# Large Room Temperature Bulk DNP of 13C via P1 Centers in Diamond

Daphna Shimon<EMAIL_ADDRESS>Institute of Chemistry, The
Hebrew University of Jerusalem, Edmond J. Safra, Givat Ram, Jerusalem, Israel.
Kelly A. Cantwell  Department of Physics and Astronomy, Dartmouth College,
Hanover, NH 03755, U.S.A.  Linta Joseph  Department of Physics and Astronomy,
Dartmouth College, Hanover, NH 03755, U.S.A.  Ethan Q. Williams  Department of
Physics and Astronomy, Dartmouth College, Hanover, NH 03755, U.S.A.  Zaili
Peng  Department of Chemistry, University of Southern California, Los Angeles,
California 90089, U.S.A.  Susumu Takahashi  Department of Chemistry,
University of Southern California, Los Angeles, California 90089, U.S.A.
Department of Physics and Astronomy, University of Southern California, Los
Angeles, California 90089, USA  Chandrasekhar Ramanathan
<EMAIL_ADDRESS>Department of Physics and Astronomy,
Dartmouth College, Hanover, NH 03755, U.S.A.

###### Abstract

We use microwave-induced dynamic nuclear polarization (DNP) of the
substitutional nitrogen defects (P1 centers) in diamond to hyperpolarize bulk
13C nuclei in both single crystal and powder samples at room temperature at
3.34 T. The large ($>100$-fold) enhancements demonstrated correspond to a
greater than 10,000 fold improvement in terms of signal averaging of the 1%
abundant 13C spins. The DNP was performed using low-power solid state sources
under static (non-spinning) conditions. The DNP spectrum (DNP enhancement as a
function of microwave frequency) of diamond powder shows features that broadly
correlate with the EPR spectrum. A well-defined negative Overhauser peak and
two solid effect peaks are observed for the central ($m_{I}=0$) manifold of
the 14N spins. Previous low temperature measurements in diamond had measured a
positive Overhauser enhancement in this manifold. Frequency-chirped
millimeter-wave excitation of the electron spins is seen to significantly
improve the enhancements for the two outer nuclear spin manifolds ($m_{I}=\pm
1$) and to blur some of the sharper features associated with the central
manifolds. The outer lines are best fit using a combination of the cross
effect and a truncated cross effect – which is known to mimic features of an
Overhauser effect. Similar features are also observed in experiments on single
crystal samples. The observation of all of these mechanisms in a single
material system under the same experimental conditions is likely due to the
significant heterogeneity of the high pressure, high temperature (HPHT) type
Ib diamond samples used. Large room temperature DNP enhancements at fields
above a few Tesla enable spectroscopic studies with better chemical shift
resolution under ambient conditions.

##  I Introduction

Nuclear magnetic resonance (NMR) spectroscopy shows exquisite chemical
sensitivity when reporting on the local magnetic environments of the spins at
atomic scales. However, it’s low detection sensitivity has long required the
use of relatively large sample volumes. Microwave-induced dynamic nuclear
polarization (DNP), a technique to produce large nuclear spin signal
enhancements via polarization transfer from electrons [1, 2, 3, 4], is driving
a technological revolution by enabling NMR and magnetic resonance imaging
(MRI) studies of low abundance, low-gamma spins and nuclei at surfaces and
interfaces for the first time [5, 6].

The electron-nuclear polarization transfer step in most DNP experiments is
typically performed at cryogenic temperatures in order to reduce the electron
spin-lattice relaxation rates below the strength of the hyperfine
interactions. This is true for both dissolution DNP, which is increasingly
being used to study room-temperature phenomena in biomedical systems [7], as
well as for high-field magic-angle sample spinning (MAS) DNP which has enabled
high-sensitivity, high-resolution NMR studies of chemistry in sample-limited
solid systems [5]. Large room temperature DNP enhancements at high field would
enable high-resolution NMR spectroscopic studies under ambient conditions.

The nitrogen-vacancy (NV) center in diamond is a promising electron spin
system for room temperature DNP applications at low field because of its long
coherence and relaxation times [8, 9, 10, 11, 12]. The electron spin of the NV
center can be optically polarized to near unity polarization at room
temperature. NV centers can also be detected (even at the single spin level)
and coherently manipulated using optically-detected magnetic resonance (ODMR).
In addition to hyperpolarizing the 13C spins locally around a single NV center
[13, 14, 15], the hyperpolarization of bulk samples via ensembles of NV
centers has been demonstrated, both at low field [16, 17, 18] and at high
magnetic fields [19, 20, 21]. However, at high magnetic fields, the magnitude
and sign of the 13C hyperpolarization were seen to depend strongly on the
orientation of the diamond crystal [21] making it difficult to hyperpolarize
bulk powders. Nanodiamonds are chemically stable and their surfaces can be
chemically functionalized, making them excellent candidates as local NMR
probes [22, 23] – similar to silicon particles [24, 25, 26, 27] – as well as
fluorescent biomarkers [9]. A key challenge to the practical use of DNP via
defects in diamond is the need to achieve high polarizations outside the
diamond surface. While the hyperpolarization of spins on the surface of
diamond samples has been demonstrated at low magnetic fields [28, 29, 30, 31],
the transfer of polarization to external spins remains challenging. Relaxation
due to surface defects and slow spin diffusion in natural abundance 13C
samples have so far been the key limiting factors to achieving high
polarizations.

In this work we study microwave-induced DNP of diamond at room temperature at
3.34 T under static (non-spinning) conditions. The P1 center is a spin-1/2
substitutional nitrogen impurity in the diamond lattice that also exhibits
long coherence and relaxation times [32, 33, 34], though it is not optically
active. There are typically at least an order of magnitude more P1 centers in
a diamond crystal than NV centers [34], though the best efficiencies for
converting P1 to NV centers can reach up to 20-25% [35, 36]. As a consequence,
most 13C nuclear spins in diamond are much closer to a P1 center than an NV
center, making the P1s potentially more efficient polarization sources. At
high magnetic fields, DNP via P1 centers can produce a significant increase in
nuclear spin polarization at cryogenic temperatures [37, 38, 32, 39, 40, 41].
Bretschneider et al. have also reported a room temperature 13C DNP enhancement
of 130 at 9.4 T under 8 kHz MAS conditions with 10 W of microwave power at 263
GHz [40]. Other high-field room temperature enhancements have also been
reported [42]. Hyperpolarization via P1 centers is also well suited to
applications when optical access is not possible. Here, we show a greater than
100-fold enhancement of the 13C spins in both single crystal and powder
diamond samples. In contrast to earlier work, these enhancements were achieved
using a solid-state source with about 240 mW of power. The DNP spectrum
exhibits multiple features indicating that several different DNP mechanisms
are operational in these systems. We elucidate the different physical
mechanisms and explain their role in both single crystal and powder samples of
diamond. Understanding these mechanisms could guide the design of more
effective hyperpolarization strategies and the improved design of diamond
substrates for polarizing external spins.

Figure 1: The 13C NMR spectrum of the diamond powder, with MW irradiation
(black line) at 93.696 GHz and without MW irradiation (blue line), resulting
in DNP enhancement of 75. With the chirped excitation the enhancement is seen
to rise to 114 (red line). The signal was recorded after a recycle delay of
3000 s for the thermal signal, and after 3000 s of MW irradiation for the DNP
and chirp DNP signals. Triangular ramp-up modulation was used with a 5 kHz
modulation frequency and a 117 MHz modulation amplitude. The pulse sequence
used to record the NMR spectra is shown in the inset, with $\Delta$ being the
delay in the saturation pulse train and $t_{\mu\text{wave}}$ the DNP build-up
time. The model of the diamond lattice shown in the figure was created using
VESTA [43].

The paper is organized as follows: Our main experimental results on the powder
sample are described in Section II, followed by a brief overview of relevant
DNP mechanisms in Section III. We discuss the fit of these mechanisms to the
observed DNP spectra in both the single crystal and powder samples in Section
IV, discuss how sample heterogeneity gives rise to the different mechanisms in
Section V, and conclude in Section VI.

Figure 2:  (a) The high-field EPR spectrum of the diamond powder, and the best
fit according to EasySpin. The simulation of the experimental EPR line used a
0.19 mT Lorentzian line broadening. (b) The 13C DNP spectrum of the diamond
powder: enhancement measured as a function of constant frequency MW (black
symbols) and chirped frequency MW irradiation (red symbols) with 240 mW power;
and constant frequency MW at 500 mw power (green symbols). The figure also
shows simulated EPR spectrum under the experimental conditions (dashed magenta
line). The simulation of the expected EPR line at 94 GHz used a 6 MHz line
broadening. Error bars are not shown (the $\sim$ 10 % errors in enhancement
are dominated by the SNR of the thermal signal).

##  II Using P1 Centers for DNP at Room Temperature

Our experiments were performed at room temperature at 3.34 T, where the 13C
Larmor frequency is 35.8 MHz. Figure 1 shows the thermal equilibrium 13C
signal from a bulk diamond powder sample (Element 6) after 128 averages with a
recycle delay of 3000 s. The The signal was acquired using the pulse sequence
shown in the inset of Figure 1. The type Ib diamond is made by high pressure,
high temperature (HPHT) synthesis. The diamond microparticles are 15–25 $\mu$m
in diameter and are specified to have a nitrogen concentration less than 200
ppm (Element 6 estimated the actual values were about 110-130 ppm).

The figure also shows the single shot DNP signal with the same 3000 s build-up
time under constant frequency irradiation and chirped millimeter-wave (MW)
irradiation centered around the frequency of 93.696 GHz. At this MW excitation
frequency the constant frequency DNP excitation resulted in a DNP enhancement
of $75\pm 8$ and the chirped excitation results in a DNP enhancement of
$114\pm 11$. The chirped excitation used a triangular ramp-up function with a
5 kHz modulation frequency and a 117 MHz modulation amplitude. The maximum
output power of our MW source is about 240 mW (see Materials and Methods -
Section VI.C).

All NMR spectra show a single peak at 37$\pm$1 ppm, which matches the
literature value for 13C nuclei in diamonds [32] (see Figure 1). The NMR peak
has a width of 1.12 kHz showing significant inhomogeneous line-broadening. It
is possible to detect several hundred echoes in a pulsed spin-lock experiment
as described in the Section I of the Supplementary Information (SI).
Stroboscopic detection of multiple echoes would significantly improve the
signal-to-noise ration (SNR).

Figure 2(a) shows the experimentally measured continuous-wave (CW) EPR
spectrum of the sample measured at room temperature using the 230 GHz EPR
system at the University of Southern California [44, 45]. The EPR spectrum
features three lines, consisting of a single electron split by the hyperfine
coupling to the spin-1 14N nucleus of the P1 center. The anisotropic hyperfine
interaction results in a powder broadening of the $m_{I}=\pm 1$ manifolds. The
figure also shows an EasySpin [46] quantum mechanical simulation of the
spectrum for this sample overlaid on the experimental spectrum. Each P1 center
was modeled as an e-14N system, with an isotropic g-factor, g=2.0024,
hyperfine coupling strengths with the 14N nucleus with principal axis
components $A_{x}^{N}=A_{y}^{N}=82$ MHz, $A_{z}^{N}$ = 114 MHz [47] (see
Section III of the SI). The 14N nuclear quadrupolar interaction was neglected.

Figure 2(b) shows the DNP spectrum (DNP enhancement as a function of
millimeter wave frequency) for 13C obtained with a build-up time of 3000 s
under three different experimental conditions. These include (i) constant
frequency MW excitation with $\sim 240$ mW power; (ii) frequency-chirped MW
excitation with $\sim 240$ mW power using the same triangular ramp-up function
described above; and (iii) constant frequency MW excitation with $\sim 500$ mW
power. The higher power sweep was obtained by using the attenuated output of
the 240 mW source to injection-lock an impatt diode source. Additional details
are provided in the Supplementary Information. The figure also shows the
simulated EPR spectrum at 3.34 T using the same sample parameters used to fit
the high-field spectra – see Section III of the SI for details. The estimated
uncertainty in the enhancement is about 10%, which is dominated by the
standard deviation of the thermal signal.

##  III DNP Mechanisms

While the DNP spectrum in Figure 2(b) is seen to broadly correlate with the
EPR spectrum, it is not immediately possible to identify the underlying DNP
mechanism(s). Here we outline the different DNP mechanisms that could play a
role. Most solid systems studied by DNP typically exhibit hyperpolarization
via one of five mechanisms [48, 49, 1, 2]. Figure 3 schematically illustrates
the first four mechanisms. In broad EPR lines, positive and negative
enhancement from the same mechanism and different mechanisms often overlap
[50, 51, 3]. Additional smaller DNP features have also been observed due to
the higher-order multi-spin processes [52].

####  III.0.1 Overhauser Effect (OE)

The OE is typically observed in metals and liquids, systems in which the
hyperfine interactions are strongly modulated in time. It has been shown,
however, that the OE can also be observed in dielectric systems with strong
localized exchange interactions [53], and in mixed-valence organic radicals
such as BDPA [54, 55, 56, 57]. Fluctuations of the hyperfine interaction
result in electron-nuclear (e-n) cross-relaxation at the double quantum (DQ:
$\omega_{e}-\omega_{n}$) or zero quantum (ZQ: $\omega_{e}+\omega_{n}$) e-n
transitions, with characteristic decay times T1DQ and T1ZQ, respectively [54,
55, 56]. When irradiating directly on the electron single quantum (SQ)
transitions, an imbalance between T1DQ and T1ZQ results in nuclear
enhancement, with positive enhancement when T1DQ $>$ T1ZQ and negative
enhancement when T1DQ $<$ T1ZQ.

####  III.0.2 Solid Effect (SE)

The SE is typically observed in isolated electron-nuclear spin systems in
insulators where anisotropic hyperfine interactions admix the nuclear spin
states. MW irradiation of the nominally “forbidden” DQ (positive enhancement)
and ZQ (negative enhancement) transitions leads to the enhancement of the
nuclear spin polarization [48, 49, 1]. If the ESR line is inhomogeneously
broadened, frequency or field modulation can produce an integrated solid
effect where the enhancements of the DQ and ZQ become additive under the
appropriate modulation conditions [58].

####  III.0.3 Cross Effect (CE)

At higher electron spin concentrations, the three-spin (two electrons + one
nucleus) CE process results from microwave irradiation of an inhomogeneously
broadened EPR line [48, 49]. The CE-DNP mechanism results in nuclear
hyperpolarization when two electrons fulfill the so called CE condition
($\omega_{e1}-\omega_{e2}=\omega_{n}$ for $\omega_{e1}>\omega_{e2}$) and have
unequal polarizations (usually due to irradiation of one of the electrons) [2,
59].

####  III.0.4 Truncated Cross Effect (tCE)

Recently, Equbal et al. observed that it is possible for the CE to masquerade
as an OE when the CE condition is satisfied by two pools of electrons, one
with a very fast T1e relaxation and the other with much slower T1e relaxation
[60]. When this happens, irradiating on the electrons that exhibit slow
relaxation results in nuclear enhancement, due to the saturation of these
electrons, and the formation of a polarization difference between the two
pools of electrons. However, irradiating on the electrons that exhibit fast
relaxation does not result in nuclear enhancement, because the electrons in
the fast relaxing pool cannot be saturated. As a result, only positive or
negative enhancement will be observed (depending on the MW frequencies of the
fast and slow electrons), and the CE will appear truncated. For this truncated
CE, the DNP enhancement is directly observed at the EPR frequency of the
electron pool with the slow relaxation.

####  III.0.5 Thermal Mixing (TM)

Finally, TM is a statistical thermodynamics description for many coupled
electron spins, and requires MW irradiation directly on a homogeneously
broadened EPR line [48, 49]. Note that TM is not expected to be significant at
the concentration of P1 centers present in this sample.

Figure 3: Schematic DNP enhancement spectra showing the positions of the SE-
DNP (e-n system), OE-DNP (e-n system), CE-DNP (e-e-n system) and truncated CE-
DNP (e-e-n system) mechanisms with respect to the EPR transitions in each
system. The DQ and ZQ transition labels represent a nucleus with a positive
gyromagnetic ratio, and an electron with a negative gyromagnetic ratio.

##  IV Analysis of the DNP Spectra

###  IV.1 Single Crystal

In order to better understand the underlying mechanisms we first attempted to
fit the DNP spectrum obtained from a single HPHT Type Ib sample (Element 6)
specified with a nominal nitrogen concentration $<200$ ppm. Fitting the single
crystal data should be simpler as we do not observe the effects of powder
averaging of the anisotropic nitrogen hyperfine interactions. We were unable
to measure a thermal NMR signal in the single crystal sample even with
extensive averaging. We estimate a lower bound to the maximum enhancement of
about 180 determined by the signal-to-noise of the DNP signal (see Section II
of the SI).

Fig. 4 shows the DNP spectrum obtained from the single crystal sample. The
spectrum shows well-resolved peaks in the $m_{I}=\pm 1$ manifold of the
nitrogen spins which allows us to easily simulate the expected ESR spectrum at
this crystal orientation. The additional electron of the P1 center lies along
one of the four equivalent C-N bonds due to the Jahn-Teller distortion. The
EPR spectrum of a single diamond crystal can show between 3 and 7 distinct
peaks, depending on the orientation of the crystal with respect to the
external field.

Figure 4: Fit of experimental constant-frequency DNP spectrum (black circles)
for a single-crystal diamond sample. The fit uses a sum (green line) of the OE
(red line), SE (magenta line), the truncated CE (blue line), and the CE (black
line). The EPR line plotted above includes line broadening of 10 MHz of the
outer EPR lines. The single crystal EPR line was simulated with EasySpin using
the Euler angles $\alpha=54.0013^{\circ}$, $\beta=134.4274^{\circ}$,
$\gamma=18.0023^{\circ}$.

In Fig. 4, we have fit the DNP spectrum using a very crude method of
convolving the EPR line with delta functions to form the basic shapes for the
SE, CE and tCE/OE DNP mechanisms, and adjusting their amplitudes to achieve
the best agreement with the experimental spectrum [61]. The shapes were
constructed for each EPR line separately, and then the relative amplitudes
were adjusted. For a detailed description of this method see Section IV of the
SI.

In the central nuclear spin manifold ($m_{I}=0$), the sharp features
correspond to an OE peak at 93.81 GHz and SE peaks (at the 13C nuclear side-
band frequencies) at 93.78 and 93.85 GHz [48, 49]. The origin of the temporal
modulation that drives OE enhancement is still not clear. One potential source
is the dynamic Jahn-Teller distortion. Early ENDOR studies suggested a
reorientation rate less than 3.5 GHz at room temperature [62]. Ammerlaan and
Bergmeister studied the reorientation rate of the P1 defect due to thermal
excitation and tunneling in the temperature regime between 78 K and 200 K [63]
while Loubser and van Ryneveld studied the rate between 600 and 1230 K [64].
Interpolating between these sets of experimental results suggests a
characteristic reorientation rate on the order of 1–10 Hz at 300 K. This is
likely to be too low to drive the observed Overhauser effect as it is
necessary to have temporal modulations at the 13C Larmor frequency to induce
an OE. Another possibility is that the OE is induced by exchange or dipolar-
coupled clusters of P1 centers [65, 53].

The outer lines are best fit using the OE or truncated CE. If it is in fact
the OE, the experimental spectrum necessitates that the OE on the low
frequency side be positive, while the OE on the high frequency side be
negative. To our knowledge, this type of effect has never been reported
previously, and the origin of the difference in sign is unclear. Therefore, we
also suggest that we may be in fact observing two truncated CE peaks.

The truncated CE is possible in this system if we have an additional pool of
very fast relaxing P1 centers that appear in the frequency range between the
outer manifolds (93.76 GHz to 93.89 GHz). If this were the case, then
irradiating on the low frequency EPR line should result in positive
enhancement (because we would be irradiating on the lower frequency EPR line
of the CE pair), and irradiating on the high frequency EPR line should result
in negative enhancement (because we would be irradiating on the higher
frequency EPR line of the CE pair), exactly as observed. These fast relaxing
spins would be difficult to observe in a standard CW-EPR experiment.

Experimental results from a second crystal orientation exhibiting the same DNP
mechanisms are shown in Section II of the SI. While no direct CE is observed
at these crystal orientations, this will not necessarily be true for all
orientations. In order for a diamond crystal to satisfy the conditions for CE
enhancement at a given orientation, there should be two EPR lines separated by
the nuclear Larmor frequency. In order to understand the DNP spectrum from the
powder, we studied how the EPR spectrum from the diamond sample changes with
orientation in the external field. Figure 5 shows EasySpin simulations of how
the single crystal spectra change as the crystal is rotated about different
axes, as well as the powder averaged spectrum [46]. There are a number of
orientations at which the separation between two of the lines in the
$m_{I}=\pm 1$ manifold is on the order of the 13C Larmor frequency. Thus two
adjacent P1 centers - with different relative orientations - can undergo a
dipolar-driven mutual spin-flip that would lead to 13C DNP. (Other CE
conditions may be fulfilled at other fields, such as those described by
Bretschneider et al.[40]). Note that the addition of electron-electron dipolar
interactions will also cause a broadening of the EPR lines, making the CE
condition easier to fulfill.

Figure 5: Easy spin simulations of the EPR spectrum of P1 centers in diamond
as a function of crystal orientation. Depending on the orientation, there are
up to 4 distinct orientations of the P1 center with respect to the magnetic
field for a single crystal orientation. The Euler angles
$(\alpha,\beta,\gamma)$ indicate the orientation of the lattice with the
external magnetic field. We have set $\gamma=\pi/4$ and the top three subplots
indicate rotation patterns as a function of $\beta$ with $\alpha=0,\pi/6$ and
$\pi/4$. The lowest curve shows the simulated powder spectrum  Figure 6: Fit
of experimental constant-frequency DNP spectrum (black circles) of the diamond
powder sample using a sum (green line) of the OE (red line), SE (magenta
line), the truncated CE (blue line), and the CE (black line). The EPR line
plotted above includes line broadening of 10 MHz of the outer EPR lines.

Section VIII.1 of the SI provides a detailed description of an e-N-C spin
system, and full quantum mechanical simulations of the DNP spectra for both
13C and 14N, including relaxation. These simulations reveal that, in general,
the 13C-SE-DNP enhancement occurs within a 14N manifold (i.e. the nitrogen
spin state does not affect the carbon DNP). For the simulations we choose to
concentrate on 13C-SE-DNP due to its relative simplicity to understand.

###  IV.2 Powder

Figure 6 shows a fit of the DNP spectrum of the powder sample. The components
of the SE, OE, tCE and CE with their respective intensities are also plotted.
As in the single crystal case, the center of the DNP spectrum can be fit using
a combination of the SE and the OE giving negative enhancement. Here the outer
lines are best fit using a combination of the CE and the OE or truncated CE.

Figure 2(b) showed that chirped DNP significantly improved the enhancements
for the two outer nuclear spin manifolds ($m_{I}=\pm 1$), and blurred some of
the sharper features associated with the central manifold ($m_{I}=0$) [66, 67,
68]. The enhancement observed under modulation could either be due to the
cross effect [66, 67] or due to the introduction of a new mechanism – the
integrated solid effect [58]. Given the low microwave power and the rapid 5
kHz modulation rate, significantly faster than the electron T1, it is unlikely
that the experiment satisfies the conditions necessary for achieving the
integrated solid effect via frequency modulation [69, 70]. Additionally the
effect is not observed in the central ($m_{I}=0$) manifold. Thus the
additional enhancement from modulation is believed to be due to the CE.

We have also characterized the build-up times and the power-dependence of the
DNP spectrum (see Sections VII and VI of the SI). Both sets of data suggest
that the observed DNP enhancements are limited by the available microwave
power.

The plurality of DNP mechanisms observed is more complex than in previous
high-field DNP experiments with P1 centers. In a diamond micropowder sample
with a P1 concentration less than 100 ppm, Bretschneider et al. observed three
SE-DNP lines, one from each EPR line, and a single positive OE line from the
central EPR line under static DNP conditions at W-band (94 GHz) and low
temperature (1.5-100 K) [40]. Similarly, Kwiatkowski et al. observed static
DNP from P1 centers at 3.5 K at both 94 GHz and 196 GHz in nanodiamonds via a
combination of the SE and a small positive OE [41]. The positive OE
enhancements measured at low temperature are opposite to the negative OE we
observe at room temperature. The origin of this difference is still unknown.

##  V Sample Heterogeneity

To our knowledge this is the first case in which the OE, SE, CE and truncated
CE have been observed in a single material system under the same experimental
conditions. This is likely due to the heterogeneity in the distribution of
nitrogen in these Type Ib HPHT diamond samples.

Li et al. recently used double electron-electron resonance (DEER) experiments
to show that single crystal HPHT diamond samples – similar to those studied
here – show significant spatial variations in their P1 concentrations [71].
One of the samples they studied was measured to have local P1 concentrations
ranging from 13 ppm to 322 ppm in different regions.

We measured the T1 and T2 of the P1 center in both our powder sample and a
similar single crystal sample to that used for DNP. The 2.5 GHz pulsed ESR
setup is described in Section IX of the SI. Figure 7 shows that for both the
Hahn-echo and the inversion recovery experiments, bi-exponential relaxation
best fits the data. The Hahn-echo data are fit with time constants of about 2
$\mu$s and 10 $\mu$s corresponding to $\sim 80$ ppm and $\sim 16$ ppm using
the relation $1/T_{2}$ ($\mu$s-1) = $\frac{1}{160}$ ($\mu$s-1ppm-1) $\times$
[P1] (ppm) [72]. Note that it is difficult to measure T2 values below 1 $\mu$s
on our system due to instrument limitations, so there could potentially be
pools with even higher local P1 concentrations present. The two T1 time
constants were about 100 $\mu$s and 1.4 ms.

This heterogeneity is key to understanding how the different mechanisms
observed above appear to co-exist in the same sample. In regions with low P1
concentration, the relatively isolated defects exhibit DNP via the solid
effect. As the P1 concentration increases, we see the appearance of the CE in
those crystallites where the orientation permits the cross effect condition to
be satisfied. Some of the local P1 clusters become fast-relaxing sites that
are then responsible for the appearance of the truncated cross effect. As
these cluster resonances can be fairly broad [73], it is possible to satisfy
the truncated cross effect conditions at most of the crystal orientations. If
the P1 in the clusters are close enough for exchange interactions to become
important, this could also explain the origin of the Overhauser effect.
Overhauser DNP has previously been observed in graphite [65] as well as in
exchange-coupled donor clusters in silicon [53]. However, a more systematic
study of the DNP spectrum as a function of magnetic field and temperature is
needed to uniquely identify the underlying mechanisms for the observed
Overhauser effects, especially in light of the different signs observed for
this effect in different experimental regimes.

Figure 7: Results from low-field pulse-EPR experiments. The fit parameters are
listed in Tables 1 & 2 in the Materials and Methods. Experimental details can
be found in Section VII.2 (Materials and Methods) and Section IX of the SI.
(a) Hahn-echo decays showing bi-exponential behavior, which suggests there are
at least two types of local environment with different P1 concentrations. (b)
Inversion recovery experiment indicating fast and slow electronic T1
relaxations. The field dependence is expected to be weak at room temperature
as it is likely to be dominated by two-phonon Raman transitions.

##  VI Conclusions

In summary, we have shown substantial 13C-DNP enhancement ($>100$) with P1
centers in diamonds at room temperature. We have also shown that the DNP
enhancement proceeds via a complex combination of SE, OE, CE and tCE DNP
mechanisms, all within the same sample. The DNP enhancements observed are
limited by the available power and could be improved by going to higher power
and potentially higher magnetic field. Additionally, it might be possible to
hyperpolarize the P1 centers via their interactions with adjacent optically-
polarized NV centers which could dramatically improve DNP enhancements even
further [74, 75].

Using DNP to increase the sensitivity of NMR has the potential to
significantly expand the application of this versatile spectroscopic technique
to ever-smaller samples. This technique will also be useful for enhancement of
NMR signals in NV-detected NMR at a high field [76] and be potentially
applicable to NV-detected NMR of external spins. Hyperpolarized NMR of Nano-
and micro-diamond tracers could prove valuable in both biomedical applications
as well as in fluid engineering. It should also be possible to transfer the
hyperpolarization to spins external to the diamond via spin diffusion [77] or
cross-polarization [29]. DNP with diamond chips would enable the use of
magnetic resonance to study oriented low-dimensional systems such as thin
films and 2D materials like graphene and its functional derivatives,
transition-metal dichalcogenides, and 2D conductive metal-organic-frameworks.
These materials are increasingly being used as catalysts and chemiresistive
devices, and may hold promise for the development of novel quantum materials.

##  VII Materials and Methods

###  VII.1 High Field CW-EPR Experiment

Room-temperature continuous-wave (cw) electron paramagnetic resonance (EPR)
lines were measured at 230 GHz. Field modulation frequency is 20 kHz and the
modulation strength is 0.02mT.

###  VII.2 Low Field Pulse-EPR Experiments

Our lab-built pulse-EPR spectrometer is designed to operate at 2.5 GHz and can
output up to 1 W of power. In Figure 7, data are shown for (a) Hahn-echo and
(b) inversion recovery experiments conducted on the powder sample and on a
single crystal macle-cut Element 6 HPHT diamond with $\textbf{B}_{0}$ parallel
to $[111]$. The data were collected with the external magnetic field tuned to
the $m_{I}=0$ manifold of the EPR line. For the Hahn-echo experiment, the
sequence is $\pi/2-\tau-\pi-\tau-\textrm{echo}$, and the interpulse delay
$\tau$ is swept. The magnitudes of the echoes are plotted as a function of the
time at which the echo comes into focus. For both the powder and the single
crystal diamond, the Hahn echo magnitudes, $S_{\text{HE}}(t_{\text{E}})$ are
fit to a bi-exponential decay equation,

$S_{\text{HE}}(t_{\text{E}})=M_{1}e^{-t_{\text{E}}/T_{2}^{1}}+M_{2}e^{-t_{\text{E}}/T_{2}^{2}}+A,$
(1)

where $t_{\text{E}}=2\tau+t_{\pi/2}/2+t_{\pi}$ is the cumulative time that
spins are undergoing $T_{2}$ relaxation, $M_{1}$ and $T_{2}^{1}$ are the
amplitude and transverse relaxation time characteristic of electrons in pool
1, $M_{2}$ and $T_{2}^{2}$ are the likewise variables for pool 2, and $A$ is
an offset that is necessarily non-zero since the echo magnitudes are used in
fitting. The fit parameter values are given in Table 1.

| $M_{1}$ |  $T_{2}^{1}$ ($\mu$s) | $M_{2}$ |  $T_{2}^{2}$ ($\mu$s) | A
---|---|---|---|---|---
Powder | $8(1)$ | $1.9(1)$ | $0.30(9)$ | $10(2)$ | $0.006(4)$
| Single
---
Crystal
$3.2(9)$ | $2.2(5)$ | $0.2(1)$ | $18(8)$ | $0.01(1)$
Table 1: Fit parameters for Hahn-echo low-field pulse-EPR experiments.
Uncertainties indicate 95% confidence intervals.

For the inversion recovery experiments, the sequence
$\pi-\tau_{1}-\pi/2\tau_{2}-\pi-\tau_{3}-\textrm{echo}$ inverts the electron
spin polarization with the first $\pi$ pulse, then after a recovery time
$\tau_{1}$, reads out the polarization with a standard Hahn-echo (note,
$\tau_{2}=\tau_{3}$). By sweeping $\tau_{1}$ from short to long values, the
echo signal transitions from a maximally inverted signal to one that is fully
recovered via $T_{1}$ relaxation processes. The echo amplitudes
$S_{\text{IR}}(\tau_{1})$ are well fit with a bi-exponential asymptotic
recovery equation,

$S_{\text{IR}}(\tau_{1})=M_{1}\left(1-2\sin^{2}(\alpha/2)e^{-\tau_{1}/T_{1}^{1}}\right)+\\\
M_{2}\left(1-2\sin^{2}(\alpha/2)e^{-\tau_{1}/T_{1}^{2}}\right),$ (2)

where $M_{1}$ and $T_{1}^{1}$ are the amplitude and longitudinal relaxation
time characteristic of electrons in pool 1, $M_{2}$ and $T_{1}^{2}$ are the
likewise variables for pool 2, and $\alpha$ is an angle whose deviation from
$\pi$ indicates imperfect inversion of the electron spin population. The
values of the fit parameters are given in Table 2.

| $M_{1}$ |  $T_{1}^{1}$ (ms) | $M_{2}$ |  $T_{1}^{2}$ (ms) |  $\alpha$ (rad)
---|---|---|---|---|---
Powder | $0.41(4)$ | $0.11(2)$ | $0.58(4)$ | $1.3(1)$ | $4.33(1)$
| Single
---
Crystal
$0.25(5)$ | $0.07(3)$ | $0.74(5)$ | $1.3(2)$ | $4.40(3)$
Table 2: Fit parameters for inversion recovery low-field pulse-EPR
experiments. Uncertainties indicate 95% confidence intervals.

###  VII.3 Referencing the 13C-NMR Spectrum

The 13C-NMR spectrum was referenced to adamantane, at 37$\pm$1 ppm using
glycerol-d5 as a secondary reference, with two peaks at 64$\pm$1 and 72$\pm$1
ppm.

###  VII.4 DNP Spectrometer

The DNP experiments were performed on a homebuilt DNP spectrometer, at a field
of 3.34 T, corresponding to an electron Larmor frequency of 94 GHz, a 1H
Larmor frequency of 142 MHz and a 13C Larmor frequency of 35.8 MHz. [78] All
experiments were performed at room temperature. The NMR pulses and detection
were controlled with a Bruker Avance AQX spectrometer.

####  VII.4.1 MW Irradiation

An Agilent 33220A arbitrary waveform generator (AWG) was used to create the
waveforms used for continuous wave (CW) MW irradiation. The AWG output was set
to 2.5 V, which was input into a Mini Circuits voltage controlled oscillator
ZX95-1480+ (VCO) for CW or chirped excitation around a central frequency of
1.012 GHz. The 1.012 GHz output of the VCO was first mixed (Marki T3 mixer)
with a variable frequency signal from the ($\sim 4$ GHz) Quonset Microwave
QM2010-4400 source to yield sidebands at $\sim 5$ GHz and $\sim 3$ GHz. The 3
GHz component mixer was filtered out using a Mini Circuits high-pass filter
VHF-3500+ that only allows frequencies above 3.9 GHz to pass through. The
variable frequency signal around 5 GHz was then mixed with an 88.56 GHz phase-
locked oscillator source to reach 94 GHz, and filtered again to remove the low
frequency sideband, using an iris filter as shown in Figure 8. This is a
modification of the Millitech MW bridge previously described in [78]. In order
to increase the available millimeter wave power we removed the voltage
controlled attenuator (1.5 dB insertion loss) and the directional coupler (1.8
dB insertion loss) to get a maximum output power of 23.8 dBm (240 mW).

In order to vary the power below 240 mW we connected a variable 30 dB
attenuator to the output to the source. In order to run the experiment at
higher power, we modified a commercial 500 mW injection-locked 94 GHz source
from Quinstar. We removed the varactor-tuned Gunn diode orignally used for the
injection locking from the source and instead used the attenuated output of
the Millitech source. We were unable to verify if the efficiency of injection-
locking was uniform across the entire sweep bandwidth.

###  VII.5 13C-NMR and DNP Experiments

The following settings were used for all the experiments, unless otherwise
noted: The DNP enhanced NMR signal was recorded with a 90-acquire pulse
sequence, using a 10 $\mu$s $\pi$/2 pulse. Eight step phase cycling was used
in all cases. The experiments began with a train of 100 30 ms saturation
pulses separated by 20 $\mu$s.

The 13C relaxation time T1 (Section V of the SI) was recorded using
saturation-recovery experiments, stepping the recovery delay and then
recording the signal, with no MW irradiation applied. The DNP enhancement
buildup time Tbu was recorded in the same manner as T1 but with MW
irradiation.

DNP spectra were recorded by keeping the 1.012 GHz VCO settings constant, and
stepping the 4 GHz source in order to cover a range of 93.63 GHz to 93.972
GHz. Data were typically taken over 102 evenly spaced frequencies points.

Figure 8: Schematic of the millimater wave source used in these experiments -
adapted from [78].

###  VII.6 NMR Data Processing

Data processing was performed in MATLAB using custom scripts. 3 points of
left-shift were used in all cases to remove switching signal from opening of
the receiver. The data was then baseline corrected, phase corrected and 300 Hz
exponential line broadening was applied. For DNP enhancement calculations we
divide the integrated intensity of the MW-on signal from the MW-off signal
(such that no enhancement is equal to 1). The MW-off signal was measured using
128 scans, except at the longest build-up times when 64 scans were used.

The reported signal intensities correspond to an average over 21 points around
the peak of the phased absorptive signal in the frequency domain. The reported
uncertainties in the NMR signal were calculated using the standard deviation
(201 point interval) from a signal-free region of the NMR spectrum.

The T1 and Tbu curves were fit using a biexponential function, using the
method of a non-linear least squares. The fitting function returns a 95 %
confidence interval which was converted to a variation of $\pm 2\sigma$
assuming a normal distribution.

The authors thank Hailey Mullen for helping acquire the DNP spectrum of the
diamond crystal and Element 6 for the donation of the powder samples used in
these experiments. We thank Professor David Cory (Waterloo) for the 500 mW
Impatt source. This work was partially supported by funding from the National
Science Foundation under cooperative agreement under grants OIA-1921199. ST
acknowledges support from the US National Science Foundation (DMR-1508661,
CHE-1611134, and CHE-2004252 with partial co-funding from the Quantum
Information Science program in the Division of Physics).

The data can be provided by the authors pending scientific review and a
completed material transfer agreement. Requests for the data should be
submitted to: Daphna Shimon or Chandrasekhar Ramanathan.

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## Supplementary Information: Large Room Temperature Bulk DNP of 13C via P1
Centers in Diamond

Daphna Shimona1, Kelly A. Cantwellb, Linta Josephb, Ethan Q. Williamsb, Zaili
Pengc, Susumu Takahashic, Chandrasekhar Ramanathanb2

a: Institute of Chemistry, The Hebrew University of Jerusalem, Edmond J.
Safra, Givat Ram, Jerusalem, Israel.

b: Department of Physics and Astronomy, Dartmouth College, Hanover, NH 03755,
U.S.A.

c: Department of Chemistry, University of Southern California, Los Angeles,
California 90089, U.S.A.

1<EMAIL_ADDRESS>
2<EMAIL_ADDRESS>
##  I 13C decoherence time

The NMR peak has a width of 1.12 kHz. This resonance shows significant
inhomogeneous line-broadening and it is possible to detect several hundred
echoes in a pulsed spin-lock experiment (using a train of $\pi/2$ pulses [79])
as shown in Figure 1(b). Stroboscopic detection of multiple echoes would allow
a significant additional improvement in the signal-to-noise ration (SNR)
obtained. The decay times measured are significantly shorter than those
recently measured by Beatrez et al. [79], potentially due to the microwaves
being continually on during the experiment.

Figure 9: The decay of a pulsed spin-locking echo train with a 10 $\mu$s
$\tau$ spacing following hyperpolarization for 60 s. The data were collected
in a two-dimensional experiment. The best fit is obtained with a 3-component
fit with time constants of $25.5\pm 1.5$ ms, $3.8\pm 0.4$ ms and $0.69\pm
0.13$ ms with relative intensities of 0.19, 0.47 and 0.33.

##  II DNP Enhancement of the Single Crystal

We tried to measure the thermal equilibrium 13C signal from the single crystal
diamond sample. Figure 10 shows average of 800 scans of the thermal signal
measured with a relaxation delay of 500 s as well as the average of 8 scans of
the DNP signal measured at 93.77 GHz with the same build-up of 500 s with
about 240 mW of microwave power. Since we are unable to see the thermal 13C
signal, we use the SNR of the DNP signal to estimate a minimum DNP enhancement
of 180 for the single crystal sample. Note the thermal signal was acquired
with a receiver gain that was 4 times larger than that used in the DNP
experiment.

Figure 10: Thermal and DNP-enhanced 13C NMR spectra from the single-crystal
diamond sample. The thermal signal is an average of 800 scans and has been
vertically scaled by a factor of 10 to better visualize the signal. The DNP
signal is an average of 8 scans and is acquired with the crystal at the
orientation shown in Figure 4.

In Figure 11 we show a fit of a single crystal at a second orientation, using
the method described in the main text, and below.

Figure 11: Fit of experimental constant-frequency DNP spectrum (black circles)
for a single-crystal diamond sample. The fit uses a sum (green line) of the OE
(red line), SE (magenta line), the truncated CE (blue line), and the CE (black
line). The EPR line plotted above includes line broadening of 10 MHz of the
outer EPR lines. The single crystal EPR line was simulated with EasySpin using
the Euler angles $\alpha=136.8000^{\circ}$, $\beta=129.7918^{\circ}$,
$\gamma=309.6000^{\circ}$.

##  III Simulating the EPR Spectrum

Given the concentration of P1 centers it is also important to account for
magnetic dipolar interactions between electron spins in the crystal. Without
knowing the specific distribution of P1 centers in the system we assume here
that the P1 centers are uniformly distributed. We used a Monte Carlo
simulation to randomly seed a diamond lattice with a 100 ppm concentration of
P1 centers and estimated the pairwise distribution of dipolar couplings in the
sample by averaging over a large number of configurations.

We used a lattice with $15\times 15\times 15$ unit cells, each with 2 atoms
per unit cell and randomly seeded the sites with P1 centers using a binomial
probability determined by the concentration. The distribution of pairwise P1
dipolar interactions was then calculated and stored. We averaged this
distribution over 10,000 random lattice configurations to estimate the
distribution of pairwise dipolar couplings in the system as shown in Figure
12.

Figure 12: Simulated distribution of pairwise dipolar couplings for a 100 ppm
P1 concentration diamond sample.

We then used EasySpin package [46] to perform quantum mechanical simulations
of pairs of P1 centers . As noted earlier, each P1 center was modeled as an
e-14N system, with an isotropic g=2.0024, hyperfine coupling strengths with
the 14N nucleus of $A_{x}^{N}=A_{y}^{N}$ = 82 MHz, A${}_{z}^{N}$ = 114 MHz
[47]. The 14N nuclear quadrupolar interaction was neglected. EasySpin
automatically computes the powder average of the spectrum and uses the 227 (F
d -3 m) space group symmetry of the diamond lattice.

For the single crystal simulation shown in Figure 4, we simulated a single
crystal orientation with Euler angles $\alpha=54.0013^{\circ}$,
$\beta=134.4274^{\circ}$, $\gamma=18.0023^{\circ}$, and the same space group,
isotropic g-value and hyperfine interactions described in the previous
paragraph. For the single crystal simulation shown in Figure 11 we simulated a
single crystal orientation with Euler angles $\alpha=136.8000^{\circ}$,
$\beta=129.7918^{\circ}$, $\gamma=309.6000^{\circ}$.

##  IV Fitting the Experimental DNP Spectrum

In the main text, we fit the DNP spectrum using a crude method of convoluting
the EPR line with delta functions to form the basic shapes for the solid
effect (SE), Overhauser effect (OE) (same shape used for tCE) and cross effect
(CE) DNP mechanisms, and changing their amplitude to achieve the best
agreement with the experimental spectrum. This method was previously described
in Banerjee et al. [61].

In order to do this, the EPR line, $g(\omega_{\text{MW}})$, was split into
three ranges:

  * •

The low frequency line: $g_{1}(\omega_{\text{MW}})$ for
$93.56\leq\omega_{\text{MW}}\leq 93.7740$ GHz

  * •

The central line: $g_{2}(\omega_{\text{MW}})$ for
$93.7740<\omega_{\text{MW}}<93.8590$ GHz

  * •

The high frequency line: $g_{3}(\omega_{\text{MW}})$ for
$93.8590\leq\omega_{\text{MW}}\leq 94.0610$ GHz

The EPR line used for the powder DNP spectrum was simulated using using a
e-14N e-14N spin system, averaged over 100 of the most probable e-e dipolar
interactions between the two systems (see Figure 12). This averaging caused a
slight broadening of the two external EPR lines (as explained above). For the
single crystal DNP spectrum, we simulated a single crystallite orientation,
again using EasySpin.

In order to mimic the effects of the effective MW irradiation strength on the
off-resonance irradiation, for each DNP mechanisms, we added Gaussian
broadening to the different OE, SE and CE lineshapes [3]. The effective
irradiation on the SE is weakest, and therefore it was broadened with a
Gaussian function with a FWHM of 0.1 MHz. The effective irradiation of the OE
and CE are much larger, and therefore they were broadened with a Gaussian
function with a FWHM of 8 MHz. The FWHM values were chosen in order to give
the best fit for the DNP spectrum. However, from perturbation theory we know
that the effective irradiation at the DQ/ZQ transition (as in the SE) is of
the order of about 1/100 of the irradiation on a single quantum transition (as
in the CE/OE), which is reflected in the values chosen [1, 2].

The basic DNP shapes used for the fitting were calculated by convoluting the
three EPR lines with delta functions at the appropriate frequency separations.
The OE shapes are just the EPR lines:

$\text{OE}_{1}(\omega_{\text{MW}})=g_{1}(\omega_{\text{MW}})$ (3)
$\text{OE}_{2}(\omega_{\text{MW}})=-g_{2}(\omega_{\text{MW}})$ (4)
$\text{OE}_{3}(\omega_{\text{MW}})=-g_{3}(\omega_{\text{MW}})$ (5)

The SE shapes are just the EPR lines convolved with delta functions at
$\omega=\omega_{\text{MW}}+\omega_{C}$ and
$\omega=\omega_{\text{MW}}-\omega_{C}$, giving:

$\text{SE}_{1}(\omega_{\text{MW}})=g_{1}(\omega_{\text{MW}}+\omega_{C})-g_{1}(\omega_{\text{MW}}-\omega_{C})$
(6)
$\text{SE}_{2}(\omega_{\text{MW}})=g_{2}(\omega_{\text{MW}}+\omega_{C})-g_{2}(\omega_{\text{MW}}-\omega_{C})$
(7)
$\text{SE}_{3}(\omega_{\text{MW}})=g_{3}(\omega_{\text{MW}}+\omega_{C})-g_{3}(\omega_{\text{MW}}-\omega_{C})$
(8)

The CE shapes are just the EPR lines convolved with delta functions at
$\omega=\omega_{\text{MW}}+\omega_{C}$ and
$\omega=\omega_{\text{MW}}-\omega_{C}$, and then convolved again with the two
outer EPR lines, giving:

$\text{CE}_{1}(\omega_{\text{MW}})=g_{1}(\omega_{\text{MW}})*[g_{1}(\omega_{\text{MW}}+\omega_{C})-g_{1}(\omega_{\text{MW}}-\omega_{C})]$
(9)
$\text{CE}_{3}(\omega_{\text{MW}})=g_{3}(\omega_{\text{MW}})*[g_{3}(\omega_{\text{MW}}+\omega_{C})-g_{3}(\omega_{\text{MW}}-\omega_{C})]$
(10)

CE from the central EPR line was not considered because the line is not broad
enough to fulfill the CE-condition of two electrons separated by the nuclear
Larmor frequency.

To reproduce the experimental DNP spectrum, a linear combination of the
different basic DNP shapes was calculated:

$\epsilon(\omega_{\text{MW}})=\epsilon_{\text{OE}}(\omega_{\text{MW}})+\epsilon_{\text{SE}}(\omega_{\text{MW}})+\epsilon_{\text{CE}}(\omega_{\text{MW}})$
(11)

where

$\displaystyle\epsilon_{\text{OE}}(\omega_{\text{MW}})$ $\displaystyle=$
$\displaystyle\epsilon_{\text{OE,1}}(\omega_{\text{MW}})+\epsilon_{\text{OE,2}}(\omega_{\text{MW}})+\epsilon_{\text{OE,3}}(\omega_{\text{MW}})$
(12) $\displaystyle=$ $\displaystyle
k_{\text{OE,1}}\text{OE}_{1}(\omega_{\text{MW}})+k_{\text{OE,2}}\text{OE}_{2}(\omega_{\text{MW}})+$
$\displaystyle\hskip 36.135ptk_{\text{OE,3}}\text{OE}_{3}(\omega_{\text{MW}})$

$\displaystyle\epsilon_{\text{SE}}(\omega_{\text{MW}})$ $\displaystyle=$
$\displaystyle\epsilon_{\text{SE,1}}(\omega_{\text{MW}})+\epsilon_{\text{SE,2}}(\omega_{\text{MW}})+\epsilon_{\text{SE,3}}(\omega_{\text{MW}})$
(13) $\displaystyle=$ $\displaystyle
k_{\text{SE,1}}\text{SE}_{1}(\omega_{\text{MW}})+k_{\text{SE,2}}\text{SE}_{2}(\omega_{\text{MW}})+$
$\displaystyle\hskip 36.135ptk_{\text{SE,3}}\text{SE}_{3}(\omega_{\text{MW}})$

$\displaystyle\epsilon_{\text{CE}}(\omega_{\text{MW}})$ $\displaystyle=$
$\displaystyle\epsilon_{\text{CE,1}}(\omega_{\text{MW}})+\epsilon_{\text{CE,3}}(\omega_{\text{MW}})$
(14) $\displaystyle=$ $\displaystyle
k_{\text{CE,1}}\text{CE}_{1}(\omega_{\text{MW}})+k_{\text{CE,3}}\text{CE}_{3}(\omega_{\text{MW}})$

In order to fit the DNP spectrum we manually adjusted the values of
$k_{\text{OE,1}}$, $k_{\text{OE,2}}$, $k_{\text{OE,2}}$, $k_{\text{SE,1}}$,
$k_{\text{SE,2}}$, $k_{\text{SE,2}}$, $k_{\text{CE,1}}$ and $k_{\text{CE,2}}$,
and determined the best fit by eye. The contribution of the tCE to the fit is
included in the OE terms for the two outer EPR lines, since the shapes are
identical for both mechanisms.

##  V Build-up of the Thermal 13C Signal

The buildup for the thermal signal (T1 curve) was recorded using a saturation-
recovery experiment. Because of the long times involved in this experiment,
the longer times were recorded with fewer scans (64 instead of 128 or 480
scans), and therefore the intensity of these points have slightly larger
error-bars. The curve was fitted with a biexponential fit, with time constants
of T${}_{1}^{\text{short}}=51\pm 29$ s and T${}_{1}^{\text{long}}=481\pm 425$
s. Note that the uncertainties in the fit are quite large due to both the low
SNR in the thermal experiment and the biexponential nature of the fit.

Figure 13: Thermal build up of NMR signal (blue diamonds) overlaid with the
biexponential fit (red line).

##  VI Power Dependence of DNP

It has been reported that different DNP mechanisms have different dependence
on the power of the MW irradiation. As such, we should be able to tell apart
the SE, OE and CE via their power dependencies [49, 5]. Figure 14 shows the
DNP spectrum as a function of applied MW power at buildup times of 300 s. For
the 240 mW source, the power was varied by changing the settings of a variable
attenuator. The figure suggests that the DNP enhancement grows linearly with
power at all MW irradiation frequencies up to about 240 mW suggesting that we
are in a low enough power regime that the enhancement has not reached
saturation for any of the DNP mechanisms [80]. At 500 mW the SE contributions
have continued to increase linearly but the enhancement starts to saturate at
other MW frequencies.

Figure 14: (a) 13C NMR Signal as a function of MW power at a DNP build-up time
of 300 s indicating that the DNP enhancement is still growing as a function of
power at all frequencies in our experiment. (b) Power dependence at specific
MW frequencies showing that the enhancement is beginning to saturate at some
frequencies.  Figure 15: (a) Surface Plot showing the build up of the DNP
spectrum as a function of MW irradiation time. (b) The build-up curves at each
MW frequency were fit using a two-component fit. The amplitudes of the two
components and their sum are shown in (b), while (c) and (d) show the best-fit
short and long time constants as a a function MW frequency. The shaded region
indicates the $\pm\sigma$ confidence interval of the fits. The fits fail when
the DNP enhancement is low and where the enhancement switches sign. There is
significant uncertainty associated with some of the longer time constants
since data was only acquired up to a maximum build-up time of 3000 s.

##  VII DNP Buildup Times

In addition, to compare the various DNP mechanisms, we also characterized the
build-up time of the hyperpolarization as a function of MW frequency at 240 mW
up to 3000 s as shown in Figure 15. Almost all the buildup curves could be fit
with a two-component fit, T${}_{bu}^{\text{short}}$ and
T${}_{bu}^{\text{long}}$. This biexponential behavior suggests that the two
components consist of 13C spins directly hyperfine-coupled to an adjacent P1
center (short time constant) and more distant spins that rely on nuclear spin
diffusion to mediate both T1 relaxation and DNP buildup (long time constant)
[81]. Only a single exponential fit was required at a few MW excitation
frequencies. The fits fail when the DNP enhancement is low such as on the
edges of the DNP spectrum and in locations where the enhancement switches
sign. The amplitudes and time constants of the two components are also shown
in the figure. The shaded region indicates the $\pm\sigma$ confidence interval
of the fitted time constants. There is significant uncertainty associated with
some of the longer time constant since data was only acquired up to a maximum
build-up time of 3000 s.

At most MW excitation frequencies, the short component is on the order of 50 s
and the long component on the order of 500 s – similar to the thermal build-up
times. At most MW frequencies, the amplitudes of the short and long time
constant components are nearly the same, except at the outer lobes around 93.7
GHz and 93.92 GHz, where the short time component is seen to be significantly
larger than the long-time component. The buildup was observed to be
particularly slow for the SE peaks.

The fact that T${}_{1}^{\text{short}}\approx$ T${}_{bu}^{\text{short}}$ and
T${}_{1}^{\text{long}}\approx$ T${}_{bu}^{\text{long}}$ is another indication
that we do not have enough MW power to drive the DNP at a rate that is faster
than T1 [1, 49].

##  VIII Simulation of DNP Mechanisms

We performed numerical simulations of the spin dynamics of two small spin
systems, an e-14N system and an e-14N-13C system. The simulations were based
on the method described by the Vega group [82, 2, 83, 3]. Numerical
simulations involving e-14N and e-14N-13C systems are described in Shimon et
al. in the context of the role the 14N nucleus plays in DNP enhancement of
spin half nuclei using Nitroxide radicals [3].

###  VIII.1 Simulation of the e-14N System

We begin by looking at an e-14N system, containing one electron that is
strongly hyperfine coupled to a 14N nucleus. In the MW rotating frame, the
Hamiltonian of the system without the MW irradiation is given by:

$H_{0}^{N}=\Delta\omega_{e}S_{z}-\omega_{N}I_{z}^{N}+A_{z}^{N}S_{z}I_{z}^{N}+A_{x}^{N}S_{z}I_{x}^{N}+A_{y}^{N}S_{z}I_{y}^{N}$

where $S$ and $I^{N}$ are the electron and nitrogen spins, respectively.
$\omega_{e}=\omega_{e}-\omega_{\text{MW}}$ is the electron off-resonance
(which is determined by the g-tensor), $\omega_{N}$ is the 14N Larmor
frequency. $A_{z}^{N}$ is the secular part of the e-N hyperfine interaction
(which includes both isotropic and anisotropic shifts) and A${}_{x}^{N}$ and
A${}_{y}^{N}$ are the pseudo-secular terms of the dipolar hyperfine
interaction (which is anisotropic). Here, we simulated each P1 center as an
e-14N system, with an isotropic g=2.0024 and hyperfine coupling strengths with
the 14N nucleus with principal axis components $A_{xx}^{N}=A_{yy}^{N}=82$ MHz,
$A_{zz}^{N}$ = 114 MHz [47]. A single crystal orientation was chosen, such
that $A_{z}^{N}$ = 98 MHz, and $A_{x}^{N}$ = -16 MHz and $A_{y}^{N}$ = 0 MHz.
In the rotating frame, the MW irradiation term is

$\omega_{\text{MW}}=\omega_{1}S_{z}.$ (15)

Note, that the nuclear quadrupolar interaction is not included in these
simulations. First, we diagonalize $H_{0}^{N}$ according to

$H_{0}^{Nd}=V^{-1}H_{0}^{N}V$ (16)

The $A_{z}^{N}$ term splits the EPR transition
$|\uparrow_{e}\rangle\leftrightarrow|\downarrow_{e}\rangle$ into three
transitions, according the nitrogen spin eigenstates
$|\chi_{N}\rangle=|-1\rangle$, $|0\rangle$ or $|1\rangle$, such that the
electron transitions can be written as
$|\uparrow_{e},\chi_{N}\rangle\leftrightarrow|\downarrow_{e},\chi_{N}\rangle$,
separated by $A_{z}^{N}$. The $A_{x}^{N}$ and $A_{y}^{N}$ terms result in weak
state mixing of adjacent (i.e., $\Delta m_{I}=\pm 1$) nitrogen spin states
within each electron manifold, such that:

$\displaystyle|\chi_{e},\pm\tilde{1}\rangle$ $\displaystyle=$ $\displaystyle
c_{N}|\chi_{e},\pm 1\rangle+s_{N}|\chi_{e},0\rangle$ (17)
$\displaystyle|\chi_{e},\tilde{0}\rangle$ $\displaystyle=$ $\displaystyle
c_{N}|\chi_{e},0\rangle+s_{N}|\chi_{e},+1\rangle-s_{N}|\chi_{e},-1\rangle$
(18)

where $|\chi_{e}\rangle=|\uparrow_{e}\rangle$ or $|\downarrow_{e}\rangle$,
$c_{N}=\cos\zeta_{N}$ and $s_{N}=\sin\zeta_{N}$, $\tan
2\zeta_{N}=\sqrt{(A_{x}^{N})^{2}+(A_{y}^{N})^{2}}/[8(\omega_{N}+A_{z}^{N})]$,
if $\sqrt{(A_{x}^{N})^{2}+(A_{y}^{N})^{2}}\ll\omega_{N}$ and $A_{z}^{N}$, from
perturbation theory [84].

Next, we transform the MW irradiation term to the same frame, according to

$H^{d}_{\text{MW}}=V^{-1}H_{\text{MW}}V$ (19)

The weak state mixing described above also results in weak effective
irradiation between double quantum and zero quantum transitions, which give
the 14N-SE-DNP enhancement. The strength of the effective irradiation is
proportional to the state-mixing, such that it is
$\omega_{1,\text{eff}}^{N}=|s_{N}|\omega_{1}$ for the 14N-SE-DNP and even
weaker for second order 14N-SE-DNP effects.

Figure 16: Simulated electron (black) and 14N (red) polarizations as a
function of the MW irradiation frequency for an e-14N spin system. The
polarizations are normalized according to the steady state electron
polarization. The MW irradiation frequency is plotted in MHz for convenience,
and is referenced to the electron Larmor frequency, $\omega_{e}=$94 GHz. The
simulation parameters: $\omega_{e}=$94 GHz, $\omega_{N}=$10 MHz,
$A_{z}^{N}=$98 MHz, $A_{z}^{N}=$98 MHz, $A_{x}^{N}$=-16 MHz, $A_{y}^{N}=$0
MHz, $\omega_{1}=$0.5 MHz, T${}_{1e}=$103 ms, T${}_{1N}=$1 s, T${}_{2e}=$10
$\mu$s and T${}_{2N}=$100 $\mu$s. No cross relaxation was added to the system.

In Fig. 16 we plot the steady state 14N nuclear polarization,
$\text{P}_{N}(\omega_{\text{MW}})$, and the electron polarization,
$\text{P}_{e}(\omega_{\text{MW}})$, during MW irradiation as a function of the
frequency of the MW irradiation. Here we normalize all electron and nuclear
polarizations to the value of the electron polarization at thermal
equilibrium, $\text{P}_{e}^{\text{eq}}=1$ (i.e., when no MW irradiation is
applied). Concentrating on the electron, it is clear that when the MW
irradiation frequency is far off resonance the electron polarization is at its
largest value. When the MW irradiation is on-resonance with one of the
electron transitions the electron polarization is reduced (i.e., the electron
is partially saturated). Far off resonance
$\text{P}_{N}(\omega_{\text{MW}})=\text{P}_{N}^{\text{eq}}\approx 0$ because
the nuclear polarization is negligible compared to the electron polarization
($\text{P}_{e}^{\text{eq}}\gg\text{P}_{N}^{\text{eq}}$). At certain
frequencies the $\text{P}_{N}(\omega_{\text{MW}})\neq 0$ is enhanced due to
the small state mixing between the nitrogen spin states, which is a result of
the $A_{z}^{N}$ term of the hyperfine interaction.

Concentrating on the 14N-DNP spectrum in Fig. 16, it can be clearly seen that
there are three distinct DNP features (marked 1,2 and 3 in the figure):

  1. 1.

Two narrow features appearing at $\omega\approx\omega_{e}\pm 2\omega_{N}$ are
second order SE-DNP transitions. Positive enhancement is achieved when
irradiating on the
$|\alpha_{e},\tilde{1}\rangle\leftrightarrow|\beta_{e},-\tilde{1}\rangle$
transition, and negative enhancement is achieved when irradiating between
$|\alpha_{e},-\tilde{1}\rangle\leftrightarrow|\beta_{e},\tilde{1}\rangle$.

  2. 2.

Four broader features appearing at $\omega=\omega_{e}\pm\omega_{N}\pm
A_{z}^{N}/2$ and $\omega=\omega_{e}\pm\omega_{N}\mp A_{z}^{N}/2$ are the SE
transitions of the central EPR line, where the separation between positive and
negative enhancement is $2\omega_{N}+A_{z}^{N}$ or $2\omega_{N}-A_{z}^{N}$.
The outer SE pair is formed as a result of irradiation on the
$|\alpha_{e},\tilde{0}\rangle\leftrightarrow|\beta_{e},-\tilde{1}\rangle$ and
$|\alpha_{e},\tilde{0}\rangle\leftrightarrow|\beta_{e},+\tilde{1}\rangle$
transitions. The inner SE pair is formed as a result of irradiation on the
$|\alpha_{e},-\tilde{1}\rangle\leftrightarrow|\beta_{e},\tilde{0}\rangle$ and
the $|\alpha_{e},\tilde{1}\rangle\leftrightarrow|\beta_{e},\tilde{0}\rangle$.
The two SE pairs are centered around $\omega_{e}$, but they have opposite
signs, such that signs of the enhancement of the inner SE pair are opposite of
those of the outer SE pair.

  3. 3.

The two broader features at $\omega=\omega_{e}\pm A_{z}^{N}$ appear on
resonance on the electron, as one would expect from the Overhauser effect, but
are in fact due to the SE. In this case, the state-mixing described in
Equations 2-3 in the main text results in electron-nitrogen cross-relaxation
terms that connect the nitrogen states within each electron manifold. When
irradiating on the low frequency electron line (i.e. on the
$|\alpha_{e},-\tilde{1}\rangle\leftrightarrow|\beta_{e},-\tilde{1}\rangle$
transition) and then positive enhancement is achieved. In a similar manner,
when irradiating on the high frequency electron line (i.e. on the
$|\alpha_{e},+\tilde{1}\rangle\leftrightarrow|\beta_{e},+\tilde{1}\rangle$
transition), $T_{1ZQ}$ forms on the
$|\alpha_{e},+\tilde{1}\rangle\leftrightarrow|\beta_{e},\tilde{0}\rangle$
transition and then negative enhancement is achieved. At the center of the DNP
spectrum (when irradiating directly at $\omega$, no enhancement is achieved).

###  VIII.2 Simulation of the e-14N-13C system

Next, we add a 13C spin to the system described above. The Hamiltonian of this
system is given by:

$H_{0}^{NC}=H_{0}^{N}-\omega_{C}I_{z}^{C}+A_{x}^{C}S_{z}I_{x}^{C}+A_{y}^{C}S_{z}I_{y}^{C}$

where $I^{C}$ is the carbon spin operator, $\omega_{C}$ is the 13C Larmor
frequency and $A_{x}^{C}$ and $A_{y}^{C}$ are the pseudo-secular terms of the
dipolar hyperfine interaction. The other terms were defined above. Note that
no e-C secular hyperfine or N-C dipolar interactions were added to the
simulation. Here, $A_{x}^{C}=A_{y}^{C}$.

Again we diagonalize the Hamiltonian $H_{0}^{NC}$, and then transform
$H_{\text{MW}}$ to the same frame, as described above. The
$A_{x}^{C}=A_{y}^{C}$ term results in weak state mixing of carbon spin spin
states within each electron-nitrogen manifold, such that:

$\displaystyle|\chi_{e},\tilde{\chi}_{N},\alpha_{C}^{*}\rangle$
$\displaystyle=$ $\displaystyle
c_{C}|\chi_{e},\tilde{\chi}_{N},\alpha_{C}\rangle+s_{C}|\chi_{e},\tilde{\chi}_{N},\beta_{C}\rangle$
(20) $\displaystyle|\chi_{e},\tilde{\chi}_{N},\beta_{C}^{*}\rangle$
$\displaystyle=c$ ${}_{C}|\chi_{e},\tilde{\chi}_{N},\beta_{C}\rangle-
s_{C}|\chi_{e},\tilde{\chi}_{N},\alpha_{C}\rangle$ (21)

where $\chi_{e}=|\alpha_{e}\rangle$ or $|\beta_{e}\rangle$,
$\tilde{\chi}_{N}=|\pm\tilde{1}\rangle$ or
$\tilde{\chi}_{N}=|\tilde{0}\rangle$ and $c_{C}=\cos\zeta_{C}$ and
$s_{C}=\sin\zeta_{C}$ and $\tan
2\zeta_{N}=\sqrt{(A_{x}^{C})^{2}+(A_{x}^{C})^{2}}/[8\omega_{C}]$, if
$\sqrt{(A_{x}^{C})^{2}+(A_{x}^{C})^{2}}\ll\omega_{N}$, from perturbation
theory [84].

The weak carbon state-mixing described above also results in weak effective-
irradiation on the e-C DQ and ZQ transitions, which results in 13C-SE-DNP
enhancement, as can be seen in Fig. 17. The strength of the effective
irradiation on the 13C-SE transitions is proportional to the state-mixing,
such that it is $\omega_{1,\text{eff}}^{C}=|s_{C}|\omega_{1}$ for the 13C-SE-
DNP and even weaker for second order 13C-SE-DNP effects.

Figure 17: Simulated electron (black), 14N (red) and 13C polarizations as a
function of the MW irradiation frequency for an e-14N-13C spin system. The
polarizations are normalized according to the steady state electron
polarization. The 14N DNP spectrum was shifted in the y-axis for clarity. The
MW irradiation frequency plotted in MHz for convenience, and is referenced to
the electron Larmor frequency, $\omega_{e}=$94 GHz. The simulation parameters:
$\Delta\omega_{e}=$94 GHz, $\omega_{N}=$10 MHz, $\omega_{C}=$34 MHz,
$A_{z}^{N}=$98 MHz, $A_{x}^{N}$=-16 MHz, $A_{y}^{N}=$0 MHz,
$A_{x}^{C}=A_{y}^{C}=$5.4 MHz (corresponds to a 15.4 nm distance),
$\omega_{1}=$0.5 MHz, T${}_{1e}=$103 ms, T${}_{1N}=$1 s, T${}_{1C}=$100 s,
T${}_{2e}=$10 $\mu$s and T${}_{2N}=$T${}_{2C}=$100 $\mu$s. No cross relaxation
was added to the system.

As can be seen in Fig. 17, the addition of the 13C nucleus only slightly
alters the 14N-DNP spectrum. The same three features described above are still
visible here (marked 1,2 and 3 in the figure), in addition to several new and
narrow DNP features. The additional narrow features are a result of second-
order SE DNP lines involving the electron, the 14N and the 13C nuclei. For
example, MW irradiation on the transition
$|\alpha_{e},\tilde{1},\alpha_{C}^{*}\rangle\leftrightarrow|\beta_{e},\tilde{0},\beta_{C}^{*}\rangle$
will result in DNP enhancement of both the nitrogen and the carbon. As such,
both the 14N and the 13C nuclei show DNP enhancement at these SE mechanisms.
These effects are beyond the scope of the current work.

In addition to the narrow second-order SE DNP lines, the 13C-DNP spectrum
exhibits three 13C-SE pairs, one from each electron line (marked SE1, SE2 and
SE3 in the figure). These SEs appear at
$\omega=\Delta\omega_{e}+A_{z}^{N}\pm\omega_{C}$ (SE1),
$\omega=\Delta\omega_{e}-A_{z}^{N}\pm\omega_{C}$ (SE2) and
$\omega=\Delta\omega_{e}\pm\omega_{C}$ (SE3). The 13C-SE-DNP mechanisms result
in positive enhancement when irradiating on the
$|\beta_{e},\tilde{\chi}_{N},\alpha_{C}^{*}\rangle\leftrightarrow|\alpha_{e},\tilde{\chi}_{N},\beta_{C}^{*}\rangle$
transition and negative enhancement when irradiating on the
$|\beta_{e},\tilde{\chi}_{N},\beta_{C}^{*}\rangle\leftrightarrow|\alpha_{e},\tilde{\chi}_{N},\alpha_{C}^{*}\rangle$
transition, for $\tilde{\chi}_{N}=-\tilde{1}$, $\tilde{0}$ or $\tilde{1}$.

In summary, the DNP simulations for an e-14N-13C system exhibit a 13C-SE for
each of the three e-14N manifolds. In each case, the 13C-SE is independent of
the 14N spin state, and does not involve the 14N spin. Using this observation,
we justify the convolution method of simulating the 13C-DNP mechanisms (OE, SE
and CE) for each e-14N manifold separately (described above). Higher order
13C-DNP enhancement features that involve both the 14N spin as well as the 13C
spin are much more sensitive to the MW irradiation strength, and therefore, we
are able to neglect them in our analysis of the experimental results.

##  IX Low-Field Pulse-EPR Spectrometer and Data Processing

The resonance frequency of 2.5 GHz is achieved by mixing a 2.476 GHz local
oscillator with the output from a Tektronix AWG 7052 which is used to define
pulse waveforms on a 24 MHz carrier. The pulses are amplified to approximately
+27 dBm, then transmitted through a circulator to an antenna. At the end of
the coax line is an exposed wire which capacitively couples to a shielded
loop-gap resonator [85] (inspired by a previously published design [86]) that
is 1.27 cm long and has an inner diameter of 0.73 cm. The received echo signal
is amplified, mixed with the local oscillator and sampled at 400 MHz with a
digitizer. In-phase and quadrature components of the pulses and echoes are
transmitted and received, respectively, via IQ mixers. On-board averaging is
performed on the digitizer, which returns to the lab computer the averaged
echo waveform for a given set of experiment parameters. For each set of
experiment parameters, the phase of the pulses is cycled through 0, $\pi/2$,
$\pi$, and $3\pi/2$, and the resulting waveforms are phase shifted and added
constructively in post-processing, thereby averaging out phase-independent
systematic noise. The echo is then multiplied by a 1.0 $\mu$s Blackman window
to suppress noise outside of the echo in the time-domain buffer. The echo is
then demodulated to baseband and Fourier transformed. The echo amplitude is
then obtained by integrating over the Fourier transform of the echo with an
integration range of 4.0 MHz. The in-phase and quadrature components of the
integrated signal are the real and imaginary components of the echo amplitude.
The uncertainties are obtained by calculating the standard deviation of the
Fourier transformed buffer in the 2 MHz ranges above and below the 4 MHz range
used to obtain the integrated signal, then multiplying by the square root of
the number of points in the signal integration part of the buffer. In the
Hahn-echo experiments, the values of $\tau$ were chosen such that values of
$\log_{10}(\tau)$ had a uniform random distribution, and the order in which
they were performed was random as well. For the diamond powder, $\tau$ ranged
from 1.95 $\mu$s to 98.1 $\mu$s. The lengths of the $\pi/2$ and $\pi$ pulses
were 200 ns and 400 ns respectively. For the single crystal macle-cut diamond,
two data sets were combined: one with 28 points with $\tau$ ranging from 1.445
$\mu$s to 99.8065 $\mu$s and one with 37 points with $\tau$ ranging from 1.445
$\mu$s to 999.63 $\mu$s. The lengths of the $\pi/2$ and $\pi$ pulses were 250
ns and 500 ns respectively. The delay between the end of one trial and the
beginning of the repeat of that trial was 10 ms. All echo magnitudes were
normalized by dividing by the number of averages and then dividing by the
maximum strength echo obtained with the powder. For each set of parameters,
$2^{14}$ trials were averaged on-board the digitizer, and with the phase-
cycling described above, the total number of averages is $2^{16}$. The
inversion recovery experiments used similar randomization to that of the Hahn-
echo experiments. The values of $\tau_{1}$ were chosen such that values of
$\log_{10}(\tau_{1})$ had a uniform random distribution and random order. For
each set of parameters tested, back-to-back tests are performed with the
inverting pulse off (amplitude set to 0) and then on, giving echo amplitudes
$S_{\text{off}}$ and $S_{\text{on}}$, respectively. The same phase correction
is applied to both by setting $S_{\text{off}}$ to be purely real. Then the
inversion recovery signal plotted in Figure 7(b) is
$S_{\text{IR}}=\textrm{Re}[S_{\text{on}}]/\textrm{Re}[S_{\text{off}}]$. For
the diamond powder and the single crystal, $\tau_{1}$ ranged from 1 $\mu$s to
60 ms, and $\tau_{2}$ was set such that the time between the middles of pulses
2 and 3 was 3 $\mu$s. The delay between the end of one trial and the beginning
of the repeat of that trial was 100 ms. For the powder, the pulses were the
same as described in the above paragraph, but for the single crystal, a
recalibration was performed which led to $\pi/2$ pulses of 330 ns and $\pi$
pulses of 660 ns being used. The need for longer pulse durations for the
single crystal is due to a different resonator and sample holder being used.