Microwave-free nuclear magnetic resonance at molecular scales

The implementation of nuclear magnetic resonance (NMR) at the nanoscale is a major challenge, as the resolution of conventional methods is limited to mesoscopic scales. Approaches based on quantum spin probes, such as the nitrogen-vacancy (NV) centre in diamond, have achieved nano-NMR under ambient conditions. However, the measurement protocols require application of complex microwave pulse sequences of high precision and relatively high power, placing limitations on the design and scalability of these techniques. Here we demonstrate NMR on a nanoscale organic environment of proton spins using the NV centre while eliminating the need for microwave manipulation of either the NV or the environmental spin states. We also show that the sensitivity of our significantly simplified approach matches that of existing techniques using the NV centre. Removing the requirement for coherent manipulation while maintaining measurement sensitivity represents a significant step towards the development of robust, non-invasive nanoscale NMR probes.

T he discovery of nuclear magnetic resonance (NMR), and its related technologies, was one of the great scientific achievements of the twentieth century, contributing to significant advances in areas ranging from materials science to healthcare. However, the limitation in sensitivity of traditional induction-based detection has required the development of different detection schemes in order to extend NMR technology to the nanoscale, where the study of processes at the molecular scale is of intense interest. The nitrogen-vacancy (NV) centre in diamond 1 has seen remarkable developments as a high-sensitivity nanoscale magnetometer [2][3][4][5][6][7][8][9][10] . In recent years, the NV centre has been utilized to achieve nanoscale NMR at sensitivities close to that required for single-proton detection [11][12][13][14][15][16] . Its roomtemperature operation also makes it an ideal candidate for biological nano-NMR 17,18 . However, current NMR protocols using the NV centre require the application of complex, high-power and high-precision microwave pulsing sequences in order to filter the environmental spectrum, placing significant constraints on nano-magnetic resonance imaging applications 19 . The application of strong microwave pulses is potentially invasive given the attendant electric fields as an inevitable by-product in the generation of the magnetic control fields 20 . In addition, achieving such quantum control on a large ensemble of NV centres over a wide field of view 21 , or on a scanning probe microscopy tip [22][23][24] , remains a challenge due to the requirement for homogeneity in the driving field. Finally, the adaptability of such high-precision control to dynamic environments such as in vitro 17 is unknown.
In this work, we demonstrate microwave-free nano-NMR on a nanoscopic sample of proton nuclear spins within an organic sample external to the diamond. We achieve this via static field tuning to the natural spin interactions between sensor and target, and measure a change in the longitudinal relaxation time, T 1 (ref. 25). The resulting all-optical microwave-free protocol can be applied in a non-invasive manner (for example, through optical excitation constrained within the diamond using total internal reflection 26 ), significantly widening the range of applications where NV-based nano-NMR can be used. We demonstrate the microwave-free NMR technique using both isotopic forms 14 NV and 15 NV, which exhibit different fundamental characteristics in this context, and use the data to estimate the NV-sample distance (10-12 nm for the studied NVs), as well as the number of protons detected (o10 5 ). In addition, we directly compare our microwave-free nano-NMR to the prevailing microwave control based nano-NMR technique, and find that both approaches offer comparable sensitivity.

Results
Principle of T 1 -based NMR. The microwave-free technique for magnetic resonance spectroscopy is based on T 1 relaxometry detection 7,27-30 and precise magnetic field tuning to bring the NV into resonance with the Zeeman split target spin transitions [31][32][33][34] . This technique was proposed and demonstrated for quantitative electron spin resonance spectroscopy using an ensemble of NV centres 25 and extended to hyperfine-coupled nuclear spin spectroscopy with single NV centres 35 . The ultimate goal of nano-NMR is the spectroscopic detection of bare nuclear spins in molecular systems (Fig. 1a). Without the assistance of strong hyperfine coupling this is a significant challenge due to the low nuclear magnetic moment 35,36 . Applying the T 1 -NMR technique to this problem requires the precise tuning of the NV probe to near its ground state level anti-crossing (GSLAC), where the system's dynamics are dominated by a relatively complex landscape of electron-nuclear spin mixing [36][37][38] , in order to bring the electronic NV transitions into resonance with the nuclear spin transition. At a resonance point (which in principle could occur both before and after the GSLAC as depicted in Fig. 1b), the longitudinal relaxation time T 1 of both the NV centre and the environmental spin(s) are significantly reduced, due to their mutual dipole-dipole interaction 25,33,35 . To probe these resonances, the strength, B, of a static background magnetic field aligned with the NV quantization axis, is swept near the GSLAC (BE1,024 G) and the T 1 decay is optically measured at each corresponding transition frequency.
The transitions associated with two simple resonances before and after the GSLAC are depicted in Fig. 1b. The relaxation rate of the initialized NV spin state |0i to | À 1i, induced at one of these resonances (over and above the intrinsic relaxation rate G 1,int , assumed constant in the field range considered), is set by the sum of the contributions of all resonant target spins, The contribution of each ith spin can be expressed as 35 where g NV and g t are the gyromagnetic ratios of the NV and (a) Schematic of the experimental setup. The protons within an organic sample external to the diamond are the targets probed by a shallow nitrogen-vacancy (NV) centre. A 532 nm green laser is used to initialize the NV spin while the red photoluminescence (PL) is measured via a single-photon detector. The background magnetic field is aligned with the NV quantization axis with a variable strength, B. (b) Schematic of the energy levels of the NV (spin states |0i and | À 1i, neglecting the hyperfine structure for clarity) and of a target nuclear spin such as 1 H (states |mi and |ki). As B is swept across the ground state level anti-crossing (GSLAC), two resonances can in principle occur where the NV and target spins can exchange energy via their mutual magnetic dipole-dipole interaction, causing an increase in their respective longitudinal relaxation rate. (c) The measurement sequence consists of laser pulses to initialize and subsequently read out the NV spin state, separated by a wait time t. (d) Polar plot of the relaxation rate induced by a single spin, G 1,ext , as a function of the angle y between the quantization axis and the NV-target separation. The solid (dashed) line corresponds to the after-GSLAC (before-GSLAC) resonance. The values are normalized by the global maximum, so that the outer circle corresponds to maximum strength. The polar plot is rotated by y ¼ 54.7°, which is the angle between an NV below a (100) diamond surface, and the closest target spin on the surface. target spins, respectively; y i is the polar angle of separation between the two spins relative to the quantization axis; r i is the separation distance; G Ã 2 is the total dephasing rate of the spin system; m 0 is the vacuum permeability; : is Planck's constant; and the ± sign refers to the resonance after ( þ ) and before ( À ) the GSLAC. Near resonance, the photoluminescence (PL) signal after an evolution time t is given by (see refs 27,28 and Supplementary Note 1) where I 0 is a normalization constant, CB0.2 is the PL contrast of the T 1 decay, and the total relaxation rate is 25 with o NV the NV transition frequency and o t ¼ g t B the Larmor frequency of the target spin, which vary with B as depicted in Fig. 1b. Equation (2) is valid when the intrinsic relaxation (G 1,int ) is dominated by magnetic noise acting on the |0i2| À 1i transition, which is generally the case near the GSLAC (Supplementary Note 1). Experimentally, rather than recording a full curve I PL (t), it is generally sufficient to probe a single, well chosen value of t, from which one can retrieve G 1,tot (B) using equation (2), provided I 0 and C are initially calibrated via measurement of a full decay trace I PL (t,B) at a given B. Such a single-point T 1 measurement is done via an initialize, wait, and read-out scheme (Fig. 1c), without any microwave pulsing of either the NV spin or target spin. We note that the relaxation rate induced by each target spin, expressed by equation (1), has a different overall angular dependence for the two resonances before and after the GSLAC, as illustrated in Fig. 1d. This difference allows y to be inferred, in the case of a single target spin, by directly comparing the transition strengths on either side of the GSLAC. The simplified picture of resonances near the GSLAC shown in Fig. 1b is in reality modified by hyperfine interactions within the NV centre, associated with the nitrogen nuclear spin which is either 14 N (spin-1) or 15 N (spin-1/2) [36][37][38] . While sensing experiments generally use implanted 15 NV centres, as they can be distinguished from native centres of the most abundant isotope, , it has become apparent from recent experiments 36 that 14 NV and 15 NV centres present distinct differences when considering their application for T 1 -NMR spectroscopy due to their different GSLAC electron-nuclear state mixing properties 36 . For this reason, both isotopic forms of the NV probe were investigated in this work.
Nano-NMR detection of 1 H spins. To demonstrate T 1 -based NMR, a custom-built confocal microscope was used, incorporating a permanent magnet mounted on a 3-axis scanning stage to precisely control the applied background field 35 . The diamond sample comprises a high purity CVD homoepitaxial layer, grown in a Seki AX6500 diamond reactor. The sample was implanted firstly with 3.5 keV 15 N þ ions and then with 3.5 keV 14 N þ ions (expected implantation depth in the range 5-15 nm (ref. 40)). Both implants were done to a dose of 0.5 Â 10 9 cm À 2 and this was followed by annealing in vacuum at 800°C and acid cleaning in a boiling mixture of sulfuric acid and sodium nitrate. The diamond has a (100) surface, so that the NV centres have their symmetry axis at 54.7°to the surface normal (Fig. 1a,d). The NV centres were identified as either 15 NV or 14 NV via their characteristic hyperfine splittings under low-power optically detected magnetic resonance (ODMR) 39,41 . As a standard proton sample, we used either the oil employed with the oilimmersion objective lens, or a layer of Poly(methyl methacrylate) (PMMA) deposited on the diamond surface 11,12 . We first report the results of T 1 -NMR using a 14 NV centre. The ODMR spectrum as a function of the background field strength (B) around 1024 G is shown in Fig. 2a, revealing a characteristic GSLAC structure resulting from hyperfine couplings and dynamic polarization of the NV nuclear spin 36,42 . The NV transitions are shown as black lines, while the 1 H spin transition is shown in green and corresponds to a Larmor frequency o H E4.4 MHz in this range of fields. Due to the NV avoided crossing before the GSLAC, there is only one measurable resonance point with 1 H (green dot in Fig. 2a). To probe this resonance, the PL intensity is measured as a function of B, using evolution times t ¼ 1 ms, which serves as reference for normalization (as no T 1 decay is expected at such time scale), and t ¼ 200 ms, optimized to probe the 1 H resonance. In the instance of an unknown signal frequency and strength, a scan with an evolution time of T1 2 would give optimal signal in the low-signal regime. The resulting T 1 -NMR spectrum is shown in Fig. 2b Fig. 2c, confirming a change in relaxation time. Fitting the two curves to equation (2) yields the values G 1,int ¼ 2.1 ± 0.2 Â 10 3 s À 1 and G þ 1;ext ¼5:9 AE 0:6Â10 3 s À 1 . The proton signal was confirmed to be associated primarily with the immersion oil, as the signal significantly reduced upon removal of the oil (Supplementary Note 4).
We now demonstrate T 1 -NMR using a 15 NV centre from the same diamond and proton sample (immersion oil) as was used in the 14 NV case. In ref. 36, it has been shown that a typical 15 NV exhibits two potential resonances with 1 H, before and after the GSLAC, but that the stronger after-GSLAC resonance overlaps with a feature intrinsic to the GSLAC structure. To circumvent this problem and allow the two resonances to be observed, we selected a 15 NV centre exhibiting a hyperfine coupling (here of E4 MHz) to a nearby 13 C, thereby shifting the intrinsic feature away from the NV-proton resonance 43 (Supplementary Note 2). The results for this particular 15 NV centre are shown in Fig. 3. The ODMR spectrum as a function of B around 1024 G is shown in Fig. 3a, revealing the characteristic 15 NV GSLAC structure 36 Fig. 3a. A T 1 -NMR spectrum recorded using evolution times t ¼ 1 ms (reference) and t ¼ 20 ms is shown in Fig. 3b and reveals three main features, labelled A, B and C. The first two dips (A and B) are seen only for t ¼ 20 ms and correspond to the cross-relaxation resonances with 1 H. The third dip, (C), exhibiting a far stronger decay, which is also visible at short time t ¼ 1 ms, corresponds to the intrinsic feature discussed above 36 .
From Fig. 3b, it can be seen that the lower-field 1 H resonance (feature A) is significantly weaker than the higher-field resonance (feature B). To resolve this resonance more clearly, a longer evolution time, t ¼ 100 ms, was employed resulting in the spectrum shown in Fig. 3c plotted against the detuning o NV À o H . Fitting the data to equation (2) along with equation (3) gives G 1,int ¼ 1.5 ± 0.4 Â 10 3 s À 1 and G À 1;ext ¼1:5 AE 0:3Â10 3 s À 1 for this resonance. Similarly, the spectrum around the 1 H resonance past the GSLAC (Fig. 3d) is fitted to give G 1,int ¼ 1.3±0.2 Â 10 3 s À 1 and G þ 1;ext ¼5:2 AE 0:6Â10 3 s À 1 . The measured ratio between the extrinsic relaxation rates of the two resonances is This is in qualitative agreement with the ratio of 6.3 predicted by integrating equation (1) over a semi-infinite bath of protons on a (100) surface. This calculation neglects the effects of state mixing due to the GSLAC structure. It has previously been shown that under optimized conditions it would take E5 min of integration to detect a single proton at a distance of 4 nm showing that single proton detection via T 1 -NMR is possible on realistic experimental timescales 35 .
Comparison to T 2 -based NMR. We now report a theoretical and experimental comparison of T 1 -NMR spectroscopy to the prevailing existing technique of T 2 -based spectroscopy, which relies on locking a dynamical decoupling pulse sequence on the NV electronic spin state (usually XY8-N where N is the number of microwave p pulses) to the nuclear spins' Larmor frequency [12][13][14][15]44 . Theoretically, the sensitivity can be compared by examining the signal-to-noise ratio (SNR) derived under the identical conditions of a shallow NV centre detecting an ensemble of nuclear spins as in the geometry of Fig. 1a. In the small signal regime (that is, G a;ext ( G a;int with a ¼ 1 for T 1 and a ¼ 2 for T 2 ), we find that the maximum SNR in T 1 and T 2 sensing schemes can be expressed as (Supplementary Note 3) respectively, where T Ã 2 ¼ 1=G Ã 2 , T 1 ¼ 1/G 1,int and T 2 ¼ 1/G 2,int are the intrinsic characteristic times of the NV centre. Note that here T 2 is the extended decoherence time under the considered dynamical decoupling sequence 45 . The constant A is given by where R is the photon count rate under continuous laser excitation, t ro ¼ 300 ns is the read-out time per pulse, T tot is the total experiment time, r is the proton density in the semi-infinite sample, and d is the NV depth. Evaluating the numeric factors, we obtain the ratio between the SNRs, For a near-surface NV centre in a bulk diamond (dE10 nm), typical approximate values are T Ã 2 ¼ 2 ms, T 1 ¼ 2 ms and T 2 ¼ 200 ms, which yields a ratio SNR T 1 ;max SNRT 2 ;max $ 1. In other words, our microwave-free T 1 -based NMR spectroscopy technique is similarly sensitive to the existing T 2 -based approach without requiring complex microwave pulse sequences. This theoretical comparison assumes a stable magnetic field in both cases.
To verify this and further compare the two approaches, we conducted a comparative measurement using a single shallow 14 NV centre, where the diamond was coated with a layer of PMMA. Figure 4 shows the hydrogen spectrum measured via T 1 relaxometry (a) and via an XY8-256 sequence (b). Both spectra were acquired in a total time of about 2 h, and show a clear feature at the 1 H frequency with a similar signal-to-noise ratio. In addition, one can compare the NV depth, d, inferred through fitting the appropriately normalized data from each method, assuming the signal comes from a semi-infinite bath of protons on a (100) surface (see Supplementary Notes 1 and 3). Using a proton density of r ¼ 56 nm À 3 , we find d ¼ 10.7 ± 0.1 nm from the T 1 data, against d ¼ 10.5 ± 0.1 nm from the XY8 data, indicating a high level of consistency between the two approaches. From the inferred depth, we deduce that 50% of the signal is generated by the E6 Â 10 4 closest protons, corresponding to a detection volume of about (10 nm) 3 (refs 12,13).
The spectral resolution of T 1 spectroscopy, however, is currently limited by the dephasing rate G Ã 2 ¼ 1/G Ã 2 (equation (3)), while it is limited by T 2 with the XY8 method, and can be improved further using correlation spectroscopy [46][47][48] . We note that both the sensitivity and spectral resolution of the T 1 approach could be dramatically improved by optimizing T Ã 2 , which motivates further work towards understanding and mitigating the decoherence of near-surface NV centres [49][50][51] .

Discussion
In summary, we have demonstrated the detection of proton spins external to a diamond using a microwave-free nano-NMR technique based on T 1 relaxometry of a single NV centre. While the electron-nuclear spin physics near the NV GSLAC are relatively complex, we have shown that the microwave-free T 1 protocol can nevertheless be implemented and the 1 H resonances observed, which we have demonstrated using both isotopic forms of the NV centre. In addition, we have shown a sensitivity comparable to an existing nano-NMR protocol which requires quantum state manipulation via microwave excitation. The sensitivity as well as the spectral resolution of our approach could be improved via engineering of the diamond surface. We note that the resulting all-optical technique can be implemented using non-invasive excitation constrained within the diamond, using total internal reflection. The removal of microwave quantum control eliminates the possibility of spurious harmonics within the measurement and opens up applications in areas where such control is inherently difficult to achieve and/or invasive, such as spectroscopic imaging over wide fields of view or in scanning probe microscopy experiments. Finally, it is worth mentioning that the demonstrated T 1 protocol can be used not only for sensing but also to hyperpolarise the target nuclear spins via spin transfer, which may have important applications in medical NMR.
Data availability. All relevant data are available from the authors on request.