Probing Spin Defects via Single Spin Relaxometry

Abstract

Spin defects in solids offer promising platforms for quantum sensing and memory due to their long coherence times and optical addressability. Here, we integrate a single nitrogen-vacancy (NV) center in diamond with scanning probe microscopy to discover, read out, and spatially map arbitrary spin-based quantum sensors at the nanoscale. Using the boron vacancy ($\mathrm{V}_\mathrm{B}^-$) center in hexagonal boron nitride$\unicode{x2013}$an emerging two-dimensional spin system$\unicode{x2013}$as a model, we detect its electron spin resonance indirectly via changes in the spin relaxation time ($T_1$) of a nearby NV center, eliminating the need for optical excitation or fluorescence detection of the $\mathrm{V}_\mathrm{B}^-$. Cross-relaxation between NV and $\mathrm{V}_\mathrm{B}^-$ ensembles significantly reduces NV $T_1$, enabling quantitative nanoscale mapping of defect densities beyond the optical diffraction limit and clear resolution of hyperfine splitting in isotopically enriched h$^{10}$B$^{15}$N. Our method demonstrates interactions between 3D and 2D spin sensors, establishing NV centers as versatile probes for characterizing otherwise inaccessible spin defects.

Figures (5)

• Figure 1: NV $T_1$ relaxometry at CR condition with $\mathrm{V}_\mathrm{B}^-$ in hBN$_\text{nat}$: (a) A scanning NV microscope containing a single NV center is brought near a 90-300 nm thick hBN$_\text{nat}$ sample that has been irradiated with He ions to create an ensemble of $\mathrm{V}_\mathrm{B}^-$ centers. The NV center's photoluminescence (PL) is collected using a confocal optical setup. A microwave field $B_\text{MW}$ is supplied to both the NV and the nearest $\mathrm{V}_\mathrm{B}^-$ centers by an antenna positioned near the cantilever tip. When the microwave frequency matches the spin resonance frequency of the NV or $\mathrm{V}_\mathrm{B}^-$ centers, transitions between the ground state sublevels $m_s=0\leftrightarrow\pm1$ states are driven coherently. (b) Calculated spin resonance dispersions of the NV and $\mathrm{V}_\mathrm{B}^-$ centers with the magnetic field oriented 29° from the surface normal. Cross-relaxation occurs near 127 G bias, where the NV $m_s = 0 \leftrightarrow +1$ transition overlaps with the $\mathrm{V}_\mathrm{B}^-$$m_s = 0 \leftrightarrow -1$ transition, highlighted by the green dot. (c) CW-ODMR spectra of the NV center before (green curve) and after (purple curve) engaging with the hBN sample, and of the $\mathrm{V}_\mathrm{B}^-$ centers in hBN (red curve), measured under the cross-relaxation condition shown in (b). All spectra are fitted using Lorentzian functions. The left and right vertical axes correspond to the NV and $\mathrm{V}_\mathrm{B}^-$ data, respectively. Only the $m_s = 0 \leftrightarrow +1$ transition of the NV is shown. The arrows denote via their colors which vertical axis each trace is plotted against. (d) NV spin $T_1$ measurement in non-CR condition (purple curve, fitted $T_1 = 1.34 \pm 0.19$ ms) and CR condition (red curve, $T_1 = 406 \pm 34\,\mu$s), both measured after engaging the hBN$_\text{nat}$ sample. Curves are single exponential fits $\propto\exp(-t/T_1)$.
• Figure 2: $T_1$-MR detection of hyperfine structure: (a) CW-ODMR spectrum of $\mathrm{V}_\mathrm{B}^-$ centers in $\mathrm{h}^{10}\mathrm{B}^{15}\mathrm{N}$ showing four hyperfine-split lines, fitted with Lorentzian functions (red). A magnetic field of 123 G is applied out-of-plane. (b) Extracted ODMR center frequencies of the NV center (red) and $\mathrm{V}_\mathrm{B}^-$ centers (black) as a function of magnetic field, with solid lines representing fitted curves. The hyperfine line positions (dashed) are calculated using the average $A_{zz}$, revealing four expected cross-relaxation conditions corresponding to the crossover points between the NV and $\mathrm{V}_\mathrm{B}^-$ transitions. (c) NV single-$\tau$$T_1$-MR detection of $\mathrm{V}_\mathrm{B}^-$ hyperfine structure by sweeping the magnetic field through the four CR conditions. The magnetic field is converted to frequency detuning between the NV and $\mathrm{V}_\mathrm{B}^-$ transitions and plotted in units of $A_{zz}$ in $\mathrm{h}^{10}\mathrm{B}^{15}\mathrm{N}$ (67 MHz). The data are fitted using a sum of four Lorentzian functions, where dips 1 and 3 share one set of parameters, and dips 2 and 4 share another (fit shown in red). Here, the free evolution time $\tau$ is chosen to be 2 ms, given that the tip's non-CR $T_1$ measured immediately before this $T_1$-MR measurement is $2.09 \pm 0.25$ ms (see Supplementary Figure S16a). (d) NV single-$\tau$$T_1$-MR measurement of hBN$_\text{nat}$ under varying magnetic field. The field axis is converted to frequency detuning and plotted in units of $A_{zz}$ in hBN$_\text{nat}$ (44 MHz). Data are fitted using a Lorentzian function (red curve). The $\tau$ in this case is 0.7 ms, and the tip's $T_1$ measured at the non-CR condition is $1.21 \pm 0.32$ ms (see Supplementary Figure S16b). (e) A short-$T_1$ NV tip's spin $T_1$ relaxation curve before engaging the sample, showing $T_1$ of $191 \pm 7$$\mu$s. (f) NV $T_1$ values measured as a function of magnetic field (blue symbols with error bars), showing four distinct cross-relaxation dips. The curve is fitted with a sum of Lorentzian functions and plotted in units of $A_{zz}$ in $\mathrm{h}^{10}\mathrm{B}^{15}\mathrm{N}$ (67 MHz).
• Figure 3: Nanoscale imaging of $\mathrm{V}_\mathrm{B}^-$ density in hBN$_\text{nat}$ using NV-$\mathrm{V}_\mathrm{B}^-$ cross relaxometry: (a) Optical microscope image of hBN$_\text{nat}$ sample on gold surface, with different colors corresponding to variations in the hBN thickness. The light-colored area in the center has thickness $\sim$90 nm compared to the surrounding pink/purple areas with thickness $\sim$190 nm. Here a portion of the right edge of the light-colored area is highlighted in a blue polygon which was measured by the scanning NV in panel (f). (b) Raman spectroscopy map showing the ratio of the $E'$ peak to the $E_{2g}$ peak across the sample area displayed in panel (a). (c) SRIM simulations of the ion energy losses (normalized per ion) of 30 keV He$^+$ (10,000 ions simulated) for 90 nm and (d) 250 nm hBN on gold, suggesting thickness-dependent non-uniform defect density distribution. (e) Monte Carlo simulation of the cross-relaxometry contribution to the NV relaxation rate $\Gamma_1^\text{CR}$ as a function of the $\mathrm{V}_\mathrm{B}^-$ density and three different NV-to-sample distances. Horizontal gray bar shows values of $\Gamma_1^\text{CR}$ associated with range of the color scale in (f). (f) $\mathrm{V}_\mathrm{B}^-$ density map, obtained as a single-$\tau$$T_1$ spatial scan over a free-evolution time $\tau=250 \,\mu$s which was converted to $\mathrm{V}_\mathrm{B}^-$ density via the Monte Carlo simulation in panel (e). The size of each pixel is 100 nm. The measurement was conducted at the CR condition. Inset: The profile of $\mathrm{V}_\mathrm{B}^-$ density as a function of position, over the line indicated by the white dashed line in (f). The data is fit to the edge-spread function (red) yielding a step width of 46 nm.
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