Zero- to low-field J-spectroscopy with a diamond magnetometer

TL;DR

This work demonstrates a magnetometer-based approach to zero- to ultra-low-field NMR by using an NV-diamond sensor to detect SABRE-hyperpolarized acetonitrile. The method achieves a sensitivity of $13\ \mathrm{pT}/\sqrt{\mathrm{Hz}}$ with a broad bandwidth up to $580\ \mathrm{Hz}$ and a sub-millimeter stand-off, enabling direct detection of $^{1}$H–$^{15}$N J-couplings at $1.7\ \mathrm{Hz}$ and $3.4\ \mathrm{Hz}$. Comparisons with a commercial optically pumped magnetometer reveal that the diamond sensor can operate at much shorter distances and provide wider bandwidth, though spectral broadening from gradients and 1/f noise present challenges. The results establish a magnet-free, portable platform for chemically specific NMR in microscopic samples, with potential applications in biomedicine, industrial sensing, and field-deployable quantum diagnostics.

Abstract

We report measurements of zero- to ultra-low-field nuclear magnetic resonance (ZULF NMR) signals at frequencies of a few hertz with a diamond-based magnetic sensor. The sensing diamond is a truncated pyramid with 0.18 mm height and a 0.5 mm x 0.5mm base. The minimum stand-off distance is < 1 mm, and the sensor sensitivity is 13 pT/(Hz)^(1/2) at frequencies f above 5 Hz with 1/f-like behavior at lower frequencies. NMR signals were generated via signal amplification by reversible exchange (SABRE) parahydrogen-based hyperpolarization resulting in zero-field signals at 1.7 Hz and 3.4 Hz corresponding to the expected hetero-nuclear J-coupling pattern of acetonitrile. This work demonstrates a magnet-free platform for detecting chemically specific NMR signals at ultra-low frequencies paving the way for portable noninvasive diagnostics in microscopic sample volumes for biomedicine, industrial sensing through metal enclosures, and field-deployable quantum analytical devices.

Figures (9)

• Figure 1: a) Signal amplification by reversible exchange (SABRE) converts the parahydrogen spin order into population imbalance within the $J$-coupled spin states of $^1$H and $^{15}$N in acetonitrile; b) Energy level diagram of the XA$_3$ spin system of acetonitrile and observable zero-field transitions; c) Experimental zero-field NMR $J$-spectra of hyperpolarized acetonitrile measured with OPM-based (blue) and NV-diamond-based (gold) magnetometers. An offset was applied to the OPM data as a visual aid. The experimental sequence is sketched in the inset. It consisted of 15 s of parahydrogen bubbling, the application of a 860 $\mu$s, 6 $\mu$T magnetic pulse applied along the x-axis (corresponding to the gray box) and 40 s of data acquisition with one of the sensors.
• Figure 2: Experimental schematic. An NMR tube ending in a spherical sample volume, with parahydrogen bubbling connection. The pink dot in the OPM and the red dot in the NV are illustrating the sensitive volume position in the respective sensor geometry. The data acquisition unit (DAQ), lock-in amplifier (LIA), pulsing setup and optical assembly are symbolically sketched. The magnetic pulse to initiate a free magnetization decay was applied using the (Helmholtz) coil pair.
• Figure 3: Comparison of the measured and simulated $J$-coupling spectra of [$^{15}$N]-acetonitrile at different ZULF fields a) 40 nT, b) 10 nT and c) 0 nT. OPM (blue) in the middle, diamond sensor (gold) at the bottom and simulation (black) at the top. Diamond data is taken at 13.3 mm distance from the NMR sample center and Fourier transformed after 50 averages in the time domain. Dashed lines indicate the 1.7 Hz ($J$) and 3.4 Hz (2-$J$) frequencies. Note that for each field the simulation, OPM data and NV data are shifted as visual aid. The allowed transitions due to the adjusted selection rules for figure b) under a 10 nT transverse magnetic field (to the quantization axis) are sketched in the level structure as an inset. For c) the energy level structure becomes more complicated.The minor disagreement between simulation and experimental data can be explained with experimental imperfections like magnetic field gradients of the applied fields and the noise properties of the sensors, in particular the 1/f noise of the diamond sensor.
• Figure 4: Scaling of the NMR spectra as a function of background magnetic field and sensor characterization. Spectra a)-f) are taken while applying fields on the NMR sample using the piercing solenoid. The $^{1}$H dominated spectra measured using the OPM are shown in blue and using the diamond sensor in gold. NV data is 50 times averaged in the time domain before Fourier transforming it into an amplitude spectrum. The NV data in this figure are all recorded at a distance of 12.8 mm from the NMR sample center. The OPM data show no response above 500 Hz. $^{15}$N related precession resonances in acetonitrile measured with the OPM sensor at 0.8 $\mu$T and 7 $\mu$T are not detectable with the NV sensor within 50 averages. In c) and d) the diamond data are vertically offset to enable a clearer comparison with the OPM data. The mean signal level in d) for instance without this offset is approximately 1.5 pT [see h)]. g) Mean center frequency of all detected $^{1}$H and $^{15}$N dominated resonances at various bias fields using the OPM data The $^{15}$N dominated resonances are not resolvable at 14 $\mu$T. h) Histogram of the diamond sensor amplitude spectrum in the range of the $^{15}$N dominated resonances at 7 $\mu$T [from Fig. \ref{['fig:4']} d)] displayed as a probability density function (PDF) and fitted with a Rayleigh distribution. i) Noise spectral density of the diamond sensor to characterize its sensitivity inside the magnetic shield. The non-magnetic noise floor was recorded without magnetic field modulation, the electronic noise floor without laser light.
• Figure 5: Distance scaling of the NMR spectra. Distance is given from sensor volume center to sample volume center. The sample is a glass sphere with a 6.25 mm radius surrounded by a piercing solenoid with a 0.5 mm wall thickness. a) Normalized signal strength of the 2J-peak measured at different distances with respect to the NMR sample for the diamond (gold) and OPM (blue) sensor. The signal strength is the baseline subtracted numerical integral of the spectra between 2.5 Hz and 6 Hz capturing the $2J$ peak for the respective sensor. For each sensor, the signal strength is normalized to the value at the distance of 14.3 mm. The closest distance possible for the OPM sensor is 11.8 mm. The closest distance for the diamond sensor is 6.8 mm, dominated by the diameter of the piercing solenoid. The normalized signal strength is compared to the expected scaling for a dipole source (black). b) Sketch of the experiment. c) Spectra recorded using the OPM for various distances. d) Spectra recorded using the NV sensor for various distances. NV data are 50 times averaged in the time domain before Fourier transforming. The spectra in c) and d) are offset as a visual aid. Note, that the OPM data are recorded with natural abundance acetonitrile leading to the much smaller signal size compared to the diamond data.