Understanding the Magnetic Resonance Spectrum of Nitrogen Vacancy Centers in an Ensemble of Randomly-Oriented Nanodiamonds, Supporting Information

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1 Understanding the Magnetic Resonance Spectrum of Nitrogen Vacancy Centers in an Ensemble of Randomly-Oriented Nanodiamonds, Supporting Information Keunhong Jeong *1,2, Anna J. Parker *1,2, Ralph H. Page 1, Alexander Pines 1,2, Christophoros C. Vassiliou 1,2, Jonathan P. King 1,2 1. Department of Chemistry, University of California, Berkeley. 2. Materials Sciences Division, Lawrence Berkeley National Laboratory * These authors contributed equally to this work jpking@berkeley.edu Materials and Methods Samples and Experimental Setup The single crystal sample is a 2 x 2 x 0.2 mm [1 0 0] surface oriented synthetic diamond produced via a high-pressure high-temperature (HPHT) synthesis (Sumitomo Electric Carbide Inc.). NV - centers were formed at a density of 7.8 ppm by irradiation with 1 MeV electrons and annealing at 800 C for 2 hours. The powder sample was 10 mg of 100 nm fluorescent diamond nanoparticles (Adamas Nanotechnologies Inc.) The experimental setup was as described previously 1 with modifications to perform 2D ODMR. The sample was mounted in a goniometer inside an electromagnet (TEL-Atomic Inc.). Optical pumping was performed with a 532 nm laser (Coherent Verdi G15) set to 1.0 W, illuminating the sample with a Gaussian beam with a waist of 1.5 mm. Microwave irradiation was supplied by a Hewlett Packard 8763C synthesized signal generator with 13 dbm output amplified by a 3 W amplifier (Mini-Circuits ZVE-3W-83+ or ZVE-3W-183+ depending on frequency). The microwave field was created at the sample with a 3 mm wire loop. Fluorescence intensity was measured by an avalanche photodiode (Thorlabs Inc.). The microwave synthesizer was operated in amplitude modulation mode with the provided by a 373 Hz sinusoid from a lock-in amplifier (Stanford Research Systems, SR830), which also detected the output of the avalanche photodiode. The microwave modulation was chosen to be sufficiently slow relative to the S1

2 dynamics of the NV - center to provide good contrast. The lock-in amplifier integration time constant was 30 ms. The signal corresponds to the in-phase component of the photodiode voltage detected at the modulation frequency. A custom software application incremented the microwave frequency and, after a 25 ms delay, recorded the lock-in amplifier signal. Single crystal data were acquired from 1 MHz to 15 GHz in 1 MHz increments. For the powder, a 0.25 MHz frequency increment was used. Fluorescence contrast was collected at a range of frequencies and magnetic field values to construct the 2D plots. For 1D overtone spectra, 100 averages were required for sufficient signal to noise ratio in the same condition. Constant frequency spurious signals manifest as vertical bands in the 2D ODMR data. These artifacts were suppressed by summing each data set over magnetic field and subtracting the resulting 1D array from each row in the 2D data. This is described further in the section titled 2D-ODMR Data Processing. Simulation All simulations and data processing were done with custom scripts written in MATLAB (The Mathworks, Inc). For a given defect orientation, the NV - spin energy eigenvalues and transition frequencies are calculated for a range of magnetic fields. The spectrum for each transition n was represented as a Gaussian function with magnitude κ and width υ #. We assume the linewidths are determined by the distribution of static magnetic fields within the sample and therefore the linewidth is proportional to the effective gyromagnetic ratio for a given transition, γ %&&,# = γ % m +,#. The linewidth may therefore be calculated using the following relation: υ # = υ, m +,#, where υ, is an empirically-determined linewidth and m +,# is the change in the z component of the electron spin angular momentum for transition n, given by: m +,# = φ &,# S 0 φ &,# φ 2,# S 0 φ 2,#. In order to generate a powder spectrum, we add spectra from various defect orientations with appropriate weighting. Assuming crystal orientations are randomly distributed, the probability density of finding a crystal axis at an angle θ with the external field is ½ sin θ. In order to achieve the appropriate weighting, we make the transformation dz = sin θ dθ or z = cos θ, so that a uniform sampling of z then approximates the random distribution of NV - axis orientations. S2

3 A misalignment of the microwave field would result in higher ODMR intensity from NV - centers oriented near 90, since the mixing of states generates a nonzero transition matrix element for the S 0 operator. Our assumed microwave field orientation resulted in a satisfactory fit to the data. To form the 2D plot, the intensity of the predicted lineshape as a function of frequency is binned by frequency (1 MHz bin width). The intensity factors provide a prediction of relative intensity, and are fit to the data with an empirical scaling factor. The empirical single-quantum linewidth υ, was estimated from the full width at half maximum (FWHM) of the 0 to +1 transition for defects in the single-crystal diamond aligned along the magnetic field (θ = 0 ). This linewidth was averaged over 15 values fitted from spectra acquired at fields ranging from G. We found υ, = 17.2 ± 1.3 MHz. For powder spectra, the magnetic field is not easily extracted from a single transition frequency as in single crystals and is therefore a parameter in the fitting along with υ,, an amplitude scaling factor (a), and a lower bound to the predicted linewidth ( υ DE ). This final factor, υ DE, is the minimum observed linewidth of a transition from an NV - center in a single randomlyoriented crystal, determined empirically. This lower bound represents the effect of transverse fields and time dependent processes causing homogeneous broadening that are not captured in the model. A least-squares fit was therefore applied to the data in Figure 4b in the main text to find the following values: a = 3.5 x 10-5 a.u., υ DE = 28.3 MHz, υ, = 54.2 MHz, and B = 1313 G (averaged squared error per point = 1.6 x a.u.). In order to simulate the 2D spectra of NV - centers in a nanodiamond powder, we uniformly sampled 10 4 values in z for 1 z 1 and converted them to values of θ (for 0 θ π) to simulate a spectrum of 10 4 crystallites (Figure 3a-c) using the values of υ DE and υ, given above. The 2D plot was generated using the same procedure as for simulating a single NV - orientation, where the 2D spectra of each value of θ are summed to give the total 2D spectrum. The magnetic field dependence of the width of the two powder patterns (one characterized by single quantum transitions and the other by overtone transitions) was analyzed by comparing the characteristic widths (σ) of the two powder patterns. The characteristic width is defined as the square root of the second moment of the distribution, which is calculated using the following relation: S3

4 σ = 1 μ, ω μ N μ, O I ω dω Here, ω is frequency, I(ω) is the spectrum of the powder pattern, and μ,/n are the zeroth and first moments of the spectrum. 2D-ODMR Data Processing Figure S1. 2D ODMR data without noise filtering. a) 2D ODMR of NV - center in diamond powder, ranging from 2 GHz to 6 GHz in magnetic fields from 0 to ~2020 G. b) 2D ODMR of NV - center in diamond powder, ranging from 6 GHz to 10 GHz in magnetic fields from 0 to ~2020 G. c) Combined data of a) and b). d) 2D ODMR of NVcenter in diamond powder, ranging from 6 GHz to 15 GHz in various magnetic fields from 0 to ~3300 G. Raw 2D ODMR data are shown in in Fig. S1. The vertical bands represent constant frequency spurious signals and do not correspond to magnetic resonance signal. The data presented in the main text was filtered by summing signal intensity at each frequency over all magnetic fields, then subtracting this value from each column. This has the effect of removing the constantfrequency signals without significantly impacting the ODMR data. S4

5 References 1. King, J. P., Jeong, K., Vassiliou, C. C., Shin, C. S., Page, R. H., Avalos, C. E., Wang, H.- J. & Pines, A. Room-temperature in situ nuclear spin hyperpolarization from optically pumped nitrogen vacancy centers in diamond. Nat. Commun. 6, 8965 (2015). S5