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Optically Detected Cross-Relaxation Spectroscopy of Electron Spins in Diamond

The application of magnetic resonance (MR) spectroscopy at progressively smaller length scales may eventually permit"chemical imaging"of spins at the surfaces of materials and biological complexes. In particular, the negatively charged nitrogen-vacancy (NV-) centre in diamond has been exploited as an optical transducer for nanoscale nuclear magnetic resonance. However, the spectra of detected spins are generally broadened by their interaction with proximate paramagnetic NV- centres through coherent and incoherent mechanisms. Here we demonstrate a detection technique that can resolve the spectra of electron spins coupled to NV- centres, namely substitutional nitrogen (NS) and neutral nitrogen-vacancy (NV0) centres in diamond, through optically detected cross-relaxation. The hyperfine spectra of these spins are a unique chemical identifier, suggesting the possibility, in combination with recent results in diamonds harbouring shallow NV- implants, that the spectra of spins external to the diamond can be similarly detected.

centres in diamond, by identifying their respective spectral characteristics in the NV − cross-relaxation ODMR spectrum. This technique is the only ODMR method that can provide detailed spectra of the detected electron spins. Such information is essential for the detection and identification of radicals or relaxation centres by the NV − centre, and for the transduction of chemically informative NMR spectra by optical means.
We demonstrate this technique on an ensemble of NV − centres in a single-crystal diamond, host to several types of paramagnetic defects that may be identified from the ODMR spectra as shown in Fig. 2 (see Methods). The measured spectra have chemically informative fine features that differ vastly from ODMR spectra based on the allowed electron spin transitions of the NV − centre alone 20,21 . The majority of the fine features can be assigned to the N S centre 16,17,19,22 (see Supplementary Information), from which almost all calculated transitions (blue lines on top of each spectrum) are present in the observed spectra. For instance, the three calculated transition frequencies at B z ~ 0 mT (i.e., ambient field), namely 18.4, 130.2, and 148.6 MHz (Fig. S1a), are matched with peaks in the ODMR spectrum (Fig. 2a). The intensity of the peaks agrees well with the 1:3 population ratio of N S centres oriented either parallel to B z (for example, the peak at 240 MHz in Fig. 2d) or ~109° relative to B z (the peak at 223 MHz in Fig. 2d). Although the N S centre is a dark spin whose hyperfine parameters were determined by electron paramagnetic resonance (EPR) 22 , our observations show that the characteristic spectra of the N S centres can also be resolved by ODMR.
With the majority of the fine spectral features assigned to the N S centre, the remaining peaks are consistent with transitions from the NV 0 centre in the spin-3/2 4  There is excellent agreement between calculations and the observed transitions at 60, 70, 84, and 92 MHz at 1.44 mT (Fig. 2b), demonstrating that the NV 0 centre is optically detected with part of its characteristic spectrum resolved. As the magnetic field increases above 2 mT, most transitions of the NV 0 centre overlap with those of the N S centre, suggesting that weak magnetic field is required to separately resolve the two species.
Although both NV − and NV 0 centres are photoluminescent 26 , the NV 0 centre has not been detected previously using ODMR (unlike the NV − centre), and EPR spectra of the NV 0 centre have been observed only recently for its 4 A 2 exited state under laser illumination 23 .
We demonstrate here that the 4 A 2 exited state of the NV 0 centre can also be detected by ODMR.
Cross-relaxation provides a generic mechanism to convert the magnetic resonance of N S and NV 0 spins into changes in the steady-state fluorescence intensity of the NV − centre. At weak magnetic field, NV − -N S or NV − -NV 0 spin flip-flop processes become possible because the transition energy can be matched through contact with the multibody dipolar degrees of freedom of the system. These flip-flop processes can also exchange angular momentum with lattice, and multiple-quantum spin-interaction elements, such as i j S S + + and i j S S − − (where i and j denote different types of paramagnetic centres), could have non-negligible contributions to the cross-relaxation 27 . Thus, when resonant RF saturates one of the N S or NV 0 spin transitions, cross-saturation then leads to enhanced spin-lattice relaxation of the NV − electron spin, and thus decreases the polarization of the "brighter" 0 sublevels, leading to decreased fluorescence intensity 1 .
In addition to the fine features in the ODMR spectra, relatively broad peaks with full-width-at-half-maximum (FWHM) of ~20 MHz are also observed. The central frequency of each broad peak agrees well with the calculated energy difference between magnetically inequivalent NV − centres that are oriented either parallel to B z or ~109° relative to B z . The calculated energy difference is labelled by asterisks in Fig. 2  Cross-relaxation between magnetically inequivalent NV − centres can be directly observed by measuring the spin-lattice relaxation time of the NV − centre parallel to B z while saturating the transition of the NV − centre ~109° relative to B z (see Methods).

The N S centre
The substitutional nitrogen defect (N S ) in diamond is also known as the P 1 centre (Fig.   S1b). Like the NV − centre, it also has four possible orientations due to the static Jahn-Teller distortion from T d to C 3v symmetry 7 . In the spin-1/2 electronic ground state, the Hamiltonian of the N S centre is given by [8][9][10] :

The NV 0 centre
The electronic structure of the NV 0 centre is less well-understood than that of the NVor N S centre (Fig. S1c). The proposed spin-1/2 2 E ground state has not been observed by EPR, probably because it is either obscured by other paramagnetic defects or broadened by the dynamic Jahn-Teller distortion 11 . A recent optically excited EPR experiment has assigned the observed transitions of a trigonal nitrogen-containing defect in diamond to the spin-3/2 4 A 2 excited state of the NV 0 centre, which should have relatively low energy and long lifetime. The Hamiltonian of the NV 0 centre is given by 11-13 : ( ) ( ) ( )

Average distance between neighbouring centres
The typical concentrations of the relevant paramagnetic centres (NV − , N S , and NV 0 ) in diamond are on the order of magnitude of ppm. In such dilute spin systems, the average distance between one NV − centre and its neighbouring centres (NV − , N S , or NV 0 ) can be estimated by setting the probability of finding no neighbouring centre within a distance r of the NV − centre to 1/2 14 : where ρ is the concentration of the relevant defect species. The average distance R is then simply given by   cross relaxation occurs between the NV − and N S centres, between the NV − and NV 0 centres, and between magnetically inequivalent NV − centres. When one of the N S or NV 0 transitions is saturated by RF radiation, the fluorescence intensity of the NV − centres will decrease, resulting in the observed ODMR spectra.