$ orientation, an optimal magnetic field is observed in proximity to 9.4 mT. This value is slightly variable based on the alignment of the magnetic field with the four NV$^-$ axes and also depends on the concentrations of impurities in a diamond. Our current setup lacks an accurate alignment system for the magnetic field direction, thus we are unable to ascertain the exact dependence pattern. Note that Figure~\ref{100vs111} does not illustrate the actual difference between $^{13}$C polarizations of $\langle 100 \rangle$ and $\langle 111 \rangle$ values, as different diamonds are employed for each measurement.
	
	\begin{figure}[h!]
		\includegraphics[width=\columnwidth]{FIGS/100vs111.pdf}
		\caption{The red data points represent $^{13}$C polarization pattern depending on magnetic field for the diamond aligned with $\langle 100 \rangle$ orientation for the -1 state. The blue data points represent $^{13}$C polarization pattern depending on magnetic field for the diamond set to a single $\langle 111 \rangle$ aligned orientation for the -1 state.
			\label{100vs111}}
	\end{figure}
	
	\section{Different sweep rates}
	
	We have conducted MW power - magnetic field dependence measurements using MW sweep rates of 2 and 15 MHz/ms (Fig.~\ref{mwratesvspower}). Notably, the optimal magnetic field is determined as 9.4 mT across all three sweep rates (the third rate is 10 MHz/ms described in the main text). However, it is imperative to underscore that the observed patterns exhibit notable differences among these sweep rates. An observation emerges from our results, showcasing that varying the MW sweep rate exerts an influence on the optimal MW power. Importantly, it should be noted that these MW powers are not entirely delivered to the MW coil owing to an impedance mismatch with our hardware system, leading to a significant portion of the power being reflected. These measurements are carried out through the excitation of the $-$1 state of NV$^-$, utilizing a MW range of 100 MHz.
	
	\begin{figure}[h!]
		\centering
		\includegraphics[width=\columnwidth]{FIGS/mwratesvspower.pdf}
		\caption{$^{13}$C polarization vs MW power at different magnetic fields for MW sweep rate: (a) 2 MHz/ms and (b) 15 MHz/ms.
			\label{mwratesvspower}}
	\end{figure}
	
	\section{Laser power}
	
	The optimal laser power density has been determined to be in the range of 30-60 mW/mm$^2$, corresponding to 1.1-2.3 W of laser power, as depicted in Figure~\ref{laser}(a). In our previous publication \cite{molecules27051700}, we also presented the dependence of $^{13}$C polarization on laser power for a different diamond. While the overall pattern is similar, the optimal value varies due to distinct diamond properties. Initially, we observe a growth in $^{13}$C polarization with increasing laser power. Once the polarization reaches its maximum value over a certain laser power range, a subsequent decline becomes apparent. This pattern can be explained as follows: when applying higher laser power, the electronic polarization of NV centers within the diamond increases, subsequently enhancing the transfer of this polarization to $^{13}$C nuclear spins. However, various factors can decrease DNP efficiency. A significant factor is the loss of $^{13}$C polarization due to heating of the diamond caused by laser irradiation. Additionally, laser polarization can break the coherence of the NV$^-$ to $^{13}$C polarization transfer by repumping the NV centers \cite{Ajoy2018}.
	
	\begin{figure}[h!]
		\centering
		\includegraphics[width=\columnwidth]{FIGS/laser.pdf}
		\caption{$^{13}$C polarization vs (a) laser power density; (b) MW power at different laser powers.}
		\label{laser}
	\end{figure}
	
	We also examined the relationship between $^{13}$C polarization and MW power at different laser power settings (Figure~\ref{laser}(b)). For laser power densities exceeding 30 mW/mm$^2$, the optimal microwave power remains fairly consistent. However, at laser power densities below 30 mW/mm$^2$, the optimal MW power exhibits a slight reduction. These measurements are carried out through the excitation of the $-$1 state of NV$^-$, utilizing a MW rate of 15 MHz/ms.
	
	\section{Polarization loss due to diamond lifting time}
	
	Following the polarization of the diamond, the subsequent step involves elevating it to a high magnetic field region (6 T) utilizing a superconducting magnet for NMR readout. This elevation is accomplished within a time frame of 1.5 seconds. Gauging the extent of polarization loss during this lifting process is crucial. To this end, we undertook measurements to quantify the $^{13}$C polarization loss by extending the lifting duration (Figure~\ref{lift}). Our measurement indicates that the incurred polarization loss during the 1.5 seconds of lift time is negligible (below 1\%).
	
	\begin{figure}[h!]
		\includegraphics[width=\columnwidth]{FIGS/lift.pdf}
		\caption{Polarization loss of $^{13}$C in the diamond during the lifting from low (9.4 mT) to high (6 T) magnetic field regions. The red line represents exponential fitting with a characteristic folding time of approximately 60 seconds.}
		\label{lift}
	\end{figure}
	
	
	
\section{Polarization combination}

In our pursuit of further enhancing \textsuperscript{13}C polarization, we investigated the feasibility of combining \textsuperscript{13}C polarization achieved through microwave (MW) sweeping of the $-$1 and $+$1 states simultaneously. These measurements are conducted utilizing optimal dynamic nuclear polarization (DNP) parameters under a magnetic field of 9.4 mT, and the corresponding optically detected magnetic resonance (ODMR) data is depicted in Figure~\ref{combination}. The outcomes of the polarization combination experiments are presented in Figure~\ref{combination}. The blue line within the graph represents the \textsuperscript{13}C polarization signal obtained through MW excitation of the $-$1 state of NV$^-$, while the red line portrays the polarization achieved from the $+$1 state. Notably, the green line denotes the combined polarization resulting from simultaneous MW excitation of both states using distinct MW sources. Upon examination of the graph, it is evident that the improvement achieved through this polarization combination is marginal.

\begin{figure}[h!]
	\centering
	\includegraphics[width=\columnwidth]{FIGS/combination.pdf}
	\caption{(a) ODMR of \textless100\textgreater diamond measured at 9.4 mT; (b) FT of \textsuperscript{13}C polarization signals obtained by MW sweeping: $-$1 (blue line); $+$1 (red line), and both states simultaneously (green line).}
	\label{combination}
\end{figure}

\section{Electron spin resonance}

The electron spin resonance (ESR) technique can be used to determine the concentration of defects in diamonds. Figure~\ref{b1esr} illustrates the ESR signal for our pure diamond, DNV-B1, sourced from Element6. Based on the ESR data and comparison with a well-known sample in our lab, we have estimated the P$_1$ concentration to be approximately 0.2 parts per million (ppm). Additionally, the levels of other impurities are similarly low, around 0.2 ppm. The NV concentration information of 0.3 ppm is provided by Element6.

\begin{figure}[h!]
	\centering
	\includegraphics[width=\columnwidth]{FIGS/b1esr.pdf}
	\caption{The ESR of a DNV-B1 diamond, aligned with the \textless100\textgreater direction, which is parallel to the direction of the magnetic field.}
	\label{b1esr}
\end{figure}

\section{Diamond temperature}

As previously noted, during the dynamic nuclear polarization measurements, no cooling is applied to the diamond sample. Consequently, exposure to high-power laser light induces heating of the diamond. We quantified the temperature of the diamond as a function of the applied laser power, as illustrated in Figure~\ref{dtemp}. Temperature measurements are obtained using optically detected magnetic resonance, allowing for precise determination of frequencies for the -1 and +1 states of NV (Figure~\ref{combination}(a)). By measuring the frequency shift of the states from the initial values at room temperature, we can determine the temperature of the diamond using the conversion factor $\frac{dD}{dT} \cong - 74$~kHz/K \cite{Acosta2010}.

\begin{figure}[h!]
	\centering
	\includegraphics[width=\columnwidth]{FIGS/dtemp.pdf}
	\caption{Temperature of the diamond as a function of laser power.}
	\label{dtemp}
\end{figure}

\newpage

\bibliographystyle{naturemag}
\bibliography{sup-references}

\begin{thebibliography}{99}
	
	\bibitem{Kavtanyuk2022}
	Vladimir V. Kavtanyuk, Hyun Joon Lee, Sangwon Oh, Keunhong Jeong, Jeong Hyun Shim,
	\textit{Optical dynamic nuclear polarization of \textsuperscript{13}C spins in diamond at a low field with multi-tone microwave irradiation},
	Molecules \textbf{27}, 1700 (2022), doi:10.3390/molecules27051700, \url{https://www.mdpi.com/1420-3049/27/5/1700}.
	
	\bibitem{Ajoy2018}
	Ajoy, A., Liu, K., Nazaryan, R., Lv, X., Zangara, P. R., Safvati, B., Wang, G., Arnold, D., Li, G., Lin, A., Raghavan, P., Druga, E., Dhomkar, S., Pagliero, D., Reimer, J. A., Suter, D., Meriles, C. A., Pines, A.,
	\textit{Orientation-independent room temperature optical \textsuperscript{13}C hyperpolarization in powdered diamond},
	Science Advances \textbf{4}, eaar5492 (2018).
	
	\bibitem{Acosta2010}
	Acosta, V. M., Bauch, E., Ledbetter, M. P., Waxman, A., Bouchard, L.-S., Budker, D.,
	\textit{Temperature dependence of the zero-field splitting of the nitrogen-vacancy center in diamond},
	Physical Review Letters \textbf{104}, 070801 (2010), doi:10.1103/PhysRevLett.104.070801, \url{https://link.aps.org/doi/10.1103/PhysRevLett.104.070801}.
	
\end{thebibliography}

\end{document}