A single spin in hexagonal boron nitride for vectorial quantum magnetometry

Nat. Commun. 16, 4947 (2025) · DOI: 10.1038/s41467-025-59642-0

License: CC BY 4.0.

Abstract

Quantum sensing based on solid-state spin defects provides a uniquely versatile platform for nanoscale magnetometry under diverse environmental conditions. Operation of most sensors used to-date is based on projective measurement along a single axis combined with computational extrapolation. Here, we show that an individually addressable carbon-related spin defect in hexagonal boron nitride is a multi-axis nanoscale sensor with large dynamic range. For this spin-1 system, we demonstrate how its spin-dependent photodynamics give rise to three optically detected spin resonances that show up to 90% contrast and are not quenched under off-axis magnetic field exceeding 100 mT, enabling μT/Hz⁻¹ᐟ² sensitivity. Finally, we show how this system can be used to unambiguously determine the three components of a target magnetic field via the use of two bias fields. Alongside these features, the room-temperature operation and the nanometer-scale proximity enabled by the van der Waals host material further consolidate this system as a promising quantum sensing platform.

Figures

29 panels with data across 4 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 (b): Confocal photoluminescence (PL) map of the hBN device, PL (kcps) against scan position ($\mu$m), showing individually addressable defects. The print has no axis ticks; as printed, the deposit's $y$ runs across and its $x$ downward. Colour scale 0 to 200 kcps as printed; brighter pixels saturate. data.csv
• panel (c): PL spectrum of the carbon-related hBN defect: PL normalised to its maximum against photon energy (eV). The deposited counts (cps) are kept in a second column. data.csv
• panel (e-1): cwODMR spectrum at $B = 0$ mT: contrast $C$ (%) against microwave frequency $\nu$ (GHz) on the printed broken axis, measured means (dark blue) with standard errors (grey bars as printed, drawn in the marker colour) and the shaded Gaussian fits to $f_{\mathrm{A}}$ and $f_{\mathrm{B}}$. data.csv
• panel (e-2): cwODMR spectrum at $B = 51$ mT, field at 51 degrees in the defect frame: contrast $C$ (%) against microwave frequency $\nu$ (GHz) on the printed broken axis, measured means (dark blue) with standard errors and the shaded Gaussian fits to $f_{\mathrm{A}}$, $f_{\mathrm{B}}$ and $f_{\mathrm{C}}$. data.csv

Fig. 2

• panel (b-1): Background-corrected second-order autocorrelation $g^{(2)}(t)$ against delay $t$ (ns): measured points (dark blue), global model fit (red) and the grey band of model predictions within 3$\times$ the minimum fit error. As printed, the delays are evenly spaced (a category axis), from $-7.7\times10^5$ to $7.7\times10^5$ ns. data.csv
• panel (b-2): Residuals of the global model fit to $g^{(2)}(t)$ against delay $t$ (ns), computed as fit minus data (the sign the print plots), on the evenly spaced delay axis of panel b-1; the print clips the axis at $\pm 0.1$. data.csv
• panel (c): Spin-dependent optical initialisation: contrast $C = \Delta$PL/PL$_0$ (%) against delay $\tau_{\mathrm{r}}$ ($\mu$s), measured means (dark blue) with one-standard-deviation error bars, the global model fit (red) and the grey band of model predictions within 3$\times$ the minimum fit error. data.csv
• panel (d): Modified spin-relaxation experiment: contrast $C = \Delta$PL/PL$_0$ (%) against delay $\tau$ ($\mu$s), measured means (dark blue) with one-standard-deviation error bars, the global model fit (red) and the grey band of model predictions within 3$\times$ the minimum fit error. data.csv
• panel (e): Simulated ODMR contrast (%) against the spin selectivity of the reverse ($k_{\mathrm{S}_0 \to \mathrm{G}_y}/k_{\mathrm{S}_0 \to \mathrm{G}}$, x) and direct ($k_{\mathrm{E}_y \to \mathrm{S}_0}/k_{\mathrm{E} \to \mathrm{S}_0}$, y) intersystem crossing rates, with the measured defects as grey circles sized by their cwODMR contrast (largest 30 %). data.csv

Fig. 3

• panel (a-1): cwODMR transition frequencies $\nu$ (GHz) against field angle $\theta$ (degree), 50 mT bias field rotated in the defect yz plane ($\phi = 90^\circ$): measured $f_{\mathrm{A}}$ (green), $f_{\mathrm{B}}$ (brown), $f_{\mathrm{C}}$ (blue) with the model curves and the pale bands the print draws around them. data.csv
• panel (a-2): cwODMR contrast of $f_{\mathrm{A}}$ normalised by the zero-field contrast of $f_{\mathrm{B}}$, against field angle $\theta$ (degree), 50 mT field in the yz plane: measured points with error bars and the contrast simulated with the model and parameters of Fig. 2. data.csv
• panel (a-3): cwODMR contrast of $f_{\mathrm{B}}$ normalised by the zero-field contrast of $f_{\mathrm{B}}$, against field angle $\theta$ (degree), 50 mT field in the yz plane: measured points with error bars and the contrast simulated with the model and parameters of Fig. 2. data.csv
• panel (a-4): cwODMR contrast of $f_{\mathrm{C}}$ normalised by the zero-field contrast of $f_{\mathrm{B}}$, against field angle $\theta$ (degree), 50 mT field in the yz plane: measured points with error bars and the contrast simulated with the model and parameters of Fig. 2. data.csv
• panel (b-1): Calculated cwODMR contrast of $f_{\mathrm{A}}$, normalised (0 to 1), as a colour map against $B_y$ and $B_z$ (mT) up to 200 mT with $B_x = 0$; the grey arc marks the 50 mT field rotated in panel (a). The print's 100 mT scale bar is replaced by axes. data.csv
• panel (b-2): Calculated cwODMR contrast of $f_{\mathrm{B}}$, normalised (0 to 1), as a colour map against $B_y$ and $B_z$ (mT) up to 200 mT with $B_x = 0$; the grey arc marks the 50 mT field rotated in panel (a). The print's 100 mT scale bar is replaced by axes. data.csv
• panel (b-3): Calculated cwODMR contrast of $f_{\mathrm{C}}$, normalised (0 to 1), as a colour map against $B_y$ and $B_z$ (mT) up to 200 mT with $B_x = 0$; the grey arc marks the 50 mT field rotated in panel (a). The print's 100 mT scale bar is replaced by axes. data.csv
• panel (c-1): cwODMR transition frequencies $\nu$ (GHz) against field angle $\phi$ (degree), 50 mT bias field rotated in the defect xy plane ($\theta = 85^\circ$): measured $f_{\mathrm{A}}$ (green), $f_{\mathrm{B}}$ (brown), $f_{\mathrm{C}}$ (blue) with the model curves and the pale bands the print draws around them. data.csv
• panel (c-2): cwODMR contrast of $f_{\mathrm{A}}$ normalised by the zero-field contrast of $f_{\mathrm{B}}$, against field angle $\phi$ (degree), 50 mT field in the xy plane: measured points with error bars and the contrast simulated with the model and parameters of Fig. 2. data.csv
• panel (c-3): cwODMR contrast of $f_{\mathrm{B}}$ normalised by the zero-field contrast of $f_{\mathrm{B}}$, against field angle $\phi$ (degree), 50 mT field in the xy plane: measured points with error bars and the contrast simulated with the model and parameters of Fig. 2. data.csv
• panel (c-4): cwODMR contrast of $f_{\mathrm{C}}$ normalised by the zero-field contrast of $f_{\mathrm{B}}$, against field angle $\phi$ (degree), 50 mT field in the xy plane: measured points with error bars and the contrast simulated with the model and parameters of Fig. 2. data.csv
• panel (d-1): Calculated cwODMR contrast of $f_{\mathrm{A}}$, normalised (0 to 1), as a colour map against $B_x$ and $B_y$ (mT) up to 200 mT with $B_z = 0$; the grey arc marks the 50 mT field rotated in panel (c). The print's 100 mT scale bar is replaced by axes. data.csv
• panel (d-2): Calculated cwODMR contrast of $f_{\mathrm{B}}$, normalised (0 to 1), as a colour map against $B_x$ and $B_y$ (mT) up to 200 mT with $B_z = 0$; the grey arc marks the 50 mT field rotated in panel (c). The print's 100 mT scale bar is replaced by axes. data.csv
• panel (d-3): Calculated cwODMR contrast of $f_{\mathrm{C}}$, normalised (0 to 1), as a colour map against $B_x$ and $B_y$ (mT) up to 200 mT with $B_z = 0$; the grey arc marks the 50 mT field rotated in panel (c). The print's 100 mT scale bar is replaced by axes. data.csv
• panel (e): Saturated cwODMR spectra for field along the defect $y$ axis up to 140 mT: each measured spectrum (dark blue points) is drawn at its field $B$ (mT) against $\nu$ (GHz), its height on the print's contrast scale (15 % for the $f_{\mathrm{A}}$ spectra, 28 % for $f_{\mathrm{B}}$), with the transition frequencies of $f_{\mathrm{A}}$, $f_{\mathrm{B}}$, $f_{\mathrm{C}}$ against $B_y$. data.csv
• panel (f-1): Spin eigen-energies (Energy/$h$, GHz) of the ground-state Hamiltonian against field $B_x$ (mT) along the defect x axis (black), with the calculated optically initialised population of each sublevel as purple circles (area relative to the largest, as printed). data.csv
• panel (f-2): Spin eigen-energies (Energy/$h$, GHz) of the ground-state Hamiltonian against field $B_y$ (mT) along the defect y axis (black), with the calculated optically initialised population of each sublevel as purple circles (area relative to the largest, as printed). data.csv
• panel (f-3): Spin eigen-energies (Energy/$h$, GHz) of the ground-state Hamiltonian against field $B_z$ (mT) along the defect z axis (black), with the calculated optically initialised population of each sublevel as purple circles (area relative to the largest, as printed). data.csv

Fig. 4

• panel (c): Simulated cwODMR spectrum under the 100 mT bias field B$_1$: contrast (%) against microwave frequency (GHz) on the printed broken axis, one window per resonance, area under the curve shaded as printed. The zoom insets with the shifts caused by each target-field component are not hosted. data.csv
• panel (d): Simulated cwODMR spectrum under the 100 mT bias field B$_2$: contrast (%) against microwave frequency (GHz) on the printed broken axis, one window per resonance, area under the curve shaded as printed. The zoom insets with the shifts caused by each target-field component are not hosted. data.csv

Cite

Carmem M. Gilardoni et al. (14 authors). A single spin in hexagonal boron nitride for vectorial quantum magnetometry. Nat. Commun. 16, 4947 (2025). https://doi.org/10.1038/s41467-025-59642-0

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