Nitrogen Substitutions Aggregation and Clustering in Diamonds as Revealed by High-Field Electron Paramagnetic Resonance

Diamonds have been shown to be an excellent platform for quantum computing and quantum sensing applications. These applications are enabled by the presence of defects in the lattice, which are also known as color centers. The most common nitrogen-based defect in synthetic diamonds is the paramagnetic nitrogen substitution (P1) center. While the majority of quantum applications rely on nitrogen-vacancy (NV) centers, the properties of the latter are heavily influenced by the presence and the spatial distribution of the P1 centers. Hence, understanding the spatial distribution and mutual interactions of P1 centers is crucial for the successful development of diamond-based quantum devices. Unlike NV centers, P1 centers do not have a spin-dependent optical signature, and their spin-related properties, therefore, have to be detected and characterized using magnetic resonance methods. We show that using high-field (6.9 and 13.8 T) pulsed electron paramagnetic resonance (EPR) and dynamic nuclear polarization (DNP) experiments, we can distinguish and quantify three distinct populations of P1 centers: isolated P1 centers, weakly interacting ones, and exchange-coupled ones that are clustered together. While such clustering was suggested before, these clusters were never detected directly and unambiguously. Moreover, by using electron–electron double resonance (ELDOR) pump–probe experiments, we demonstrate that the latter clustered population does not exist in isolation but coexists with the more weakly interacting P1 centers throughout the diamond lattice. Its presence thus strongly affects the quantum properties of the diamond. We also show that the existence of this population can explain recent hyperpolarization results in type Ib high-pressure, high-temperature (HPHT) diamonds. We propose a combination of high-field pulsed EPR, ELDOR, and DNP as a tool for probing the aggregation state and interactions among different populations of nitrogen substitution centers.


T Field Swept ED -EPR of Diamond A
The asymmetry in signal intensity between the left and right sides of the experimental spectrum of diamond A in Figure 2a, as well as the remaining discrepancy in signal intensity between the simulation and the experiment, are due to the dependence of power output on the mm-wave frequency and the presence of standing waves in the quasi-optical system.For accurate signal intensity, we measured an echodetected (ED) field sweep EPR spectrum at a constant frequency (Figure S1), which indeed shows the expected symmetric EPR spectrum.The ED field-swept EPR spectrum was measured using the same pulse sequence and parameters as the frequency-stepped EPR spectrum.In order to confirm that the resolved lines observed at low-field CW EPR experiments between the resolved outer

T ED-EPR of Diamond B
An EPR spectrum of diamond B acquired at 13.8 T overlaid with the corresponding simulation is shown in Figure S3.An additional signal marked with an asterisk belongs to the NV center and is thus not accounted for by the simulation.

Calculation of the g-tensor
The g-tensor was determined from the simulation of the frequency sweep at 13.8 T. To accurately calculate the magnetic field we used the measured radio frequency (RF) of the diamond NMR signal.Since the gyromagnetic ratio is defined for the free atom, we need to account for the chemical shift (CS) of diamond relative to it.For  13 NMR all CS values are reported relative to the reference sample of Tetramethylsilane (TMS) in deuterated chloroform (Me4Si in CDCl3), thus we began by calculating the CS of TMS relative to the free  13 atom and then accounted for the CS of diamond relative to TMS.We used the literature value for the theoretical Larmor frequency of free   The  0 for the ED-EPR spectra was calculated using this value.
Both CS values result in final g-tensor values of  ⊥ = 2.00220 ± 0.00001;  ∥ = 2.00218 ± 0.00001 with the difference in the two CS values manifesting itself as the difference in the gtensor values of 0.000006-0.000007,which is smaller than the error.

Figure S1 .
Figure S1.Field swept ED-EPR spectrum of P1 centersin diamond A acquired at 6.9 T.

Figure S2 .
Figure S2.(a) and (b) show CW field sweep of HPHT diamonds A and B acquired at X-band.The magentacolored arrows point to the additional transitions between the resolved  14 hyperfine lines, which are visible only with high microwave power.
14 hyperfine lines belong to a different exchange-coupled species than those responsible for the broad signal in pulsed EPR spectra, we recorded CW EPR spectra 34 T. Sharp, resolved lines appear between the   = ±1 and   = 0 lines in CW EPR spectra acquired with high microwave power as shown in FiguresS2a and b.Therefore both types of exchange-coupled P1 centers exist in Diamond A and Diamond B samples, but the two have very different EPR spectra.

Figure S3 .
Figure S3.Overlay of experimental and simulated ED-EPR spectrum of P1 centers in diamond B acquired at 13.8 T.An additional non-P1 peak is marked with an asterisk.

Figure
Figure S4 shows ELDOR with   = 193.45GHz, corresponding to the excitation of the exchange-coupled population on the right side of the EPR spectrum.The spectrum in the figure mirrors the one shown in Figure 4b of the main text and corroborates our conclusions.

Figure S4 .
Figure S4.ELDOR spectrum acquired at 193.450 GHz of P1 centers in diamond A overlaid with the experimental EPR line.The asterisks mark the positions of non-eSD  14 peaks.Spin-Lattice Relaxation MeasurementsAn example of saturation recovery experimental data, measuring spin-lattice relaxation time  1 , for  − = 193.397GHz is shown in FigureS5.The experiment was recorded using the pulse sequence in the inset with parameters listed in the materials and method section in the main text.The data in FigureS5was fitted using monoand stretched-exponential functions showing a clear preference for the latter.

13
atom of 25.1504 MHz, and the experimental frequency of 1% Me4Si in CDCl3 sample 25.145020 MHz, both at the magnetic field strength where proton NMR signal of TMS equals 100.0 MHz.(All values taken from Bruker NMR properties of selected isotopes table) Diamond CS relative to TMS is known as 33 or 36 ppm1,2 , thus the CS of diamond relative to the free atom is -180.913or -177.913ppm which for the 100 MHz proton field give 25.14588 MHz.

Table S1 .
The relaxation times measured at the other  − frequencies for diamond A are summarised in TableS1and Figure3in the main text.Summary of  1 and   relaxation times measured across the EPR spectrum of diamond A, with  as the stretching exponent for the stretched exponential fit of the  1 relaxation.