Limits of absolute vector magnetometry with nitrogen-vacancy centers in diamond

Phys. Rev. Res. 8, 013054 (2026) · DOI: 10.1103/28t7-7gcn · arXiv: 2504.20750

License: CC BY 4.0.

Abstract

The nitrogen-vacancy (NV) center in diamond has become a widely used platform for quantum sensing. The four NV axes in mono-crystalline diamond specifically allow for vector magnetometry, with magnetic-field sensitivities reaching down to fT/sqrt(Hz). The current literature primarily focuses on improving the precision of NV-based magnetometers. Here, we study the experimental accuracy of determining the magnetic field from measured spin-resonance frequencies via solving the NV Hamiltonian. We derive exact, analytical, and fast-to-compute formulas for calculating resonance frequencies from a known magnetic-field vector, and vice versa, formulas for calculating the magnetic-field vector from measured resonance frequencies. Additionally, the accuracy of often-used approximations is assessed. Finally, we promote using the Voigt profile as a fit model to determine the linewidth of measured resonances accurately. An open-source Python package accompanies our analysis.

Figures

13 panels with data across 7 figures. Each panel page shows the plot, its columns and its files; each data.csv begins with a header naming the paper, the panel, the source, the license and the provenance route.

Fig. 1

• panel (a): ODMR map of the four NV axes of a monocrystalline diamond: relative fluorescence (%) against magnetic-field value (mT) and MW frequency (MHz), for a field of fixed direction. The white dashed lines, labelled Theory, are the resonance frequencies from the analytical solution of Eq. (7). data.csv
• panel (b): ODMR map of the four NV axes of a monocrystalline diamond: relative fluorescence (%) against magnetic-field angle (rad) and MW frequency (MHz), as the magnetic-field vector rotates. The white dashed lines are the resonance frequencies from the analytical solution of Eq. (7). data.csv

Fig. 2

Illustrative figure, no extractable data. Shown in the paper PDF.

Fig. 3

• panel (1): Heatmap of the systematic error (nT) of the approximation, Eq. (20), that the field is aligned with the NV axis, against magnetic-field absolute value $|\vec{B}|$ (mT) and misalignment angle $\theta$ (°), log axes and log scale. White lines are contours at $10^1$ to $10^6$ nT; their printed labels and the 1.5 bottom tick of the printed scale are not shown. data.csv

Fig. 4

• panel (a): Histogram of the computation time ($\mu$s) of the analytical approach: number of occurences, as printed, against computation time, for 600 benchmark points, each the average over 500 runs. data.csv
• panel (b): Histogram of the computation time ($\mu$s) of a typical numerical approach: number of occurences, as printed, against computation time, for 600 benchmark points, each the average over 500 runs. data.csv

Fig. 5

• panel (1): An example ODMR resonance: relative fluorescence (%) against MW frequency (MHz), data as markers, with three fits drawn as lines, labelled Voigt $R^2 = 0.989$, Lorentz $R^2 = 0.985$ and Gauss $R^2 = 0.964$. data.csv

Fig. 6

• panel (a): Voigt fit parameters of the example ODMR resonance of Fig. 5 against MW power (dBm): contrast $C_\text{V}$ (%) on the left axis and FWHM linewidth $\alpha_\text{V}$ (MHz) on the right axis, one marker per power step. data.csv
• panel (b): FWHM linewidth (MHz) against MW power (dBm), three series: the Lorentzian part $\alpha_\text{L}$ and the Gaussian part $\alpha_\text{G}$ of the Voigt fit, and the total $\alpha_\text{V}$. data.csv
• panel (c): Broadening factor $d$ (left axis) and magnetic-field sensitivity $\eta$ ($\mu$T$/\sqrt{\text{Hz}}$) (right axis) against MW power (dBm), from the Voigt fits of panel (a). data.csv

Fig. 7

• panel (a): Computed angle $\theta$ (deg) against magnetic-field absolute value (mT) for a field parallel to the NV axis, three curves as in the legend: correct value ($\theta = 0°$), Approximation $D \gg E$ and our Equation (11). data.csv
• panel (b): Computed angle $\theta$ (deg) against magnetic-field absolute value (mT) for a field perpendicular to the NV axis, three curves as in the legend: correct value ($\theta = 90°$), Approximation $D \gg E$ and our Equation (11). The approximation is absent where it is unsolvable; the gray band marking that region in the print is not drawn. data.csv

Fig. 8

• panel (b): ODMR spectrum recorded with only the y coil turned on, at 4 A: relative fluorescence (%) against MW frequency (MHz), with the fit, labelled $R^2 = 0.991$. data.csv
• panel (c): ODMR spectrum recorded with only the z coil turned on, at 4 A: relative fluorescence (%) against MW frequency (MHz), with the fit, labelled $R^2 = 0.983$. data.csv

Cite

Dennis Lönard, Isabel Cardoso Barbosa, Stefan Johansson, Jonas Gutsche, Artur Widera. Limits of absolute vector magnetometry with nitrogen-vacancy centers in diamond. Phys. Rev. Res. 8, 013054 (2026). https://doi.org/10.1103/28t7-7gcn

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