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arXiv:2607.17734

Depth Determination of Individual Shallow NV-Centers via Spin-Lock NMR

Aaron Daniel, Beat Bürgler, Patrick Maletinsky, Patrick Potts

cond-mat.mes-hallquant-phSubmitted Jul 20, 2026• Announced Jul 21, 2026• 0 citations
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Abstract

Quantitative quantum sensing with shallow electron spins, such as those hosted by nitrogen-vacancy (NV) centers in diamond, requires accurate knowledge of the spin's depth below the host material's surface. A widely used approach infers this depth from the 1H nuclear magnetic resonance (NMR) signal of immersion oil on the diamond surface that can be detected using dynamical decoupling sequences such as XY8. However, finite-width pulses make XY8 sensitive to subharmonic responses, including unwanted contributions from nearby 13C spins, and its instrument-limited spectral resolution provides only sparse sampling of the narrow 1H NMR lineshape. Here, we introduce Spin-Lock NMR as an alternative approach to single-NV depth determination. By tuning the Spin-Lock Rabi frequency to the 1H Larmor frequency, the NV probes the 1H NMR signal through the Hartmann-Hahn resonance without the harmonic ambiguities of pulsed decoupling sequences and with substantially higher instrument-limited spectral resolution. We derive a quantitative Spin-Lock NMR fit function from a Markovian master equation that directly relates the measured spectrum to the NV depth. Our approach yields NV depth estimates in excellent agreement with the established XY8-based protocol across multiple NV centers and establishes Spin-Lock NMR as a robust alternative for quantitative single-NV depth determination. To demonstrate its applicability, we employ our method to investigate the 1H nuclear spin signal that is regularly reported to be present on diamond, even in the absence of immersion oil.

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Quantitative quantum sensing with shallow electron spins, such as those hosted by nitrogen-vacancy (NV) centers in diamond, requires accurate knowledge of the spin's depth below the host material's surface. A widely used approach infers this depth from the 1H nuclear magnetic resonance (NMR) signal of immersion oil on the diamond surface that can be detected using dynamical decoupling sequences such as XY8. However, finite-width pulses make XY8 sensitive to subharmonic responses, including unwanted contributions from nearby 13C spins, and its instrument-limited spectral resolution provides only sparse sampling of the narrow 1H NMR lineshape. Here, we introduce Spin-Lock NMR as an alternative approach to single-NV depth determination. By tuning the Spin-Lock Rabi frequency to the 1H Larmor frequency, the NV probes the 1H NMR signal through the Hartmann-Hahn resonance without the harmonic ambiguities of pulsed decoupling sequences and with substantially higher instrument-limited spectral resolution. We derive a quantitative Spin-Lock NMR fit function from a Markovian master equation that directly relates the measured spectrum to the NV depth. Our approach yields NV depth estimates in excellent agreement with the established XY8-based protocol across multiple NV centers and establishes Spin-Lock NMR as a robust alternative for quantitative single-NV depth determination. To demonstrate its applicability, we employ our method to investigate the 1H nuclear spin signal that is regularly reported to be present on diamond, even in the absence of immersion oil.
We report the formation of perfectly aligned, high-density, shallow nitrogen vacancy (NV) centers on the (111) surface of a diamond. The study involved step-flow growth with a high flux of nitrogen during chemical vapor deposition (CVD) growth, which resulted in the formation of a highly concentrated (>1019 cm−3) nitrogen layer approximately 10 nm away from the substrate surface. Photon counts obtained from the NV centers indicated the presence of 6.1 × 1015–3.1 × 1016 cm−3 NV centers, which suggested the formation of an ensemble of NV centers. The optically detected magnetic resonance (ODMR) spectrum confirmed perfect alignment (more than 99%) for all the samples fabricated by step-flow growth via CVD. Perfectly aligned shallow ensemble NV centers indicated a high Rabi contrast of approximately 30% which is comparable to the values reported for a single NV center. Nanoscale nuclear magnetic resonance demonstrated surface-sensitive nuclear spin detection and provided a confirmation of the NV centers' depth. Single NV center approximation indicated that the depth of the NV centers was approximately 9–10.7 nm from the surface with error of less than ±0.8 nm. Thus, a route for material control of shallow NV centers has been developed by step-flow growth using a CVD system. Our finding pioneers on the atomic level control of NV center alignment for large area quantum magnetometry.
High spatial resolution quantum sensing of near-surface nitrogen vacancy (NV) centers in diamond has enabled detection of magnetic, electrical, and thermal signals at the nanoscale. At depths of just a few nanometers, NV centers serve as localized quantum probes for external spins or low-dimensional materials, but their proximity to the surface also enhances decoherence caused by fluctuating nuclear spins. While advances in surface engineering have stabilized the charge state of NV centers at depths of tens of nanometers, achieving both ultra-shallow implantation (0.5-2 nm) and long-term spin coherence remains a central challenge. In this work, we show using first-principles modeling that, by exploiting the interaction of surface-induced strain and weak dc magnetic fields, the spin coherence times of 1-nm-deep NV centers can be greatly improved near the spin-phonon-confined regime at room temperature in 12C-rich diamonds. We also demonstrate that this protocol benefits ~ 10-nm-deep NV centers in natural diamond, enabling vector magnetometry at the nanoscale. Shallow NV centers in diamond are advantageous for quantum sensing but suffer from surface magnetic noise. Using first-principles simulations supported by experiments, the authors show that a combination of small magnetic fields and surface strain can significantly enhance spin coherence of 1 nm-deep NV centers.
Nitrogen vacancy centers in diamond (NVs) are point defects well suited to quantum sensing of magnetic fields. NV spin states can be initialized and read out optically with high spatial resolution, enabling detection of pL-scale volumes of nuclear spins. Using Coherently Averaged Synchronized Readout (CASR), standard NMR spectroscopy techniques such as free decay, spin echo, and PGSE have been performed with Hz-scale spectral resolution using NV-diamond sensors. However, using NV detection for conventional high-resolution NMR at multi-tesla fields is challenging due to the need to manipulate NV electronic spins at resonance frequencies 100 GHz or higher. Low-field J-coupling spectroscopy provides an alternative path to chemical resolution in a regime more easily accessible to NVs. Here, we demonstrate homonuclear and heteronuclear J-coupling spectroscopy using an NV-NMR spectrometer based on permanent magnets operating at $\sim$890 kHz proton Larmor frequency (bias magnetic field $\sim21mT).ThisfieldstrengthenableschemicalcharacterizationbasedonJ−couplingusingsequencessuchasSynchronizedEcho(SyncE)andSpin−EchoDoubleResonance(SEDOR),whichdonotrequirethestrongchemicalshiftdispersionandpristinefieldhomogeneityofhigh−fieldNMR.ThefrequencyrangeiseasilydetectedbyNVsusingstandardXYdynamicaldecouplingsequencesandiswell−suitedforapplyingOverhauserDNP,whichcanboostprotonsignalbytwoordersofmagnitude.WeacquireinitialNV−NMRmeasurementsofT21 mT). This field strength enables chemical characterization based on J-coupling using sequences such as Synchronized Echo (SyncE) and Spin-Echo Double Resonance (SEDOR), which do not require the strong chemical shift dispersion and pristine field homogeneity of high-field NMR. The frequency range is easily detected by NVs using standard XY dynamical decoupling sequences and is well-suited for applying Overhauser DNP, which can boost proton signal by two orders of magnitude. We acquire initial NV-NMR measurements of T21mT).ThisfieldstrengthenableschemicalcharacterizationbasedonJ−couplingusingsequencessuchasSynchronizedEcho(SyncE)andSpin−EchoDoubleResonance(SEDOR),whichdonotrequirethestrongchemicalshiftdispersionandpristinefieldhomogeneityofhigh−fieldNMR.ThefrequencyrangeiseasilydetectedbyNVsusingstandardXYdynamicaldecouplingsequencesandiswell−suitedforapplyingOverhauserDNP,whichcanboostprotonsignalbytwoordersofmagnitude.WeacquireinitialNV−NMRmeasurementsofT_1,T, T,T_2,andOverhauserDNPinglycerolbeforeadvancingtoSEDORspectroscopyofmethanol−, and Overhauser DNP in glycerol before advancing to SEDOR spectroscopy of methanol-,andOverhauserDNPinglycerolbeforeadvancingtoSEDORspectroscopyofmethanol−^{13}Candamethanol−C and a methanol-Candamethanol−^{13}C/acetonitrile−2−C/acetonitrile-2-C/acetonitrile−2−^{13}$C mixture at sample volumes $\sim$50 pL, in which we demonstrate measurement of 1JCH^1J_\text{CH}1JCH​ couplings and resolution between species. We also acquire a homonuclear J-coupling spectrum of a natural-abundance propylene carbonate sample.
Abstract The nitrogen-vacancy (NV) center in diamond is the most promising candidate for quantum sensing because of its beneficial properties. For quantum-sensing applications, a shallow NV center is critical for approximating the sensing target on a diamond surface. Such shallow NV centers are strongly affected by the diamond surface termination. The properties of shallow NV centers in hydrogen-, oxygen-, and fluorine-terminated diamond have been well studied. In recent years, silicon-terminated diamond has also been investigated; however, the effect of silicon-terminated diamond on the properties of shallow NV centers remains unclear. Recently, the suitability of nitrogen-terminated diamond for shallow NV centers has been theoretically and experimentally examined; however, quantum sensing has not yet been performed. In this work, we evaluated the effect of silicon and nitrogen termination on shallow NV centers. The negatively charged state of shallow NV centers was unstable below silicon termination. In contrast, the properties of shallow NV centers in nitrogen-terminated diamond were satisfactory for quantum sensing and enabled 1H NMR detection. Our results are in good agreement with previous reports on silicon and nitrogen terminations and provide the perspective that the stability of shallow NV centers highly depends on the polarity of electron affinity of the diamond surface.
Precise positioning of nitrogen-vacancy (NV) centers is crucial for their application in sensing and quantum information. Here we present a new purely optical technique enabling determination of the NV position with nanometer resolution. We use a confocal microscope to determine the position of individual emitters along the optical axis. Using two separate detection channels, it is possible to simultaneously measure reflected light from the diamond surface and fluorescent light from the NV center and statistically evaluate both signals. An accuracy of 2.6 nm for shallow NV centers was achieved and is consistent with other techniques for depth determination.
Nitrogen vacancy centers (NV) in proximity to diamond surfaces are promising nanoscale quantum sensors. However, their coherence properties are negatively affected by magnetic and electric surface noise, whose origin and detailed impact have remained elusive. Using atomistic models of diamond surfaces derived with density functional theory, together with decoherence time calculations with cluster correlation expansion methods, we quantify the effects of surface crystallographic orientation and functionalization, and of the density of unpaired electrons on the NV Hahn-echo time T2T_2T2​. We determine a crossover depth at which T2T_2T2​ ceases to be limited by surface nuclear spins and recovers the bulk-limited value. We find that for static surface-electron baths, the ratio between the NV depth and the separation between surface electron spins determines a transition from fast-fluctuating to quasi-static noise, leading to a dependence of T2T_2T2​ on orientation for specific surfaces. We also find that the modulation of T2T_2T2​ by spin-phonon relaxations leads to motional-narrowing at sub-microsecond relaxation times. Importantly, our calculations show that it is only when accounting for surface-spin in-sequence hopping that measured T2T_2T2​ values as a function of depth can be reproduced, thus highlighting the importance of hopping-mediated models to describe the surface spin noise affecting NV sensors. Overall, our work provides clear guidelines for engineering diamond surfaces to achieve enhanced NV coherence for quantum sensing and information processing applications.