# Fileset

[CShineiComMater6-66(2025)-2.pdf](https://mdr.nims.go.jp/filesets/969fad6b-11b9-4862-9c42-400a6ef7a0f6/download)

## Creator

[Chikara Shinei](https://orcid.org/0000-0003-4926-8641), Yuta Masuyama, Hiroshi Abe, [Masashi Miyakawa](https://orcid.org/0000-0002-0838-8156), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), Takeshi Ohshima, [Tokuyuki Teraji](https://orcid.org/0000-0002-7731-0547)

## Rights

[Creative Commons BY-NC-ND Attribution-NonCommercial-NoDerivs 4.0 International](https://creativecommons.org/licenses/by-nc-nd/4.0/)

## Other metadata

[Homogeneous spin-dephasing time of NV− centre in millimetre-scale 12C-enriched high-pressure high-temperature diamond crystals](https://mdr.nims.go.jp/datasets/e261ff78-1741-479e-a845-99262644e3e8)

## Fulltext

Homogeneous spin-dephasing time of NV− centre in millimetre-scale 12C-enriched high-pressure high-temperature diamond crystalscommunicationsmaterials ArticleA Nature Portfolio journalhttps://doi.org/10.1038/s43246-025-00782-7Homogeneous spin-dephasing timeofNV−centre in millimetre-scale 12C-enrichedhigh-pressure high-temperature diamondcrystalsCheck for updatesChikara Shinei 1,2 , Yuta Masuyama 3, Hiroshi Abe 3, Masashi Miyakawa1, Takashi Taniguchi 1,Takeshi Ohshima 3 & Tokuyuki Teraji 1Negatively charged nitrogen vacancy (NV−) centres in diamond crystals are promising colour centresfor high-sensitivity quantum sensors. A long dephasing time (T2* > 10 μs) is essential for achievingincreased sensitivity and higher uniformity of T2* in millimetre-scale diamond is strongly desired forfemto-tesla weak magnetic field detection. High uniformity of T2* for NV− centres is achieved herein.The median value of T2*, <T2*>, in the 12C-enriched high-pressure, high-temperature (HPHT) growndiamondwith a nitrogen concentration of 1.3 ± 0.4 ppm is 4.5 μs. The varianceofT2* is only 10%over amillimetre-scale region (1.1 × 1.1 mm2)within the 0.4 mm thick {111} growth sector. <T2*> is ~2/3 timesthe value limited by the dipole-dipole interaction from the electron-spin bath of nitrogen impurities,suggesting that the residual strain gradient in the HPHT diamond crystal partially limits T2*. Reducingthe strain gradient in diamond crystals provide a pathway to achievement of high sensitivitymagnetometry using NV quantum sensing.The quantum superposition states (QSS) of electron and nuclear spins inpoint defects in wide-gap semiconductors are stable at room temperature1.These superposition states in semiconductors can prospectively be used forvarious quantum applications such as quantum computation2, and quan-tum sensing1,3,4. In quantum sensing, a type of quantum technology, themagnitude of external fields such as magnetic fields, electric fields, andtemperature are measured by detecting phase changes of the QSS. In gen-eral, QSS reflecting quantum effects are expected to provide higher-sensitivity measurements than classical sensing1. To achieve higher sensi-tivity in quantum sensing using QSS, extending both the number of sensorsand the spin-dephasing time, T2*, are essential.The QSS of the electron spins of NV− centres formed in diamond areattractive quantum systems because the ensemble of electron spins has anextremely long T2* of tens of microseconds at room temperature5. For NV−centres, T2* is relatively long even at room temperature because of theextremely small nuclear spin concentration of 1.1% indiamond6,7. The valueofT2* has been extended using 12C isotopically enriched diamondwith [13C]<500 ppm8–10, and a quantum sensor for measuring weak magnetic fieldshas been demonstrated using optically excited NV− centres created in12C-enricheddiamond11. In addition to the elongationT2*of theNV− centre,the crystal size of optically excited diamond, which determines the totalnumber of excited NV− centres, must be enlarged to achieve highmagneticsensitivity. In recent research12, a minimum detectable magnetic field sen-sitivity (MDMFS) of 9.4 pT Hz−1/2 was reported in a relatively small exci-tation volume of 0.004 mm3. This sensitivity was the best reported value intheDC frequency range of 5‒100Hz. In the previous report, a longT2*of theNV− centre ensemble (~2 μs) was achieved by 12C isotopic enrichment. Theachieved sensitivity corresponds to the shot noise limit, which is a quantum-limitingMDMFS. The long T2* and reduction in PL intensity noise by lasermainly contributed for the achieved the best reported sensitivity. Here, weproposed that enlargement of the reported excitation volume: 0.004mm3could lead to higher sensitivitywhilemaintaining the factors contributing tothe best reported sensitivity; long T2* (~2 μs) and PL intensity noise can-celling. Arai et al. reported a relatively large excitation diamond crystalvolume of 0.19mm3 for NV sensing13. The excitation volume was achievedby laser beam spot size being ~0.4mm in diameter with high laser power(2W) and constructing a reflection pass of excitation laser in a diamondcrystal13. Here, the increase in excitation volume contributes to improve theshot noise limit1. Based on the relationship that the shot-noise limit theo-retically improves by a factor of the square root of the excitation volume1National Institute for Materials Science, Tsukuba, Ibaraki, 3050044, Japan. 2University of Tsukuba, Tsukuba, Ibaraki, 3058577, Japan. 3National Institutes forQuantum Science and Technology, Takasaki, Gunma, 3701292, Japan. e-mail: shinei.chikara.fb@u.tsukuba.ac.jp; TERAJI.Tokuyuki@nims.go.jpCommunications Materials |            (2025) 6:66 11234567890():,;1234567890():,;http://crossmark.crossref.org/dialog/?doi=10.1038/s43246-025-00782-7&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s43246-025-00782-7&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s43246-025-00782-7&domain=pdfhttp://orcid.org/0000-0003-4926-8641http://orcid.org/0000-0003-4926-8641http://orcid.org/0000-0003-4926-8641http://orcid.org/0000-0003-4926-8641http://orcid.org/0000-0003-4926-8641http://orcid.org/0000-0002-1733-095Xhttp://orcid.org/0000-0002-1733-095Xhttp://orcid.org/0000-0002-1733-095Xhttp://orcid.org/0000-0002-1733-095Xhttp://orcid.org/0000-0002-1733-095Xhttp://orcid.org/0000-0001-9659-8382http://orcid.org/0000-0001-9659-8382http://orcid.org/0000-0001-9659-8382http://orcid.org/0000-0001-9659-8382http://orcid.org/0000-0001-9659-8382http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-7850-3164http://orcid.org/0000-0002-7850-3164http://orcid.org/0000-0002-7850-3164http://orcid.org/0000-0002-7850-3164http://orcid.org/0000-0002-7850-3164http://orcid.org/0000-0002-7731-0547http://orcid.org/0000-0002-7731-0547http://orcid.org/0000-0002-7731-0547http://orcid.org/0000-0002-7731-0547http://orcid.org/0000-0002-7731-0547mailto:shinei.chikara.fb@u.tsukuba.ac.jpmailto:TERAJI.Tokuyuki@nims.go.jpwww.nature.com/commsmatincrease rate, NV sensing using the reported large excitation volume of0.19mm3 with high laser power and NV− centre with a long T2* of ~ 2 μscould lead to higher magnetic sensitivity (<1 pT Hz−1/2). There are severalfactors that substantially reduce magnetic sensitivity when the excitationvolume is increased.One of them is significant increase of PL intensity noisedue to larger laser power. To increase the excitation volume while main-taining the higher emission rate of each NV− centre, the laser power has tobe increased. The PL intensity noise by high laser power is expected to becancelledbyabalancedphotondetection technique12,13.Another is the straindistribution, which becomes more pronounced as the excitation volumeincreases. The estimation of the improvement in sensitivity due to theincrease in the excitation volume was based on a condition that the NVcentres in the increased excitation volume have a long T2* with uniformedspatial distribution. Here, imperfection of diamond crystal such as straininhomogeneities1 andmagnetic noise by spin bath1 cause shorten ofT2*. Forexample, defects such as dislocations and plastic deformation defects dis-tributed over sub-millimetre-sized areas are formed during the synthesis ofdiamonds with millimetre-sized volumes14. These defects cause inhomo-geneous strain distribution and reduce the T2* of the NV− centre in theexcitation volume14. Therefore, we concluded that increasing the excitationvolume and spatial homogeneity of T2* by reducing the imperfection ofdiamond crystal in the excitation volume at the same time would be the keyto constructing highly sensitive magnetometers.For example, the achievement of human magnetoencephalographyunder ambient conditions is a major milestone in quantum sensing using aNV− centres12. An MDMFS of less than 10 fT15 is required for humanmagnetoencephalographymeasurements. Herein, the crystal size needed toobtain a sensitivity of 10 fT is estimated. The sensitivity is expressed as theDC shot noise limit ðηensemblesp Þ as represented by Eq. 11,13,ηensemblesp ¼ 1γNV1C × ffiffiffiffiffiffiffiffinavgp ×ffiffiffiβp 1ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiV × NV�½ �×T�2p ð1ÞγNV, C, navg, β and V are gyromagnetic ratio of the NV− centre spin of1.76 × 1011 Hz T−1, the spin-dependent NV− centre PL contrast, averagenumber of photons collected per NV− centre per measurement, photoncollection efficiency, and excitation diamond crystal volume, respectively.The product ofV and [NV−] represents the total number of NV− centres inthe excitation volume of the diamond crystal. The concentration of NV−centres is typically limited by the total nitrogen concentration in the dia-mond. The reported maximum efficiency for the conversion of nitrogen toNV− centres is about 50%16,17. TheT2* value of theNV− centre ensemblewaslimited by the total nitrogen concentration when the 13C concentration andstrain spatial distribution were significantly small18. T2* was found to beinversely proportional to the total nitrogen concentration, with an inversecoefficient of 9.9 μs ppm (corresponding to dephasing rate per density:101 kHz ppm−1)10. Using themaximumconversion efficiency [NV−]/[N] of0.5 and theT2* value limited by the total nitrogenconcentration expressed as9.9/[N], the shot noise limit equation (Eq. 1) can be transformed to Eq. 2.ηensemblesp ¼ 1γNV1C × ffiffiffiffiffiffiffiffinavgp ×ffiffiffiβp 1ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiV × 0:5× 9:9p ð2ÞThe product of the PL contrast and square root of the average photoncounts of theNV− centre ensemble shown inEq. 2, C × navg1/2 is an indicatorof the photon readout fidelity for the NV− centre. This readout fidelity isunity under ideal condition, which is the spin projection limiting value1.However, in the typical photon readout fidelity for NV− centres, C× navg1/2was reported to have a significant lower value 1/5000‒1/10001 than the spinprojection limiting value. By using the total reflection of the photon emis-sion of the NV− centre in diamond, a value of 1/67 as C× navg1/2 wasachieved19,which is twoorders ofmagnitude larger than the typical reportedvalues. This two-magnitude improvement in the photon readout fidelitycontributed to enhancing the magnetic sensitivity19. For the excitation ofmillimetre-sized diamond volumes, this total internal reflection method isthought to be essential. And photon collection efficiency can be improved to65% by using a trapezoidal-cut diamond crystal and a parabolicconcentrator20.Using the shotnoise limits inEq. 2withphotonicparametersas C × navg1/2 = 1/67 and β = 0.65, to achieve a magnetic sensitivity below 10fT, the minimum excitation diamond volume V was estimated to be~ 2.6 mm3.The estimation of the minimum excitation diamond volume forhuman magnetoencephalography using the shot noise limit equation doesnot consider high-fidelity spin-rotation operations for high-precisionquantum sensing. During quantum sensing, the protocol of spin half-rotation in a Bloch sphere is essential for preparing QSS. The phase of theQSS fluctuates when the half π-rotation time (Tπ/2), that is, the generationtime of the QSS, is significantly larger than the spin-dephasing time, T2*. Toavoid phase fluctuation, in general, Tπ/2 must be set to a value significantlyshorter than T2*. This criterion suggests that the spin rotation is completedwell before phase coherence is lost. In order to perform high-fidelity spinrotation, the value of T2* needs to be over two orders of magnitude longerthan Tπ21. For achieving high sensitivity using NV sensing, so far, someprevious reports showed spin π-rotation time of ~ 50 ns22 and ~ 100 ns23,24.Because the spin π-rotation time of the NV− centre in this study isapproximately 100 ns, the minimum spin-dephasing time required forhigh-fidelity spin rotation is estimated to be 10 μs. To achieve a π rotationtime of ~ 100 ns, a driving microwave (MW) magnetic field amplitude of0.18 ~ 0.21mT23,24 was applied to the NV− centre ensemble. The spin-rotation time is determined by the strength of themicrowavemagnetic fieldapplied to the NV− centre. The larger the amplitude of the microwavemagneticfield applied to theNV− centre, the faster the spin rotation is. AT2*of over 10 μs is expected when the total nitrogen concentration is below1 ppm because the total nitrogen concentration and T2* are inversely pro-portional in this nitrogen doping range. From the shot noise limit andcriteria for high-fidelity spin rotation, millimetre-sized diamond crystalsand T2* > 10 μs are essential for 10 fT human magnetoencephalography.Previous research has been conducted using diamonds synthesised bychemical vapourdeposition (CVD), a commondiamondgrowthmethod, toincrease the T2* of NV− centres formed in millimetre-sized diamond singlecrystals and improve their spatial uniformity. Indeed, T2* spatial mappinghas reportedly been carried out within an area of 1mm× 1mm in the {001}plane of 0.1 µm thick diamond, where non-uniform T2* spatial distributionwas observed18. In that study, the T2* inhomogeneity was caused by a straingradient in thediamondcrystal.Oneof the factors contributing to the spatialdistribution of strain in CVD diamonds is the dislocation distribution. In aprevious report, high-density dislocation distributions ranging from 104 to106 cm−2 were observed inCVDdiamondcrystals usingX-ray topography25.Furthermore, Kehayias et al. reported the distribution ofNV− centres with ashort and non-uniform T2* in the dislocation area in CVD diamondcrystals14. High-pressure, high-temperature (HPHT) synthesis is anothercommon method for diamond growth. In the HPHT method, diamond issynthesised under equilibrium conditions; therefore, it is thought that theformation of high-density dislocation defects as observed in CVD diamondis unlikely, as there have been reports of millimetre-sized HPHT diamondsingle crystals with low dislocation densities of less than 102cm−2 26,27.Therefore, NV− centres with a uniformly distributed, long T2* are expectedto be obtained in HPHT nitrogen-doped diamonds. In previous report,strain imaging by NV sensing were carried out with millimetre-sizednitrogen doped CVD diamond18. The imaging cross-sectional area was 1mm2 and the doped nitrogen concentration was 0.75 ppm. The obtainedstrain imaging indicated partial sub-millimetre-sized large strain distribu-tions. This sub-millimetre-sized distribution caused degradation of T2* anda significant large variation of T2* (1‒10 μs) was also reported in that pre-vious study. The large variation of T2* could cause degradation of theaveragedT2* in excitedmillimetre-sizeddiamondcrystal volume.Therefore,expected millimetre-sized homogeneous T2* distribution in HPHT dia-mond crystal is essential for human magnetoencephalography.In this study, low-strain, nitrogen-doped diamond crystals are syn-thesised using HPHT synthesis method. These low-strain HPHT diamondhttps://doi.org/10.1038/s43246-025-00782-7 ArticleCommunications Materials |            (2025) 6:66 2www.nature.com/commsmatcrystals are used for millimetre-size T2* imaging and to clarify themillimetre-size distributed dephasing factor of NV− centre spin coherence.Finally, high uniformity of the spin dephasing time of NV− centres inmillimetre-scale area was achieved using 12C-enriched nitrogen dopedHPHTdiamond crystals, and in region of nitrogen impurity concentrationsless than ~ 1 ppm, it was found that the strain gradient in HPHT diamondcrystals partially limits spin dephasing time.Results and discussionSynthesis of HPHT diamond crystalsIn order to form an ensemble of NV− centres that contributes to magne-toencephalography, it is necessary to extend T2* to over 10 μs. To achievethis, the density of the doped nitrogenmust be controlled, and the nitrogenconcentration should be reduced to less than 1 ppm. In general, the nitrogenconcentration can be controlled by adding nitrogen-gettermetals such as Tiand Al to the solvent-metal during HPHT synthesis. The nitrogen-gettermetal and solvent-metal are described in the sample preparationofMethodssection. Precise nitrogen concentration control ranging from0.2 to 100 ppmwas achieved by controlling the amount of the nitrogen-getter metal28.DuringHPHT synthesis of diamond, when the growth rate was higher than6‒7mg h−1, the solvent-metal used in HPHT synthesis was incorporatedinto the growing diamond, resulting in the formation of metal inclusions29.These metal inclusions become a source of strain gradients distributed overmillimetre-sized areas. To suppress the formation of metal inclusions andsynthesis large diamond crystal, the lower growth rate than 6‒7mg h−1 andlong growth time: over several tens of hours are required29. When growingdiamond crystals for a long time to obtain high-quality crystals, changes ingrowth rate due to temperature fluctuations can be a problem. To avoid thetemperature fluctuation, a modified belt-type, high-pressure apparatus wasused28,30,31, in which cooling water was available for temperature stabilisa-tion. In this study, HPHT diamond crystals were synthesised using amodified belt-type, high-pressure apparatus, in the temperature range of1300‒1350 °C. The temperature fluctuation was less than ± 7.5 °C. Thegrowth time and growth rate were 40‒80 h and ~1mg h−1, respectively inthis study.Sequence of T2* spatial mapping for NV− centresT2* was measured in the millimetre-scale region of the diamond. Acolumnar excitation fluorescence microscope23 was used to excite theNV− centres throughout the thickness direction of the diamond crystal,which is typically 400 μm. Because the 532 nm laser diameter and depthof the excitation region in the employedmicroscope are designed to be 20and 500 μm23, respectively, the ensemble of NV centres was excited at thesame time, as shown in Fig. 1a. The spatial distribution of T2* in the {111}plane was evaluated as follows: (1) Optically detected magnetic resonance(ODMR)measurements were performed at each excited position. Duringthe measurements, an external magnetic field of 2.5 mT was appliedalong the direction of the [111] diamond crystal. The obtained ODMRfrequency was generally ~ 2.8 GHz. (2) Subsequently, spatial Rabi mea-surements were performed at the same excited position. The MW fre-quency was set to the ODMR frequency obtained at the same excitedposition. The typical duration of the microwave π/2 pulse in the Rabioscillation was ~ 50 ns. (3) Finally, free-induction decay (FID) mea-surements were performed at the same excited position, where theduration of the microwave π/2 pulse was obtained from Rabi measure-ment at the same excited position. A typical FID signal was shown inFig. 1c. T2* was estimated by fitting the obtained FID signal to thedamped oscillation function18, shown in Eq. 3:SFID τð Þ ¼ exp � τT�2� � Xi¼1;2;3Ai sin 2π f i þ δi� �ð3Þwhere f1, f2 and f3 are the frequencies of the hyperfine splittingmagneticfielddue to the 14N atom in the NV− centres. The typical values of f1, f2 and f3 are0.9, 3 and 6MHz, respectively.As shown in Fig. 1b, the distance between each laser excited positionwas set to 100 µm for T2* spatial mapping within the millimetre-scale {111}growth sector.T2* spatial mapping in the millimetre-scale {111} planeFigure 1d shows the PL intensity imaging for the NV− centre in the HPHTdiamond with [Ns0]initial = 1.3 ppm. The HPHT diamond crystal has flat-areas indicated as Fig. 1d-i, ii, and also has tapered-area indicated as Fig. 1d-iii. The growth sector indicated as Fig. 1d-i including the red square area(1.1mm× 1.1mm for T2* spatial mapping below) was primarily the {111}growth sector. In this red square area, the distribution of PL intensity wasnearly homogeneous, and the PL intensity was significantly larger than thatof the othergrowth sectors as indicated inFig. 1d-ii except for growth sectorsin tapered-area as indicated in Fig. 1d-iii. From the relationship between thereported uptake of nitrogen for different growth sectors32 and the obtainedPL intensity from the growth sector in Fig. 1d-ii was {110} or {113} growthsector. The details for PL intensity in multi-growth sectors in flat-areas andthe relationship between PL intensity and growth sector in the tapered areawere explained in PL intensity of NV− centres in multi-growth sectors ofMethods section.Next, T2* spatial mapping was performed in themillimetre-scale {111}plane region of the red square (1.1mm× 1.1mm) in Fig. 1d. Figure 1eshows the T2* spatial distribution in this 1.1 mm× 1.1mm region. T2*presented here is the average value of four T2* measurements at the sameposition (for details, see the Supplementary Note 1). No significant low T2*region was detected in the mapped millimetre-scale area shown in Fig. 1e.This means that the number of millimetre-scale structural defects, such asdislocation bundles and plastic deformation zones observed by Kehayias etal.14, is quite small in themillimetre-scale {111} growth sector of the presentspecimens. On the surface of a diamond crystal, ubiquitous defects causemagnetic noise at the NV− centre located within 100 nm of the surface33. Inthe present study, most of the detected NV− centres were located inside thediamond crystal with ~400 μm thickness, far away from the surface.Therefore, the degradation of the examined T2* caused by the surfacemagnetic noisewasneglected in this study. PL intensity imaging canprovideinformation on the distribution of non-radiative defects near the NV−centre because NV− photons are transferred from the excited-state level oftheNV− centre to thenon-radiativedefect level. This photon transfer causedby non-radiative defects leads to a decrease in the PL intensity. In addition,non-radiative defects may shorten T2* of the NV− centre due to magneticnoise or lattice strain from these defects. The PL imaging of {111} growthsector as indicated red square in Fig. 1d showed no area with significantlylow PL intensity, demonstrating that the distribution of high-density, non-radiative defects was negligible. Furthermore, there was no obvious corre-lation between the PL intensity and T2* image in the {111} growth sector, asshown in Fig. 1d and e. This result suggests that non-radiative defectsprimarily do not limit the T2* distribution in the {111} sector. Birefringenceimaging detects microdefects such as dislocations and dislocation bundles.The birefringence imaging in the {111} growth sector is presented in Sup-plementary Note 2. In birefringence imaging, the distributions of disloca-tions and dislocation bundles cannot be resolved. This birefringence imagealso shows that the examined HPHT diamond crystal has high crystallinity(see Supplementary Note 2). Figure 1f shows a histogram of T2* obtainedfrom T2* spatial mapping in the millimetre-scale {111} growth sector. Thesolid line represents the Gaussian curve fitted to the histogram. Themedian<T2*> of this Gaussian distribution was 4.5 µs, with a standard deviation ofless than 10% of <T2*>. The 10% variation in T2* indicates that the HPHTdiamond used in this study has a highly uniform spatial distribution of T2*.The obtained spatial variation in T2* was significantly smaller than thepreviously reported T2* variation of 35 %. The reported variation wasobtained byT2*mapping in 150 µm× 150 µmregion in {001} plane of CVDdiamond with [NT] ~ 20 ppm34.The phase of theQSS of theNV− centre fluctuates owing to the dipole-dipole interaction (DDI) from the electron-spin bath of nitrogenimpurities1,10,18. The fluctuation of the QSS phase led to a decrease in T2*.https://doi.org/10.1038/s43246-025-00782-7 ArticleCommunications Materials |            (2025) 6:66 3www.nature.com/commsmatFig. 1 | T2* spatial mapping in {111} plane of diamond using columnar excitationfluorescence microscope. a 532 nm laser excitation volume in diamond for oneexcited position using columnar excitation fluorescence microscope. b Schematic ofspatial T2* mapping in {111} plane of diamond. c Circle symbol indicates repre-sentative FID signal respective to free precision time and solid line shows dampingoscillation curve as per Eq. 3 for fitting the FID signal. d Spatial distribution of PLintensity ofNV− centremapped in {111} plane of diamond crystal. Red square regionindicated as (i) shows {111} growth sector in diamond crystal. The lower PL intensityarea indicated as (ii) was the {110} or {113} growth sector. The tapered area indicatedas (iii) was {110} or {113} growth sector. e SpatialT2*mapping in {111} growth sectorwithin the red square (1.1 mm × 1.1 mm) as shown in this figure. fHistogram of T2*from spatial T2*mapping in {111} growth sector of diamond, as shown in this figure.g Histogram of Mz obtained from spatial Mz mapping in {111} growth sector, asshown in this figure. ΔMz represents FWHM of Mz.https://doi.org/10.1038/s43246-025-00782-7 ArticleCommunications Materials |            (2025) 6:66 4www.nature.com/commsmatThis phenomenon becomes dominant when the nitrogen concentrationexceeds 1 ppm. The spin-dephasing rate, 1/T2*{NT}, due to this DDI fromthe electron-bath of nitrogen impurities is described as follows:1T�2fNTg¼ DNT× NT� �ð4Þwhere DNT¼ 101 ± 12ms�1ppm�1 and [NT] is the total concentration ofnitrogen impurities in thediamond.The experimentally obtained<T2*>was4.5 μswhich is smaller thanT2*{NT} = 7.6 ± 0.9 μs estimated fromEq. 4with[NT] = [Ns0]initial = 1.3 ± 0.4 ppmfor the examinedHPHTdiamond sample,as seen in the filled orange area in Fig. 1f. This result indicates that thedephasing rate for T2* is affected by sources other than the electron-spinbath of nitrogen impurities. Previous studies reported that the straingradient in diamond crystals reduces T2* through the interaction betweenthe electronic dipole and the electron spin of the NV− centre14,35. Thedephasing rate due to this strain gradient, which is termed 1/T2*{straingradient} in this study, corresponds to the spatial dispersion of theinteraction Mz between the electron spins and diamond crystal strain. Ingeneral,Mz is one component of theODMRresonance frequency ðf± Þ of theNV− centre (Eq. 5).f± ¼ DþMz ± γNVBz ð5Þf± is composed of the zero-field splitting (D) of the electron spin (S = 1)of theNV− centre, the spin-strain interaction (Mz), and theZeeman splittingcaused by the external magnetic field (Bz)18,35. Strain gradients in diamondcrystals have been observed as resonance frequency shifts in ODMR14,35. Inthis study,Mz was obtained from Eq. 6 using the value of f± obtained fromthe ODMR measurements.Mz ¼ ð fþ þ f�Þ=2� D ð6ÞHere, 2.87 GHz was used for D1,36 in Eq. 6. Mz mapping in the {111}sector area was used to study the strain gradient in the HPHT diamond, asindicated by the red rectangle in Fig. 1d. The PL intensity image of the NV−centre, T2*, Mz, and birefringence in the {111} sector are compared inSupplementary Note 2. There was no obvious correlation between theimaging data. In future studies, other defect imagingmethods such as X-raytopography and cathodoluminescence will be used to determine the causesof the partial distribution of the relatively low T2* observed in Fig. 1e. Fig-ure 1g shows the histogram obtained fromMz spatial mapping in the {111}growth sector, where T2*mapping was performed. The solid line representsthe Gaussian function fitted to the histogram. The result indicates that thediamond crystal strain was uniformly distributed throughout the HPHTdiamond. The full width at half maximum (FWHM) ofMz in the Gaussiandistribution, that is, ΔMz, was 0.06MHz. Note that the calculated ΔMzincludes not only in-plane variance of the strain, but also depth variance ofthe strain. The depth variance arises from the examined excited depth of~400 μm. Assuming that strain is hydrostatic, the strain gradient in thedepth direction of the examined HPHT diamond is expected to be com-parable to that obtained by in-plane Mz imaging in this study. In futurestudies, the strain gradient in thedepthdirection should bedirectly observedby ODMR using a conventional confocal microscope having a depthresolution of 1 μm. Here, the spatial dispersion of the strain related ODMRshift, ΔMz, induces inhomogeneous broadening of the ODMR spectrum oftheNV− centre18. Thus,ΔMz corresponds to the dephasing rate of the straingradient 1/T2*{strain gradient}18 in the whole T2* spatial mapping region(Fig. 1e). The slope of the strain gradient in the {111} plane direction of thediamond crystal was estimated to be 0.06MHz/1100 μm= 0.05 kHz μm−1.This value is approximately one order of magnitude smaller than the straingradient of 2.8 kHz µm−1 for nitrogen-doped CVD diamond with[NT] = 0.75 ppm reported by Bauch and coworkers18. In this study, thecritical synthesis parameter for improvement of homogeneity of T2* andstrain gradient in examined HPHT diamond crystals were not clear. It ispossible that reducing the growth rate to ~1mg h−1, which is smaller thanreported value29, led to the high quality of the diamond single crystal. Thislow growth ratemay cause reduction of defects such as dislocation. In futureworks, an investigation of the relationship between formation of defect andvarious synthesis parameters such as growth rate is expected.Here, strain gradients in diamond crystals caused by high doping withimpurities such as boron and phosphorus have been reported37–39. There-fore, in the next section, the dependence of the strain gradient observed inthis study on the nitrogen impurity concentration is discussed.Dependence of strain gradient in diamond on concentration ofnitrogen impuritiesThe dependence of the strain gradient in diamond crystals on the con-centration of nitrogen impurities was investigated. The green triangles inFig. 2a show the relationship betweenΔMz and [Ns0]initial. To determine thestrain gradient,ΔMz, in-plane {111} spatialMz mapping was carried out fornine 12C-enriched HPHT diamond crystals with different [Ns0]initial. Theresulting ΔMz ranged from 0.06 to 0.1MHz and did not have a strongdependence on [Ns0]initial, indicating that the strain gradient in the diamondcrystal was not caused by uptake of nitrogen under the [Ns0]initial rangingfrom 0.7 to 14 ppm. When strain gradient is independent of nitrogenconcentration, dephasing effect due to strain gradient becomes negligiblewhennitrogen concentration is larger, e.g., 10 ppm, leading to improvementof shot-nose limit. But, in practical sensing, as well as improving shot noise,spin manipulation with high fidelity is also one of essential key technologyFig. 2 | Effect of concentration of nitrogen impurities on spin-dephasing rate.aDependence of initial neutral substitutional nitrogen concentration, [Ns0]initial, ontwo-spin dephasing rate component. Black dashed line and green triangles showdipole-dipole interaction (DDI) from electron-spin bath of nitrogen impurities andstrain gradient in diamond crystal, respectively. b Dependence of initial neutralsubstitutional nitrogen concentration [Ns0]initial on spin-dephasing time, T2*. Redsquare, orange rhombus, and blue triangle, respectively, show experimental spin-dephasing time as T2*{exp. 12C} and T2*{exp. CNat. Abu.} from12C-enriched andcarbon natural-abundance HPHT diamond, and spin dephasing time obtained bysubtracting spatial strain gradient in diamond crystal from T2*{exp. 12C}: T2*{strainsubtract}. The black dashed line shows the dephasing time limited by DDI from theelectron-spin bath of nitrogen impurities, T2*{NT}. The vertical error bars forT2*{exp. 12C} and T2*{exp. CNat. Abu.} indicate the standard deviation of the Gaussiandistribution. The horizontal error bars for T2*{exp. 12C}, T2*{exp. CNat. Abu.} andT2*{strain subtract} indicate the EPR estimation error for initial Ns0 concentration.https://doi.org/10.1038/s43246-025-00782-7 ArticleCommunications Materials |            (2025) 6:66 5www.nature.com/commsmatfor high sensitivity as explained in the introduction part. In the case of spinrotation time ~100 ns in this study, T2* over 10 μs is needed for high fidelityof spin manipulation. Therefore, the reduction of strain gradient in dia-mond with lower nitrogen concentration less than 1 ppm is desirable forpractical sensing. The obtained strain gradient ΔMz ranging from 0.06 to0.1MHz corresponds to stress ranging from 5 to 8MPa, assuming that thestrain is hydrostatic40. Sumiya et al. reported that an Ib-diamond containingseveral tens to hundreds of ppm of nitrogen impurities has a larger inho-mogeneous strain distribution41. This fact suggests that nitrogen-dopeddiamond has relatively large strain gradient. This inhomogeneous straindistribution could shift the resonance frequency of the NV− centre.Therefore, in Ib-diamond crystals, the inhomogeneous strain distributionshortens T2* of the NV− centre. To determine the effect of the nitrogen-impurity concentration and strain gradient onT2*, the spin-dephasing rates1/T2*{NT} estimated using Eq. 4 were superimposed on Fig. 2a, as indicatedby the black dotted line. As shown in Fig. 2a, 1/T2*{NT} was approximately10 times larger than the strain-gradient dephasing rate, ΔMz, at[Ns0]initial ≈ 10 ppm. The difference between ΔMz and 1/T2*{NT} becamesmaller as [Ns0]initial decreased, and the values of both were comparable at[Ns0]≈ 1 ppm. This suggests that in the region of a relatively small [Ns0]initial(~1 ppm),T2* is expected to be governednot only byDDI from the electron-spin bath of nitrogen impurities but also by the strain gradient in the dia-mond crystal. To verify this T2* dephasing model, the relationship betweenthe experimentally-obtained spin-dephasing time of the 12C-enrichedHPHT diamond crystal (T2*{exp. 12C}) and [Ns0]initial was investigated.Here, T2*{exp. 12C}, which is plotted in Fig. 2b as red rectangles, is themedian value of T2*, <T2*>, in a Gaussian distribution, as shown in Fig. 1f.Thevertical error bars forT2*{exp. 12C} indicate the standarddeviationof theGaussian distribution; they are much smaller than themarker size. T2*{exp.12C} decreased with increasing [Ns0]initial (Fig. 2b). This suggests that theDDI from the electron-spin bath of nitrogen impurities was significantdephasing contribution respect to the other dominant contributionsincluding strain gradient. TheT2*{exp.CNat. Abu.} data obtained fromcarbonnatural-abundance HPHT diamond samples were plotted in the figure asorange rhombuses. T2*{exp. CNat. Abu.} also decreased with an increase in[Ns0]initial. Furthermore, T2*{exp. CNat. Abu.} became significantly smallerthan T2*{exp. 12C} with a decrease in [Ns0]initial. This significant decrease ofT2*{exp. CNat. Abu.} from T2*{exp. 12C} was caused by the presence of mag-netic noise from the 13C nuclear spin in carbon natural-abundance HPHTdiamond samples. It means that 12C enrichment is indispensable forobtaining T2* of larger than 1 μs. The relationship between T2*{NT} and[Ns0]initial shown in Eq. 4 is superimposed on Fig. 2b using a black dashedline. The difference between T2*{exp. 12C} and T2*{NT} became significantlylarger with a decrease in [Ns0]initial. As discussed above, one possiblemechanism that shortens T2*{exp.} is the strain gradient of the diamondcrystals. To eliminate the strain-gradient dephasing rate (ΔMz) from 1/T2*{exp. 12C}, T2*{strain subtract} was estimated, as defined below:1T�2fstrain subtractg �1T�2 exp : 12C  � ΔMz ð7ÞT2*{strain subtract}, which is plotted as blue triangles in Fig. 2b, hadapproximately the same value as T2*{NT} (Fig. 2b), as indicated by the blackdashed line, based on Eq. 4. This result shows that reducing the straingradient extendsT2* to a value limitedbyDDI fromthe electron-spinbathofnitrogen impurities, as shown in Eq. 8:1T�2fstrain subtractg �1T�2fNTgð8ÞReducing the strain gradient in diamond crystals is essential for furtherimproving T2*, especially in the nitrogen-impurity concentration rangebelow 1 ppm. Furthermore, reducing strain and strain gradient in the lowernitrogen impurity concentration is essential for high-performance quantumcomputation and quantum telecommunication using a single NV− centre.The electronic noise from the strain shifts the ODMR frequency and zerophonon line wavelength42 of a single NV− centre, and this shift causesfluctuation of the quantum state of a single NV− centre, leading to thedegradation in the performance of these quantum applications. Here,T2*{strain subtract} at an [Ns0]initial of <1 ppm was slightly larger thanT2*{NT}, as indicated by the black dashed line as shown in Fig. 2b. T2*{NT}was obtained from N-doped CVD diamond crystals6,10 with [13C] ~500 ppm. The dephasing rate by 13C nuclear spin with [13C] ~ 500 ppmwas~ 1/20 μs−1 using the reported coefficient between [13C] and 13C dephasingrate1. This rate is significant for the NV− centre spin dephasing in diamondcrystals with [Ns0]initial of less than 1 ppm. In this study, the dephasing rateby 13C nuclear spin with [13C] ~ 50 ppmwas ~ 1/200 μs−1. The one order ofmagnitude higher isotopically 12C enrichmentmay cause the observed slightelongation of T2*{strain subtract} relative to T2*{NT} with [Ns0]initial of lessthan 1 ppm in Fig. 2b. Furthermore, we considered the effects of defectsinherent in the CVD growth on T2*. Previous studies have demonstratedthat nitrogen-doped CVD diamond crystals with nitrogen-impurity con-centrations below 1 ppm contain various vacancy-impurity complexes43–46.To date, these defects have not been observed in nitrogen-doped HPHTdiamond crystals, including those examined in this study. The non-formation of the vacancy-impurity complexes in HPHT diamond crystalsmay cause a slight elongation of T2*{strain subtract} from T2*{NT}at an[Ns0]initial of <1 ppm in Fig. 2b.In conclusion, high uniformity of theT2* ofNV− centres inmillimetre-scale area was demonstrated using 12C-enriched HPHT diamond crystals.The median value of T2*, <T2*>, for the NV− centres formed in the high-pressure, high-temperature diamond was 4.5 μs when the nitrogen con-centration in diamond crystal was 1.3 ppm. The spatial variance of T2* wasas small as 10% over a millimetre-scale region (1.1 × 1.1 mm2) within the{111} growth sector with a thickness of 0.4 mm. The value of <T2*> wasapproximately 2/3 times the value limitedby theDDI from the electron-spinbath of the nitrogen impurities, suggesting that the strain gradient in thediamond crystal partially limitsT2*. The strength of the interaction betweenthe electron spins of the NV− centre and strain in the diamond crystal,Mz,wasmeasuredwithin the {111} growth sector, whereT2*was estimated. Thespatial variance of Mz, which corresponds to the strain gradient, was0.06MHz. The dephasing rate originating from the strain gradient wascomparable to that originating from the electron-spin bath of nitrogenimpurities. The effect of the nitrogen-impurity concentration on the straingradient was investigated using several HPHT diamond crystals with[Ns0]initial ranging from 0.7 to 14 ppm. The strain gradient was independenton the nitrogen impurity concentration ranged in over one order of mag-nitude. Especially, T2* is limited by the electron-spin bath of nitrogenimpurities with [Ns0] > 2 ppm because the dephasing rate due to theelectron-spin bath of the nitrogen impurities is larger than the obtaineddephasing rate of the strain gradient. On the other hand, T2*was limited bythe strain gradient in the diamond crystals when [Ns0]initial <~1 ppm. Thus,reducing the strain gradient is essential for further improvementofT2*whenthe nitrogen-impurity concentration is relatively small (<1 ppm), which is arequirement for achieving high-sensitivity magnetometry by NV quantumsensing.MethodsSample preparation12C isotopically enrichedHPHT synthesized diamond was examined in thisstudy28. 12C-enrichedCVDpolycrystalline diamondwas used as the startingmaterial (carbon source) because 12C isotopically enriched graphite is notcommercially available47. The reduced 13C concentration was assumed to be50 ppm. The concentration of nitrogen impurities in the examined dia-monds was controlled by the amount of Ti or Al (nitrogen-getter metal)added to the solvent-metals such as Fe and Co28. Diamond single-crystalswere grown on (001) plane seed crystals in Co-Ti-Cu, Fe-Co-Ti-Cu, Fe-Al,Fe-Co-Al (99.98%–99.999%, RARE METALLIC Co., Ltd.) solvents via atemperature-gradient method at 5.5 GPa in the temperature range of 1300‒https://doi.org/10.1038/s43246-025-00782-7 ArticleCommunications Materials |            (2025) 6:66 6www.nature.com/commsmat1350 °C for 40‒80 h. A small temperature fluctuation less than ± 7.5 °C wasachieved by using cooling water in the modified belt-type, high-pressureapparatus. When Ti was added as a nitrogen getter, Cu was added to thesolvent. TheCu additive suppressed the formation of Ti-C inclusion defectsin the grownHPHTdiamond48. The synthesised diamonds were then laser-cut parallel to the {111} plane. The spin coherence time was maximisedwhen the external magnetic field was parallel to NV− centre’s dipole-oriented axis of [111]. For NV sensing, {111} oriented diamond crystal istypically used12,49–51 because the precise alignment of the external magneticfield parallel to the NV axis of [111] is easier than that of {001}, {110}oriented diamond crystal. A magnet can be arranged in a compact mannerusing a {111}-oriented diamond, leading to the miniaturisation of the NVsensing system49. Laser cutting caused non-diamond phase carbon such asgraphite and amorphous carbon defects to form on the surfaces of thediamond samples. The amorphous carbon defect has paramagneticproperties52 and could cause degradation ofT2* ofNV− centre distributed insurface of diamond crystal. After laser cutting, acid treatment(H2SO4:HNO3 = 1:1 at 360 °C for 2 h) was used to remove the graphite andthe surface amorphous carbon from thediamond samples. The in-plane sizeof the cut diamonds was approximately 2mm× 2mm and the thickness inthe [111] direction was 400 ± 100 µm. In this study, nine HPHT diamondswere laser-cut.The concentrationofnitrogen impuritieswas thenquantifiedfor these nine diamond samples. Most of the nitrogen impurities in thediamonds synthesized by the HPHT method are in the form of neutralsubstitutional nitrogen (Ns0)53. Electron paramagnetic resonance (EPR)wasused to determine the concentration of NV centres and Ns0 53,54. Here, theconcentration of NV− centres and Ns0 obtained by EPR were lower thanthose in the {111} sector because EPRwas performedwithHPHTdiamondscontainingmultiple sectors, as shown in Fig. 1d. Themultisector composedof not only the {111} growth sector but also contains {110} and {113} growthsectors.TheNs0 concentration in the {110} and {113} growth sectorswas oneorder of magnitude smaller than that in the {111} growth sector32. Thus, theEPR intensity obtained from the examined multi growth sector HPHTdiamondsmainly originated fromNs0 andNV− centres in the {111} growthsector. To correct theunderestimationof [Ns0] and [NV−], the volumeof themulti-sectors (that is, the {110} and {113} growth sectors) was subtractedfrom the total volume of the examined HPHT diamond samples. For someHPHT diamond samples in this study, the {111} growth sector was isolatedby laser cutting and [Ns0] and [NV−] were directly estimated. The estimatederror in [Ns0] and [NV−] for the {111} growth sector was within ± 30%.Here, the concentration of the NV centres formed during the HPHTsynthesiswas the detection limit for theEPRmeasurements in the examinedHPHT diamond samples. In HPHT synthesis, the formation of vacancies isless likely to occur than in CVD synthesis. In the CVD synthesis, NV andNVH centres were typically observed54,55. The concentration of neutralsubstitutional nitrogen, [Ns0]initial, before formation of the NV centres inthese crystals ranged from 0.7 to 14 ppm. Electron-beam irradiation fol-lowedbypost-annealing (1000 °C2 h)was carriedout to formNVcentres inthe examineddiamond54. The examinedfluencewas ranged from1 × 1017 to5 × 1017 e cm−2. The concentrations of NV− centres formed by this post-process ranged from 0.1 to 2 ppm. The obtained maximum conversionefficiency [NV−]/[Ns0]initial was approximately 20% in this study. The idealconversion efficiency is 50%16,17. By using electron-beam irradiation duringhigh-temperature annealing, the best reported conversion efficiency of 45%was obtained for the Ib-diamond sample with [Ns0]initial = 100 ppm16,17. Theenhancement of conversion efficiency has been investigated with only overnitrogen concentration of 30 ppm56. In future work, in diamond sampleswith nitrogen concentrations less than 1 ppm, the conversion efficiency isexpected to be enhanced by electron-beam irradiation during high-temperature annealing.Experimental setupFree induction decaymeasurements were conducted using a home-built PLsystem with a pulsed microwave module (Synth NV PRO; WindfreakTechnologies, LLC/arbitrary waveform generator M3202A; Keysight Inc.).A 532 nm laser (gem 532; Laser Quantum Inc.) was pulsed using anacoustic–optic modulator (#35 250-0.2-0.53-XQ; Gooch & Housego). Redfluorescence emitted from the NV− centre by pulsed green laser excitationwas collectedusinganachromatic lens (AC254-030-AB-ML;Thorlabs, Inc.)and detected using an avalanche photodiode (APD410A/M;Thorlabs, Inc.).PL intensity of NV− centres in multi-growth sectorsHere, we additionally explained the relationship between PL intensity andgrowth sectors as indicated in Fig. 1d-ii, iii.The PL intensity distributed around the three triangular verticesindicated as Fig. 1d-ii is over one order of magnitude lower than that in the{111} growth sector indicated as Fig. 1d-i, indicating that the three triangularvertex areas was corresponding to the {113} or {110} sectors. It has beenreported that thenitrogendensity in the {113} and {110} growth sector is oneorder of magnitude lower than that in the {111} growth sectors32. Thetapered area indicated as Fig. 1d-iii is {110} or {113} growth sector as fol-lowing general HPHT diamond text. But PL intensity distributed in thetapered areawas comparable to or slightly larger than {111} growth sector inFig. 1d-i. The PL intensity in the tapered area was not corresponding totypical variation of uptake of nitrogen impurities between multi-sectors.This controversial result in this study was caused by the excitation laserreflecting and refracting at the tapered area. The laser reflecting andrefracting at the tapered area, entered a {111} growth sector in central area,and thePL emission from the {111} growth sector returned to the entry-passand was subsequently detected.Data availabilityThe datasets generated during and/or analysed in this study are availablefrom the corresponding authors upon reasonable request.Code availabilityThe codes used for this study are available from the corresponding authorsupon reasonable request.Received: 3 April 2024; Accepted: 14 March 2025;References1. Barry, J. F. et al. Sensitivity optimization for NV-diamondmagnetometry. Rev. Mod. Phys. 92, 015004 (2020).2. Kubo, Y. et al. Hybrid quantum circuit with a superconducting qubitcoupled to a spin ensemble. Phys. Rev. Lett. 107, 220501 (2011).3. Gottscholl, A. et al. Spin defects in hBN as promising temperature,pressure and magnetic field quantum sensors. Nat. Commun. 12,4480 (2021).4. Castelletto, S. et al. Quantum systems in silicon carbide for sensingapplications. Rep. Prog. Phys. 87, 01401 (2023).5. Barry, J. F. et al. Sensitive ac and dc Magnetometry with nitrogen-vacancy-center ensembles in diamond. Phys. Rev. Appl. 22, 044069(2024).6. Edmonds, A. M. et al. Characterisation of CVD diamond with highconcentrations of nitrogen for magnetic-field sensing applications.Mater. Quantum Technol. 1, 025001 (2021).7. Mizuochi, N. et al. Coherence of single spins coupled to a nuclear spinbath of varying density. Phys. Rev. B 80, 041201 (2009).8. Teraji, T. High-quality and high-purity homoepitaxial diamond (100)film growth under high oxygen concentration condition. J. Appl. Phys.118, 115304 (2015).9. Nakamura, K. et al. Single-crystal synthesis of highly thermalconductive 12C-enriched diamond from pyrolytic carbon powder bythe high-pressure, high-temperature method. Diam. Relat. Mater. 16,1765–1769 (2007).10. Bauch, E. et al. Decoherence of ensembles of nitrogen-vacancycenters in diamond. Phys. Rev. B 102, 134210 (2020).https://doi.org/10.1038/s43246-025-00782-7 ArticleCommunications Materials |            (2025) 6:66 7www.nature.com/commsmat11. Balasubramanian, G. et al. Ultralong spin coherence time inisotopically engineered diamond. Nat. Mater. 8, 383–387 (2009).12. Sekiguchi, N. et al. Diamond quantum magnetometer with dcsensitivity of sub-10 pT Hz−1/2 toward measurement of biomagneticfield. Phys. Rev. Appl. 21, 064010 (2024).13. Arai, K. et al. Millimetre-scale magnetocardiography of living rats withthoracotomy. Commun. Phys. 5, 1–10 (2022).14. Kehayias, P. et al. Imaging crystal stress in diamond using ensemblesof nitrogen-vacancy centers. Phys. Rev. B 100, 174103 (2019).15. Aslam, N. et al. Quantum sensors for biomedical applications. Nat.Rev. Phys. 5, 157–169 (2023).16. Choi, J. et al. Depolarization Dynamics in a Strongly Interacting Solid-State Spin Ensemble. Phys. Rev. Lett. 118, 093601 (2017).17. Choi, S. et al. Observation of discrete time-crystalline order in adisordered dipolar many-body system. Nature 543, 221–225 (2017).18. Bauch, E. et al. Ultralong Dephasing Times in Solid-State SpinEnsembles via Quantum Control. Phys. Rev. X 8, 031025 (2018).19. Le Sage, D. et al. Efficient photon detection from color centers in adiamond optical waveguide. Phys. Rev. B 85, 121202 (2012).20. Wolf, T. et al. Subpicotesla diamond magnetometry. Phys. Rev. X 5,041001 (2015).21. Yoneda, J. et al. A quantum-dot spin qubit with coherence limited bycharge noise and fidelity higher than 99.9%. Nat. Nanotechnol. 13,102–106 (2018).22. Masuyama, Y. et al. Extending coherence time of macro-scalediamond magnetometer by dynamical decoupling with coplanarwaveguide resonator. Rev. Sci. Instrum. 89, 125007 (2018).23. Masuyama, Y. et al. Columnar excitation fluorescencemicroscope foraccurate evaluation of quantum properties of color centers in bulkmaterials. Sci. Rep. 14, 18135 (2024).24. Wang, P. et al. High-resolution vector microwave magnetometrybased on solid-state spins in diamond.Nat. Commun. 6, 6631 (2015).25. Friel, I. et al. Control of surface and bulk crystalline quality in singlecrystal diamond grown by chemical vapour deposition. Diam. Relat.Mater. 18, 808–815 (2009).26. Sumiya, H. & Tamasaku, K. Large Defect-Free Synthetic Type IIaDiamond Crystals Synthesized via High Pressure and HighTemperature. Jpn. J. Appl. Phys. 51, 090102 (2012).27. Burns, R. C. et al. HPHT growth and x-ray characterization of high-quality type IIa diamond. J. Phys. Condens.Matter 21, 364224 (2009).28. Miyakawa,M.et al. Nitrogenconcentrationcontrol in diamondsgrownin Co–(Fe)–Ti/Al solvents under high-pressure and high-temperature.Jpn. J. Appl. Phys. 61, 045507 (2022).29. Sumiya, H. et al. Growth rate of high-quality large diamond crystals. J.Cryst. Growth 237–239, 1281–1285 (2002).30. Kanda, H. et al. Surface structures of synthetic diamonds. J. Mater.Sci. 15, 2743–2748 (1980).31. Kanda,H. Large diamonds grown at high pressure conditions.Braz. J.Phys. 30, 482–489 (2000).32. Burns, R. C. et al. Growth-sector dependence of optical features inlarge synthetic diamonds. J. Cryst. Growth 104, 257–279 (1990).33. Sangtawesin, S. et al. Origins of Diamond Surface Noise Probed byCorrelating Single-Spin Measurements with Surface Spectroscopy.Phys. Rev. X. 9, 031052 (2019).34. Hart, C. A. et al. N-V–Diamond Magnetic Microscopy using a DoubleQuantum 4-Ramsey Protocol. Phys. Rev. Appl. 15, 044020 (2021).35. Tsuji, T. et al. Extending spin dephasing time of perfectly alignednitrogen‐vacancy centers by mitigating stress distribution on highlymisoriented chemical‐vapor‐deposition Diamond. Adv. QuantumTechnol. 7, 2300194 (2024).36. Loubser, J. et al. Electron spin resonance in the study of diamond.Rep. Prog. Phys. 41, 1201–1248 (1978).37. Wojewoda, T. et al. Doping-induced anisotropic lattice strain inhomoepitaxial heavily boron-doped diamond.Diam. Relat. Mater. 17,1302–1306 (2008).38. Mermoux, M. et al. Characterization of〈111〉 diamond thin films bymicro-Raman spectroscopy. Diam. Relat. Mater. 13, 886–890 (2004).39. Shinei, C. et al. Nearly degenerate ground state of phosphorus donorin diamond. Phys. Rev. Mater. 4, 024603 (2020).40. Barson, M. S. J. et al. Nanomechanical Sensing Using Spins inDiamond. Nano Lett. 17, 1496–1503 (2017).41. Sumiya, H. et al. Distribution of internal strain and fracture strength invarious single-crystal diamonds. Diam. Relat. Mater. 134, 109781(2023).42. Alaerts, L. et al. First-principles study of the Stark shift effect on thezero-phonon line of the NV center in diamond. Phys. Rev. Mater. 8,106201 (2024).43. Coxon, D. J. L. et al. An Ultrafast Shakedown Reveals the EnergyLandscape, Relaxation Dynamics, and Concentration of theN3VH0 Defect in Diamond. J. Phys. Chem. Lett. 11, 6677–6683 (2020).44. Glover, C. et al. Hydrogen incorporation in diamond: The nitrogen-vacancy-hydrogen complex. Phys. Rev. Lett. 90, 185507 (2003).45. Green,B. L. et al. Electronparamagnetic resonanceof theN2V−defectin 15N-Doped synthetic diamond. Phys. Rev. B 92, 165204 (2015).46. Glover, C. et al. Hydrogen Incorporation in Diamond: The vacancy-hydrogen complex. Phys. Rev. Lett. 92, 135502 (2004).47. Teraji, T. et al. Effective Use of Source Gas for Diamond Growth withIsotopic Enrichment. Appl. Phys. Express 6, 055601 (2013).48. Sumiya, H. & Satoh, S. High-pressure synthesis of high-puritydiamond crystal. Diam. Relat. Mater. 5, 1359–1365 (1996).49. Kainuma,Y. et al. CompactandStableDiamondQuantumSensors forWide Applications. Adv. Quantum Technol. 7, 2300456 (2024).50. Hatano, Y. et al. Transverse magnetic field effects on diamondquantum sensor for EV battery monitor. Front. QuantumSci. Technol.3, 1432096 (2024).51. Kubota, K. et al. Wide temperature operation of diamond quantumsensor for electric vehicle batterymonitoring.Diam. Relat.Mater. 135,109853 (2023).52. Show, Y. et al. Structural characterization of CVDdiamond films usingthe ESR method. Thin Solid Films 274, 50–54 (1996).53. Shinei, C. et al. Equilibrium charge state of NV centers in diamond.Appl. Phys. Lett. 119, 254001 (2021).54. Shinei, C. et al. Nitrogen related paramagnetic defects: Decoherencesource of ensemble of NV− center. J. Appl. Phys. 132, 214402 (2022).55. Teraji, T. & Shinei, C. Nitrogen-related point defects in homoepitaxialdiamond (001) freestandingsingle crystals.J.Appl. Phys.133, 165101(2023).56. Capelli, M. et al. Increased nitrogen-vacancy centre creation yield indiamond through electron beam irradiation at high temperature.Carbon 143, 714–719 (2019).AcknowledgementsThis work was supported by MEXT Q-LEAP (JPMXS0118068379 andJPMXS0118067395). T. Teraji acknowledges the support of, JST CREST(JPMJCR1773), MIC R&D for construction of a global quantum crypto-graphy network (JPMI00316), JSPS KAKENHI (Nos. 20H02187, 20H05661,and 19H02617), and JST Moonshot R&D (JPMJMS2062).Author contributionsC.S. performed the experiments on the NV centres, assisted by M.Y., H.A.,M.M., T.O. and T.T. (Takashi Taniguchi). M.M. and T.T. (Takashi Taniguchi)grew the HPHT diamond samples. H.A. and T.O. carried out electron beamirradiation to form the NV− centres. M.Y. primarily designed and examinedthe optical setup. C.S. performed the data analysis and conceived thesupplementary information. T.T. (Tokuyuki Teraji) supervised this study.C.S.and T.T. (Tokuyuki Teraji) wrote themanuscript, and all authors discussed it.Competing interestsThe authors declare no competing interests.https://doi.org/10.1038/s43246-025-00782-7 ArticleCommunications Materials |            (2025) 6:66 8www.nature.com/commsmatAdditional informationSupplementary information The online version containssupplementary material available athttps://doi.org/10.1038/s43246-025-00782-7.Correspondence and requests for materials should be addressed toChikara Shinei or Tokuyuki Teraji.Peer review information Communications Materials thanks Wei Liu,Christian Giese and the other, anonymous, reviewer(s) for their contributionto the peer review of this work. Primary Handling Editors: Sunkook Kim andAldo Isidori. A peer review file is available.Reprints and permissions information is available athttp://www.nature.com/reprintsPublisher’s note Springer Nature remains neutral with regard tojurisdictional claims in published maps and institutional affiliations.Open Access This article is licensed under a Creative CommonsAttribution-NonCommercial-NoDerivatives 4.0 International License,which permits any non-commercial use, sharing, distribution andreproduction in any medium or format, as long as you give appropriatecredit to the original author(s) and the source, provide a link to the CreativeCommons licence, and indicate if you modified the licensed material. Youdo not have permission under this licence to share adapted materialderived from this article or parts of it. The images or other third partymaterial in this article are included in the article’s Creative Commonslicence, unless indicated otherwise in a credit line to thematerial. If materialis not included in thearticle’sCreativeCommons licenceandyour intendeduse is not permitted by statutory regulation or exceeds the permitted use,you will need to obtain permission directly from the copyright holder. Toview a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.© The Author(s) 2025https://doi.org/10.1038/s43246-025-00782-7 ArticleCommunications Materials |            (2025) 6:66 9https://doi.org/10.1038/s43246-025-00782-7http://www.nature.com/reprintshttp://creativecommons.org/licenses/by-nc-nd/4.0/http://creativecommons.org/licenses/by-nc-nd/4.0/www.nature.com/commsmat Homogeneous spin-dephasing time of NV− centre in millimetre-scale 12C-enriched high-pressure high-temperature diamond crystals Results and discussion Synthesis of HPHT diamond crystals Sequence of T2* spatial mapping for NV− centres T2* spatial mapping in the millimetre-scale 111 plane Dependence of strain gradient in diamond on concentration of nitrogen impurities Methods Sample preparation Experimental setup PL intensity of NV− centres in multi-growth sectors Data availability Code availability References Acknowledgements Author contributions Competing interests Additional information