Isotope engineering for spin defects in van der Waals materials

Spin defects in van der Waals materials offer a promising platform for advancing quantum technologies. Here, we propose and demonstrate a powerful technique based on isotope engineering of host materials to significantly enhance the coherence properties of embedded spin defects. Focusing on the recently-discovered negatively charged boron vacancy center (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{{{{{{{\rm{V}}}}}}}}}_{{{{{{{{\rm{B}}}}}}}}}^{-}$$\end{document}VB−) in hexagonal boron nitride (hBN), we grow isotopically purified h10B15N crystals. Compared to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{{{{{{{\rm{V}}}}}}}}}_{{{{{{{{\rm{B}}}}}}}}}^{-}$$\end{document}VB− in hBN with the natural distribution of isotopes, we observe substantially narrower and less crowded \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{{{{{{{\rm{V}}}}}}}}}_{{{{{{{{\rm{B}}}}}}}}}^{-}$$\end{document}VB− spin transitions as well as extended coherence time T2 and relaxation time T1. For quantum sensing, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{{{{{{{\rm{V}}}}}}}}}_{{{{{{{{\rm{B}}}}}}}}}^{-}$$\end{document}VB− centers in our h10B15N samples exhibit a factor of 4 (2) enhancement in DC (AC) magnetic field sensitivity. For additional quantum resources, the individual addressability of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{{{{{{{\rm{V}}}}}}}}}_{{{{{{{{\rm{B}}}}}}}}}^{-}$$\end{document}VB− hyperfine levels enables the dynamical polarization and coherent control of the three nearest-neighbor 15N nuclear spins. Our results demonstrate the power of isotope engineering for enhancing the properties of quantum spin defects in hBN, and can be readily extended to improving spin qubits in a broad family of van der Waals materials.

Introduction-Optically-addressable spin defects in solid-state materials have emerged as one of the leading prospects for expanding the boundary of modern quantum technologies [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17].Recently, spin defects in atomically-thin van der Waals materials have attracted significant research interest for their innate ability to integrate with heterogeneous optoelectronic and nanophotonic devices [18][19][20][21][22][23][24].Among a wide range of two-dimensional host materials, hexagonal boron nitride (hBN) stands out as a promising candidate owing to its large bandgap (∼ 6 eV) and exceptional mechanical, thermal, and chemical stability [25,26].Unlike established host materials such as diamond and silicon carbide, neither nitrogen nor boron has stable isotopes with zero nuclear spin, potentially to the detriment of spin defects in hBN.In particular, the presence of such a dense nuclear spin bath can substantially broaden electronic transitions and shorten the coherence time of spin defects.To this end, prior experimental works have focused on designing dynamical decoupling sequences to isolate spin defects from the local nuclear spin environment in hBN [24,27].
In this work, we demonstrate isotope engineering of hBN as a more fundamental way of strengthening the capability of spin defects for quantum applications.By carefully optimizing the isotope species and preparing hBN samples with 15 N and 10 B , we drastically improve the spin coherent properties of the recently discovered negatively charged boron-vacancy defect (V − B ) [18,19].
We note that a prior study has investigated the effect of changing only boron isotopes in hBN and do not observe significant improvements in the spin properties of V − B [28].Importantly, this technique of isotope engineering is fundamental because of its full compatibility with other ongoing V − B optimization efforts, making it an necessity for future V − B improvement and applications.Although here we focus on a specific spin defect in hBN, we would also like to highlight that the approach is exemplary for engineering other spin defects in general host materials.
Optimal Isotopes of hBN -We start with identifying the optimal isotope species in hBN for the embedded V − B defects.The V − B center harbors an electronic spin triplet ground state, |m s = 0, ±1⟩, which can be optically initialized and read out at room temperature [18].The Hamiltonian of the system, including both the electronic degree of freedom and nearby nuclear spins, can be written as where D gs = (2π) × 3.48 GHz is the ground state zerofield splitting between |m s = 0⟩ and |m s = ±1⟩, B z is the external magnetic field aligned along the out-of-plane c axis of hBN (ẑ direction), S and S z are the electronic spin-1 operators, I j and I j z are the spin operators for the j th nuclear spin (including both nitrogen and boron) with hyperfine tensors A j , and γ e = (2π)×2.8MHz/G and γ j n are the electronic and nuclear spin gyromagnetic ratios arXiv:2307.06441v2[quant-ph] 4 Jan 2024 (Fig. 1a,c).We note that, for nuclei with I ≥ 1, there is a small additional nuclear spin dependent energy shift corresponding to higher multipole moments.Nevertheless, this term only acts on the nuclear spin degree of freedom and thus has no effect on the measured electronic spin transitions to leading order.
Throughout our experiment, we consistently operate within magnetic fields of B z ≲ 760 G such that the energy splitting (D gs ± γ e B z ) ≳ (2π) × 1.35 GHz between the electronic ground state levels |m s = 0⟩ and |m s = ±1⟩ is much greater than the hyperfine interaction strength, i.e. |A j | ≲ (2π) × 100 MHz.As a result, the hyperfine term can be approximated as j SA j I j ≈ j A j zz S z I j z = ( j A j zz I j z )S z to leading order, where all remaining terms are suppressed under the secular approximation.This term leads to an energy shift of the electronic spin transition that is dependent on the nuclear spin configuration; averaging across all different configurations gives rise to spectral crowding [29,30] of the electronic spin transition with an overall width proportional to 2|γ n I| (see Methods).
Fig. 1a summarizes the nuclear spin quantum numbers and gyromagnetic ratios of four stable atomic isotopes in hBN.Intuitively, a lower nuclear spin quantum number leads to fewer hyperfine states and contributes to less spectral crowding, with all other factors being equal.Accordingly, the nitrogen isotope 15 N (I = 1/2) induces a narrower transition linewidth of V − B than its naturally abundant counterpart, 14 N (I = 1).However, we note that the gyromagnetic ratio is equally important in isotope engineering, and although 11 B (I = 3/2) has a lower spin quantum number compared to 10 B (I = 3), its gyromagnetic ratio is much larger, which results in a broader linewidth.Therefore, to minimize the spectral crowding of V − B , we predict that h 10 B 15 N is the optimal host material.
Experimental Characterization-To experimentally validate the effect of isotope engineering on the V − B center, we grow single h 10 B 15 N crystals with isotopically purified 15 N and 10 B sources (purity > 99.7 % for 15 N and > 99.2 % for 10 B, see Methods) [31][32][33][34].We exfoliate the hBN crystal into thin flakes with thickness ranging from 20 − 70 nm.V − B defects are created via He + ion implantation with energy 3 keV and dosage 1 ion/nm 2 , resulting an estimated V − B concentration around 150 ppm [24].In the experiment, the fluorescence signal of V − B is collected using a home-built confocal microscope, and the microwave is delivered via a coplanar waveguide (see Supplementary Note 1).Most of the experiment in this work are performed at room temperature other than that specified (Fig. 2c).
The spin transitions of V − B can be probed via electron spin resonance (ESR) spectroscopy: by sweeping the frequency of the applied microwave drive while monitoring the fluorescence signal of V − B , we expect a fluorescence drop when the microwave is resonant with an electronic spin transition.Figure 1c compares the ESR spectra of V − B in our isotopically engineered h 10 B 15 N and conventional naturally abundant hBN nat (99.6%/0.4% for 14 N/ 15 N and 20%/80% for 10 B/ 11 B) under a small external magnetic field (B ≈ 87 G).As expected, the ESR measurements for both |m s = 0⟩ ↔ |m s = ±1⟩ transitions on h 10 B 15 N show much less crowded spectra than hBN nat .In particular, there are two strik- ing features.First, instead of an ordinary 7-resonance spectrum observed in the naturally abundant sample [18,35], we resolve 4 distinct hyperfine lines for V − B in h 10 B 15 N.This structure stems from the hyperfine interaction between V − B and the three nearest-neighbor 15 N nuclear spins ( , where I j z can take the values of ± 1 2 .Accounting for all nuclear spin configurations, there are a total of 4 hyperfine lines (split by |A 15

N
zz |) with degeneracy {1:3:3:1} corresponding to the total nuclear spin number m I = {− 3 2 , − 1 2 , 1 2 , 3 2 } (Fig. 1b,c).By fitting the spectrum to the sum of four equally-spaced Lorentzians with amplitudes proportional to the aforementioned degeneracy ratio, we extract the hyperfine coupling A 15 N zz = (2π) × [−65.9 ± 0.9] MHz, where the negative sign originates from the negative gyromagnetic ratio of 15 N.In comparison, the nearestneighbor 14 N hyperfine interaction strength in hBN nat is A The second feature of the V − B spectrum in h 10 B 15 N is its dramatically narrower transitions.Specifically, the full width at half maximum (FWHM) linewidth for each hyperfine resonance is (2π)×[55±2] MHz, almost a factor of two lower than that of the naturally abundant hBN nat sample, (2π) × [95 ± 2] MHz.The linewidth originates from the hyperfine couplings to boron and nitrogen nuclear spins beyond the three nearest-neighbor atoms.To quantitatively capture the measured ESR linewidth, we perform numerical simulations by summing over the couplings to the nearest 36 nuclear spins for four different kinds of isotopically distinct hBN samples (see Meth-ods and Supplementary Information) [36].The simulated spectra for h 10 B 15 N and hBN nat are in good agreement with the experimental data (Fig. 1c).Importantly, the narrower and less crowded hyperfine lines in h 10 B 15 N substantially boosts the sensitivity of V − B for quantum sensing applications [37].
Enhanced Quantum Sensing-Taking magnetic field sensing as an example, we now evaluate the DC and AC magnetic field sensitivity enhancement of V − B in h 10 B 15 N.The static magnetic field sensitivity of ESR measurement takes the form [38,39] where R denotes the photon detection rate, C(ν) the ESR measurement contrast at microwave frequency ν, C m the maximum contrast, and ∆ν the FWHM linewidth assuming a single Lorenztian resonance.If one directly compares the fitted FWHM from h 10 B 15 N and hBN nat , we find a factor of ∼ 1.8 improvement in sensitivity.Moreover, the hyperfine transitions of V − B in hBN nat significantly overlap with each other, while for V − B in h 10 B 15 N the resonances are individually resolvable.Therefore, a more accurate comparison instead takes the steepest slope, max | ∂C(ν)  ∂ν |, into consideration, with which we conclude a factor of ∼ 4 improvement in sensitivity using isotope purified h 10 B 15 N.By optimizing the laser and microwave power, we estimate a static magnetic field sensitivity η DC ≈ 10 µT Hz − 1 2 .We note that the sensitivities reported in this work are sample specific, and one can further optimize the sensitivity by increasing the number of V − B defects used in experiment (see Supplementary Information).
Next, we characterize the spin echo coherence of V − B in h 10 B 15 N and hBN nat for AC field sensing.The spin echo coherent timescale, T E 2 , of V − B has been previously understood to be limited by the magnetic fluctuations from the nearby nuclear spin bath [24,28,40], and the isotope engineering technique should precisely alleviate such decoherence.For a robust and systematic comparison, we prepare three h 10 B 15 N flakes (sample S1-S3) and three naturally abundant hBN nat flakes (sample S4-S6) onto the same microwave stripline (see Methods).Figure 2a shows the measured spin echo decays on h 10 B 15 N sample S1 and hBN nat sample S4, where the extension of spin echo timescales T E 2 exceeds twofold, from T E 2,S4 = 87 ± 9 ns to T E 2,S1 = 186 ± 22 ns. Figure 2b summarizes the experimentally measured spin echo coherence timescales T E 2 across all six hBN flakes, revealing a consistent improvement of coherence time in our isotopically purified samples.We also perform the spin echo measurement using h 11 B 15 N samples and find T E 2 ≈ 119 ± 6 ns, lying in between h 10 B 15 N and hBN nat (see Supplementary Fig. 13).
The AC magnetic field sensitivity η AC ∝ T −1 2 exhibits improvement of more than a factor of 2 in our h 10 B 15 N samples.By employing an advanced dynamical decoupling sequence, XY8, which exploits a series of echo pulses with alternating phases, we further extend the coherence time of V − B in h 10 B 15 N samples to T XY 2 ≈ 500 ns (Fig. 2b Inset).This improves the estimated AC magnetic field sensitivity to η AC ≈ 7 µT Hz − 1 2 for a signal at frequency ∼ (2π) × 12 MHz (see Supplementary Note 4).
We now turn to investigate the spin relaxation time, T 1 , of V − B in different isotopic samples.At room temperature, we find T 1 of V − B across all six samples to be comparable (T 1 ≈ 15 µs) and nearly independent of isotope choice (Fig. 2b).To further explore the isotope effect on T 1 , we also explore the temperature-dependence of the V − B relaxation using an optical cryostat (Fig. 2c).The measured T 1 in both h 10 B 15 N and hBN nat increases monotonically with decreasing temperatures.Interestingly, when the temperature goes below ∼ 170 K, there is a clear improvement of T 1 in the h 10 B 15 N sample compared to natural abundant sample.At the lowest temperature 10 K, we find T 1 = (1.00 ± 0.07) ms for V − B in h 10 B 15 N, around 50 % longer than T 1 = (0.63 ± 0.04) ms measured in hBN nat (Fig. 2c Inset).The current theoretical understanding of the spin relaxation process of V − B identifies spin-phonon interaction as the main limitation [19,41,42], which is consistent with the observed monotonic increase of T 1 with decreasing temperature in both samples.One possible explanation for the improved T 1 of V − B in h 10 B 15 N is that the nearest-neighbouring 15 N nuclei are slightly heavier in mass, leading to a weaker spin-phonon coupling strength [43,44].However, the detailed underlying mechanism of isotope and temperature dependent of V − B spin lifetime invites more future studies.Nevertheless, the extension of T 1 from isotope effect facilitates the use of V − B as a noise magnetometer to diagnose different phases of material, such as magnetic insulators and superconductivity at low temperature [14,[45][46][47].
Polarizing Three Nearest 15 N Nuclear Spins-Next, we demonstrate the polarization and coherent control of the three nearest-neighbor 15 N nuclear spins using V − B .
Nuclear spins feature exceptional isolation from external environments and offer long-lived systems for quantum simulation and computation applications.In contrast to V − B in naturally abundant hBN samples, our isotopically purified host h 10 B 15 N presents a unique advantage: the hyperfine levels are individually addressable with a much less crowded spectrum.
We start by dynamically polarizing the 15 N nuclear spins at the electronic spin level anti-crossing (esLAC).Under an external magnetic field B z ≈ 760 G, the V − B excited state levels |m s = 0⟩ and |m s = −1⟩ are nearly degenerate [48][49][50].In this regime, the secular approximation no longer holds, and we need to consider the full hyperfine interaction Hamiltonian, To understand the nuclear spin polarization process, we can rewrite the hyperfine terms using ladder operators as where xy , S ± and I ± are the ladder operators (see Supplementary Information).
To experimentally probe the nuclear spin polarization, we measure ESR spectra at a range of different laser powers.Here, we focus on the ESR transitions from |m s = 0⟩ to |m s = +1⟩ to avoid any fluorescence modulation due to esLAC and thus accurately characterize the nuclear spin population [51].At low laser power (0.3 mW), the ESR spectrum exhibits a symmetric four-peak structure with amplitudes {1:3:3:1}, similar to the low field measurement, indicating no nuclear spin polarization (Fig. 3b).Once the laser power, and hence the optical pumping rate, increases, the ESR spectrum manifests an asymmetry skewed toward the two resonances at lower frequencies.This indicates that the three nearest-neighbor 15   nuclear spins are significantly polarized to the |m I = ↑⟩ state.
To quantify the nuclear spin polarization, we assume each nuclear spin is independently initialized to |m I = ↑⟩ with probability P (|↑⟩) and |m I = ↓⟩ with probability 1−P .In this case, the population distribution of the four hyperfine resonances follows a ratio of {P 3 : 3P 2 (1 − P ) : 3P (1 − P ) 2 : (1 − P ) 3 } (See Methods).This model yields excellent agreement with the experimental data (Fig. 3b), allowing us to extract the nuclear spin polarization probability P at different laser powers.The nuclear polarization saturates at a laser power of around 10 mW, giving a maximum extracted nuclear spin polarization probability P = (63.2± 0.3)% (Fig. 3c).The nuclear spin polarization is also sensitive to the magnetic field alignment relative to the c-axis of the h 10 B 15 N, as a transverse magnetic field induces mixing between the nuclear spin states (Fig. 3c inset).We notice a small overall shift (∼ 5 MHz) of the entire ESR spectrum at high laser power originating from the laser-induced heating effect of the sample [37].Nevertheless, the well-resolved hyperfine lines in our isotopically purified h 10 B 15 N enables us to faithfully capture any temperature-induced shift that may have been previously difficult to distinguish in the spectrum of naturally abundant hBN nat .
We further study the nuclear spin depolarization dynamics via pulsed ESR measurements.After initializing the V − B electronic spin and the three 15 N nuclear spins at esLAC with a 5 µs laser pulse, we wait for a time t before applying a microwave π-pulse with varying frequency to probe the hyperfine transitions, as shown in Figure 3d.By fitting the ESR spectra, we observe that the nuclear spin population P exhibits almost no decay within 15 µs, the T 1 time of V − B .The longevity of nuclear spin polarization may serve as a vital attribute for future applications such as quantum registers [52].
Coherent Control of the Nuclear Spins-Next, we illustrate the direct control and detection of the three nearest-neighbor 15 N nuclear spins.After polarizing the V − B to |m s = 0⟩ state via optical pumping, we apply a nuclear spin selective microwave π-pulse to transfer |m s = 0, m I = 1  2 ⟩ population into |m s = −1, m I = 1 2 ⟩ followed by a radio-frequency (RF) π-pulse to drive the nuclear spin states (Fig. 4a).A final microwave π-pulse ⟩ for nuclear spin detection.
Figure 4b shows the measured 15 N nuclear spin resonance spectrum obtained by sweeping the frequency of the RF pulse.The clear nuclear spin transition at around (2π) × 66.6 MHz is consistent with the sum of the measured 15 N hyperfine interaction strength and the nuclear spin Zeeman shift |A 15 N zz + γ n B z | ≈ (2π) × 66.2 MHz.By parking the RF pulse at this frequency and increasing the pulse duration, we obtain coherent Rabi oscillations of the nearest three 15 N nuclear spins with Rabi frequency Ω N = (2π) × (1.67 ± 0.02) MHz (Fig. 4c).
Here, we would like to emphasize a few points.First, the nuclear spin Rabi signal contains a clear beating that does not fit to a single frequency oscillation.This originates from the interaction between nuclear spins which can be captured using a more sophisticated model containing V − B and three 15 N nuclear spins (see Supplementary Note 6.3).Second, the transverse hyperfine interaction enhances the effective nuclear gyromagnetic ratio to [35,53] enabling us to achieve a fast nuclear spin manipulation (see Supplementary Note 6.1).
From our experiment, we estimate γ eff n /γ n ≈ 99, suggesting A 2 xx + A 2 yy + 2A 2 xy ≈ (2π) × 30 MHz, a factor approximately 5 times lower than the values predicted by abinitio calculations [35,36] (see Supplementary Note 6.2).Another piece of evidence is that the measured nuclear spin resonance spectrum is consistent with the estimated transverse hyperfine parameters (Fig. 4b), while if we include the ab-initio predicted values, the simulated spectrum deviates from the measurement at B ≈ 760 G (Supplementary Fig. 9).Prior work using 14 N nuclear spins in natural abundant hBN nat has reported a ∼ 30 % discrepancy between experiment and the ab-initio calculated transverse hyperfine coefficients [35].However, the measured 14  Looking forward, our work also opens the door to a few highly promising directions.First, we believe that almost all previous works using V − B for sensing applications could greatly benefit from simply switching to our newly prepared h 10 B 15 N sample.The demonstrated sensitivity improvement is also fully compatible with other ongoing optimization efforts on V − B sensors, such as dynamical decoupling protocols to extend T 2 [24,27], coupling V − B to optical cavities [54][55][56] and increasing V − B number and density [24,57,58] to improve fluorescent signals.Second, the individual addressability of V − B hyperfine transitions in h 10 B 15 N allows the utilization of nearby nuclear spins as valuable quantum resources and provides a promising platform to realize multi-qubit quantum registers in two-dimensional materials.Finally, we highlight that our isotope engineering method can be readily extended to other spin defects in hBN [59,60] as well as the broader family of van der Waals materials [61].For instance, the recent search for quantum spin defects in transition metal dichalcogenides [62] will greatly benefit from a careful selection of host isotopes, which may even create a nuclear spin-free environment.
Note added : During the completion of this work, we became aware of complementary work studying boronvacancy centers in both nitrogen and boron isotopes purified hBN crystals (Vincent Jacques, private communication) [63].
High-quality h 10 B 15 N flakes are grown via precipitation from a molten Ni-Cr flux as detailed in [1].Ni, Cr, and isotopically pure 10 B powders in the mass ratio 12:12:1 [Ni:Cr:B] are first loaded into an alumina crucible, then heated at 1550°C for 24 hours in a continuously flowing Ar/H 2 atmosphere to melt all three components into a homogenous ingot and remove oxygen impurities.Next, this ingot is heated at 1550 °C for 24 hours in a static 15 N 2 /H 2 atmosphere to saturate the molten flux with 15 N, then slowly cooled at 1°C/hr to precipitate hBN from the solution.Since isotopically pure 10 B (> 99.2%) and 15 N (> 99.7%) are the only sources of boron and nitrogen in the system, the hBN single crystals that precipitated have the same isotopes.
We first exfoliate hBN nanosheets using tapes and then transfer them onto the Si/SiO 2 wafer.The wafer is pretreated with O 2 plasma at 50 W for 1 minute (flow rate 20 sccm).The tapes and wafers are heated to 100 • C for 1 minute before samples are carefully peeled off for maximum hBN flake yield [2].The wafers with hBN nat and h 10 B 15 N are then sent to CuttingEdge Ions LLC for 4 He + ion implantation with energy 3 keV and dose density 1 ion/nm2 to create V − B defects with estimated density ∼ 150 ppm [3].After implantation, the hBN flakes with thicknesses ranging from 20 − 70 nm are transferred onto the coplanar waveguide using polycarbonate (PC) stamps.Specifically, the temperature is raised in a stepwise manner to facilitate the transfer of hBN flakes.After successful transfer, the waveguide is immersed in chloroform for cleaning, removing any residual PC films.For a systematic comparison between V − B in isotopically purified h 10 B 15 N and naturally abundant hBN nat , we transfer three h 10 B 15 N flakes (S1-S3) and three hBN nat flakes (S4-S6) onto a single waveguide for measurement (Figure 1).

I.3. Fabrication of Coplanar Waveguide
An impedance-matched (50 Ω) coplanar waveguide is fabricated onto a 400 µm thick sapphire wafer for microwave delivery (Figure 1).Specifically, photoresist layers (LOR 1A/S1805) are first applied to the sapphire wafer at a spin rate 4000 rpm for 1 minute.A carefully designed waveguide pattern with a 50 µm wide central line is then developed using a direct-write lithography system (Heidelburg DWL66+), followed by an O 2 plasma cleaning process to remove resist residue.A 10 nm chromium adhesion layer and a 160 nm gold layer are deposited using thermal evaporation, followed by a lift-off process.To quantitatively capture the measured ESR spectra in hBN samples with different isotopes, we numerically simulate the V − B transitions by accounting for its hyperfine couplings to the nearest 36 nuclear spins.At small external magnetic fields, the hyperfine terms from main text Eqn.(1), can be approximated as j SA j I j ≈ j A j zz S z I j z = ( j A j zz I j z )S z , which leads to an effective energy shift of the electronic spin state depending on the nearby nuclear spin configurations.Considering the hyperfine interaction between V − B and an individual nuclear spin with spin number I, the averaged spectrum for the electronic spin transition |m s = 0⟩ ↔ |m s = ±1⟩ will exhibit 2I + 1 resonances with splitting A zz assuming the nuclear spin is in a fully mixed state (to be expected at room temperature).We note that the value of the hyperfine coupling is proportional to the gyromagnetic ratio of the nuclear spin, i.e.A zz ∝ γ n ; therefore, the overall bandwidth of the transition is proportional to 2I × |γ n |. Figure 2 shows a schematic ESR spectrum assuming the V − B couples to a single 14 N or 15 N nuclear spin.To achieve a smaller overall linewidth of the V − B transitions, the value 2|γ n I| must be minimized for each atomic species in the host material (main text Figure . 1a).
Following this approximation, we proceed to compute the V − B ESR spectrum by summing over the hyperfine couplings to the 18 nearest nitrogen and 18 nearest boron nuclear spins.The values of A zz for 14 N and 11 B have been previously predicted using a Density Functional Theory (DFT) calculation [4].To calculate A zz for 15 N and 10 B nuclear spins, we only need to account for the differences between gyromagnetic ratios.Direct summation of all nuclear configurations yields (2I N + 1) 18 × (2I B + 1) 18 individual resonances, where I N and I B represent the nuclear spin numbers of the corresponding nitrogen and boron isotopes, respectively.To mitigate the computational cost, we employ Fourier transformation to simplify the calculations (see Supplementary Note 2).The final ESR spectrum is obtained by binning transition frequencies with bin size 0.5 MHz. Figure 3   To further verify that h 10 B 15 N is the ideal host regarding the V − B coherence timescales, we prepare another sample with h 11 B 15 N, which is predicted to be the second best host material.Unsurprisingly, the ESR spectrum of V − B in h 11 B 15 N exhibits a slightly broader transition linewidth in comparison with h 10 B 15 N (Fig. 4a).By measuring the Spin Echo coherence time, V − B in h 11 B 15 N indeed shows T E 2 = 119 ± 6 ns, in between the values measured from h 10 B 15 N and h 10 B 15 N (Fig. 4b).A previous work [5] has also shown that V − B in h 10 B 14 N and h 11 B 14 N did not exhibit a clear improvement in spin echo T 2 compared to natural abundant hBN.Therefore, we believe that h 10 B 15 N is indeed the optimal isotope selection for improving the coherence time of V − B .

III. QUANTIFYING NUCLEAR POLARIZATION
To quantify the nuclear spin polarization of the nearest three 15 N , we assume each nuclear spin is individually prepared to |m I =↑⟩ with probability P (|↑⟩) and |m I =↓⟩ with probability 1−P (|↑⟩).The energy sublevels accounting for the three 15 N spins should effectively follow a bionomial distribution with n = 3, the total number of a sequence of independent events.For a random variable X defined as the number of 15  |m I = ↑⟩ in a single observation, the probability mass function is For example, the four possible nuclear spin configurations correspond to m I = − 3 2 , − 1 2 , 1 2 , 3 2 and X = 0, 1, 2, 3. Therefore, the theoretical probability distribution follows { When there is no nuclear spin polarization (P = 0.5), we obtain amplitudes {1 : 3 : 3 : 1} for the ESR spectra.
To quantitatively extract the nuclear polarization, we first fit the ESR spectrum using the sum of four equally spaced Lorentzian distribution whose amplitude follows the aforementioned ratio.However, we note that the gyromagnetic ratio for 15 N is negative, which reverses the order of the sublevels in the ESR spectrum.In this case, for the V − B transition between electronic |m s = 0⟩ and |m s = +1⟩ states, the lowest-frequency resonance corresponds to m I = 3 2 or X = 3 (main text Figure 3b).
We note here that previous studies have predicted a reduction of symmetry in the V − B excited state manifold from D 3h to C 2v due to Jahn-Teller effect [4,6,7].This can lead to a different hyperfine interaction for one of the 15 N nuclear spins compared to the other two.To this end, we also investigate the fitting of the experimental spectra assuming two of the 15 N nuclear spins are polarized to |m I = ↑⟩ with probability P 1 and the third 15 N is polarized with probability P 2 .The corresponding probability distribution for the four hyperfine resonances takes the form 5 illustrates a comparison between the two different fitting methods, and we find that both models capture the experimental spectra almost identically well.Thus, the addition of the parameter P 2 does not significantly enhance agreement with experiment.Furthermore, the two-parameter fit has much greater uncertainty in the extracted values of P 1 and P 2 compared to the single-parameter fit and the net nuclear spin polarization amount remains almost exactly the same between the two cases.Therefore, we utilize the first model with minimal fit parameters throughout the manuscript.Further studies are required to experimentally distinguish whether a parameter such as P 2 is required.
(purple dashed lines).Inset: computed residuals between experimental data and two fits.
we find that the coupling term between nuclear spin sublevels can be written as

FIG. 1
FIG. 1. V − B electron spin resonance spectra in isotopically distinct hBN samples (a) Schematic of an individual V − B center (red spin) in an isotopically purified h 10 B 15 N crystal.ẑ is defined along the c-axis (perpendicular to the lattice plane) and x and ŷ lie in the lattice plane, with x oriented along one of the three V − B Nitrogen bonds.The table lists the nuclear spin quantum number (I), gyromagnetic ratio (γn), and overall electronic spin transition width (∝ 2|γnI|) of four stable atomic isotopes in hBN.(b) Energy level diagram of the V − B electronic ground state coupled to the three nearest-neighbor 15 N nuclear spins (I = 1 2 ) under an external magnetic field Bz.For each electronic spin transition |ms = 0⟩ ↔ |ms = ±1⟩, the hyperfine interaction leads to four distinct resonances with total nuclear spin magnetic quantum number mI = {− 3 2 , − 1 2 , 1 2 , 3 2 } of degeneracy {1, 3, 3, 1}.(c) Measured ESR spectra of V − B in h 10 B 15 N and naturally abundant hBNnat at magnetic field Bz ≈ 87 G. Solid lines represent multi-peak Lorentzian fits, and shaded regions represent numerically simulated transitions considering the 36 nearest nuclear spins (18 nitrogen and 18 boron atoms; see Methods).Insets: ESR spectra at Bz = 0 G.

FIG. 3 .
FIG. 3. Dynamic polarization of nearest-neighbor15 N nuclear spins (a) Left: schematic of the nuclear spin polarization process of15 N spins at esLAC (Bz = 760 G).The hyperfine term (A1S+I− + h.c.) (red) is much stronger than (A2S+I+ + h.c.) (blue).Under laser pumping (green), which continuously polarizes the electronic spin to |ms = 0⟩, each nuclear spin will be preferentially polarized to |mI = ↑ ⟩.Right: calculated excited state energy spectrum of V − B as a function of magnetic field (see Supplementary Information).Inset: closeup of energy levels around esLAC (760 G).(b) Measured ESR spectra of the |ms = 0⟩ ↔ |ms = +1⟩ transition at esLAC under different laser powers.Inset: ESR spectrum of the |ms = 0⟩ ↔ |ms = −1⟩ transition at a laser power ∼ 10 mW.Dashed lines represent best fits assuming each 15 N nucleus is independently polarized to | ↑ ⟩ with probability P .(c) Extracted P (| ↑ ⟩) as a function of laser power.Inset: P (| ↑ ⟩) as a function of the magnetic field alignment angle θ relative to the c-axis of hBN.(d) Measured depolarization dynamics of nuclear spin as a function of wait time t.Inset: pulsed-ESR spectra at t = 2 µs and 10 µs. N

1 FIG. 4 .
FIG. 4. Coherent control of 15 N nuclear spins (a) Experimental pulse sequence and schematic for the control and detection of nuclear spins.(b) Resulting 15 N nuclear spin resonance spectra at 760 G and 210 G (Inset).Dashed lines represent simulated spectra (see Supplementary Information).(d) Measurement of nuclear spin Rabi oscillations.The dashed line corresponds to a cosine fit with exponentially decaying amplitude.

FIG. 1 .
FIG. 1. Optical image of the coplanar waveguide (a) Overview of the coplanar waveguide before transferring the hBN flakes.(b) Zoomed-in microscope image of the coplanar waveguide after transferring the hBN samples.The six flakes studied in this work are labeled as S1-S6.(c) Fluorescence confocal scan of sample S1, S4, and S5.
II. COMPARISON OF V − B IN HBN WITH DIFFERENT ISOTOPES II.1.Simulation of ESR spectrum FIG. 2. Schematic ESR Spectrum A schematic ESR spectrum of V −B coupling to a single 14 N (orange) or 15 N (blue) nuclear spin with a overall bandwidth of the transitions proportional to 2|( γn 2π )I|.

FIG. 3 .
FIG. 3. Simulated ESR Spectra for Different Isotopes Simulated ESR spectra of V − B in the four different possible isotopically purified hBN crystals (a) h 10 B 15 N, (b) h 11 B 15 N, (c) h 10 B 14 N, (d) h 11 B 14 N, and (e) in hBNnat.

− γ n 2 Bγ n 2 B 1 I , m 2 I , m 3 I 6 FIG
FIG. S5.Nuclear Spin Resonance Measurement (a) Hyperfine parameters A of the three nearest 15 N nuclear spins.The first three rows are from ab-initio calculations [4, 5]; the last three list the adjusted values by rescaling the transverse components (Axx, Ayy, Axy) by a factor of 4.8.(b) 15 N nuclear spin resonance spectra at 760 G and 210 G (Inset).Dashed lines show the numerical simulations using the ab-initio predicted hyperfine values.
N nuclear spin transitions contain multiple resonances and are much broader than what we have observed here using 15 N nuclei.Future work is required to resolve such discrepancy between experiment and ab-initio results.For instance, one can perform highresolution ESR spectroscopy near the ground-state anticrossing (gsLAC) with magnetic field B ≈ 1200 G.At such field, the V − B electronic spin state |0⟩ and | − 1⟩ are close to degenerate, and one expects the effect of transverse hyperfine coefficients to become evident.Outlook -In conclusion, we present isotope engineering as a versatile and foundational tool to improving spin properties of V − B .On the quantum sensing front, V − B centers in isotope-engineered h 10 B 15 N feature substantially narrower spin transitions and enhanced spin coherent time compared to conventional hBN nat , enabling a universal enhancement factor of ∼ 4(2) in DC (AC) magnetic field sensitivity.Additionally, we demonstrate the dynamical polarization and coherent control of the nearest neighboring three 15 N nuclear spins.
N nuclear spins being measured to be FIG.4. h 11 B 15 N characterization.(a) The ESR spectra of V − B in h 10 B 15 N and h 11 B 15 N. (b) The spin echo measurement.T E 2 ≈ 186 ± 22, 119 ± 6, 76 ± 7 ns for h 10 B 15 N, h 11 B 15 N, and hBNnat respectively.Error bars represent 1 s.d.accounting statistical uncertainties.Source data are provided as a Source Data file.