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Hao Gu, [Moeta Tsukamoto](https://orcid.org/0000-0002-0708-6308), [Yuki Nakamura](https://orcid.org/0000-0002-9038-468X), [Shu Nakaharai](https://orcid.org/0000-0002-6329-3942), [Takuya Iwasaki](https://orcid.org/0000-0002-1103-2433), [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), Shinichi Ogawa, Yukinori Morita, [Kento Sasaki](https://orcid.org/0000-0002-5880-2116), [Kensuke Kobayashi](https://orcid.org/0000-0001-7072-5945)

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[Systematic characterization of nanoscale <math display="inline">  <mi>h</mi></math>-BN quantum sensor spots created by helium-ion microscopy](https://mdr.nims.go.jp/datasets/b278a733-2094-41aa-97a6-8e89d85119b9)

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Systematic characterization of nanoscale h-BN quantum sensor spots created byhelium-ion microscopyHao Gu,1 Moeta Tsukamoto,1 Yuki Nakamura,1 Shu Nakaharai,2 Takuya Iwasaki,3 Kenji Watanabe,4Takashi Taniguchi,5 Shinichi Ogawa,6 Yukinori Morita,6 Kento Sasaki,1 and Kensuke Kobayashi1, 7, 81Department of Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan2Department of Electric and Electronic Engineering, Tokyo University of Technology,1404-4 Katakuramachi, Hachiohji, Tokyo 192-0982, Japan3Research Center for Materials Nanoarchitectonics,National Institute for Materials Science, 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan4Research Center for Electronic and Optical Materials,National Institute for Materials Science, 1-1 Namiki, Tsukuba Ibaraki 305-0044, Japan5Research Center for Materials Nanoarchitectonics,National Institute for Materials Science, 1-1 Namiki, Tsukuba Ibaraki 305-0044, Japan6National Institute of Advanced Industrial Science and Technology,1-1-1 Umezono, Tsukuba, Ibaraki 305-8568, Japan7Institute for Physics of Intelligence, The University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan8Trans-scale Quantum Science Institute, The University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan(Dated: November 19, 2024)The nanosized boron vacancy (V −B ) defect spot in hexagonal boron nitride (h-BN) is promisingfor a local magnetic field quantum sensor. One of its advantages is that a helium-ion microscope canmake a spot at any location in an h-BN flake with nanometer accuracy. In this study, we investigatethe properties of the created nanosized V −B defect spots by systematically varying three conditions:the helium-ion dose, the thickness of the h-BN flakes, and the substrate on which the h-BN flakesare attached. The physical background of the results obtained is successfully interpreted usingMonte Carlo calculations. From the findings obtained here, a guideline for their optimal creationconditions is obtained to maximize its performance as a quantum sensor concerning sensitivity andlocalization.I. INTRODUCTIONInvestigating the magnetism arising from the cooper-ative behavior of microscopic spins has been a centraltopic in solid-state physics [1]. Many magnetic mate-rials with various magnetic orders are known, such asferromagnets, antiferromagnets, frustrated systems, andso on [2]. In addition to conventional bulk materials,magnetic domains, nanomagnets, atomically thin van derWaals magnets, and their application to spintronics de-vices tell us how diverse magnetic properties manifestthemselves [3, 4]. Thus, versatile methods and inno-vations are necessary for their experimental study. Inparticular, magnetic force microscopy and magneto-opticKerr effect microscopy are representative methods todirectly observe magnetism, which have been powerfultools for many years [5, 6].Quantum sensors based on the nitrogen-vacancy (N-V )centers in diamond can detect local magnetic fields usingthe optically detected magnetic resonance (ODMR) tech-nique [7, 8]. Either N-V center ensembles or a single N-Vcenter in a scanning probe can be used to image the strayfield from the target material quantitatively. The time-dependent magnetic responses and fluctuation in the tar-get materials can also be measured by devising quantumcontrol of quantum sensors. Since the first proposals ofthe NV-center-based magnetometry in 2008 [9–11], themethod has been successfully applied to condensed mat-ter physics. For example, it has been used to quanti-tatively observe the stray fields from magnetic domainwalls in antiferromagnets [12, 13] and superconductingvortices [14–16], which has been challenging to do withother existing methods.Boron vacancy (V −B ) defects in hexagonal boron nitride(h-BN), shown in Fig. 1, were recently demonstrated towork as quantum sensors [17–19]. Because h-BN is avan der Waals material, very thinly cleaved h-BN flakescan easily adhere to a magnetic material to be measured.Thus, V −B defects hosted within a flake as thin as tens ofnanometers can sense magnetic fields that remain steepand strong near the sample on nanometer order. Addi-tionally, the thickness of the flake can be precisely mea-sured, allowing us to determine the stand-off distance.This parameter is crucial for accurately reconstructingthe magnetization and current in the target material [20].For these reasons, V −B sensors are expected to be appliedto detect minute magnetic orders. Several reports on theimaging of van der Waals magnets using V −B defects cre-ated inside an h-BN flake or its surface have already beenreported [21–24].To maximize the potential of the V −B sensors, we shouldsystematically investigate both the defect creation meth-ods and the sensing configurations. V −B defect spots (V −Bspots) are created in h-BN crystals by neutron [17] or ionirradiation [25, 26]. It has been reported that the sen-sor properties, such as photoluminescence (PL) intensity,relaxation time, and strain, depend on irradiation condi-tions, including ion species, dose, and acceleration [25].arXiv:2411.10717v1  [cond-mat.mes-hall]  16 Nov 20242FIG. 1. Schematic of magnetic field imaging using a V −B spotin an h-BN flake as thin as t nm with the ODMR technique.Therefore, investigating the damage caused by ion irra-diation when creating V −B sensors is essential. Regardingthe sensing configuration, the h-BN flake thickness andsubstrate surface to which the h-BN flakes are attachedare vital. The flake thinner than 100 nm is conventionallyused but if the flake becomes too thin, the total amountof V −B defects is reduced unfavorably. The effect of thesubstrate surface is also critical, as it has been demon-strated to increase sensitivity significantly by increasingthe signal intensity of V −B defects on the gold (Au) sub-strate film [27]. Also, in Ref. [28], the effect of the SiO2substrate surface on the PL spectrum of V −B centers cre-ated by He ion irradiation was observed.In addition, we emphasize the importance of the size ofthe created V −B spot, which directly affects the locality ofthe detected magnetic field. The locality in the magneticfield detection is essential to capture changes in the mag-netic field that become steeper as the spot gets closer tothe target. When V −B sensors are uniformly created in h-BN flakes, the measurement spot size is typically as largeas the optical spot, whose size is similar to the PL wave-length (submicrometers). To overcome this issue, Sasakiet al. [29] limited the actual defect spot size by ion ir-radiation to nanosize (l = 25–200 nm square), using ahelium ion microscope (HIM), leading to a high localityof magnetic field detection. This method is also advanta-geous as HIM can create a sensor at a designed positionwith nanometer accuracy. Although some works [28–30]have investigated V −B creation using a HIM, a systematicinvestigation of spin properties and substrate effects atpractical h-BN flake thicknesses has not been shown.In this study, we show the dependence of sensor prop-erties on helium ion doses in the nanosized V −B defect cre-ation by HIM, following our previous work [29]. For dosesover three orders from 1014 cm−2 to 1017 cm−2, we sys-tematically characterize the sensor properties of sensitiv-ity, intensity, contrast, strain, and spin relaxation time.Additionally, we investigate different h-BN flake thick-nesses and substrates and observe substrate-dependentsensor properties. We find that the static magnetic fieldsensitivity is best at the dose of 1016 cm−2 for a 47 nmthick h-BN flake on an Au film. We compare the exper-imental results with Monte Carlo simulations [Stoppingand Range of Ions in Matter (SRIM)] [31] calculatingdefect formation and discuss the effect of ion backscat-tering from the substrate. The obtained findings provideguidelines for arranging V −B sensors using HIM.This paper is organized as follows. We describe theexperimental setup in Sec. II and explain the underly-ing physics for the characterization of V −B in Sec. III.The experimental results are presented in Sec. IV. Sec-tions IVA and IVB discuss the sensor properties ob-tained from ODMR spectra. Section IVC reports thespin relaxation time. Section IVD discusses the size ac-curacy of V −B spots and substrate dependence based onSRIM. Section IVE shows the results related to the PLintensity. Section IVF summarizes guidelines for creat-ing V −B defects using HIM based on the observation andsimulations shown in Sec. IV, and, finally, Sec. V providesthe conclusion of this work.II. EXPERIMENTSWe use HIM to create V −B spots by local ion irradia-tion of h-BN flakes on a substrate. We systematicallyadopt several different fabrication conditions of h-BNflake thickness (t), substrate surface (Au or SiO2), andHe ion dose (dHe) as listed in Table I. Section IIA de-scribes the preparation of h-BN flakes, Sec.II B describesthe V −B defect creation using HIM, and Sec. II C explainsthe confocal microscope to evaluate the properties of thecreated V −B spots as quantum sensors.Parameters ConditionsSubstrate film Au, SiO2h-BN flake thickness, t (nm) 9, 47, 256He ion dose, dHe (cm−2) 1014, 1015, 1016, 1017TABLE I. Parameter list of the V −B defect creation.A. Device fabrication with h-BN flakesWe prepare thin h-BN flakes by cleaving h-BN bulkcrystals with Scotch tape and transferring them onto asilicon substrate. A 100 nm thick Au wire (width 4 µm) isfabricated on a silicon substrate with a 285 nm thick ox-ide film using photolithography, and the h-BN flakes arestamped on top of it using the bubble-free method [32].Figure 2(a) is an optical micrograph of a typical fabri-cated device. The h-BN flake is large enough comparedto the Au wire to have areas of adhesion to both Au andSiO2. An atomic force microscope (AFM) is used to mea-sure the h-BN flake thickness t. Figure 2(b) shows a pro-file corresponding to the white dashed line in Fig. 2(a).3A few steps due to the h-BN flake and the Au wire (Aufilm) are observed. We estimate the h-BN flake thicknessof the device shown in Fig. 2(a) to be t = 47 nm. Simi-larly, we fabricate devices of h-BN flakes with t = 9 nmand t = 256 nm.FIG. 2. Overview of the h-BN device. (a) Left panel: Opticalmicrograph of the Au wire (Au film) covered by an h-BN flakewith t = 47 nm. Right panel: Schematic representation of themeasurement configuration. The squares and the numbers in-side them denote the irradiated regions and the exponentialportion of the helium dose, namely log10 dHe, respectively. Acopper wire for applying microwaves (MW) is arranged par-allel to the Au wire, as schematically shown. (b) AFM profileacross the white dashed line in panel (a). (c) PL intensitymapping of the irradiation region with dHe = 1015 cm−2 ofthe device with t = 256 nm, which is obtained using a confo-cal microscope. Each spot inside the yellow frame is a 100 nmsquare irradiated with ions, which we evaluate in this study.B. V −B defect creation using HIMWe use an Orion Plus HIM (Carl Zeiss MicroscopyLLC, Peabody, MA, USA) with a helium ion beam ofnominal width 0.3 nm and create V −B spots on the h-BN flakes on the fabricated Au wire devices. HIM isa technique to irradiate a target object with a focusedbeam of helium ions for processing and imaging with highspatial resolution [33]. The irradiation by helium ions,which are light, is reasonable for creating small V −B spotsdue to less surface scattering than electron irradiationand less damage on the material structure than heavy-atom irradiation [28].First, we precisely determine the position of the h-BNflake on the Au film by observing the secondary electronsemitted from the device using HIM. Then, the targetpositions at the h-BN flakes are irradiated with heliumions as designed in square-shaped spots of 100 nm oneach side at an acceleration voltage of 30 keV. Thus, eachspot consists of many V −B defects. The 30 keV voltagewas a value used previously for the V −B defect creationwith HIM [29] and conventional ion irradiation [26]. Thefocused helium ion beam is discretely raster scanned withan interval of 3.2 nm so that the average helium ion dosein the spot is dHe (cm−2). Each h-BN flake is irradiatedat multiple positions in contact with Au and SiO2 atdHe = 1014, 1015, 1016, and 1017 cm−2, as shown in theright panel of Fig. 2(a) (see also Table I). Only for thedevice with t = 9 nm, we use dHe = 1015, 1016, and1017 cm−2.C. Confocal microscope systemWe utilize a home-built confocal microscope sys-tem [34] to characterize the created V −B spots. The PLof V −B defects occurs in the wavelength range of 750–1000 nm [17], and it can be detected using a bandpassfilter and a single photon counting module while irradi-ating a green laser. The laser wavelength is 515–532 nmfor Sec. IVE and 532 nm otherwise. The laser poweris 0.7 mW in ODMR and spin relaxation time measure-ments. It is sufficiently weaker than the typical power(on Au, 7.6 mW and on SiO2, far stronger laser poweris needed to saturate) at which the PL from V −B defectssaturates in our confocal system. Only in Sec. IVE, thelaser power is set to 3.0 mW to increase the signal inten-sity.Figure 2(c) displays an example of the PL intensitymapping of a fabricated device with t = 256 nm anddHe = 1015 cm−2. Bright spots correspond to the createdV −B spots. The spots surrounded by the yellow box inFig. 2(c) are 100 nm square size irradiated spots. ThePL intensity of the spots is more prominent on Au thanon SiO2.To perform ODMR, we apply microwaves (MW) anda static magnetic field to the devices. The MW is irradi-ated from a 50 µm-diameter copper wire beside the Auwire, as shown in the right panel of Fig. 2(a). This con-figuration allows a strong and uniform MW irradiationto the V −B spots. We examine spots with different dosesdHe made on h-BN of different thicknesses t (see Table I).They are located along the same copper wire, as shown4in the right panel of Fig. 2(a). Thus, the influence ofMW amplitude variation on the sensitivity evaluation isminimized. The static magnetic field is applied using acoil. The direction of the coil’s magnetic field is perpen-dicular to the surface of the h-BN flake and parallel tothe quantization axis of V −B , and its maximum intensityis 12 mT. We measure spin relaxation time by pulsingMW and the laser, as described in Sec. IVC.III. CHARACTERIZATION OF BORONVACANCY DEFECTSIn this study, we measure five parameters, PL inten-sity (I), PL contrast (C), strain (E), resonance linewidth(∆ν), and spin relaxation time (T1). This section ex-plains their meanings and the evaluation methods.We determined C, E, and ∆ν using ODMR measure-ment. We briefly outline the principle of the ODMRmea-surement based on the effective model of energy levelsand optical transition, which includes the ground state,the excited state, and the metastable state, as illustratedin Fig. 3 (a) [35, 36]. We apply this model, initially devel-oped for diamond N-V centers, to V −B defects, assumingthat they behave as an S = 1 system, with the groundand excited states as spin triplets and the metastablestate as a spin singlet. The spin triplet is quantized inthe out-of-plane direction of the h-BN flake, and mS = 0,+1, and −1 in that direction can be used to distinguishstates as magnetic quantum numbers.The sensor state transitions from the ground state tothe excited state with the green laser while the mag-netic quantum number is preserved [green arrows inFig. 3(a)] [17]. There are two relaxation pathways fromthe excited state to the ground state. One pathwayis the relaxation with red photon emission while main-taining the magnetic quantum number [red arrows inFig. 3(a)]. This emission constitutes the PL signal ob-served using a confocal microscope system. The otherpathway is through a metastable state [dashed black ar-rows in Fig. 3(a)], where the magnetic quantum numbersare not conserved without red emission. The mS = ±1state in the excited state selectively goes through thispathway to the mS = 0 state in the ground state. Be-cause of this selectivity, the mS = ±1 state exhibits aweaker PL intensity than the mS = 0 state. In addition,the sensor state is polarized or initialized to the mS = 0state with repeated excitation.The ODMR measurement relies on the above behav-iors, utilizing continuous irradiation of green light andMW. The optical excitation initializes the mS = 0 stateand simultaneously yields the PL intensity. When theMW frequency matches the electron spin resonance fre-quency of the ground state, a part of the mS = 0 statetransitions to the mS = ±1 state, leading to the PL in-tensity reduction. Therefore, the intensity as a functionof the MW frequency, the so-called ODMR spectrum,corresponds to an electron spin resonance spectrum. Fig-FIG. 3. Principles of ODMR measurement. (a) An effectivemodel that includes energy levels and their optical transition.(b) An example of the ODMR spectrum. The data are takenat a spot irradiated with dHe = 1016 cm−2 in the device witht = 9 nm on the Au film. The applied magnetic field in thiscase is 10.2 mT. The blue markers denote experimental data,and the red line represents the result of the double-Lorentzianfit.ure 3(b) is an example ODMR spectrum of V −B under amagnetic field. The vertical axis is the ratio of the PLintensity with and without MW irradiation. Two dipscorrespond to the resonance between the mS = 0 stateand the mS = ±1 states. The resonance frequency andthe linewidth (full width at half maximum) are ν± and∆ν, respectively. The amount of the PL ratio change isthe contrast C.In quantum sensing, we estimate the magnetic fieldbased on electron spin resonance frequencies ν±. TheHamiltonian of the spin-triplet in the ground state isgiven by [37]Ĥ = DgsŜ2z + E(Ŝ2x − Ŝ2y) + γeBzŜz, (1)where Ŝj is the S = 1 operator for j direction (j =x, y, z), Dgs is the zero-field splitting, E is the strain,and the γe = 28 MHz/mT is the electron gyromagneticratio. Bz is the magnetic field applied along the z direc-tion, which is the out-of-plane direction of the h-BN flake[see right panel of Fig. 2(a)]. The second term, E, ariseswhen defect symmetry is broken by a crystal strain or anelectric field from charge impurities. Thus, it can dependon irradiation damage [38]. The third term is the Zeemanterm, which gives rise to the magnetic field dependence ofthe sensor. Here, we neglect the influence of nuclear spinsnear the V −B defects, which additionally split energy lev-5els [17–19]. Since this does not significantly impact thediscussion in our study, we do not give a detailed expla-nation. By diagonalizing the Hamiltonian, the resonancefrequencies are obtained asν± = Dgs ±√(γeBz)2 + E2. (2)Therefore, if the strain Dgs and E are known, we candetermine the magnetic field Bz from the difference.How sensitive the resonance frequency is affected bymagnetic fields defines the sensitivity, as follows,∣∣∣∣∂ν±∂Bz∣∣∣∣ =∣∣∣∣∣ γ2eBz√(γeBz)2 + E2∣∣∣∣∣ . (3)This equation shows that sensitivity depends on thestrain E. The value decreases as the effect of magneticfield strength is sufficiently small compared to the strain(Bz ≪ E/γe). The strain limits the range on the low-field side where the V −B can function as a sensor; thesmaller the strain, the more sensitivity the V −B can retainat lower magnetic fields. Thus, the strain is a key param-eter to characterize the sensor performance. The strainE can be estimated as half of the difference in resonancefrequencies ν+ − ν− near zero fields (|Bz| ≪ 0.3 mT).The result will be discussed in Sec. IVB. Note that Ecould be determined by fitting the change in resonancefrequency with the magnetic field according to Eq. (2).The sensitivity also depends on the precision of esti-mating the resonance frequencies from the ODMR spec-trum. The resonance frequencies are obtained as thecenter frequencies of the double-Lorentzian fitted to theODMR spectrum [the red line in Fig. 3(b)]. The precisionincreases when each resonance dip is sharp, i.e., as the PLcontrast C increases and the linewidth ∆ν narrows. Wededuce C and ∆ν from the lower frequency (ν−) dip. Thesensitivity is subject to the noise per unit time when ob-taining the ODMR spectrum, which depends on the PLintensity I. We deduce it from the PL intensity withoutMW, including the value obtained by PL mapping. Thestatic magnetic field sensitivity expression and its resultswill be detailed in next Sec. IVA. While it is beyond thescope of the present study, the sensitivity for other typesof measurements is also proportional to (C√I)−1 [26].Note that the experimentally observed PL intensity Iincludes V −B fluorescence Is and other background signalsIb. The background contributes to the reduction of C.We estimate and discuss the amount of the V −B createdusing HIM based on Is in Sec. IVE.Finally, we explain the spin relaxation time T1 as a keyparameter of sensor performance. This time T1 definesthe time it takes for the spin state to reach thermal equi-librium. In the experiment, the laser is turned off oncethe spin is optically initialized to the mS = 0 state. Aftera waiting time, τ , we measure how much mS = 0 statesremain. The decay of the PL intensity Iw(τ) at readoutlaser pulse as a function of τ behaves exponentially asIw(τ) ∝ exp(−τ/T1) + offset. (4)The longer T1 becomes, the longer the upper limit ofsensing duration is, which is advantageous regarding sen-sitivity and frequency resolution of ac magnetic field andmagnetic field noise detection [7]. The spin relaxationtime is suppressed with the ion irradiation dose [39]. Sec-tion IVC discusses T1.IV. RESULTS AND DISCUSSIONSA. Magnetic field sensitivity using ODMRWe discuss the ODMR results obtained on the V −Bspots on the device with a flake thickness t = 47 nm,which is a suitable thickness for h-BN flakes in magneticimaging applications [29]. We estimate the shot-noise-limited static magnetic field sensitivity η through ODMRmeasurements under a sufficient bias field (Bz ≫ E/γe),using the following expression [40, 41],η =43√31γe∆νC√I. (5)The increase in the contrast C and PL intensity I andthe decrease in ∆ν directly contribute to the increase insensitivity.Figure 4(a) shows the ODMR spectra for the V −B spotson Au with various doses dHe. We note that C decreasesas the dose increases. We obtain C = 12.7, 12.2, and9.2 for dHe = 1015, 1016, and 1017 cm−2, respectively,as shown in Fig. 4(b). The decrease in C with increas-ing dHe is also observed for different t, which is also thecase for the h-BN flakes on SiO2. The degradation islikely caused by suppression of spin lifetime or by in-creased photoluminescence from non-V −B defects due tolarge dHe. Amorphous defects in the h-BN lattice cre-ated by He ion irradiation have been reported to affectthe luminescence intensity [28], which may be related tothe present observation.In contrast to C, I increases monotonically with dHeas shown in Fig. 4(b). We obtain I = 2 × 102 kcps,1.1× 103 kcps, and 1.3× 103 kcps for dHe = 1015 cm−2,1016 cm−2, and 1017 cm−2, respectively. The estimatedbackground Ib is sufficiently weak < 20 kcps comparedto the V −B signal [see Sec. IVE]. Therefore, the numberof V −B defects increases with the amount of dose. In thisway, there is a clear trade-off between C and I in thedose range we investigate. Nevertheless, the increase ofI is not proportional to dHe; the intensity is increased 5.4times from dHe = 1015 to 1016 cm−2, while it is only 1.1times from dHe = 1016 to 1017 cm−2. The aforementionedamorphous defects may have prevented the formation ofV −B [28].The linewidth ∆ν is almost insensitive to dHe, as shownin Fig. 4(a); only a 5 variation in ∆ν (136–143 MHz) isdetected within the investigated dHe. This implies thatthe nuclear spin primarily determines ∆ν. Since the reso-nance is broadened by huge (several hundred MHz) level6FIG. 4. Analysis of ODMR spectrum and sensitivity for thespots with t = 47 nm. (a) ODMR spectra under Bz = 9.7 mTfrom three devices with different dHe. The markers denote ex-perimental data, and the lines denote double-Lorentzian fit.The blue, red, and green colors correspond to V −B spots cre-ated at dHe = 1015, 1016, and 1017 cm−2, respectively. (b)Dose-dependent PL intensity I (cyan, left axis) and PL con-trast C (yellow, right axis). (c),(d) Dose-dependent (c) staticmagnetic field sensitivity η and (d) strain E. The red andblue markers denote the spots on Au and SiO2, respectively.splitting due to nuclear spins [17–19, 26], the influenceof the other factors is negligibly small. Further investi-gation of the ODMR spectra for the isotope-controlledh-BN [42–44], where nuclear spins have less impact thanconventional ones, might enable us to observe the dosedependence of linewidths.We estimate the sensitivity η using Eq. (5), as shownin Fig. 4(c). It is obtained to be 61.9 µT/√Hz,30.2 µT/√Hz, and 38.2 µT/√Hz for dHe = 1015 cm−2,1016 cm−2, and 1017 cm−2, respectively. In Ref. [29], thesensitivity of 73.6 µT/√Hz is obtained for the spots onAu in the h-BN flake with t = 66 nm irradiated withdHe = 1015 cm−2, being consistent with the present ob-servation (61.9 µT/√Hz) obtained for the similar con-dition. We get the best sensitivity, the minimum valueof η, of 30.2 µT/√Hz for the spots on Au with dHe =1016 cm−2. The V −B density estimated by the SRIM sim-ulation is 6.1 × 1016 in the single spot. The sensitivityis 2.5 times better than before [29]. It is an advantageof HIM that a dose as high as 1016 cm−2 can be realizedwith local ion irradiation in a reasonable time and cost.Figure 4(c) also shows the sensitivity of the V −B spotson SiO2. While the MW intensity is expected to differsignificantly between on a metal (Au) and on an insulator(SiO2), the contrast of the spots on SiO2 is maintainedat around 71–83% of that on Au (not shown here). Incontrast, I on SiO2 is only about 1–3% of that on Au,as discussed later in Sec. IVE. As a result, η is approx-imately an order of magnitude worse than the optimalsensitivity obtained on Au [Fig. 4(c)].B. StrainFigure 4(d) shows the dHe dependence of the strain Eobtained for the spots on the device with t = 47 nm.We notice two facts. First, increasing dHe leads to anincrease in strain. For example, the strains of the spotson Au are obtained as 53 MHz and 66 MHz for dHe =1015 cm−2 and 1017 cm−2, respectively. Similarly, we getE on SiO2 as 58 MHz and 64 MHz for dHe = 1016 cm−2and 1017 cm−2, respectively. Second, for a given dHe, thespots on Au exhibit 3–10% larger E than those on SiO2.This observation might indicate the substrate-dependentdamage to the h-BN flakes. We will consider these resultswith simulation in Sec. IVD.In Ref. [25], the dose dependence of nitrogen irradia-tion at an accelerating voltage of 30 keV to the 10–100 nmthick h-BN flakes on a silicon substrate was investigated.They observed that strain E increases from about 60 to80 MHz as the dose increases from 1013 to 1015 cm−2.In contrast, E is as small as 60–65 MHz for the dose of1017 cm−2 in our study. The difference may be mainlydue to the difference in the ion mass. The nitrogen ion isabout seven times heavier than the helium ion, leading tomore considerable irradiation damage in the h-BN flakes.The large error bars in Fig. 4(d) are due to the double-Lorentzian fit of the ODMR spectra near zero fieldsin determining strain E. The double-Lorentzian shapeis insufficient to reproduce the experimentally observedODMR spectra, so the fitting precision needs to bemore satisfactory. A more appropriate analytical ex-pression for zero-field ODMR spectra, such as discussedbefore [45], will enhance the estimation precision of thesensor parameters.C. Spin relaxation timeWe measure the spin relaxation time T1 using the pulseprotocol depicted in Fig. 5(a) inset. The spin state pop-ulation is estimated from the PL intensity at the first7200 ns of the readout laser pulse. Figure 5(a) shows theresults for the spots irradiated with dHe = 1017 cm−2 atthe device with t = 47 nm. The vertical axis is the nor-malized PL intensity Iw so that Iw = 1 at τ = 0 ns andIw = 0 when τ is sufficiently long. Their behaviors arewell explained by Eq. (4). Remarkably, the PL intensitydecays faster in the spots on Au (red, T1 = 7.7 µs) thanthose on SiO2 (blue, T1 = 14.7 µs). These values aretypical for T1 of V −B centers [21, 27, 46].FIG. 5. (a) Relaxation behavior of a V −B spot with t = 47 nmand dHe = 1017 cm−2. Red and blue colors represent the re-sults on Au and on SiO2, respectively. Points represent exper-imental data, and lines indicate exponential fits using Eq. (4).The inset shows the measurement protocol, consisting of ini-tialization, waiting (τ), and readout. (b) Spin relaxation timeT1 as a function of dHe. Red and blue markers indicate thespots on Au and SiO2, respectively. (c) Relaxation behaviorcorresponding to panel (a) in the case of t = 256 nm.We also investigate the dHe dependence of T1, as pre-sented in Fig. 5(b). We notice two trends. First, T1becomes smaller for larger dHe. This observation agreeswith previous studies [25, 39], which discussed that theT1 degradation is caused by lattice damage during irradi-ation. For the spots on Au, changing dHe from 1015 cm−2to 1016 cm−2 results in a 27% degradation, and chang-ing from 1016 to 1017 cm−2 leads to a 35% degradation.For the spots on SiO2, changing dHe from 1016 cm−2to 1017 cm−2 results in an 11% degradation. Clearly, thedegradation is more pronounced for the spots on Au thanon SiO2. Second, for a given dHe, the spots on SiO2 havea 1.4–1.9 times longer T1 than those on Au.Figure 5(c) shows the spin relaxation of the spots onthe device with a thicker h-BN of t = 256 nm with dHe =1017 cm−2. In contrast to the case with t = 47 nm shownin Fig. 5(a), the decays for the spots on Au and on SiO2are almost identical.The above results suggest that irradiation damage de-pends on the substrate and h-BN thickness. This insightis further investigated by the Monte Carlo simulationsnext.D. Monte Carlo simulationsWe run a Monte Carlo simulation package, Stoppingand Range of Ions in Matter [31] (SRIM), where the colli-sion events and the resultant vacancy distribution createdby ion irradiation are calculated. SRIM treats atomic col-lisions as classical two-body ones, including the atomicinteractions and the cascade effect where one scatteredatom scatters another. Since the ion irradiation spot sizeof HIM is extremely small, the spreading effect of ionsrandomly colliding in the target material should be care-fully treated in estimating the actual V −B spot size.Figure 6(a) shows the simulation configuration, wherehelium ions are directed perpendicular to the h-BN flakefrom left to right and enter it perpendicularly from theincident position. There, R and D indicate the distancefrom the incident axis and the depth from the surface,respectively. The flake is attached to a sufficiently thickAu or SiO2 film. The backscattering of ions at the sub-strate film plays an important role in the defect creation.We set the acceleration voltage to 30 keV and the h-BN,SiO2, and Au densities at 2.3 g/cm3 [47], 2.1 g/cm3 [48],and 19.3 g/cm3. We consider V −B positions to be thoseof the removed boron atoms. We analyze the results ofirradiating each device with a total of 104 helium ions.The top panel of Fig. 6(b) shows the histogram of thedensity of the created V −B defects per unit length as afunction of R for the device with t = 47 nm. In therange R < 12 nm [indicated by the vertical dot-dashline in Fig. 6(b)], the V −B defect density distribution isnearly the same for the h-BN flakes on Au and SiO2.In contrast, for R > 12 nm, more V −B defects tend tobe created for the flake on Au than on SiO2. In total,the V −B defects are created 2.0 times more on the formerthan on the latter, which means that the total damageis higher for the flake on Au. Au has a higher densitythan SiO2, so backscattering is more significant, leadingto increased irradiation damage. In Secs. IVB and IVC,we discussed larger E and shorter T1 for devices on Authan on SiO2. This is consistent with our simulation thatlattice damage depends on the substrate film.The bottom panel of Fig. 6(b) shows the normalizedcumulative distribution as a function of R. For the h-BN(t = 47 nm) on Au, three-fourths (75%) of all V −B defects8FIG. 6. (a) Configuration of ion irradiation in SRIM. Ionsenter the h-BN flake perpendicularly from the incident posi-tion. The distance from the incident axis and the depth fromthe surface are indicated by R and D, respectively. The flakeis attached to a sufficiently thick Au or SiO2 film. (b) Toppanel: Histogram of the V −B defects created per unit length forR of the device with t = 47 nm. Bottom panel: Normalizedcumulative distribution of V −B defects. The horizontal dashedline indicates 75%. (c) Top panel: Histogram of the V −B de-fects per unit length for D of the device with thick h-BN flake(t = 1 µm). The blue and red colors indicate the cases of thick(1 µm) and thin (47 nm) h-BN flakes on SiO2, respectively.The vertical dotted lines represent the two thicknesses (47and 256 nm) used in our experiment. Bottom panel: Normal-ized cumulative distribution of V −B defects. The h-BN flakethickness does not affect the distribution of V −B defects in theSiO2 case.are created scattered over an area up to R ∼ 76 nm, asindicated by the horizontal dashed line in the figure. Sucha spreading of the V −B defects degrades the localizationof the sensor. In contrast, on SiO2, the same amount ofV −B defects is concentrated only in an R < 6 nm area.Using the SiO2 substrate with less backscattering wouldhelp create a V −B spot as small as a few nm.Figure 6(c) shows the depth (D) dependence of thedefect creation for a thick h-BN flake (t = 1 µm). Almostall of V −B defects are created shallower than D = 256 nmin a thick h-BN flake, as indicated by a vertical dashedline in the bottom panel of Fig. 6(c). This means thatthe backscattering from the substrate (Au or SiO2) isalmost negligible in an h-BN flake thicker than this. Thedifference in the defect creation between Au and SiO2 ina 256 nm thick h-BN flake is only 1% (data not shown).It is also interesting to focus on a small D region. Thenormalized cumulative distribution from the surface isonly 7% at depth D = 47 nm. Thus, for the thin h-BNflake with t = 47 nm, most V −B defects are produced byions that have undergone backscattering.The above observations can explain several experimen-tal findings discussed in Secs. IVB and IVC. Au tends tobackscatter ions more than SiO2, so a thin h-BN flake onAu is more subject to backscattering damage than one onSiO2. This agrees with a larger strain E for t = 47 nm inthe Au case than in the SiO2 case, shown in Fig. 4(d) fora given dHe. We can also claim that the backscatteringeffect is responsible for the shorter spin relaxation timeT1 of the t = 47 nm flake on Au than on SiO2, as shownin Fig. 5(a). In sharp contrast, T1 is almost the sameon Au and SiO2 in a thick h-BN flake (t = 256 nm) [seeFig. 5(c)], which is concordant with the calculation thatthe fraction of V −B defects created by backscattering isreduced for thicker flakes. Thus, the SRIM results nicelyillustrate the experimental results.E. PhotoluminescenceWe evaluate the PL intensity at the irradiated spot forvarious conditions. For this investigation only, we set thelaser power to 3.0 mW, our maximum available power,to enhance the signal. Note that we do not treat theresult of the spots of the device with t = 47 nm anddHe = 1014 cm−2 and of the device with t = 9 nm onSiO2, as they do not provide a sufficient luminescencesignal from the analysis. As mentioned in Sec. III, theoverall PL intensity I includes background fluorescenceother than V −B . We separate the spot luminescence Isfrom the background Ib to focus only on the increase inluminescence due to ion irradiation.We separate Is from Ib in the following way. Fig-ure 7(a) shows a typical PL mapping as an XY planeat a V −B spot on the h-BN flake. The spot shape canbe fitted using a two-dimensional Gaussian distributionwith a peak contribution of Ipeak, including an offset ofIb. Figures 7(b) and (c) show the cross sections of thePL intensity across the peak along the X and Y axes, re-spectively. The markers represent the experimental data,and the lines represent the fitting result. The dashed linecorresponds to Ib. Then, we find Is as Ipeak − Ib.Figures 7(d) and (e) show the dose dependence of Is forthe spots on Au and SiO2, respectively. Is shows a mono-tonic increase in dHe for all devices with t = 9, 47, and256 nm. The rise in Is becomes smaller for higher dHe.9FIG. 7. PL intensity without background Is. (a) TypicalPL mapping as an XY plane at a V −B spot on the h-BN flakewith t = 256 nm and dHe = 1015 cm−2. (b),(c) Cross sectionsalong the (b) horizontal (X) and (c) vertical (Y ) directionsacross the peak. The markers represent experimental data,and the lines represent the two-dimensional Gaussian fittingwith an offset. (d),(e) The dHe dependence of Is on (d) Auand (e) SiO2. The dotted blue, dashed red, and solid magentalines are the data of the devices with t = 9, 47, and 256 nm,respectively. (f),(g) PL intensity per unit thickness Is/t on(f) Au and (g) SiO2.It corresponds to a decrease in V −B defect creation effi-ciency at high doses and agrees with the discussion givenfor Fig. 4(b) in Sec. IVA. It is known that amorphizationof substrates and h-BN crystals occurs at helium doses of1017 cm−3 with an acceleration voltage of 30 keV [49, 50],and such defects may prevent V −B defect creation.Next, we compare Is of the spots on Au and on SiO2in Figs. 7(d) and (e), respectively. For the spots witht = 47 nm and dHe = 1017 cm−2, Is is about 22 timeslarger on Au than on SiO2. The enhancement is peculiarbecause the simulation results in Sec. IVD naively pre-dict that the V −B defect creation efficiency on Au is abouttwo times larger than on SiO2. This marked enhance-ment is due to the luminescence enhancement on Au. Ina previous study [27], for an h-BN flake with t ∼ 50 nm,the luminescence on Au is 10–15 times stronger than onSiO2. Thus, it is reasonable that Is increases about 20times more on Au than on SiO2.In contrast, the Is is only 2–3 times larger on Au thanon SiO2 for the device with t = 256 nm. This agreeswith the fact that the luminescence enhancement on Auis suppressed at an h-BN as thick as 200 nm [27]. Also,as discussed in Sec. IVD, a thick flake has no significantenhancement due to backscattering from the substrate inthe V −B defect creation.Finally, in Figs. 7(f) and (g), we compare Is per unitflake thickness, i.e., Is/t. In the devices on Au, the valueis maximized for t = 47 nm, being 1.6–5.4 times higherthan for t = 256 nm and 5.9–8.4 times higher than fort = 9 nm. This result is attributed to the compos-ite effects of the backscattering [Sec. IVD] and the t-dependent luminescence enhancement on Au [27]. In thedevices on SiO2, in contrast, Is/t is bigger for t = 256 nmthan for t = 47 nm. This is consistent with the fact thatthe depth at which most boron vacancies are created isD = 150–250 nm for an acceleration voltage of 30 keV,as shown in the top panel of Fig. 6(c). When the h-BNis very thin on SiO2, the He ion goes through withoutdefect creation.F. Optimum conditionsWe now summarize the results obtained so far and pro-vide guidelines for creating V −B spots using HIM.First, we discuss the choice of the substrate. The ad-vantage of selecting Au is that, even at a low dHe, theeffective dose increases due to significant backscatteringfor an h-BN flake with a thickness well below 256 nm.Additionally, Au significantly enhances the PL intensity,which is beneficial for high magnetic-field sensitivity. Theoptimum dose that maximizes sensitivity in the condi-tions investigated in this study is about 1016 cm−2 (TableII). The optimal condition could be further investigatedwith different spot sizes and acceleration voltages.ParametersSubstrate film AuHe ion dose, dHe (cm−2) 1016Acceleration voltage of He beam (keV) 30Sensitivity (µT/√Hz) 30.2TABLE II. Best sensitivity condition for V −B on 47 nm h-BN.On the other hand, the advantage of SiO2 is that SiO2causes less backscattering than Au, and a well-localized10spot can be created. The spot size is expected to besmaller than 10 nm for devices with a thickness of 47 nm[see Fig. 6(b)]. The optimum dose for this purpose is1017 cm−2, which gives a sensitivity of ∼ 250 µT/√Hz[Fig. 4(c)]. Further fine-tuning of dose and verification athigher doses may yield even better sensitivity. In prin-ciple, high localization and sensitivity can be obtainedsimultaneously by irradiating h-BN flakes on SiO2 withhelium ions to create V −B spots and then stamping themon Au.Second, we comment on the choice of flake thicknesst. Consider the case where flakes are sufficiently thin(say, t ≪ 256 nm) and irradiated at a given dHe; asshown in Fig. 6(c), in that case, the thicker the flake, themore the V −B defects are created. On the other hand,as the thickness increases, the spot size increases due tocollision processes inside the flake and the backscatteringat the substrate film (Au or SiO2). Fortunately, if we usean h-BN flake on Au, the luminescence enhancement issubstantial at t ∼ 50 nm, so there is no need to increasethe thickness of the flakes any further.V. CONCLUSIONTo conclude, we have investigated sensor parametersof V −B spots created using HIM under various conditions,fixing only the acceleration voltage of 30 keV. From theexperimental and simulation results, we obtain the fol-lowing three findings. First, we find the optimal dose forthe h-BN on Au to achieve high static magnetic field sen-sitivity. Second, the sensor performance depends on thesubstrates, Au and SiO2. The ion backscattering fromAu significantly affects sensor parameters such as strainE and spin relaxation time T1 for thin flakes. However,the effect of backscattering becomes negligible in a suffi-ciently thick flake. Third, based on simulations, the V −Bspot is localized more on SiO2 than on Au. These re-sults help optimize sensing configuration using V −B spotscreated with HIM. Notably, many of the discussions inthe present paper apply to general cases of V −B defectcreation using HIM and conventional ion irradiation.The original purpose of the present work is to improvethe effective spatial resolution of the stray magnetic fieldby localizing the sensor. The created quantum sensorsusing this approach allow adjustable and rigid determi-nation of the stand-off distance and in-plane position be-tween the quantum sensor and the target object. De-signing appropriate patterns for V −B spots is expected tocreate new probes for studying condensed matter-physicsusing nanosized quantum sensor spots, such as investigat-ing microscopic spatial correlations in magnetic materi-als [51]. As an application, arranging V −B spots in anarray and employing a high-performance camera couldenable simultaneous high-precision magnetic field imag-ing at multiple spots [29]. Moreover, by refining the anal-ysis methods, there is a possibility of independently ex-amining signals from spots that approach or surpass theoptical resolution.ACKNOWLEDGMENTSWe thank Tomohiko Iijima (AIST) for the usage ofAIST SCR HIM for the helium-ion irradiations, Toshi-hiko Kanayama (AIST) for helpful discussions since theintroduction of HIM at AIST in 2009, and Kohei M. Itoh(Keio University) for letting us use the confocal micro-scope system. This work was partially supported by JST,CREST Grant No. JPMJCR23I2, Japan; Grants-in-Aidfor Scientific Research (Grants No. JP24KJ0692, No.JP24KJ0880, No. JP23K25800, No. JP22K03524, No.JP22KJ1059, No. JP19H00656 and No. JP19H05826);“Advanced Research Infrastructure for Materials andNanotechnology in Japan (ARIM)” (Proposal No. JP-MXP1222UT1131) of the Ministry of Education, Cul-ture, Sports, Science and Technology of Japan (MEXT);the Mitsubishi Foundation (Grant No. 202310021);Kondo Memorial Foundation; JSR Corporation; DaikinIndustries, Ltd.; and the Cooperative Research Projectof RIEC, Tohoku University. K.W. and T.T. acknowl-edge support from the JSPS KAKENHI (Grants No.21H05233 and No. 23H02052) and World Premier In-ternational Research Center Initiative (WPI), MEXT,Japan. H.G., Y.N., and M.T. acknowledge financial sup-port from FoPM, WINGS Program, The University ofTokyo, and JSPS Young Researcher Fellowship. H.G.acknowledge financial support from JSR Fellowship, TheUniversity of Tokyo.[1] R. M. White, Quantum Theory of Magnetism (SpringerBerlin Heidelberg, 2007).[2] B. D. Cullity and C. D. Graham, Introduction to mag-netic materials (John Wiley & Sons, 2011).[3] J. M. Coey and S. S. Parkin, Handbook of magnetism andmagnetic materials (Springer International Publishing,2021).[4] K. S. Burch, D. Mandrus, and J.-G. Park, Magnetism intwo-dimensional van der waals materials, Nature 563, 47(2018).[5] O. Kazakova, R. Puttock, C. Barton, H. Corte-León,M. Jaafar, V. Neu, and A. Asenjo, Frontiers of magneticforce microscopy, Journal of Applied Physics 125, 060901(2019).[6] Z. Q. Qiu and S. D. Bader, Surface magneto-optic Kerreffect, Review of Scientific Instruments 71, 1243 (2000).[7] C. L. Degen, F. Reinhard, and P. Cappellaro, Quantumsensing, Reviews of Modern Physics 89, 035002 (2017).[8] F. Casola, T. van der Sar, and A. Yacoby, Probingcondensed matter physics with magnetometry based onhttps://doi.org/10.1007/978-3-540-69025-2https://doi.org/10.1038/s41586-018-0631-zhttps://doi.org/10.1038/s41586-018-0631-zhttps://doi.org/10.1063/1.5050712https://doi.org/10.1063/1.5050712https://doi.org/10.1063/1.1150496https://doi.org/10.1103/RevModPhys.89.03500211nitrogen-vacancy centres in diamond, Nature ReviewsMaterials 3, 17088 (2018).[9] J. M. Taylor, P. Cappellaro, L. Childress, L. Jiang,D. Budker, P. R. Hemmer, A. Yacoby, R. Walsworth, andM. D. Lukin, High-sensitivity diamond magnetometerwith nanoscale resolution, Nature Physics 4, 810 (2008).[10] G. Balasubramanian, I. Y. Chan, R. Kolesov, M. Al-Hmoud, J. Tisler, C. Shin, C. Kim, A. Wojcik, P. R. Hem-mer, A. Krueger, T. Hanke, A. Leitenstorfer, R. Brats-chitsch, F. Jelezko, and J. Wrachtrup, Nanoscale imagingmagnetometry with diamond spins under ambient condi-tions, Nature 455, 648 (2008).[11] C. L. Degen, Scanning magnetic field microscope with adiamond single-spin sensor, Applied Physics Letters 92,243111 (2008).[12] N. Hedrich, K. Wagner, O. V. Pylypovskyi, B. J. Shields,T. Kosub, D. D. Sheka, D. Makarov, and P. Maletinsky,Nanoscale mechanics of antiferromagnetic domain walls,Nature Physics 17, 574 (2021).[13] M. S. Wörnle, P. Welter, M. Giraldo, T. Lottermoser,M. Fiebig, P. Gambardella, and C. L. Degen, Coexistenceof Bloch and Néel walls in a collinear antiferromagnet,Physical Review B 103, 094426 (2021).[14] Y. Schlussel, T. Lenz, D. Rohner, Y. Bar-Haim,L. Bougas, D. Groswasser, M. Kieschnick, E. Rozenberg,L. Thiel, A. Waxman, J. Meijer, P. Maletinsky, D. Bud-ker, and R. Folman, Wide-field imaging of superconduc-tor vortices with electron spins in diamond, Physical Re-view Applied 10, 034032 (2018).[15] S. E. Lillie, D. A. Broadway, N. Dontschuk, S. C.Scholten, B. C. Johnson, S. Wolf, S. Rachel, L. C. L. Hol-lenberg, and J.-P. Tetienne, Laser modulation of super-conductivity in a cryogenic wide-field nitrogen-vacancymicroscope, Nano Letters 20, 1855 (2020).[16] S. Nishimura, T. Kobayashi, D. Sasaki, T. Tsuji,T. Iwasaki, M. Hatano, K. Sasaki, and K. Kobayashi,Wide-field quantitative magnetic imaging of supercon-ducting vortices using perfectly aligned quantum sensors,Applied Physics Letters 123, 112603 (2023).[17] A. Gottscholl, M. Kianinia, V. Soltamov, S. Orlin-skii, G. Mamin, C. Bradac, C. Kasper, K. Krambrock,A. Sperlich, M. Toth, I. Aharonovich, and V. Dyakonov,Initialization and read-out of intrinsic spin defects in avan der waals crystal at room temperature, Nature Ma-terials 19, 540 (2020).[18] A. Gottscholl, M. Diez, V. Soltamov, C. Kasper, A. Sper-lich, M. Kianinia, C. Bradac, I. Aharonovich, andV. Dyakonov, Room temperature coherent control of spindefects in hexagonal boron nitride, Science Advances 7,eabf3630 (2021).[19] A. Gottscholl, M. Diez, V. Soltamov, C. Kasper,D. Krauße, A. Sperlich, M. Kianinia, C. Bradac,I. Aharonovich, and V. Dyakonov, Spin defects in hBNas promising temperature, pressure and magnetic fieldquantum sensors, Nature Communications 12, 4480(2021).[20] D. Broadway, S. Lillie, S. Scholten, D. Rohner,N. Dontschuk, P. Maletinsky, J.-P. Tetienne, and L. Hol-lenberg, Improved current density and magnetizationreconstruction through vector magnetic field measure-ments, Phys. Rev. Appl. 14, 024076 (2020).[21] M. Huang, J. Zhou, D. Chen, H. Lu, N. J. McLaughlin,S. Li, M. Alghamdi, D. Djugba, J. Shi, H. Wang, andC. R. Du, Wide field imaging of van der waals ferromag-net fe3gete2 by spin defects in hexagonal boron nitride,Nature Communications 13, 5369 (2022).[22] A. J. Healey, S. C. Scholten, T. Yang, J. A. Scott, G. J.Abrahams, I. O. Robertson, X. F. Hou, Y. F. Guo,S. Rahman, Y. Lu, M. Kianinia, I. Aharonovich, andJ.-P. Tetienne, Quantum microscopy with van der waalsheterostructures, Nature Physics 19, 87 (2022).[23] P. Kumar, F. Fabre, A. Durand, T. Clua-Provost,J. Li, J. Edgar, N. Rougemaille, J. Coraux, X. Marie,P. Renucci, C. Robert, I. Robert-Philip, B. Gil, G. Cass-abois, A. Finco, and V. Jacques, Magnetic imaging withspin defects in hexagonal boron nitride, Physical ReviewApplied 18, L061002 (2022).[24] J. Zhou, H. Lu, D. Chen, M. Huang, G. Q. Yan,F. Al-matouq, J. Chang, D. Djugba, Z. Jiang,H. Wang, and C. R. Du, Sensing spin wave exci-tations by spin defects in few-layer-thick hexagonalboron nitride, Science Advances 10, eadk8495 (2024),https://www.science.org/doi/pdf/10.1126/sciadv.adk8495.[25] N.-J. Guo, W. Liu, Z.-P. Li, Y.-Z. Yang, S. Yu, Y. Meng,Z.-A. Wang, X.-D. Zeng, F.-F. Yan, Q. Li, J.-F. Wang,J.-S. Xu, Y.-T. Wang, J.-S. Tang, C.-F. Li, and G.-C.Guo, Generation of spin defects by ion implantation inhexagonal boron nitride, ACS Omega 7, 1733 (2022).[26] H. Gu, Y. Nakamura, K. Sasaki, and K. Kobayashi,Multi-frequency composite pulse sequences for sensitivityenhancement in hexagonal boron nitride quantum sensor,Applied Physics Express 16, 055003 (2023).[27] X. Gao, B. Jiang, A. E. L. Allcca, K. Shen, M. A.Sadi, A. B. Solanki, P. Ju, Z. Xu, P. Upadhyaya, Y. P.Chen, S. A. Bhave, and T. Li, High-contrast plasmonic-enhanced shallow spin defects in hexagonal boron nitridefor quantum sensing, Nano Letters 21, 7708 (2021).[28] S. Sarkar, Y. Xu, S. Mathew, M. Lal, J.-Y. Chung,H. Y. Lee, K. Watanabe, T. Taniguchi, T. Venkatesan,and S. Gradečak, Identifying luminescent boron vacan-cies in h-BN generated using controlled he+ ion irradia-tion, Nano Letters 24, 43 (2023).[29] K. Sasaki, Y. Nakamura, H. Gu, M. Tsukamoto, S. Naka-harai, T. Iwasaki, K. Watanabe, T. Taniguchi, S. Ogawa,Y. Morita, and K. Kobayashi, Magnetic field imaging byhBN quantum sensor nanoarray, Applied Physics Letters122, 244003 (2023).[30] H. Liang, Y. Chen, C. Yang, K. Watanabe, T. Taniguchi,G. Eda, and A. A. Bettiol, High sensitivity spin defectsin hbn created by high energy he beam irradiation, Ad-vanced Optical Materials 11, 2201941 (2022).[31] J. F. Ziegler, M. Ziegler, and J. Biersack, SRIM – thestopping and range of ions in matter (2010), Nuclear In-struments and Methods in Physics Research Section B:Beam Interactions with Materials and Atoms 268, 1818(2010).[32] T. Iwasaki, K. Endo, E. Watanabe, D. Tsuya, Y. Morita,S. Nakaharai, Y. Noguchi, Y. Wakayama, K. Watan-abe, T. Taniguchi, and S. Moriyama, Bubble-free transfertechnique for high-quality graphene/hexagonal boron ni-tride van der Waals heterostructures, ACS Applied Ma-terials & Interfaces 12, 8533 (2020).[33] G. Hlawacek, V. Veligura, R. van Gastel, andB. Poelsema, Helium ion microscopy, Journal of VacuumScience, Technology B, Nanotechnology and Microelec-tronics: Materials, Processing, Measurement, and Phe-nomena 32, 020801 (2014).[34] D. Misonou, K. Sasaki, S. Ishizu, Y. Monnai, K. M. Itoh,https://doi.org/10.1038/natrevmats.2017.88https://doi.org/10.1038/natrevmats.2017.88https://doi.org/10.1038/nphys1075https://doi.org/10.1038/nature07278https://doi.org/10.1063/1.2943282https://doi.org/10.1063/1.2943282https://doi.org/10.1038/s41567-020-01157-0https://doi.org/10.1103/PhysRevB.103.094426https://doi.org/10.1103/physrevapplied.10.034032https://doi.org/10.1103/physrevapplied.10.034032https://doi.org/10.1021/acs.nanolett.9b05071https://doi.org/10.1063/5.0169521https://doi.org/10.1038/s41563-020-0619-6https://doi.org/10.1038/s41563-020-0619-6https://doi.org/10.1126/sciadv.abf3630https://doi.org/10.1126/sciadv.abf3630https://doi.org/10.1038/s41467-021-24725-1https://doi.org/10.1038/s41467-021-24725-1https://doi.org/10.1103/PhysRevApplied.14.024076https://doi.org/10.1038/s41467-022-33016-2https://doi.org/10.1038/s41567-022-01815-5https://doi.org/10.1103/PhysRevApplied.18.L061002https://doi.org/10.1103/PhysRevApplied.18.L061002https://doi.org/10.1126/sciadv.adk8495https://arxiv.org/abs/https://www.science.org/doi/pdf/10.1126/sciadv.adk8495https://doi.org/10.1021/acsomega.1c04564https://doi.org/10.35848/1882-0786/acd1d1https://doi.org/10.1021/acs.nanolett.1c02495https://doi.org/10.1021/acs.nanolett.3c03113https://doi.org/10.1063/5.0147072https://doi.org/10.1063/5.0147072https://doi.org/10.1002/adom.202201941https://doi.org/10.1002/adom.202201941https://doi.org/10.1016/j.nimb.2010.02.091https://doi.org/10.1016/j.nimb.2010.02.091https://doi.org/10.1016/j.nimb.2010.02.091https://doi.org/10.1016/j.nimb.2010.02.091https://doi.org/10.1021/acsami.9b19191https://doi.org/10.1021/acsami.9b19191https://doi.org/10.1116/1.4863676https://doi.org/10.1116/1.4863676https://doi.org/10.1116/1.4863676https://doi.org/10.1116/1.486367612and E. Abe, Construction and operation of a tabletopsystem for nanoscale magnetometry with single nitrogen-vacancy centers in diamond, AIP Adv. 10, 025206 (2020).[35] L. Robledo, H. Bernien, T. van der Sar, and R. Han-son, Spin dynamics in the optical cycle of single nitrogen-vacancy centres in diamond, New Journal of Physics 13,025013 (2011).[36] A. Gupta, L. Hacquebard, and L. Childress, Efficient sig-nal processing for time-resolved fluorescence detection ofnitrogen-vacancy spins in diamond, Journal of the Opti-cal Society of America B 33, B28 (2016).[37] M. W. Doherty, N. B. Manson, P. Delaney, F. Jelezko,J. Wrachtrup, and L. C. Hollenberg, The nitrogen-vacancy colour centre in diamond, Physics Reports 528,1 (2013).[38] E. E. Kleinsasser, M. M. Stanfield, J. K. Q. Banks,Z. Zhu, W.-D. Li, V. M. Acosta, H. Watanabe, K. M.Itoh, and K.-M. C. Fu, High density nitrogen-vacancysensing surface created via He+ ion implantation of 12Cdiamond, Applied Physics Letters 108, 202401 (2016).[39] R. Gong, G. He, X. Gao, P. Ju, Z. Liu, B. Ye, E. A. Hen-riksen, T. Li, and C. Zu, Coherent dynamics of stronglyinteracting electronic spin defects in hexagonal boron ni-tride, Nature Communications 14, 3299 (2023).[40] A. Dréau, M. Lesik, L. Rondin, P. Spinicelli, O. Arcizet,J.-F. Roch, and V. Jacques, Avoiding power broadeningin optically detected magnetic resonance of single NVdefects for enhanced dc magnetic field sensitivity, Phys.Rev. B 84, 195204 (2011).[41] J. F. Barry, J. M. Schloss, E. Bauch, M. J. Turner, C. A.Hart, L. M. Pham, and R. L. Walsworth, Sensitivity op-timization for NV-diamond magnetometry, Reviews ofModern Physics 92, 015004 (2020).[42] K. Sasaki, T. Taniguchi, and K. Kobayashi, Nitrogen iso-tope effects on boron vacancy quantum sensors in hexag-onal boron nitride, Applied Physics Express 16, 095003(2023).[43] T. Clua-Provost, A. Durand, Z. Mu, T. Rastoin,J. Fraunié, E. Janzen, H. Schutte, J. H. Edgar, G. Seine,A. Claverie, X. Marie, C. Robert, B. Gil, G. Cassabois,and V. Jacques, Isotopic control of the boron-vacancyspin defect in hexagonal boron nitride, Physical ReviewLetters 131, 126901 (2023).[44] R. Gong, X. Du, E. Janzen, V. Liu, Z. Liu, G. He, B. Ye,T. Li, N. Y. Yao, J. H. Edgar, E. A. Henriksen, andC. Zu, Isotope engineering for spin defects in van derwaals materials, Nature Communications 15, 104 (2024).[45] Y. Matsuzaki, H. Morishita, T. Shimooka, T. Tashima,K. Kakuyanagi, K. Semba, W. J. Munro, H. Yamaguchi,N. Mizuochi, and S. Saito, Optically detected magneticresonance of high-density ensemble of NV centers in dia-mond, Journal of Physics: Condensed Matter 28, 275302(2016).[46] X. Gao, S. Vaidya, P. Ju, S. Dikshit, K. Shen, Y. P. Chen,and T. Li, Quantum sensing of paramagnetic spins inliquids with spin qubits in hexagonal boron nitride, ACSPhotonics 10, 2894 (2023).[47] E. K. Sichel, R. E. Miller, M. S. Abrahams, and C. J.Buiocchi, Heat capacity and thermal conductivity ofhexagonal pyrolytic boron nitride, Phys. Rev. B 13, 4607(1976).[48] S. Sze and K. N. Kwok, Mosfets, in Physics of Semi-conductor Devices (John Wiley and Sons, Ltd, 2006) pp.293–373.[49] R. Livengood, S. Tan, Y. Greenzweig, J. Notte, andS. McVey, Subsurface damage from helium ions as afunction of dose, beam energy, and dose rate, Jour-nal of Vacuum Science & Technology B: Microelectron-ics and Nanometer Structures Processing, Measurement,and Phenomena 27, 3244 (2009).[50] D. Fox, Y. Chen, C. C. Faulkner, and H. Zhang, Nano-structuring, surface and bulk modification with a focusedhelium ion beam, Beilstein Journal of Nanotechnology 3,579 (2012).[51] J. Rovny, Z. Yuan, M. Fitzpatrick, A. I. Abdalla, L. Fu-tamura, C. Fox, M. C. Cambria, S. Kolkowitz, and N. P.de Leon, Nanoscale covariance magnetometry with dia-mond quantum sensors, Science 378, 1301 (2022).https://doi.org/10.1063/1.5128716https://doi.org/10.1088/1367-2630/13/2/025013https://doi.org/10.1088/1367-2630/13/2/025013https://doi.org/10.1364/JOSAB.33.000B28https://doi.org/10.1364/JOSAB.33.000B28https://doi.org/https://doi.org/10.1016/j.physrep.2013.02.001https://doi.org/https://doi.org/10.1016/j.physrep.2013.02.001https://doi.org/10.1063/1.4949357https://doi.org/10.1038/s41467-023-39115-yhttps://doi.org/10.1103/PhysRevB.84.195204https://doi.org/10.1103/PhysRevB.84.195204https://doi.org/10.1103/revmodphys.92.015004https://doi.org/10.1103/revmodphys.92.015004https://doi.org/10.35848/1882-0786/acf7aahttps://doi.org/10.35848/1882-0786/acf7aahttps://doi.org/10.1103/PhysRevLett.131.126901https://doi.org/10.1103/PhysRevLett.131.126901https://doi.org/10.1038/s41467-023-44494-3https://doi.org/10.1088/0953-8984/28/27/275302https://doi.org/10.1088/0953-8984/28/27/275302https://doi.org/10.1021/acsphotonics.3c00621https://doi.org/10.1021/acsphotonics.3c00621https://doi.org/10.1103/PhysRevB.13.4607https://doi.org/10.1103/PhysRevB.13.4607https://doi.org/10.1116/1.3237101https://doi.org/10.1116/1.3237101https://doi.org/10.1116/1.3237101https://doi.org/10.1116/1.3237101https://doi.org/10.3762/bjnano.3.67https://doi.org/10.3762/bjnano.3.67https://doi.org/10.1126/science.ade9858 Systematic characterization of nanoscale h-BN quantum sensor spots created by helium-ion microscopy Abstract Introduction Experiments Device fabrication with h-BN flakes VB- defect creation using HIM Confocal microscope system Characterization of boron vacancy defects Results and Discussions Magnetic field sensitivity using ODMR Strain Spin relaxation time Monte Carlo simulations Photoluminescence Optimum conditions Conclusion Acknowledgments References