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Shuji Ito, Moeta Tsukamoto, Kensuke Ogawa, [Tokuyuki Teraji](https://orcid.org/0000-0002-7731-0547), Kento Sasaki, Kensuke Kobayashi

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[Optical-power-dependent Splitting of Magnetic Resonance in Nitrogen-vacancy Centers in Diamond](https://mdr.nims.go.jp/datasets/0ce9c0b1-c6e0-4cc4-9af5-af267b70e66b)

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Optical-power-dependent splitting of magnetic resonance in nitrogen-vacancy centersin diamondShuji Ito,1 Moeta Tsukamoto,1 Kensuke Ogawa,1 Tokuyuki Teraji,2 Kento Sasaki,1 and Kensuke Kobayashi1, 3, 41Department of Physics, The University of Tokyo, Bunkyo-ku, Tokyo, 113-0033, Japan2National Institute for Materials Science, Tsukuba, Ibaraki 305-0044, Japan3Institute for Physics of Intelligence, The University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan4Trans-scale Quantum Science Institute, The University of Tokyo, Bunkyo-ku, Tokyo 113-0033, JapanNitrogen-vacancy (NV) centers in diamonds are a powerful tool for accurate magnetic field mea-surements. The key is precisely estimating the field-dependent splitting width of the opticallydetected magnetic resonance (ODMR) spectra of the NV centers. In this study, we investigate theoptical power dependence of the ODMR spectra using NV ensemble in nanodiamonds (NDs) and asingle-crystal bulk diamond. We find that the splitting width exponentially decays and is saturatedas the optical power increases. Comparison between NDs and a bulk sample shows that while thedecay amplitude is sample-dependent, the optical power at which the decay saturates is almostsample-independent. We propose that this unexpected phenomenon is an intrinsic property of theNV center due to non-axisymmetry deformation or impurities. Our finding indicates that diamondswith less deformation are advantageous for accurate magnetic field measurements.I. INTRODUCTIONA nitrogen-vacancy (NV) center in a diamond is a de-fect where a nitrogen atom replaces a carbon atom inthe lattice with a vacancy at its neighboring site. TheNV center has an electron spin S = 1, and its peculiarspin-dependent optical transitions enable the optical ini-tialization and readout of the ground-state spin. Thisproperty has been applied to the quantum sensing of lo-cal magnetic fields [1–8] and temperature [9–11]. Re-searchers have applied the technique to measure variousphysical properties, such as observing the electron flow ingraphene [12, 13] and the stray fields from magnetic do-main walls of a single-crystal antiferromagnet Cr2O3 [14].The basis for these achievements is the ability to accu-rately measure local magnetic fields on the order of µTusing NV centers.Optically detected magnetic resonance (ODMR) is atypical and basic measurement technique for quantumsensing using NV centers. This technique measures themicrowave (MW) frequency dependence of the photolu-minescence (PL) intensity (red) when the NV centers arecontinuously irradiated with an excitation light (green)and MW. The ODMR spectrum presents a magneticresonance signal between the ground state spin levelsmS = 0 and mS = ±1. The resonance frequency splitsagainst the magnetic field due to the Zeeman effect [1–8] and shifts in the same direction against temperaturechange [9–11]. In addition, the splitting of the reso-nance frequency is affected by crystal strain [15], electricfield [16, 17], and hyperfine interactions [18]. Therefore,it is essential for accurate sensing to estimate the splittingwidth purely due to the magnetic field from the ODMRspectra. Commonly used diamond samples are single-crystal bulk diamonds and nanodiamonds (NDs) withgrain sizes ranging from tens to hundreds of nanome-ters [19, 20]. Depending on whether the diamond is abulk crystal or nanoparticles, there are variations in crys-tal strains, impurity density, and crystal orientation.The ODMR spectra of NV centers vary with the excita-tion light power. For example, the contrast and linewidthvary with the degree of initialization and spin relaxationassociated with optical excitation [21, 22]. These depen-dencies only affect sensitivity but not accuracy.Recently, however, it was reported that the ODMRspectra of NV centers in NDs at low magnetic fieldschange with the optical power, degrading the accuracyof temperature measurements [23]. They found that achange in the ODMR splitting up to 2.8 MHz (equivalentto Zeeman splitting for 50 µT) occurred depending onthe optical power. This unexpected observation directlyaffects the accuracy of the conversion of the ODMR split-ting to magnetic field, which is a critical issue in achiev-ing the µT-order magnetic field measurements necessaryfor the physical properties measurements. In particular,in wide-field imaging of magnetic field and temperatureusing a CMOS camera and NV ensembles [15, 24–26],inhomogeneity of the optical power within the field ofview could result in degradation of the measurement ofthe magnetic field and temperature distributions. Thus,it is crucial to investigate the extent to which this phe-nomenon is universal for various samples, i.e., bulk dia-monds as well as NDs.In this study, we investigate the dependence of theODMR splitting on the optical power using several NVensemble samples. We first investigate the NV ensemblesin NDs with a grain size of 100 nm, the same size as in theprevious study [23]. We confirm the reported behavior ofthe ODMR splitting to decrease with increasing opticalpower. In addition, we measure the ODMR spectra overa broader optical power range than in the previous study.We thereby find the splitting decays exponentially withthe optical power and saturates at a constant value. Weobserve similar behavior in NDs with a different grain sizeof 50 nm. We then investigate NV ensembles in a single-crystal bulk diamond with much fewer impurities andstrain than NDs and find a weaker but similar behavior. Journal of the Physical Society of Japan Confidential 2We prove the irrelevance of magnetic field and tempera-ture on this observation and discuss possible mechanismsto account for this phenomenon. Finally, we propose thepossibility that repetitive photoionization of impuritiesaverages the local non-axisymmetry environment of NVcenters and a systematic method to deal with this phe-nomenon.This paper is organized as follows. Sec. II describesthe experimental setup and defines the optical power inthis study. Sec. III A reproduces the previous study [23]using NDs and confirms that the ODMR spectra changewith optical power. Sec. III B shows that a similar phe-nomenon occurs even in the single-crystal bulk diamond.Sec. III C analyzes the dependence of the ODMR split-ting on the optical power. In Sec. IIID, we discuss theinfluence of the magnetic field and temperature, possi-ble mechanisms, and implications of the present finding.Sec. IV presents our conclusions.II. EXPERIMENTSFigure 1(a) shows an overview of the experimentalsetup [27]. All measurements in this study are performedin a confocal system at room temperature. A green laserwith a wavelength of 520 nm (Oxxius, LBX-520-70-CSB-PPA) is applied for initialization and readout of the NVcenters. The intensity of the green laser is adjusted usingseveral fixed neutral density filters as appropriate. Theintensity of the red emission from the NV centers is de-tected by an avalanche photodiode (APD) after passingthrough a dichroic mirror, a 514 nm notch filter, a 650 nmlong-pass filter, and an 800 nm short-pass filter. Whenmeasuring NV centers in nanodiamonds, the red emis-sion counts were suppressed using a fixed neutral densityfilter to match the APD measurement range. We use aMW antenna for spin manipulation of the NV centers,which is a coplanar waveguide with ground consisting ofa 1.6 mm thick PCB substrate and an 18 µm thick cop-per foil with a 2 mm width centerline terminated with a50 Ω resistor. The antenna is impedance matched so thatno frequency dependence of the MW power at a sampleposition is present during the measurement. We confirmthat from S11 parameter. Microwaves are output from avector signal generator at approximately −13 dBm andinput to a microwave antenna after passing through anMW amplifier (typ. +45 dB). In all measurements in thispaper, the microwave power is fixed at the above values.We use three types of diamond samples, #1, #2, and#3, in the present study: NDs with nominal grain sizesof ϕ50 nm (#1) and of ϕ100 nm (#2), and NV ensemblein a bulk diamond film (#3).The NDs are those commercially available fromAdámas Nanotechnologies, NDNV50nmHi10ml for #1and NDNV100nm10ml for #2. In the measurements of#1 and #2, we prepare a ND film [see Fig. 1(b)], whichis the NDs spin-coated on a cover glass at 600 rpm [26].The thickness of the ND film made by this method is typ-0 0.5 1 1.5 2x [μm]00.511.52y[μm]Single NV0 5 10 15PL Intensity [kcps]typ. 386 nm0 2 4 6 8 10x [μm]0246810y[μm]NDs 50 nm #1 3005007009001100PLIntensity[kcps](a)Objective LensLaserAntennaCover glassNanodiamondsCoilPhotoluminescence(c)(b)1 mmNDs 50 nm #1Cover glassFIG. 1. (a) Experimental setup. A wavelength of the greenlaser is 520 nm. The MW antenna is a coplanar waveguidewith ground. The two coils beside and beneath the sam-ple stage are for applying the magnetic fields perpendicularand parallel to the optical axis, respectively. Nanodiamondsspin-coated on the cover glass (#1 and #2) are fixed to theantenna with carbon tape and placed on the sample stage asshown here. In the case of the bulk diamond film (#3), wefix it directly to the antenna with carbon tape. (b) The up-per figure shows an optical microscope image of a spin-coatedND film (#1). The lower figure shows a PL intensity map ofthe spot surrounded by a red frame in the top image. Thecolor bar indicates PL intensity in a unit of kilo counts persec (kcps). The red circle is the ODMR measurement spot.(c) Determination of the irradiation area for the optical powercalibration. The color map shows the PL intensity distribu-tion from a single NV center. The cross sections of the colormap are shown in markers in the top and side panels with theresults of the 2D Gaussian fitting (solid line).ically about 200–1000 nm [26, 28]. The number of NDsin #1 and #2 within a laser irradiation area is estimatedto be several hundred and more than 20, respectively.The ND film is fixed to the antenna with carbon tape. Asurface of the ND film is at a height of 0.44 mm abovethe antenna.In addition to NDs, this study investigates a bulk dia-mond film (#3). It was synthesized using a custom-builtmicrowave plasma chemical vapor deposition (MPCVD)system [29]. High-pressure and high-temperature type-Ib(100) single crystalline diamond plates were used as sub-strates. 12C concentrated (> 99.95%) methane gas wasused as a carbon source. First, an undoped thick filmwith a total thickness of ∼70 µm was grown on the sub-3strate by chemical vapor deposition (CVD). A 15N dopedCVD layer was then overgrown on the undoped film witha gas ratio of 15N/C of 4000 ppm. An expected 15N con-centration is ∼10 ppm and a film thickness is ∼5 µm.This nitrogen density is consistent with the NV’s coher-ence T2 = 29 µs obtained by Hahn echo [30]. We fix #3directly to the antenna with carbon tape for the measure-ment. A surface of the bulk diamond film is at a heightof 0.73 mm above the antenna. In this study, NV cen-ters spontaneously formed during the MPCVD processare used for characterization.We perform the present study under three differentmagnetic fields: a zero field (A), an environmental field(B), and a biased field (C). We apply magnetic fieldsfor the conditions A and C. We use two coils beside andbeneath the sample stage to generate magnetic fields per-pendicular and parallel to the optical axis, respectively,as shown in Fig. 1(a). Using a tesla meter (Lake ShoreCryotronics F71), we evaluate the magnetic fields at thesample position as 6.3 µT, 88.7 µT, and 196.7 µT for theconditions A, B, and C, respectively.The upper panel of Fig. 1(b) shows an optical micro-scope image of the spin-coated NDs ϕ50 nm (#1). Thelower panel shows the PL intensity map at the spot sur-rounded by a red frame in the upper panel. The colorbar indicates PL intensity in a unit of kilo counts persec (kcps). The data set for #1 is obtained using thestandard ODMR measurement at the red circle.As the dependence of the ODMR spectra on the op-tical power of the excitation light is the central topic inthis study, it is important to calibrate the optical power(Popt). We evaluate Popt from the green laser intensityand the irradiated area with an accuracy of 10%. Thegreen laser intensity is measured between the objectivelens and the diamond sample using an optical power me-ter (Thorlab, Power Meter PM100D, sensor S121C). Theirradiation area is estimated as the spot size of the redluminescence from a single NV center near the surface ofa high quality bulk diamond provided by H. Watanabe inAIST, Japan [31]. The spot size is calculated as a circlewhose diameter is the full width at half maximum of theintensity distribution. Figure 1(c) presents an exampleof the PL intensity map from a single NV center usedto determine the spot size, where the diamond surfaceis defined as the xy-plane. Ten PL intensity maps of asingle NV center are fitted by the two-dimensional (2D)Gaussian function, and the obtained average of their fullwidth at half-maximum, 386 ± 2 nm, is used as thelaser spot diameter. The cross sections of the experi-mental data (markers) and the 2D Gaussian fitting (solidline) are shown in the upper side and right side panels ofFig. 1(c). Both panels show that the fits are consistentwith the experimental data.All the experimental conditions in this study are com-piled in Table I. NDs ϕ100 nm #2’ in Table I indicatesthe data set obtained at a different location of the samesample as NDs ϕ100 nm #2. The estimated densities ofnitrogen, [N], and NV center, [NV], are also given in Ta-Condition zero (A) envir. (B) biased (C)NDs ϕ50 nm #1[N] ∼ 100 ppm[NV] ∼ 2 ppm1A - -NDs ϕ100 nm #2, #2’[N] ∼ 100 ppm[NV] ∼ 3 ppm2A2’A2BRef. [23]2CBulk diamond #3[N] ∼ 10 ppm[NV] ∼ 4 ppb3A - -TABLE I. #1, #2, and #3 correspond to the NDs ϕ50 nm,ϕ100 nm, and the bulk diamond film, respectively (see text).[N] and [NV] are given for each. #2’ means the data setobtained at a different location of the sample #2. The mag-netic field conditions A, B, and C correspond to a zero field(6.3 µT), an environmental field (88.7 µT), and a biasedfield (196.7 µT), respectively. The experimental conditionof Ref. [23] is classified in 2B in the present study.ble I. We include the previous study (Ref. [23]) in Table Iin the same cell as 2B as their measurements were carriedout in an environmental geomagnetic field (∼ 50 µT) us-ing NDs ϕ100 nm supplied by Adámas Nanotechnologies.III. RESULTS AND DISCUSSIONSA. ODMR Spectra of Nanodiamond NVsThe upper panel of Fig. 2(a) is the ODMR spec-trum as a function of the MW frequency obtained atPopt = 0.55 kW/cm2 shown by markers. This result isfor 2A (see Table I). The vertical axis indicates the PLcontrast, namely the normalized contrast of the PL inten-sities with and without MW. In this measurement, theswept frequency range is 60 MHz. The splitting betweendips in the ODMR spectrum is due to crystal strain andelectric fields that break the axial symmetry of the NVcenters. The impacts of such non-axisymmetry deforma-tion were treated in Refs. [15–17]. Below we call thesefactors as “deformation”.We note that similar observations for the NDs ensem-ble were reported before, for example, in Fig. 1(d) ofRef. [15]. Their shapes are generally consistent withours, while the splitting is slightly larger than that inthe present study as they applied a magnetic field of 100µT. Also, similar ODMR spectra obtained in a singleND were reported in Fig. 3(a) of Ref. [23].From now on, we focus on splitting quantitativelybased on the values obtained from fitting with a dou-ble Lorentzian function. This fitting method is mean-ingful because it is often used for magnetometry usingNVs. We will discuss the validity and limitations of thismethod later in Sec. IIID. The solid line in the upperpanel of Fig. 2(a) is a fitted curve. We define the differ-ence in frequencies between the two dip values obtainedby this fitting as the difference ∆. ∆ is 11.5±0.2 MHz in4FIG. 2. ODMR spectra of NDs ϕ100 nm at zero mag-netic fields (the condition 2A). (a) Spectra measured atPopt = 0.55 kW/cm2 in the upper panel and that at Popt =38.4 kW/cm2 in the lower panel are shown in markers. Thesolid cuved lines are the results of the fitting. The dashedand solid vertical lines are drawn at the dip positions de-duced from the fitting in the upper and lower panels, re-spectively. This clearly indicates that ∆ decreases as Poptincreases. (b) ODMR spectra at various Popt’s. They areincrementally shifted from bottom to top in the order ofPopt = 0.55, 2.12, 4.24, 8.21, 15.2, and 31.3 kW/cm2 as shownby the numbers in the right column. Markers are experimen-tal data, and solid lines are the spline interpolation curvesinstead of the fitted ones. Cross markers (+) indicate the dippositions in the interpolated curve.this specific case, which is consistent with the literaturevalues of 10–20 MHz for NDs [15, 23].We measure the ODMR spectra by increasing Poptfrom 0.55 kW/cm2. The lower panel of Fig. 2(a) showsthe spectrum for 2A obtained at Popt = 38.4 kW/cm2,which is the maximum optical power used in the presentstudy. We discuss later that the temperature increasedue to laser heating is inconsequential within the presentoptical power range. As in the upper panel, the markersshow experimental data, and the solid curved line resultsfrom a double Lorentzian fitting. The PL contrast de-creases from 2.7% at Popt = 0.55 kW/cm2 to 0.5% atPopt = 38.4 kW/cm2 because the increase in the opti-cal power enhances the spin initialization rate, i.e., thetransition rate from mS = ±1 to mS = 0. The spectrumalso possesses two dips, but careful inspection reveals aslight change in shape between the upper and lower pan-els. The dashed and solid vertical lines show the dippositions obtained by the fitting at Popt = 0.55 kW/cm2and Popt = 38.4 kW/cm2, respectively. ∆ is determinedto be 9.4 ± 0.3 MHz for Popt = 38.4 kW/cm2. Thus, ∆decreases with increasing Popt.Similar behavior was reported in Fig. 3(a) of Ref. [23],suggesting that ∆ of NVs in NDs actually depends onthe optical power, which is usually not considered. Inour case, ∆ changes by approximately 2.1 MHz betweenthe two different Popt. Significantly, ignoring deforma-tion, this variation corresponds to about 38 µT accordingto a magnetic field conversion widely used in the NV re-search field. Therefore, this phenomenon can be relevantin applying NVs to magnetic field measurements.The above finding is not an artifact caused by adouble Lorentzian fitting. To confirm this, Fig. 2(b)presents the ODMR spectra measured at Popt =0.55, 2.12, 4.24, 8.21, 15.2, and 31.3 kW/cm2, which areincrementally shifted from bottom to top. The markersare the experimental data, where the spline interpola-tion curves are superposed by the solid lines. Since thePL contrast varies depending on Popt, we appropriatelynormalize the spectra to focus only on the shape. Thecross markers (+) point to the dip positions in the splineinterpolation curves. Their behavior again supports thatthe two dips become closer for a larger Popt.While we do not show the data, the results of the con-dition 2’A and the NDs of ϕ50 nm (1A) are consistentwith the results of 2A. Some results are later shown inFigs. 4(d), 4(e), and 4(f).B. ODMR Spectra of Bulk Diamond NVsWe focus on the bulk diamond film #3 to investigatewhether or not the optical power dependence observedin NDs is relevant here. The upper panel of Fig. 3presents the ODMR spectrum for the condition 3A ob-tained at Popt = 0.55 kW/cm2. The horizontal axis rangeis 10 MHz, much smaller than that in Fig. 2(a). The ob-tained spectrum shown by the markers has two sharpdips, as expected for the NVs in bulk diamonds. As per-formed for the analysis of NDs, we fit the experimentaldata with a double Lorentzian function. We estimate thesplitting between the two dips to be ∆ = 3.55±0.02 MHz,a comparable value to the width of 3.03 MHz due to thehyperfine interaction in 15N [18]. Presumably, the defor-mation is much less than 1 MHz because it is buried inthis hyperfine splitting. Thus, the bulk diamond differsfrom NDs because the hyperfine interaction prevails overthe deformation. In addition, the resonance line widthis significantly narrower than in the NDs. This reflects50.880.920.961Bulk 3A0.55 kW/cm2experimenttted curve2865 2867.5 2870 2872.5 2875Frequency [MHz]0.920.961PLContrast(arb.unit)38.4 kW/cm2experimenttted curveFIG. 3. ODMR spectra of the bulk diamond film #3 atzero magnetic fields (the condition 3A, see Table I) mea-sured at Popt = 0.55 kW/cm2 in the upper panel and Popt =38.4 kW/cm2 in the lower panel. The markers are the ex-perimental data with the fitted curve shown by the solid line.The dashed and solid vertical lines are drawn at the fitted dipvalues in the upper and lower panels, respectively.that the density of impurities, such as nitrogen impuri-ties (P1 centers), which cause the decoherence [8], is lowin #3. Indeed, the typical nitrogen concentration of atype 1b diamond, the raw material of NDs, is about 100ppm, whereas the single-crystal diamond in this study isabout 10 ppm.Now, we discuss the ODMR spectra at increased opti-cal powers. The lower panel in Fig. 3 shows the ODMRspectrum by the markers in the condition 3A obtainedat Popt = 38.4 kW/cm2. The markers are experimen-tal data, and the solid curved line results from a doubleLorentzian function fitting. As seen in NDs, the con-trast decrease is also due to a larger initialization ratein larger optical power. In Fig. 3, the dashed and solidvertical lines indicate the dip positions obtained by thefitting at Popt = 0.55 kW/cm2 and Popt = 38.4 kW/cm2,respectively. ∆ is now 3.44 ± 0.01 MHz, smaller than∆ = 3.55 ± 0.02 MHz. As in the NDs case, ∆ becomessmaller in the larger optical power in the bulk diamond.Interestingly, the optical power dependence is presenteven when the 15N hyperfine interaction causes the split-ting. However, the reduction of ∆ in the bulk diamondis much smaller than in NDs.C. Analysis of SplittingWe systematically examine the dependence of ∆ onPopt. We start with the condition 2A. The upward tri-angle markers in Fig. 4(a) show the experimentally ob-served ∆ as a function of Popt between 0.55 kW/cm2and 38.4 kW/cm2. We already showed the results of ∆at the minimum (Popt = 0.55 kW/cm2) and maximum(Popt = 38.4 kW/cm2) optical powers in the upper andNDs BulkRef. [23]NDs 100nm 2ABulk 3AFIG. 4. (a) Behavior of ∆ as a function of Popt. The ex-perimental data of 2A and 3A are shown by the markers (△and ×), respectively. For comparison, the data of Ref. [23]is superposed with the markers (+). The dotted lines resultfrom the fitting to Eq. (1). The inset is a magnified view ofthe data of the bulk diamond 3A to clarify the exponentialdecaying behavior. (b) Experimental data and the fitted re-sults for 2A and 3A in (a) are presented in the semi-log plot.The constant offsets ∆0 have been subtracted from the data.(c) PL intensity from NDs in the condition 2A is shown asa function of Popt. (d), (e), and (f): Fitted parameters (d)A, (e) P0, and (f) ∆0 for the conditions 1A, 2A, 2’A, and 3A[see Table I] are shown. Note that the error bars of the datapoints indicate 1σ for all the figures (a)–(f).lower panels in Fig. 2(a), respectively. Figure 4(a) clearlytells that ∆ monotonously decays with increasing Poptand saturates at Popt ≳ 15 kW/cm2.Previous study [23] reported a similar dependence of∆ on Popt. Their results are superposed in Fig. 4(a) bythe markers (+). Significantly, the decaying behavior isalmost the same between their results and ours, whilethey did not reach the optical power to saturate ∆.It is well established that the PL intensity from an NVcenter, which is determined by the relaxation rate pecu-6liar to its optical process, saturates for a large Popt [21].However, the present observation is irrelevant as we per-form the experiment using a sufficiently small laser inten-sity such that the PL intensity is linear to Popt. Figure4(c) confirms that the PL intensity from NDs in the con-dition 2A is proportional to Popt. Ref. [23] also treatedthis sufficiently small optical power region. The opticalpower dependence in such a very small intensity regionis unexpected. Our work has quantitatively confirmedRef. [23] for a wider optical power region.It was previously reported [22] that the linewidth ofthe ODMR spectrum of the NV ensemble decreases withincreasing Popt for an optical power as small as in thepresent study. However, they did not mention a decreasein ∆ of the ODMR spectra. While we observe a system-atic change in ∆, no systematic change in the linewidthis detected.For more quantitative discussion, we analyze the be-havior of 2A shown in Fig. 4(a) using the following ex-ponential fit.∆(Popt) = A exp(−Popt/P0) + ∆0, (1)where A, P0, and ∆0 are the amplitude, the saturationpower, and the offset, respectively. The dotted line inFig. 4(a) is the result of this fitting. A semi-log plot ofonly the first term of Eq. (1) is shown in Fig. 4(b) with thesame markers as Fig. 4(a). The linear variation is con-sistent with the exponential function. Unlike Fig. 4(a),Fig. 4(b) does not include the previous result [23] becauseno convergence value (offset ∆0) is available.Then, how about the behavior of the bulk diamondfilm (the condition 3A)? Figure 4(a) shows the Popt de-pendence of ∆. While the decrease of ∆ is not as signif-icant as in NDs (2A), the magnified view in the inset ofFig. 4(a) proves that an exponential decay of ∆ is alsopresent in the bulk diamond case. Figure 4(b) depicts thedecaying component extracted by the fitting to Eq. (1),which looks very similar to the 2A case. The fact suggestsa common mechanism behind the present exponential de-cay of ∆ in the NDs and the bulk diamond, even thoughdifferent reasons cause the dip splitting.We find similar behavior in all the measured conditionsat zero fields (1A, 2A, 2’A, and 3A in Table I) and obtainthe parameters A, P0, and ∆0. Figure 4(d) shows theobtained amplitude A for the four conditions. From leftto right, the bars indicate the conditions 1A, 2A, 2’A,and 3A, and the vertical axis is expressed on a semi-logscale. Comparing 1A, 2A, and 2’A, the A values arealmost the same for NDs with different grain sizes. Onthe other hand, the bulk diamond (3A) has A, one orderof magnitude smaller than those of NDs (about 1/20).Figure 4(e) shows the saturation power P0 for differentconditions. While the amplitude A significantly differsbetween NDs and the bulk diamond, there is relativelylittle difference in P0 between the two; P0 ∼ 3.8 kW/cm2for NDs and P0 ∼ 7.4 kW/cm2 for the bulk diamond.It is vital that the values of P0 are close for differentdiamonds. The offsets ∆0 are shown in Fig. 4(f). Theyreduce in the order of conditions 1A, 2A, 2’A, and 3A,which seems to coincide with the degree of deformation ofNVs. We intuitively expect that the smaller the crystalsize is, the greater the deformation tends to be, affectingthe sensitivity of the NVs to the optical power. We comeback to this fact later.With the results and analysis explained so far, we haveestablished that the ODMR spectra of NVs depend onthe excitation light power even when the power is suf-ficiently small. This phenomenon occurs in both NDsand the bulk diamond. The amplitude of the decay (A)largely depends on the samples, but the behavior of expo-nentially decaying with the optical power characterizedby P0 seems an essential feature of NVs. The quantita-tive establishment of the universality of this phenomenonis the main achievement of the present study. The factalso means that the excitation light power can be relevantfor accurate magnetic field measurements using NVs.D. Possible MechanismsWe are interested in the possible causes of the observedoptical power dependence. The zero-field splitting (ZFS),the coupling between the NV spin and the magnetic field,and the deformation are the most critical factors in defin-ing the energy structure of an NV center in the groundstate [32]. The hyperfine interaction between the NV spinand the neighboring nuclear spins is also often relevant.Therefore, it is essential as a starting point to investigatewhether the present phenomenon is related to these fourfactors. This section will examine them individually andthen explore other possibilities.We start with the ZFS, which might be subject to theoptical power through the heating by the laser. We de-fine the ZFS as the average of the frequencies of thetwo dips obtained by a double Lorentzian fit. Aroundroom temperature at zero magnetic fields, the ZFS inthe ODMR spectrum decreases linearly with increasingtemperature [9]. The dependences of ZFS on the opti-cal power in the conditions 1A, 2A, and 3A are shown inFigs. 5(a), (b), and (c), respectively. The figures indicateno signal of systematic change in ZFS due to the opti-cal power. Indeed, the variation of ZFS is much smallerthan the amplitude A in Fig. 4(d). Thus, heating bylaser irradiation is not responsible for the present opticalpower dependence. We estimate the maximum temper-ature change in this experiment to be about 12 K sincethe maximum frequency shift observed is approximately850 kHz, as shown in Fig. 5(a).Next, we discuss the influence of the magnetic field.The upper and lower panels of Fig. 6 show the ODMRspectra in conditions 2A (zero magnetic field) and 2C (bi-ased magnetic field of 196.7 µT), respectively [the spec-trum shown in the upper is the same as that in the upperpanel in Fig. 2(a)]. Both are obtained with the minimumoptical power (Popt = 0.55 kW/cm2). The markers areexperimental data, and the solid curved lines are fitted bykensukeハイライト表示7286728682869ZFS[MHz]3 MHzNDs 50 nm 1A286828692870ZFS[MHz]3 MHzNDs 100 nm 2A0 5 10 15 20 25 30 35 40Optical Power [kW/cm2]286928702871ZFS[MHz]3 MHzBulk 3A(a)(b)(c)FIG. 5. Dependence of the ZFS of ODMR spectra for (a)NDs ϕ50 nm (1A), (b) NDs ϕ100 nm (2A), and (c) the bulkdiamond film (3A) as a function of the optical power Popt.The range on the vertical axis is fixed to 3 MHz for (a), (b),and (c).0.980.991NDs 100 nm6.3 μT 2Aexperimenttted curve2840 2860 2880 2900Frequency [MHz]0.960.981PLContrast(arb.unit)196.7 μT 2Cexperimenttted curveFIG. 6. ODMR spectra of NDs ϕ100 nm obtained at Popt =0.55 kW/cm2 in the conditions 2A (the upper panel) and 2C(the lower panel). The markers are the experimental data,and the solid curved lines result from the fitting. The dashedand solid vertical lines indicate the fitted dip positions in theupper and lower panels, respectively, supporting that ∆ in-creases in the magnetic field.a double Lorentzian function. The dashed and solid ver-tical lines show the dip positions obtained by the fit for2A and 2C, respectively. As expected from the Zeemaneffect, the solid vertical lines are outside the two dashedlines, confirming that ∆ increases in the magnetic field.We obtain the spectra for the conditions 2A, 2B, and2C as Popt is modulated. The acquired behaviors of ∆are plotted as a function of Popt in the inset of Fig. 7(a).Due to the Zeeman effect, ∆ vertically shifts from 2A toFIG. 7. (a) ∆−∆0 as a function of Popt. Markers are exper-imental data for 2A (△), 2B (▷), and 2C (▽). The dashedlines result from the fitting to Eq. (1). The inset shows thedependence of ∆. (b), (c), and (d) Fitted parameters A, P0,and ∆0 in the different magnetic fields (2A, 2B, and 2C), re-spectively.2B to 2C. Importantly, there is no significant variationin the spectral shapes of 2A, 2B, and 2C except for thisvertical shift. We obtain the offset ∆0 by the fitting toEq. (1) and plot ∆−∆0 against Popt in the main panel ofFig. 7(a). The behavior of 2A, 2B, and 2C are superposedon each other almost perfectl1y. We plot the amplitudeA, the saturation power P0, and the offset ∆0 for eachfield obtained by the fitting in Figs. 7(b), (c), and (d),respectively. ∆0 increases with increasing magnetic field[Fig. 7(d)], reflecting the Zeeman effect, although furtherquantitative analysis is complicated in this magnetic fieldregion due to the considerable influence of deformationin NDs [26]. On the other hand, A and P0 do not changesignificantly as shown in Figs. 7(b) and (c), respectively.Thus, in our examined regime, there is no visible cor-relation between the optical power dependence and themagnetic field.Third, we consider the hyperfine interaction. The op-tical power dependence in the bulk diamond NVs is min-imal, only about 1/20 of that in the nanodiamond NVs[see Figs. 4(a) and 4(d)]. However, the contribution of8the hyperfine interaction to ∆ is reasonably assumed tobe almost similar in the two types of diamonds. There-fore, if the hyperfine interaction was responsible for thepresent phenomenon, it would be difficult to explain themarked difference between both. Consequently, we canconclude that the hyperfine interaction is not the leadingcause of this phenomenon.As the final factor, we examine the deformation. InNDs, the deformation is about 10 MHz [Figs. 2(a) and4(a)], while the value is well below 1 MHz in the bulk di-amond, as discussed in Sec. IIIB. Now, the amplitude Ato characterize the optical power dependence is ∼ 2 MHzfor NDs and ∼ 0.1 MHz for the bulk diamond [Fig. 4(d)].For the former, the ratio of A to the deformation is about2/10 = 0.2. For the latter, the ratio is at least 0.1/1 = 0.1and is comparable to the NDs’ case. The ratio of ND tobulk diamond deformation also corresponds to the ra-tio of nitrogen impurity density [see Table I]. This sug-gests that either the deformation/impurity itself or theimpurity-derived deformation would be responsible forthis phenomenon. Although this argument is not fullyquantitative, it suggests a correlation between the defor-mation/impurity and the optical power dependence.We infer a reasonable idea of the possible mechanismbased on the deformation caused by impurities. Previ-ous work on single NV centers indicated that the electricfield from charge traps causes deformation [33]. Thismight also be the cause with the deformations in the NVensemble case in our study. If the charge traps originatefrom impurities, the magnitude of the deformation willcorrelate with the impurity density, consistent with ourobservations. It is known that the charge state of im-purities changes with photoionization. For example, asthe optical power is increased, the time that the NV cen-ter retains its charge state decreases exponentially on themillisecond scale [34]. As this charge generated by pho-toionization moves around, the electric field would betime-averaged, suppressing deformation. The relation-ship between the ionization rate at thermal equilibriumand the photoionization rate determines the coefficient ofthe exponential change. When the optical power is suf-ficiently large, the electric field and crystal strain, whichcannot be averaged, remain as a finite deformation.Ref. [33] also noted that deformation due to chargecan change the shape of the ODMR spectrum to a non-Lorentzian distribution. This is consistent with thefact that the ODMR spectrum deviates from the dou-ble Lorentzian fitting, and its shape changes with opticalpower [see Figs. 2(a) and (b)]. Investigating both the dipposition and its shape will help to elucidate the mecha-nism.We note further experimental and theoretical effortsare needed because many parameters could be involvedin the mechanism. On the experimental side, compar-ing bulk samples with systematically varying impuritiesand deformations and investigating this optical power-dependent splitting in a single NV center with charge-induced deformation [33] are helpful. The magnetic fieldcan be swept over a sufficiently wide range compared tothe deformation for bulk samples. This will clarify whichparameters of the ground-state Hamiltonian appear todepend on optical power. Pulsed ODMR [21] will provideinformation on the time the effect of the laser irradiationremains, which can be used to validate the mechanism.On the theoretical side, it is helpful to investigate whatfitting function is appropriate to reproduce the ODMRspectral shape and what defects are candidates for pho-toionization.IV. CONCLUSIONWe investigate the optical power dependence of split-ting of the ODMR spectra using various NV ensemblesamples. In addition to reproducing the previous studyusing NDs [23], we find that the optical power depen-dence saturates in a larger optical power than in theirstudy. Since we also observe the same phenomenon inthe single-crystal diamond, which has very few impuritiesand non-axisymmetry deformation compared to NDs, weconsider our observation due to the NV center’s intrinsicnature. We quantitatively discuss the parameters thatcould be responsible for this phenomenon and infer thatdeformation is an important parameter. We point outthe possible responsibility of slow dynamics in the opti-cal excitation and emission process of single NV centers.The present optical power dependence can be criticalin accurate magnetometry using NVs. This effect maydegrade the accuracy of the magnetometry using NDsby about a few ten µT. Even when using high-qualitybulk diamonds, we must be careful when discussing afew µT magnetic fields around zero magnetic fields. Wecan minimize degradation by introducing strong opticalpower based on the phenomenological exponential behav-ior discussed here. Also, we suggest that using diamondswith fewer impurities and deformation can reduce theinfluence on the accurate magnetic field measurement.Further experimental verification and theoretical discus-sion on deformation, impurity densities, and a compre-hensive range of magnetic fields will help to identify themechanism of this phenomenon.ACKNOWLEDGEMENTSWe thank K. M. Itoh for letting us use the confo-cal microscope system, and H. Watanabe for his highquality diamond, which we used in the estimation ofthe spatial resolution of our system [Fig. 1(c)]. Weappreciate the fruitful discussion with J. Inoue. Wealso thank MEXT-Nanotechnology Platform Program“Microstructure Analysis Platform” for technical sup-port. K.S. acknowledges the support of Grants-in-Aidfor Scientific Research No. JP22K03524. 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