Abstract
Spin defects in foils of hexagonal boron nitride are an attractive platform for magnetic field imaging, since the probe can be placed in close proximity to the target. However, as a IIIV material the electron spin coherence is limited by the nuclear spin environment, with spin echo coherence times of ∽100 ns at room temperature accessible magnetic fields. We use a strong continuous microwave drive with a modulation in order to stabilize a Rabi oscillation, extending the coherence time up to ∽ 4μs, which is close to the 10 μs electron spin lifetime in our sample. We then define a protected qubit basis, and show full control of the protected qubit. The coherence times of a superposition of the protected qubit can be as high as 0.8 μs. This work establishes that boron vacancies in hexagonal boron nitride can have electron spin coherence times that are competitive with typical nitrogen vacancy centres in small nanodiamonds under ambient conditions.
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Introduction
Hexagonal boron nitride (hBN) is a widebandgap Van der Waals material used as an insulator in twodimensional electronic devices^{1}. Recently, there has been a growing interest in optically detected magnetic resonance (ODMR) experiments on spin defects. There are several reasons why. Firstly, ODMR provides a useful tool for identifying defects, and has been instrumental in identifying the boron vacancy in hBN^{2,3}. Secondly, a good magnetic field sensor or spinphoton interface^{4} requires a defect with both good optical and spin properties. There is mounting evidence that some hBN defects have excellent optical properties, with high brightness of up to 87% quantum efficiency^{5} at visible wavelengths wellmatched to silicon detectors^{6}, and suggestions of transformlimited transitions with a high fraction of emission occurring through the zerophonon line^{7,8}. Thirdly, as a twodimensional material it may be possible to make magneticfield sensing foils that allow the spindefect to be placed in closeproximity to the target of interest^{9,10,11}. In the leading platform, nanodiamonds, the spin coherence properties are adversely affected by the surface states, typically limiting spin echo coherence times to a few μs for diameters of a few nm^{12}.
In hBN, there are a few recent studies on single bright ODMRactive defects^{13,14,15}, which are possibly carbon related. But so far, most ODMR work in hBN has focused on ensembles of boron vacancies^{2,9,16,17,18,19}, because although they suffer low brightness, they are easy to generate^{19}, their internal energy levels have been theorized^{18,20,21} and allow facile spinpumping by a green laser.
In any IIIV material the nuclear spin environment is expected to limit the electron spin coherence times. So far, in hBN there have been claims of spin echo times in the μsregime, at room temperature and moderate magneticfield^{16,22}, which is competitive with negatively charged nitrogen vacancy (NV)centres in small nanodiamonds^{12}. However, this has been challenged by experiments that show sub100 ns spin echo times in isotopically purified material, which are further supported by calculations of the decoherence expected from the electronnuclear interactions^{3}. Since nuclear spin dephasing is largely a property of the host material^{23}, the boron vacancy serves as a model spin system to evaluate the potential of hBN as a host.
Here, we present a study of the spin properties of ensembles of negatively charged boron vacancies (\({V}_{B}^{}\)) in hBN. We confirm the findings of Haykal et al.^{3} that the majority of the spin echo coherence is lost in T_{echo} < 100 ns at room temperature and milliTesla magnetic fields. However, we propose and demonstrate a solution. We show that by using a strong continuous microwave field, a method often referred to as continuous concatenated dynamic decoupling (CCD), we can define a protected qubit basis with favourable coherence properties, allowing the Rabi oscillation damping time to be extended up to 4 μs. This method has previously been used in NVcentres in diamond^{24,25,26,27,28,29,30,31}, but here we show that it works extremely well in a IIIV material with hostile nuclear environment, by using a Rabi drive stronger than the hyperfine coupling. Furthermore, we define a protected qubit basis in terms of an electron spin that rotates inphase or outofphase with the expected Rabi oscillation. We then demonstrate full control of this protected qubit to show coherence times, T_{pRabi}, of up to 0.8 μs. The method avoids the use of cryogenic superconducting magnets, and is therefore suitable for room temperature applications. Whilst the boron vacancy may not ultimately be suitable for single spin applications, due to its low quantum efficiency and broad photoluminescence spectrum^{17,18}, ODMR on other single spin defects has been reported^{13,14,15}. The CCD method presented here should be insensitive to the details of the nuclear bath, and therefore applicable in general to spin defects in hBN, and to other IIIV materials with harsh nuclear spin environments.
Results
Boron vacancy optically detected magnetic resonance
Our device consists of flakes of hBN placed on top of a coplanar waveguide (CPW) fabricated on a sapphire substrate^{17}. Following the recipe of ref. ^{19}, boron vacancies are generated by carbonion irradiation at 10 keV and a dose of 1 × 10^{14}cm^{−2}. A DC magnetic field of 20 mT is applied along the caxis of the hBN flakes, and an AC field is applied inplane through the CPW. The coupling is sufficient to achieve Rabi frequencies in excess of 100 MHz. The sample is located beneath a microscope at room temperature and in air. Photoluminescence (PL) is excited using a 532 nm laser, modulated using an acoustooptic modulator, and detected with a SiAPD module.
Only \({V}_{B}^{}\) is expected to be optically active in the range of our detection system^{32}. A sketch of the optical pumping cycle for optically detected magnetic resonance (ODMR) is shown in Fig. 1a. The \({V}_{B}^{}\) has two unpaired electrons in an S = 1 triplet ground state. Excitation with a 532 nm laser preferentially optically pumps the \({V}_{B}^{}\) into the m_{s} = 0 state, whose PL is slightly brighter than the m_{s} = ± 1 states, allowing ODMR detection of the electron spin resonance. The PL is broadband and centred at ~850 nm, see Fig. 1b.
The Hamiltonian of the crystal groundstate can be expressed as H = H_{e} + H_{n} + H_{en}. The electron Hamiltonian,
is composed of a zerofield splitting with D = 3.479GHz, and E = 59 MHz (see Supplementary Fig. 2) and an electron Zeeman term with gyromagnetic ratio γ_{e} ≈ 28 MHz/mT. S_{j} are the S = 1 electron spin operators. D is consistent with previous works^{2}. E is relatively large, perhaps due to high level of strain caused by use of carbonirradiation to generate the defects, and is consistent with reports for ionimplanted samples^{33}. The nuclear spin Hamiltonian is
I^{k} is the nuclear spin of nuclei k. The first term is a nuclear Zeeman term, and Q^{k} is a quadrupolar tensor. H_{en} is the electronnuclear hyperfine interaction.
It is dominated by the three nearest neighbour nitrogen atoms with A^{nn} = 47 MHz, and I(^{14}N) = 1^{2}. The next nearest neighbour interactions have been calculated to be up to 6.8 MHz in ref. ^{21}. In our CWODMR measurements, see Fig. 1c, the hyperfine structure is not resolved, but the FWHM is similar to 3A, corresponding to three nearest neighbours with I = 1.
Unprotected electron spin
To start our investigation of the spin properties of \({V}_{B}^{}\) we measure a Rabi oscillation, see Fig. 1d. The Rabi oscillation is sensitive to all inhomogeneities and noise sources, and has a coherence time of T_{Rabi} < 60 ns, which depends on the microwave power (Fig. 1f). At high microwave power, the dephasing rate is proportional to the Rabi frequency possibly due to fluctuations in the power of the microwave source. At low microwave power, the Rabi damping is dominated by fluctuations in the detuning^{34}.
To evaluate the intrinsic coherence times, we perform spinecho measurements, see Fig. 1e. In principle, the measurement is insensitive to low frequency variations in the detuning, and errors in the pulsearea. However, at a moderate magnetic field of B = 20 mT, we find a T_{echo} < 100 ns, that saturates at high Rabi frequencies with fast pulses. We note that the T_{echo} is comparable to the T_{Rabi} times. These numbers are similar to those of Haykal et al.^{3}, who report that T_{echo} is sensitive to ^{11}B content, and therefore limited by nuclear spins. In the high microwavepower regime our T_{echo} = 100 ns is a close match to their calculations for a natural 20:80 mix of ^{10}B and ^{11}B isotopes. We note that data reported by Liu et al.^{35} is compatible with T_{echo} of < 100 ns under similar conditions. In refs. ^{16,22} a longer μsscale T_{echo} was reported. However, these T_{echo} were extracted from low contrast data for times larger than 200 ns. We could not observe a longlived tail in the spin echo (see Supplementary Note 4 and Supplementary Fig. 3). At cryogenic temperature and few Tesla magnetic fields, T_{echo} = 15 μs has been reported^{36}.
Stabilized Rabi oscillation
An important question for quantum devices based on hBN spin defects is whether one can create a protected qubit that is isolated from the nuclear spins, and thereby access a longer electron spin coherence. There exists an extensive literature on how to mitigate the impact of nuclear spins in IIIV quantum dots^{37,38,39}, and for defects in groupIV materials^{24,29,40,41}. For the boron vacancy, the electronnuclear interaction is dominated by the three nearest nitrogen atoms and a strong hyperfine interaction of ~47 MHz. This few nuclei situation, contrasts with the case of a GaAs quantum dot, where a few thousand nuclei provide a bath of nuclear spins. It also contrasts with the case of groupIV materials, where the majority of nuclei have no nuclear spin, and electron spin dephasing due to hyperfine coupling is relatively weak.
To this end, we trial the use of a strong microwave field to create a protected spinqubit subspace, and use concatenated continuous driving methods to coherently control the protected qubit^{24,29} (see Supplementary Notes 1–3). This involves applying a continuous AC magnetic field along the xdirection to give a control Hamiltonian of the form:
The first term is the usual Rabi drive. The second term adds an amplitude modulated field in quadrature with the Rabi drive, and when ω_{m} = Ω this acts to stabilize the Rabi oscillation. This can be understood by considering only the m_{s} = 0, m_{s} = + 1 electron spin states near resonance with the Rabi drive, and switching to the first rotating frame of the Rabi drive: \({H}_{c}^{{\prime} }={e}^{i\omega t{\sigma }_{z}/2}{H}_{c}{e}^{i\omega t{\sigma }_{z}/2}\). In the case ϕ = 0,
where \({\sigma }_{\alpha }^{{\prime} }\) are the Pauli spin1/2 matrices, and the superscript identifies the frame. The counterrotating term has been neglected. The Ωterm drives a Rabi oscillation in the y’z’plane. The ϵ_{m} term applies a corrective rotation about the y’axis, at a clock frequency of ω_{m}.
Making a second rotating frame approximation to rotate into the dressed states basis, \({H}_{c}^{{{\prime\prime}} }={e}^{i{\omega }_{m}t{\sigma }_{x}^{{\prime} }/2}{H}_{c}^{{\prime} }{e}^{i{\omega }_{m}t{\sigma }_{x}^{{\prime} }/2}{\omega }_{m}{\sigma }_{x}^{{\prime} }/2\).
In the second rotating frame, the control field is equivalent to a DC magnetic field of magnitude ϵ_{m} that is oriented using the phases of the drive θ_{m} and ϕ. By setting the drive such that Ω = ω_{m}, θ_{m} = ϕ = 0, the Hamiltonian reduces to \({H}_{C}^{{{\prime\prime}} }=\frac{1}{2}{\epsilon }_{m}{\sigma }_{z}^{{{\prime\prime}} }\). In this frame, an error in the Rabi frequency (Ω − ω_{m}) results in a rotation about the x^{″}axis, and a spread in Rabi frequencies leads to a divergence in the rotation angle, and a damping of the unprotected Rabi oscillation. However, if an ϵ_{m}drive is applied, an error in the Rabi frequency results in a small tilt in the effective magnetic field, limiting the spread in the Bloch vector, resulting in a longlived Rabi oscillation.
For a spin with no drive, the qubit is protected from bitflip errors by an energy gap ω_{0}. However, against phaseflips, the qubit is vulnerable to fluctuations in the energy gap. By dressing the qubit, the qubit is rotating about twoaxes, at different frequencies, such that both bit and phaseflip errors are protected by an energy gap (see Supplementary Notes 1–3, Supplementary Fig. 1 and Supplementary Movie 1, for further discussion of the theory).
Figure 2a presents a comparison of unprotected Rabi oscillation (red), and a protectedqubit Rabi oscillation using a CCD drive with θ_{m} = 0, ϕ = 0 (black), with a close up shown in Fig. 2b. The former is exponentially damped with T_{Rabi} = 31 ns. For the CCD scheme, after the first cycle, the amplitude of the Rabi oscillation has stabilized. The stabilized Rabi oscillation is also exponentially damped, but with an extended time of T_{CCD} = 2.2 μs. In addition to this amplitude decay, there is also an overall decay of the contrast towards ~− 5%. This is attributed to T_{1} relaxation and also affects the conventional Rabioscillation, as previously reported for ensembles of NVcentres in diamond^{31} (see also Supplementary Note 5 and Supplementary Fig. 4).
In the Fourier domain, the stabilized Rabi oscillation narrows the Ω frequency component of the signal, and gives rise to two weak sidebands at Ω ± ϵ_{m}. Figure 2c compares the stabilized Rabi oscillation in the case with θ_{m} = 0, π/2. For θ_{m} = π/2, the stabilization ϵ_{m}term adds in phase with the Rabiterm resulting in an amplitude modulated Rabi drive, and an unprotected Rabi oscillation with strong damping. In the Fourier domain, the phase θ_{m} controls the magnitude of the centre band, and the sidebands, see Fig. 2d. Figure 2e, f show maps of the modulation phase (θ_{m}) and frequency (ω_{m}) dependence of the signal in the frequency domain with θ_{m} = π/2, respectively. The main feature is a Mollowtriplet^{29} with centre frequency ω_{m}, and sidebands \({\omega }_{m}\pm \sqrt{{({\omega }_{m}{{\Omega }})}^{2}+{\epsilon }_{m}^{2}}\). A feature at ϵ_{m} and a counterrotating term at 2ω_{m} can also be seen. At high ω_{m}, additional side bands at \({\omega }_{m}\pm \sqrt{{({\omega }_{m}{{{\Omega }}}_{{m}_{I}})}^{2}+{\epsilon }_{m}^{2}}\), \({{{\Omega }}}_{{m}_{I}}^{2}={{{\Omega }}}^{2}+{({m}_{I}{A}^{nn})}^{2}\), are observed, and attributed to transitions where the nearest neighbour nuclei are in total nuclear spin state m_{I} = ± 1.
To characterize the lifetime of the stabilized Rabi oscillation, we plot the coherence time of the centre and sidebands as a function of stabilization field strength 2ϵ_{m} (Fig. 2g). For an amplitude modulation with θ_{m} = 0, when 2ϵ_{m} > 10 MHz the energygap of the protected qubit exceeds the nextnearest neighbour electronnuclear hyperfine coupling strengths of ~6.8 MHz^{21}, and the centreband coherence time increases to better than a microsecond, as the electron spin is isolated from the majority of nuclear spins. At 2ϵ_{m} ≈ A = 47 MHz, there is a dip when the 2ϵ_{m} sidebandsplitting matches the nearestneighbour hyperfine interaction, before rising to a maximum value of T_{CCD} ≈ 2 μs. The sidebands are far broader, and the optimum coherence time of the sidebands occurs at 2ϵ_{m} ≈ 20 MHz with T_{CCD±} = 0.27 μs. We interpret the sidebands as providing the stabilization of the Rabi oscillation, and need a faster response to stabilize the electron spin. Using amplitude modulation, 2ϵ_{m} is limited by the available power.
A similar control can be achieved using phase modulation^{42}, where the control Hamiltonian is: \({H}_{c}={{\Omega }}\cos (\omega t+\phi \frac{2{\epsilon }_{m}}{{{\Omega }}}\sin ({\omega }_{m}t{\theta }_{m})){S}_{x}\). This has the advantage of not requiring so much power, allowing us to extend the range of 2ϵ_{m}. Qualitatively, the coherence time dependence for phase modulation imitates the amplitude modulation case. However, an additional dip in coherence time is observed at about 100 − 140 MHz, which corresponds to 2ϵ_{m} ≈ 2Ω − A. When ϵ_{m} > Ω the stabilization stops working. Overall, the phase modulation scheme works better, possibly because the frequency stability of the function generator is better than the power stability, and reaches a maximum of T_{CCD} = 4.4 μs, a >150fold improvement on T_{Rabi} ≈ 25 ns of the conventional Rabi oscillation.
Coherent control of protected electron spin
So far, we have shown that at room temperature and milliTesla magnetic field, an ensemble of electron spins in boron vacancies decohere on a timescale of T_{echo} ≈ 100 ns, due to a strong electronnuclear hyperfine interaction. However, by using a CCD scheme it is possible to stabilize the Rabi oscillation of the electron spin, increasing the damping time of the Rabi oscillation up to several μs. Regarding applications in metrology or as a spin qubit, the question is, do we simply lock the spin to a Rabi oscillation, or can we define a fully controllable protected qubit, and if so, how coherent is that qubit?
To address this question, we define a protected qubit basis in the second rotating frame. When the drive is set to ‘idle’ with θ_{m} = ϕ = 0, and Ω = ω_{m}, the effective field \({H}_{c}^{{{\prime\prime}} }=\frac{{\epsilon }_{m}}{2}{\sigma }_{z}^{{{\prime\prime}} }\) points along the z^{″}axis, see eqn (6). The protected qubit states are defined as \(\left{0}^{{{\prime\prime}} }\right\rangle=\cos ({\omega }_{m}t/2)\left{0}^{{\prime} }\right\rangle i\sin ({\omega }_{m}t/2)\left{1}^{{\prime} }\right\rangle\), and \(\left{1}^{{{\prime\prime}} }\right\rangle=i\sin ({\omega }_{m}t/2)\left{0}^{{\prime} }\right\rangle+\cos ({\omega }_{m}t/2)\left{1}^{{\prime} }\right\rangle\). In the lab frame, these states are observed as a Rabi oscillation that is in/out of phase with a clock rotation in S_{z} that starts at t = 0, when the drive is turned on, and has a frequency ω_{m}. If the electron spin is in a superposition state, this will show up as modulation sidebands with frequency component Ω ± ϵ_{m}.
To measure a Rabi oscillation in the protected basis, the experiment has initialization, control and readout steps, as illlustrated in Fig. 3a. To initialize the spin in state \(\left{0}^{{{\prime\prime}} }\right\rangle\), the drive is turned on in the ‘idle’ state, and left for 94 ns. This is a time of several periods of the Rabi oscillation giving the system time for the frequency to be well defined. To effect a Rabi oscillation, the control field is tilted into y^{″}direction by setting θ_{m} = π/2 for time 94 ns < t < t_{c} + 94 ns, and then switched back to ‘idle’. This causes the spin to rotate about the y^{″}axis for a time t_{c} creating a superposition of \(\left\,{0}^{{{\prime\prime}} }\right\rangle,\left{1}^{{{\prime\prime}} }\right\rangle\). For readout, the PL contrast is measured as a function of total MWpulse length T, and the resulting state of the protected qubit is inferred from the phase of the Rabi oscillation.
Figure 3b, compares the Rabi oscillation after a control pulses of duration (t_{c} = 45 ns, ϵ_{m}t_{c} = π), and (t_{c} = 90 ns, ϵ_{m}t_{c} = 2π), and shows that the phase of the Rabi oscillation has been shifted by π. More generally, we measure the PL contrast as a function of the total MWpulse width T and the control pulse length t_{c}, see the colour map of Fig. 3c. To analyze this we consider the dataset 1000 ns < T < 1400 ns, and make a Fourier transform with respect to T, see Fig. 3d. The centre band oscillates with the control pulse length at a frequency ϵ_{m}, the sidebands oscillate in quadrature with the centre peak, and appear when the protected spin points along the y″direction. As shown in Fig. 4a, the centre peak decays with a time T_{pRabi} = 487 ns.
To show rotation of the protected spin about a second axis, a Ramsey interference experiment is performed, using the pulse sequence shown in Fig. 3a. The MWpulse is applied for a total time 1 < T < 1.4 μs. Again, to initialize the protected spin in state \({0}^{({{\prime\prime}} )}\rangle\) the MWfield is applied in the ‘idle’ state for a short time. To apply a π/2pulse, θ_{m} is switched to θ_{m} = π/2 for a time τ_{90} = π/2ϵ_{m}, and then switched back to the θ_{m} = 0 idle state. A pair of π/2pulses with a timedelay t_{d} are applied, and the final state is deduced by analyzing the signal as the total time T and the timedelay t_{d} are varied, see Fig. 4e. A Ramsey interference showing rotation about z^{″}axis with a frequency of ϵ_{m} is observed, with a T_{pRam} = 706 ns, demonstrating full control of the protected spin.
To evaluate the potential coherence time of the protected spin, we measure the damping time of the protected Rabi oscillation as a function of the modulation 2ϵ_{m}, see Fig. 4c. The best coherence time T_{pRabi} = 0.8 μs is observed at low ϵ_{m}, which is ~8 times better than the unprotected spin echo time.
Discussion
To conclude, the spin echo coherence time of ensembles of boron vacancies in room temperature hexagonal boron nitride is limited by electronnuclear interactions to under 100 ns at sub 100 mT Bfields. To overcome this issue, we trial a CCD scheme to stabilize the Rabi oscillation, extending the Rabi damping time up to T_{CCD} = 4.4 μs = 0.44T_{1}. This time is similar to the spin echo coherence times of InAs/GaAs quantum dots at helium temperatures^{43,44}, and NVcentres in 10–35 nm diameter nanodiamonds at room temperature^{45}, and is close to the limit of 0.5T_{1}, reported for NVcentres in diamond^{46} where T_{1} is limited by twophonon induced spin relaxation. We note that Gottscholl et al.^{16} report a temperature^{−2.5} dependence of T_{1}. This is close to the exponent of − 3 expected for twophonon induced spin relaxation in the case of a 2D phonon bath. Therefore a similar limit may apply for the case of S = 1 boron vacancy in hBN. In that case, reducing the temperature should improve T_{CCD}. Further improvements could also be made by adding higher order drive terms^{25}.
Furthermore, we define a protected qubit basis, show twoaxis control, and show that the arbitrary superpositions of the protected qubit can survive for up to 800 ns. This demonstrates that the protection scheme is compatible with applications of the spin as a quantum memory, and with ac Bfield sensing schemes^{42}. The method avoids the use of cryogenic superconducting magnets, and is therefore suitable for room temperature applications. It should be insensitive to the details of the nuclear bath, and applicable to other spin defects in hBN or other IIIV materials with harsh nuclear spin environments.
Methods
Sample
The sample consists of a chromium/gold (20/170 nm thick) coplanar waveguide (CPW), with a 10 μm wide central conductor, on a sapphire substrate. An hBN flake, ~100 nm thick, is placed on top of the CPW using the PDMS transfer method. Boron vacancies are generated/activated using C ion irradiation with an energy of 10 keV and dose of 1 × 10^{14}cm^{−2}. Further details can be found in Baber et al.^{17}.
Experimental setup
Photoluminescence is excited using a 532 nm diodepumped solidstate laser, modulated by an acoustooptic modulator. The laser is coupled to a long working distance objective lens (N.A. = 0.8) which focuses the light to a diffractionlimited spot ~1 μm in diameter. The luminescence is collected with the same objective via a 750 nm long pass filter, to a fibre coupled single photon avalanche diode (SPAD). The intensity is recorded using a timecorrelated single photon counting module. The microwave waveforms are generated using an arbitrary waveform generator, amplified (30 dB amplification, maximum output power 30 dBm) and applied to the CPW on the sample. The optical and microwave excitation and photon collection are synchronised using a digital pattern generator.
Data availability
Source data are provided with this paper. All other data that supports the findings of this study are available from the corresponding author upon reasonable request. Source data are provided with this paper.
Code availability
The codes used for the analysis included in the current study are available from the corresponding author upon reasonable request.
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Acknowledgements
This work was supported by the Engineering and Physical Sciences Research Council [Grant numbers EP/S001557/1 (I.J.L.), EP/L015331/1 (A.J.B.) and EP/T017813/1 (A.J.B.)] and Partnership Resource Funding from the Quantum Computing and Simulation Hub [EP/T001062/1 (I.J.L. and A.J.B.)]. Ion implantation was performed by Keith Heasman and Julian Fletcher at the University of Surrey Ion Beam Centre. We thank Dr J. P. Hadden for useful discussions at an early stage of the project, and James Haigh for help with the SI Movies.
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I.J.L. and A.J.R. conceived and designed the experiments. S.B. fabricated the sample. I.J.L, R.H. and C.J.P. built the experimental setup and performed the measurements. I.J.L., A.J.R. and A.J.B. supervised the project. I.J.L., C.J.P., A.J.B., R.H. and A.J.R. analysed and discussed the experimental results. A.J.R. and D.R.M.A.S. performed calculations. A.J.R. wrote the manuscript with contributions from I.J.L and A.J.B.
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Ramsay, A.J., Hekmati, R., Patrickson, C.J. et al. Coherence protection of spin qubits in hexagonal boron nitride. Nat Commun 14, 461 (2023). https://doi.org/10.1038/s41467023361967
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DOI: https://doi.org/10.1038/s41467023361967
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