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Zilong Zhang, Keyun Gu, Zhijian Zhao, Zhengyan Lei, Yi-Hsiu Kao, [Meiyong Liao](https://orcid.org/0000-0003-1361-4266), Takahito Ono, Masaya Toda

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[Ultrasensitive and Reliable Diamond MEMS Magnetic Force Sensor with 3D Imaging at Room Temperature](https://mdr.nims.go.jp/datasets/20f8e9cb-da70-48b4-b4a8-0c4189371517)

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Ultrasensitive and Reliable Diamond MEMS Magnetic Force Sensor with 3D Imaging at Room TemperatureRESEARCH ARTICLEwww.advmattechnol.deUltrasensitive and Reliable Diamond MEMS Magnetic ForceSensor with 3D Imaging at Room TemperatureZilong Zhang, Keyun Gu, Zhijian Zhao, Zheng-Yan Lei, Yi-Hsiu Kao, Meiyong Liao,Takahito Ono, and Masaya Toda*Developing magnetic force sensors with a simple structure, high sensitivity,and exceptional reliability at room temperature remains challenging due tofrequency fluctuations and noise suppression issues. In this work, anultra-sensitive and highly reliable magnetic force sensor is presented byintegrating a single-crystal diamond (SCD) MEMS resonator with apermanent magnetic particle. The magnetic particle serves as the sensingelement, enabling precise detection of magnetic field gradients under a fieldbath. The SCD-based MEMS sensor exhibits outstanding performance,achieving an ultra-low detectable force of 1.8 × 10−16 N/Hz1/2, a highmagnetic sensitivity of 0.303%/(mT/mm), and a response time of 98.8 ms inthe first mode at room temperature. Notably, the resonant frequencyfluctuation is remarkably low, reaching 7.89 × 10−4 Hz at room temperature,ensuring stable and reliable operation. Furthermore, a 3D magnetic forceimaging sensor based on the SCD platform, capable of visualizing the 3Ddistribution of magnetic forces is demonstrated. This work lays a solidfoundation for the advancement of SCD MEMS-based magnetic imagingsensors, offering unparalleled sensitivity, reliability, and tunable spatialresolution for next-generation magnetic imaging applications.1. IntroductionMagnetic force sensors play a crucial role in various applica-tions, including precise measurements of magnetic fields, ma-terial properties, and forces in sensitive environments. Espe-cially, the weak magnetic force sensors have high sensitivityZ. Zhang, Z. Zhao, Z.-Y. Lei, Y.-H. Kao, T. Ono, M. TodaGraduate School of EngineeringTohoku University6-6-01 Aramaki-Aza-Aoba, Aoba-ku, Sendai, Miyagi 980-8579, JapanE-mail: toda@tohoku.ac.jpK.Gu,M. LiaoResearchCenter for Electronic andOpticalMaterialsNational Institute forMaterials Science (NIMS)1-1Namiki, Tsukuba, Ibaraki 305-0044, JapanThe ORCID identification number(s) for the author(s) of this articlecan be found under https://doi.org/10.1002/admt.202500470© 2025 The Author(s). Advanced Materials Technologies published byWiley-VCH GmbH. This is an open access article under the terms of theCreative Commons Attribution-NonCommercial License, which permitsuse, distribution and reproduction in any medium, provided the originalwork is properly cited and is not used for commercial purposes.DOI: 10.1002/admt.202500470and accuracy, which makes them es-sential for advancements in fields suchas medical diagnostics, aerospace, andindustrial automation.[1–3] Currentweak-force magnetic sensors, suchas atomic magnetometers, supercon-ducting quantum interference device(SQUID), magnetoresistive sensor,nitrogen-vacancy (NV) sensor, and reso-nant magnetic force sensors, are widelyutilized. Highly sensitive magneticsensor, known as SQUID, is exten-sively utilized in detecting biomagneticsignals from human organs. But theSQUID requires cryogenic cooling withcomplex equipment and is suscepti-ble to electromagnetic interference.[4]Magnetoresistive sensors are compact,highly sensitive, and easily integratedinto electronic systems, but they aresensitive to temperature variations andexternal magnetic disturbances.[5,6] ForNV sensors, they can achieve a highsensitivity of aN/Hz1/2 level. But they aredifficult to control and integrate with other electronics.[7–9]Atomic magnetometers offer exceptional sensitivity in detectingweak magnetic fields but are prone to environmental noises andrequire careful shielding for optimal performance.[10]Magnetic resonance force microscopy (MRFM) employs acantilever-type resonant magnetic force sensor that convertsmagnetic forces into measurable displacements or frequencychanges, offering exceptional spatial resolution and the abilityto probe nanoscale structural phenomena. However, it is lim-ited by complex setups, environmental noise, and slow opera-tional speed.[11–13] Typically, the state-of-the-art silicon resonatorscan achieve force sensitivities of 10−16 N/Hz1/2 at room temper-ature and 10−18 N/Hz1/2 at millikelvin temperatures.[14] In or-der to achieve high force sensitivity (≈zN/Hz1/2), advancementshave been made in the development of vertical structure de-vices at low temperatures, including suspended carbon nanotubeoscillators,[2] silicon nanowires,[15] and trapped ion oscillators.[1]These innovations represent significant progress in the field.Magnetic force sensors typically operate at low temperatures,where reduced thermal noise and higher quality (Q) factor signif-icantly improve their performance.[16,17] However, most practicalapplications require room-temperature operation, where mag-netic force sensors offer notable advantages.[18] These includethe elimination of uneconomical and complex cryogenic coolingAdv. Mater. Technol. 2025, 2500470 2500470 (1 of 10) © 2025 The Author(s). Advanced Materials Technologies published by Wiley-VCH GmbHhttp://www.advmattechnol.demailto:toda@tohoku.ac.jphttps://doi.org/10.1002/admt.202500470http://creativecommons.org/licenses/by-nc/4.0/http://crossmark.crossref.org/dialog/?doi=10.1002%2Fadmt.202500470&domain=pdf&date_stamp=2025-05-12www.advancedsciencenews.com www.advmattechnol.desystems, simpler operation, and compatibility with portable andwearable devices. A promising approach involves resonant mag-netic force sensors with mechanical resonators, which convertweak forces into resonance frequency shifts. This design mini-mizes thermal noise and mechanical drift, ensuring high stabil-ity and scalability while enabling precise force measurements atultra-low levels, even at room temperature. Currently, most res-onant magnetic force sensors are fabricated from silicon, whichsuffers from oxidation and limited reliability under demandingconditions. These limitations highlight the need for more robustmaterials to improve sensor performance and durability in vari-ous applications.Single-crystal diamond (SCD), a distinctive semiconductormaterial for micro-electromechanical systems (MEMS) devices,has attracted significant interest due to its remarkable proper-ties, such as excellent thermal conductivity, chemical stability,and biocompatibility. These characteristics make diamond anideal substrate for resonant magnetic force sensors, enablinghigh resonant frequency and high Q factor, while improvingdurability and reliability in dynamic operating conditions.[19,20]Neodymium-Iron-Boron (NdFeB) particles are known for theirhigh magnetic energy density, strong coercivity, excellent rema-nence, and temperature stability, making them well-suited forhigh-performance MEMS magnetic sensors that require stablemagnetic fields. Additionally, the magnetic field gradient effect,arising from the interaction between a material’s magnetic mo-ment and an external magnetic field, is particularly advantageousfor high-frequency operations, offering exceptional sensitivity tosmall magnetic forces.In this work, we introduce a novel magnetic force imagingsensor that integrates a diamond MEMS resonator with an Nd-FeB magnetic particle, utilizing the magnetic field gradient ef-fect. The magnetic particle is positioned at the tip of the SCDMEMS resonator. By combining the exceptional properties ofSCDMEMS with the strong magnetic interactions of NdFeB par-ticles, the sensor achieves enhanced magnetic force response.The sensor demonstrates outstanding performance, including alow detectable force of 1.80× 10−16 N/Hz1/2, a highmagnetic sen-sitivity of 0.303%/(mT/mm), and a response time of 98.8 ms inthe first mode. Additionally, the resonant frequency fluctuationreaches an ultralow value of 7.89 × 10−4 Hz at room temperature.A 3D magnetic force imaging sensor based on the SCD-basedplatform was also developed to map 3D magnetic force distribu-tions. This work presents a promising approach for designinghigh-performance MEMS magnetic force sensors with reliableand facile structures, showcasing their potential for applicationsrequiring precise and stable magnetic force measurements.2. Results and Discussion2.1. Device Concept and AssemblyThe SCD cantilevers were fabricated by a smart-cutmethod[21] based on the ion-implantation assisted lift-off(IAL) technology[22]. It initiated with the ion-implantation intohigh temperature and high pressure (HTHP) type-Ib (100) SCDsubstrate with root mean square (RMS) surface roughness lowerthan 1 nm. The fabrication process is shown in detail in FigureS1 (Supporting Information). The growth of the SCD epilayerwas accomplished by using a microwave plasma chemical vapordeposition (MPCVD) system. The advantages of the epilayergrowth are 1) the great enhancement in crystal quality of dia-mond compared to HTHP diamond, and 2) the accurate controlof the thickness of the diamond resonator. The ion-damagedlayer was converted to a graphite-like layer during the CVDgrowth process.The SCD resonators provide a high-reliability, compact, andadvanced platform for fabricating high-performance magneticsensors. By integrating the SCD cantilever with a NdFeB perma-nent magnetic particle, we realize a magnetic force sensor withenhanced functionality. NdFeB particles exhibit a unique combi-nation of high magnetic energy density, strong coercivity, excel-lent remanence, and exceptional temperature stability, makingthem ideal for high-performance MEMS magnetic force sensorsoperating in magnetic field gradients. These gradients are par-ticularly suited for high-frequency applications and exhibit highsensitivity to small magnetic forces.By combining the properties of SCD and NdFeB particles, weleverage their strengths to develop highly sensitive and reliabledevices. In this work, we present a magnetic force sensor de-signed to detect weakmagnetic fields, utilizing an SCD resonatorcoupled with an NdFeB particle, as illustrated in Figure 1a. Tofacilitate heterogeneous integration and lay the foundation forfuture functional expansion, the fabricated diamond cantileverwas transferred to the edge of a Si substrate. A glass needle isutilized to cut the as-fabricated SCD cantilever on the SCD sub-strate to form the free SCD cantilever. Subsequently, a glass nee-dle controlled by a micromanipulator is used to transfer the freeSCD cantilever onto a Si substrate, as shown in Figure 1a. Thisnon-destructive transfer method ensures the precise and stablerelocation of the SCD cantilever, which is then secured with asmall amount of conductive glue. The NdFeB particle was se-curely attached to the tip of the SCD cantilever using a smallamount of conductive adhesive. The 2D Raman imaging tech-nique enables precise assessment of the quality of the SCD epi-layer. The peak position (Ppeak) was determined by fitting the Ra-man spectra of each measurement point with a Lorentzian func-tion. The full width at half maximum (FWHM) was obtained byevaluating the dispersion of the Raman spectra using the sameLorentz fitting. The average Ppeak and FWHMvalues were derivedfrom the corresponding histograms by applying a Gaussian func-tion fitting. The Raman Ppeak and FWHM 2D images of a 120μm-long diamond cantilever are shown in Figure 1b. The his-tograms for Ppeak and FWHM are presented in Figure 1c,d, re-spectively, with the color bars in Figure 1b indicating the valueranges for both Ppeak and FWHM. While the measured area con-tains a small region with defective SCD epilayer, the average Ppeakfor the area is 1332.62 cm−1. The crystal quality of the epilayercan be evaluated through the FWHM of the Raman spectra. Asshown in Figure 1d, the average FWHM for the measured areais 1.84 cm−1, which is lower than that of the high-pressure andhigh-temperature (HPHT) substrate before the ion implantation,which is 2.15 cm−1 (Figure S2, Supporting Information). The re-duced FWHM of the epilayer compared to the original HPHTsubstrate is attributed to the improved crystalline quality of theepilayer. TheHTHP substrate inherently contains defects such asdislocations or strain fields, which broaden the Raman peak. Incontrast, theMPCVDgrowth process yields a high-purity epilayerAdv. Mater. Technol. 2025, 2500470 2500470 (2 of 10) © 2025 The Author(s). Advanced Materials Technologies published by Wiley-VCH GmbH 2365709x, 0, Downloaded from https://advanced.onlinelibrary.wiley.com/doi/10.1002/admt.202500470 by Meiyong Liao - National Institute For , Wiley Online Library on [10/07/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advmattechnol.dewww.advancedsciencenews.com www.advmattechnol.deFigure 1. Fabrication process and sensing principle of single-crystal diamond (SCD)-based magnetic force sensor. a) Illustration of the fabricationmethod of integrating an SCD resonator with a permanent magnetic particle for a magnetic force sensor. The SCD resonator was fixed on the Siliconsubstrate, and the particle was put on the tip of the SCD resonator via the conductive glue. b) 2D mapping of the Raman Ppeak and full width halfmaximum (FWHM) of a 120 μm-length diamond cantilever. c) Histogram distribution of Raman Ppeak. d) Histogram distribution of FWHM. e) Opticalimage of a 120 μm length-magnetic force sensor through coupling a SCD cantilever with an NdFeB particle. f) Magnetic force sensing principle ofthe SCD-based magnetic force sensor. The magnetic force, stemmed from the interaction of the magnetic field gradient and the permanent magneticparticle, is employed for tuning the resonance frequency of this SCD-based sensor. The resonance frequency can shift toward high frequency and lowfrequency due to the repulsion force and attraction force, respectively.with lower defect density and reduced internal stress, resulting ina small FWHM. For a one-clamped rectangular micro-resonatorwithout an external force, the resonance frequencymode is givenby:[23,24]f = k tL2√E𝜌(1)where k takes the values 0.162 and 1.013 for the first and sec-ond vibration modes, respectively. E and 𝜌 represent the effec-tive Young’s modulus and the effective mass density of the can-tilever, respectively, while t and L denote its thickness and length,respectively. Alternatively, the minimum detectable force of theresonator, as limited by thermomechanical noise, can also be ex-pressed as:[14,25]Fmin = t√wlQ4√E𝜌√kBTB (2)kB, T, and B represent the Boltzmann constant, temper-ature, and bandwidth, respectively. The magnetic sensingmechanism relies on the interaction between a magneticparticle affixed to the cantilever tip and an external mag-netic field oriented perpendicular to the cantilever’s plane,as illustrated in Figure 1e. The as-transferred diamond can-tilever has a width of 10 μm and a thickness of 700 nm.The magnetic force exerted on the particle is expressed asfollows:[13,26]F = mz𝜕B𝜕z(3)The particle possesses a magnetic moment, mz, which alignswith an external magnetic field. This magnetic moment, a vectorrepresenting the particle’s magnetization M, can be calculatedby multiplying the magnetization of the particle by its volume V.Adv. Mater. Technol. 2025, 2500470 2500470 (3 of 10) © 2025 The Author(s). Advanced Materials Technologies published by Wiley-VCH GmbH 2365709x, 0, Downloaded from https://advanced.onlinelibrary.wiley.com/doi/10.1002/admt.202500470 by Meiyong Liao - National Institute For , Wiley Online Library on [10/07/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advmattechnol.dewww.advancedsciencenews.com www.advmattechnol.deThe relationship is given by the equation: mz = MV. The mag-netic force gradient can be expressed as:F′z =dFzdz= mz𝜕2B𝜕2z(4)It is noted that the change in the spring constant arisesnot from a static magnetic force, but from the magneticforce gradient acting on the vibrating NdFeB particle. Thisgradient, F’z, directly modifies the effective restoring forceexperienced by the cantilever during oscillation, thereby al-tering its effective spring constant, keff. It is described bythe equation:keff = k + F′z (5)Consequently, the resonance frequency shift Δf of the Nd-FeB/SCD sensor, resulting from the magnetic force, is pre-sented as (the detailed derivation is given in SupportingInformation):Δf = fB − f0 ≈ −f0F′z2k(6)f0 and fB represent the resonance frequencies of the sensor inthe absence and presence of a magnetic field gradient, respec-tively. Alternatively, the magnetic sensitivity can be defined bythe resonance shift in the sensor’s response to varying mag-netic field gradients, as shown in Figure 1f. The resonance fre-quency of the sensor can shift toward high frequency and lowfrequency under the repulsion force and attraction force, respec-tively. The magnetic sensitivity is characterized by the expres-sions as follows: |Δf/(f0∂B/∂z)|. The ∂B/∂z indicates the mag-netic field gradient. The SCD-based MEMS resonator, utiliz-ing the magnetic field gradient effect, offers a promising sys-tem for a high-sensitivity and high-reliability magnetic forcesensor.2.2. Effect of Transfer Method on Vibration PerformanceThe vibration performance and magnetic sensing were exam-ined through the laser optical system based on the Doppler ef-fect. Figure 2a exhibits the measurement setup for the magneticforce sensor. The magnetic field gradients were generated via acoil connected to a DC source. The as-transferred SCD resonatorexhibits good vibration performance with a resonance frequencyof 172.592 kHz and a Q factor of 3500, as shown in Figure 2b.It is disclosed that the transferred method via the glass needleoffers a useful and facile way to transfer the SCD resonator toheterogeneous substrates. In addition, the Q factor is enhancedfrom 3500 to 6400 through the combination of a magnetic parti-cle on the tip of the SCD cantilever (Figure 2b,c). The increase inQ factor after magnetic particle integration can be attributed toa combination of mechanisms, including the added mass effectand dissipation dilution. The presence of the particle introduceslocalized strain, which modifies the mode shape and reduces in-trinsic energy dissipation, leading to an overall enhancement inQ factor.[27–30] The resonance frequency of the SCD cantilever sig-nificantly shifts toward a lower frequency by integrating with aparticle. Based on Equation (2), the spring constant and themini-mum detectable force (per unit bandwidth) of the magnetic forcesensor are 9.0 × 10−3 N m−1 and 1.8 × 10−16 N/Hz1/2 at roomtemperature. Figure 2d,e shows the relationship between the res-onance spectrum and actuation voltage of the SCD cantileverwithout and with a magnetic particle, respectively. The peak am-plitude of the resonance frequency exhibits a linear dependenceon voltage (the insets of Figure 2d,e). Alternatively, the magneticproperties of the NdFeB magnetic particle were examined by thevibrating sample magnetometer (VSM). This magnetic particlewas magnetized by a uniform magnetic field before the VSMmeasurement. The hysteresis loop of themagnetic particle is dis-played in Figure 2f. The coercive fieldHc and the saturationmag-netization Ms of the particle are 1333.1 Oe and 111.9 emu g−1,respectively. This Ms is similar to that of 116 emu g−1 of Nd-FeB particle.[31,32] The higher magnetic energy product (BH)maxof this particle can achieve a value that contributes to highmagnetic sensing response of the NdFeB/SCD magnetic forcesensor2.3. Magnetic Force SensingThe SCD MEMS resonator coupled with an NdFeB particle wasemployed formagnetic sensing through themagnetic field gradi-ent effect. The sensor architecture guarantees both excellent sta-bility and high sensitivity, attributable to 1) the robust, thermal-stable SCD resonator with a temperature coefficient of resonancefrequency (TCF) lower than 5 ppm K−1[19,33] and 2) the outstand-ing magnetic properties of the NdFeB particle. The dependenceof relative resonance frequency shift on magnetic field gradient,|Δf/(f0∂B/∂z)|, was utilized to indicate the magnetic sensitivityof the SCD-based sensor. In this work, we observed two vibra-tion modes (the first mode and the second mode) of this SCD-based magnetic sensor. The magnetic particle is located at theresonator tip, as shown in Figure 1a, which serves as an antin-ode for the first vibration mode but not for the second vibrationmode. In the first mode, the resonator exhibits a simpler andmore uniform motion, resulting in larger vibration amplitudesat the magnetic particle’s position. This enhances the couplingbetween themagnetic particle and the resonator, thereby increas-ing the sensor’s sensitivity to weak magnetic forces. In contrast,in the second mode, the magnetic particle is not positioned at anantinode and therefore experiences smaller vibration amplitudes.The increased stiffness and more complex displacement profileof this mode further limit its sensitivity to small variations inmagnetic force. Figure 3a,b shows the resonance frequency spec-tra shift of the 1st mode and 2nd mode of the SCD-based mag-netic sensor caused by applying various magnetic field gradientsat room temperature, respectively. The amplitudes of the spectraare normalized. Within the positive field gradient range, the fre-quency shift toward low frequency, showcasing the occurrenceof attraction force on the particle. While the frequency moves to-ward high frequency under negative field gradients, meaning theapplied repulsion force on the particle Figure S3 (Supporting In-formation). Totally, it is elucidated that the resonance frequencyshift increases with themagnetic field gradients. TheQ factors ofthese two modes of the SCD-based magnetic sensor exhibit weakchange with varying magnetic field gradients (Figure 3c,d).Adv. Mater. Technol. 2025, 2500470 2500470 (4 of 10) © 2025 The Author(s). Advanced Materials Technologies published by Wiley-VCH GmbH 2365709x, 0, Downloaded from https://advanced.onlinelibrary.wiley.com/doi/10.1002/admt.202500470 by Meiyong Liao - National Institute For , Wiley Online Library on [10/07/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advmattechnol.dewww.advancedsciencenews.com www.advmattechnol.deFigure 2. a) Schematic image of measurement setup for vibration and magnetic sensing. b,c) Resonance spectra of the as-transferred SCD resonatorwithout and with a particle, respectively. d,e) Dependences of resonance spectra of the SCD resonator without and with a magnetic particle on theactuation voltage applied to the PZT actuator, respectively. f) In-plane hysteresis loopmeasured by VSM at room temperature of the permanent magneticparticles.Through the resonance spectra response to field gradients, thedependences of resonance frequencies of the 1st mode and the2nd mode of the magnetic force sensor on field gradient areexhibited in Figure 4a,b. It can be seen that the resonance fre-quency shifts linearly increase with magnetic field gradients.The slopes of plots are 70.3 and 231.9Hz/(mT/mm) for the 1stmode and the 2nd mode, respectively. According to the sen-sitivity expression, the magnetic sensitivity of the 1st modeis 0.303%/(mT/mm), surpassing the 2nd mode’s sensitivity of0.157%/(mT/mm). This indicates that the magnetic sensitivityof the sensor cannot be effectively enhanced by employing the2nd mode, which is attributed to the impact of the vibration ofthe magnetic particle within these two vibration modes on themagnetic sensitivity. Compared to the 2nd mode, the 1st modeexhibits larger displacement amplitudes under the same forceand typically benefits from a higher Q factor, leading to lowerenergy dissipation. These characteristics enhance the sensitivityand reduce the minimum detectable force, making the 1st modepreferable for high-resolution magnetic force detection. In sens-ing applications, the smallest detectable frequency shift, Δfmin,depends on the accuracy of the resonance frequency measure-ment system. Therefore, identifying and quantifying any noisethat affects the frequency stability of the resonator is essentialfor sensor design.[34] In this work, the Allan deviation is a sta-tistical measure used to quantify the frequency stability of theSCD-based resonant sensor over different averaging times. It isdefined as the square root of the Allan variance, which is givenby:[34,35]𝜎A (𝜏) =√12 (N − 1)∑N−1i=1(fi+1 − fi)2(7)where N represents the total number of resonance frequencysamples, f1, f2,…, fN, each calculated as an average over the inte-gration time 𝜏. The Allan deviation of the 1st mode and the 2ndAdv. Mater. Technol. 2025, 2500470 2500470 (5 of 10) © 2025 The Author(s). Advanced Materials Technologies published by Wiley-VCH GmbH 2365709x, 0, Downloaded from https://advanced.onlinelibrary.wiley.com/doi/10.1002/admt.202500470 by Meiyong Liao - National Institute For , Wiley Online Library on [10/07/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advmattechnol.dewww.advancedsciencenews.com www.advmattechnol.deFigure 3. a,b) Resonance spectrum shifts of the 1st mode and 2nd mode of the SCD-based sensor upon positive magnetic field gradients, respectively.c,d) Q factor variations of the 1st mode and 2nd mode of the SCD-based sensor without and with applying magnetic field gradients, respectively.mode of the magnetic force sensor are presented in Figure 4c,d.The analysis reveals that the minimum frequency fluctuations,Δfmin of the 1stmode and the 2ndmode are 7.89× 10−4 and 2.76×10−2 Hz, respectively. Using the plot slopes in Figure 4a, themini-mumdetectablemagnetic field gradients are calculated to be 1.12× 10−5 and 1.19 × 10−4 mT mm−1 for the 1st mode and the 2ndmode, respectively. Furthermore, based on Equation (3), themin-imum detectable forces at room temperature are determined tobe 6.32 × 10−14 and 6.70 × 10−13 N for the 1st mode and the 2ndmode, respectively. For themagnetic force sensor, which consistsof an SCD cantilever coupled with a magnetic particle, the 1stmode demonstrates superior performance in achieving a mini-mal frequency shift and higher force detection sensitivity. Table 1displays the sensing performances of representative magneticforce sensors with a resonator-based structure. It is revealed thatat room temperature, the present SCD-basedmagnetic force sen-sor in our work exhibits excellent force sensitivity and low de-tection force limitation. Moreover, as indicated by Equation (2),reducing the thickness and achieving a higher Q factor in theSCD-based resonator significantly enhances the detection forceof the resonator-based sensor. By reducing the thickness of theresonator to below 100 nm while maintaining a Q factor of onemillion, the sensor is expected to reach a magnetic force sensi-tivity as low as ≈aN/Hz1/2. However, a thinner resonator mayexperience a decline in Q factor due to the surface friction.[14,36]Therefore, careful consideration is required to balance the trade-off between reducing thickness and preserving a high Q factor.Alternatively, the response times of the sensor are evaluated byintermittently applying a magnetic field gradient, allowing foran assessment of its performance under dynamic conditions, asshown in Figure 4e,f. The magnetic field gradient was gener-ated using a coil driven by a DC voltage from a signal generator,and was manually switched on and off with a 4-s interval. Thesensor exhibits response times of 98.8 ms for the 1st mode and164.8 ms for the 2nd mode, highlighting the faster response ofthe 1st mode.2.4. Magnetic Force ImagingMagnetic force imaging sensors play a vital role in detectingnanoscale magnetic field distributions with exceptional sensitiv-ity and spatial resolution. They are essential tools for advancingmaterial characterization, biomedical diagnostics, and quantumtechnology applications.[2,16] Among these, diamond-based sen-sors stand out for their remarkable durability in extreme envi-ronments and their seamless integration with cutting-edge imag-ing techniques. In this work, a mechanical force technique basedon magnetic field gradient is utilized to image the 3D magneticforce distributions. The present magnetic force sensor consistsof an SCD MEMS resonator coupled with a permanent mag-netic particle (NdFeB). The magnetic fields are generated by ashaped magnet (3 × 3 × 3 mm3). The 3D magnetic force imag-ing was conducted by manually moving the magnet, using a 3Dmotorized stage with an interval of 1 mm in the xoy coordinateplane, as shown in Figure 5a. The recorded magnetic responseat each position was used to directly generate the 3D map us-ing the visualization software, without additional reconstruction.Adv. Mater. Technol. 2025, 2500470 2500470 (6 of 10) © 2025 The Author(s). Advanced Materials Technologies published by Wiley-VCH GmbH 2365709x, 0, Downloaded from https://advanced.onlinelibrary.wiley.com/doi/10.1002/admt.202500470 by Meiyong Liao - National Institute For , Wiley Online Library on [10/07/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advmattechnol.dewww.advancedsciencenews.com www.advmattechnol.deFigure 4. a,b) Dependences of resonance frequency shift of the 1st mode and 2nd mode of the SCD-based sensor upon magnetic field gradients,respectively. The magnetic sensitivity can be expressed in two ways, as indicated by the slopes of the plots. c,d) Allan deviations of the 1st mode and2nd mode of the SCD-based sensor, respectively. The minimum resonance frequency fluctuation can be obtained at the lowest point of the curves. e,f)Response times of the 1st mode and 2nd mode of the SCD-based sensor to the magnetic field gradient of 5.75 mT m−1.Each red square represents each movement coordinate position(Figure 5a). Initially, the distance between the magnetic forcesensor and the magnet is Z0 = 10 mm. For the 3D force imag-ing, this distance changes from Z0, Z0 + 1 mm, to Z0 + 2mm. Figure 5b,c exhibits the resonance spectra shift with chang-ing x coordinate position as the y = 0 mm and Z = Z0 = 10mm. The peak amplitude of each resonance spectrum is nor-malized. It is disclosed that the resonance frequency varies withdifferent x coordinate positions and the Q factor can maintaina week change with the sensor movement. The dependences ofthe resonance frequency shifts response to magnetic field gra-dients on the coordinate positions was calculated via the res-onance spectra changes. Based on the magnetic sensitivity of70.24Hz/(mT/mm) for the 1st mode of the magnetic sensor, themagnetic field gradient, (dB/dz)(x ,y) for a specific coordinate posi-tion (x, y) is calculated with the known resonance frequency shift,Δf(x, y). Through Equation (3), the magnetic force, F(x, y), for thiscoordinate position is evaluated. Figure 5d–f showcases the mag-netic force distributions of a 10 × 10 mm2 area detected by theSCD-based magnetic force sensor with the Z coordinate varyingas Z0, Z0 + 1 mm, and Z0 + 2 mm. The magnetic force decreaseswith the distance between the sensor and the magnet increasing(Figure 5d–f). It is disclosed that the minimum detectable mag-netic force achieves a low value of 5.5 pN at room temperature.The magnetic force sensor made of an SCD resonator with a par-ticle is capable of realizing 3D magnetic force with ≈pN forcelevel, which hosts the promising potential in detecting biologi-cal molecules, for example, DNA molecules.[3,41] The spatial res-olution and actual detectable force level are constrained by themovement method. Considering the minimum detectable mag-netic force for this sensor, it can achieve the fN force level forimaging.Adv. Mater. Technol. 2025, 2500470 2500470 (7 of 10) © 2025 The Author(s). Advanced Materials Technologies published by Wiley-VCH GmbH 2365709x, 0, Downloaded from https://advanced.onlinelibrary.wiley.com/doi/10.1002/admt.202500470 by Meiyong Liao - National Institute For , Wiley Online Library on [10/07/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advmattechnol.dewww.advancedsciencenews.com www.advmattechnol.deTable 1. Comparison of magnetic force sensing performances of various resonator-based sensors.Materials Structure Principle f [Hz] Q Sensitivity[N/Hz1/2]Limitation[N]Temperature[°C]Refs.Si/NdFeB NEMS(mirror)MRFM 5746 4900 1.3 × 10−15 – 25 [18]Si/NdFeB MEMS(cantilever)MRFM 1640 230 1.1 × 10−13 – 25 [37]Si/NdFeB NEMS(mirror)MRFM 8000 5000 1.9 × 10−16 – 25 [38]Si NEMS(cantilever)MRFM 4976 150000 0.82 × 10−18 – −273.13(220 mK)[39]Si/Diamond NEMS(nanowire)MRFM 7600 130000 2.5 × 10−18 – −269.15 [40]Diamond NEMS MRFM 32140 1510000 0.54 × 10−18 – −273.14(100 mK)[14]Si/Fe NEMS(cantilever)Torque 33977 12000 3.6 × 10−16 4.6 × 10−13 25 [26]Diamond/NdFeBMEMS(cantilever)Field gradient 23170 6400 1.8 × 10−16 6.3 × 10−14 25 This work3. ConclusionIn this work, we developed a highly sensitive and reliablemagnetic force sensor by integrating a SCD MEMS resonatorwith a permanent magnetic particle. The magnetic particleserved as a sensing head, enabling the detection of magneticfield gradients. The SCD-based MEMS magnetic transducerdemonstrated exceptional performance, achieving a low de-tectable force of 1.8 × 10−16 N/Hz1/2, a high magnetic sensi-tivity of 0.303%/(mT/mm), and a response time of 98.8 msin the first mode. Additionally, the resonant frequency fluctua-tion reaches an ultralow value of 7.89 × 10−4 Hz at room tem-perature. To extend its capabilities, we developed a 3D mag-netic force imaging sensor on the SCD platform, enabling vi-sualization of magnetic force distributions in three dimensions.The magnetic sensing performance can be further enhancedby reducing the thickness of the resonator to less than 100nm while maintaining a high Q factor. This work establishesa foundation for advanced magnetic imaging sensors basedon SCD MEMS resonators integrated with permanent mag-netic particles. Owing to its high sensitivity, spatial resolution,and ambient operability, this sensor holds promise for a rangeof applications such as magnetic resonance imaging (MRI)-inspired sensing, non-invasive biomedical magnetic detection,and localized field mapping in microelectronic and spintronicsystems.4. Experimental SectionFabrication Process for High Q-Factor Diamond Micro-Cantilevers: Inthis work, SCD microresonators were fabricated using the smart-cuttechnique.[19,20] The process began with the growth of a diamond epilayeron HtTHP SCD substrates. Before diamond deposition, the HTHP SCDsubstrates underwent thorough cleaning, which included boiling in a mix-ture of acids (H2SO4 +HNO3), followed by rinsing with acetone, ethanol,and deionized water. Following cleaning, the carbon ions with an energy of180 keV and a dose of 1016 cm−2 were implanted into the substrates. SCDepilayers were then deposited onto these ion-implanted substrates usinganMPCVD system. The specific parameters for theMPCVDprocess were amethane concentration of 0.5%, a hydrogen flow of 500 sccm, amicrowavepower of 1 kW, a working temperature of 840 °C, and a growth duration of3 h. During growth, a graphite-like layer≈200 nm thick formed beneath thediamond surface due to the ion implantation treatment. This layer servedas a sacrificial layer to facilitate the release of the resonator structure. Next,a 150 nm-thick aluminum film was deposited onto the SCD epilayer, act-ing as a metal mask for patterning the epilayer.[24] The patterned SCD wasthen dry-etched using reactive ion etching (RIE) with an inductively cou-pled plasma (ICP) system in a pure oxygen environment. To complete theresonator structure, the metal mask was removed by boiling the samplesin an acid mixture (H2SO4 + HNO3).After the fabrication process, the SCD sample was annealed at 1100 °Cfor 3 h under ultrahigh vacuum conditions (<10−7 Pa) to reduce de-fects caused by ion implantation, thus enhancing the Q-factors of theresonators. However, the presence of a non-diamond layer resulting fromion implantation still limited the Q-factor. To address this, oxygen etchingwas employed to effectively remove defective surface layers, including non-diamond and other imperfections.[42] These surface imperfections had asignificant impact on the resonator’s performance. Following this treat-ment, the resonators were annealed again at 650 °C for 10 h in an oxygenenvironment to further improve Q-factors.A Smart Method for Transferring a Free Resonator or a Particle on Hetero-Substrates: The magnetic force sensor was configured by coupling anSCD MEMS resonator with an NdFeB particle, as illustrated in Figure 1a.The free SCD cantilever stems from the as-fabricated SCD cantilever on theSCD substrate, which was cut by a glass needle. Then, through an opticalmicroscope, a glass needle controlled by a micromanipulator was utilizedto pick up the free SCD cantilever from the Si substrate. The SCD can-tilever was precisely and stably transferred via this non-destructive transfermethod, and fixedwith a small amount of conductive glue. The sample washeated up to 180 °C to fix the SCD cantilever on the Si substrate. After theabove process, a 14 μm-diameter NdFeBmagnetic particle was also pickedup and placed on the tip of the SCD cantilever using a glass needle. Thetransferred method is similar to that of the free SCD cantilever. Prior to thevibrating sample magnetometer (VSM) measurement, the NdFeB particlewas in an annealed state and magnetized using a 694 mT magnetic field.The magnetic moment, which is a vector quantity of the magnetizationmof the magnetic particle, can be calculated from the magnetization M ofthe particle and the volume of the magnetic particle V, using the followingequation of m =MV.Adv. Mater. Technol. 2025, 2500470 2500470 (8 of 10) © 2025 The Author(s). Advanced Materials Technologies published by Wiley-VCH GmbH 2365709x, 0, Downloaded from https://advanced.onlinelibrary.wiley.com/doi/10.1002/admt.202500470 by Meiyong Liao - National Institute For , Wiley Online Library on [10/07/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advmattechnol.dewww.advancedsciencenews.com www.advmattechnol.deFigure 5. a) Schematic image of movement steps along the x coordinate and the y coordinate with a 1 mm interval in the xoy plane for magnetic forcesensing. b,c) Dependences of the resonance spectrum and Q factor of the magnetic force sensor on the x position as the y position is fixed at 0 mm,respectively. The distance between the sensor and the magnet is Z0 = 10 mm. d–f) Magnetic force imaging of the magnetic force sensor with changingof Z coordinate as Z0, Z0 + 1 mm, and Z0 + 2 mm.Materials Characterization and Readout of Resonance Signals: The hys-teresis loop of the permanent magnetic particle was measured usinga VSM (TM-VSM5050-SMS, Japan). The system was equipped with a1800 lines/mm monochromator grating and a cooled charge-coupleddevice detector. To assess the out-of-plane resonance performance ofthe SCD cantilever, both with and without a magnetic particle, an opti-cal setup based on the Doppler effect was employed, as illustrated inFigure 2a. This setup used a focused He–Ne laser (633 nm, <1 mW)directed vertically onto the substrate. A lock-in amplifier (HF2LI fromZurich Instruments) was used to capture the resonance signal. Allexperiments were conducted in a vacuum chamber with a pressurebelow 10−2 Pa. The resonators were driven by a lead zirconate ti-tanate (PZT) actuator. For magnetic sensing measurements, magneticfield gradients were applied using a coil connected to a DC powersource.Supporting InformationSupporting Information is available from the Wiley Online Library or fromthe author.AcknowledgementsThe authors greatly thanked Dr. Meiyong Liao (NIMS) for his help inoffering the diamond MEMS cantilevers. This work was partially sup-ported by a Grant-in-Aid of JSPS KAKENHI (Grant Nos. 24K00828 and24H00287).Conflict of InterestThe authors declare no conflict of interest.Data Availability StatementAll data needed to evaluate the conclusions in the paper are present inthe paper and/or the Supplementary Information. Other relevant data ofthis study are available from the corresponding author upon reasonablerequest.Adv. Mater. Technol. 2025, 2500470 2500470 (9 of 10) © 2025 The Author(s). Advanced Materials Technologies published by Wiley-VCH GmbH 2365709x, 0, Downloaded from https://advanced.onlinelibrary.wiley.com/doi/10.1002/admt.202500470 by Meiyong Liao - National Institute For , Wiley Online Library on [10/07/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advmattechnol.dewww.advancedsciencenews.com www.advmattechnol.deKeywords3D imaging, magnetic force sensor, resonator, single-crystal diamondReceived: March 5, 2025Revised: April 30, 2025Published online:[1] M. J. Biercuk, H. Uys, J. W. Britton, A. P. VanDevender, J. J. Bollinger,Nat. Nanotechnol. 2010, 5, 646.[2] J. Moser, J. Güttinger, A. Eichler, M. J. Esplandiu, D. Liu, M. Dykman,A. Bachtold, Nat. Nanotechnol. 2013, 8, 493.[3] T. Liu, T. Cai, J. Huo, H. Liu, A. Li, M. Yin, Y. Mei, Y. Zhou, S. Fan, Y.Lu, Nucleic Acids Res. 2024, 52, 86.[4] H. Weinstock,in SQUID Sensors: Fundamentals, Fabrication and Appli-cations, Springer Science + Business Media, Berlin, Germany 2012.[5] S. Yang, J. Zhang, Chemosensors 2021, 9, 211.[6] L. Jogschies, D. Klaas, R. Kruppe, J. Rittinger, P. Taptimthong, A.Wienecke, L. Rissing, M. C. Wurz, Sensors 2015, 15, 28665.[7] F. Casola, T. Van Der Sar, A. Yacoby, Nat. Rev. Mater. 2018, 3, 1.[8] J. L. Webb, L. Troise, N. W. Hansen, J. Achard, O. Brinza, R. Staacke,M. Kieschnick, J. Meijer, J.-F. Perrier, K. Berg-Sørensen, Front. Phys.2020, 8, 522536.[9] K. Yamakawa, Y. Ochiai, T. Ono, M. Toda, Functional Diamond 2024,4, 2389801.[10] X. Bai, K. Wen, D. Peng, S. Liu, L. Luo, Front. Phys. 2023, 11,1212368.[11] D. Rugar, R. Budakian, H. Mamin, B. Chui, Nature 2004, 430, 329.[12] M. R. Koblischka, U. Hartmann, Ultramicroscopy 2003, 97, 103.[13] M. Toda, T. Ono, J. Magn. Reson. 2021, 330, 107045.[14] Y. Tao, J. M. Boss, B. Moores, C. L. Degen, Nat. Commun. 2014, 5,3638.[15] J. M. Nichol, E. R. Hemesath, L. J. Lauhon, R. Budakian, Appl. Phys.Lett. 2008, 93, 193110.[16] M. Poggio, C. L. Degen, Nanotechnology 2010, 21, 342001.[17] O. Kazakova, R. Puttock, C. Barton, H. Corte-León, M. Jaafar, V. Neu,A. Asenjo, J. Appl. Phys. 2019, 125, 060901.[18] M. Toda, G. Xue, T. Ono, IEEJ Trans. Sens. Micromach. 2022, 142, 224.[19] Z. Zhang, H. Wu, L. Sang, Y. Takahashi, J. Huang, L. Wang, M. Toda,I. M. Akita, Y. Koide, S. Koizumi, ACS Appl. Mater. Interfaces 2020, 12,23155.[20] Z. Zhang, H. Wu, L. Sang, J. Huang, Y. Takahashi, L. Wang, M. Imura,S. Koizumi, Y. Koide, M. Liao, Carbon 2019, 152, 788.[21] M. Liao, S. Hishita, E. Watanabe, S. Koizumi, Y. Koide, Adv. Mater.2010, 22, 5393.[22] P. Olivero, S. Rubanov, P. Reichart, B. C. Gibson, S. T. Huntington, J.Rabeau, A. D. Greentree, J. Salzman, D. Moore, D. N. Jamieson, Adv.Mater. 2005, 17, 2427.[23] W. Weaver Jr, S. P. Timoshenko, D. H. Young, in Vibration Problems inEngineering, John Wiley & Sons, Hoboken, NJ, USA 1991.[24] M. Liao, Functional Diamond 2022, 1, 29.[25] S. Castelletto, L. Rosa, J. Blackledge, M. Z. Al Abri, A. Boretti, Mi-crosyst. Nanoeng. 2017, 3, 1.[26] T. Ono, M. Esashi, Rev. Sci. Instrum. 2003, 74, 5141.[27] A. H. Ghadimi, S. A. Fedorov, N. J. Engelsen, M. J. Bereyhi, R.Schilling, D. J. Wilson, T. J. Kippenberg, Science 2018, 360, 764.[28] L. Sang, M. Liao, X. Yang, H. Sun, J. Zhang, M. Sumiya, B. Shen, Sci.Technol. Adv. Mater. 2020, 21, 515.[29] A. Beccari, D. A. Visani, S. A. Fedorov, M. J. Bereyhi, V. Boureau, N. J.Engelsen, T. J. Kippenberg, Nat. Phys. 2022, 18, 436.[30] R. Shaniv, S. K. Keshava, C. Reetz, C. A. Regal, Phys. Rev. Appl. 2023,19, L031006.[31] R. Kuchi, V. Galkin, S. Kim, J.-R. Jeong, S.-j. Hong, D. Kim, IEEEMagn.Lett. 2022, 13, 1.[32] V. Galkin, R. Kuchi, S.-J. Kwon, T.-h. Kim, J.-g. Lee, J.-R. Jeong, D. Kim,J. Magn. 2024, 29, 1.[33] Z. Zhang, Y. Wu, L. Sang, H. Wu, J. Huang, L. Wang, Y. Takahashi, R.Li, S. Koizumi, M. Toda,Mater. Res. Lett. 2020, 8, 180.[34] M. Sansa, E. Sage, E. C. Bullard, M. Gély, T. Alava, E. Colinet, A. K.Naik, L. G. Villanueva, L. Duraffourg,M. L. Roukes,Nat. Nanotechnol.2016, 11, 552.[35] P. Sadeghi, A. Demir, L. G. Villanueva, H. Kähler, S. Schmid, Phys.Rev. B 2020, 102, 214106.[36] K. Y. Yasumura, T. D. Stowe, E. M. Chow, T. Pfafman, T. W. Kenny, B.C. Stipe, D. Rugar, J. Microelectromech. Syst. 2000, 9, 117.[37] G. Xue, M. Toda, X. Li, X. Wang, T. Ono, IEEE Sens. J. 2021, 21, 22578.[38] Y.-J. Seo,M. Toda, Y. Kawai, T. Ono, IEEJ Trans. Sens. Micromach. 2014,134, 166.[39] H. Mamin, D. Rugar, Appl. Phys. Lett. 2001, 79, 3358.[40] Y. Tao, C. L. Degen, Nano Lett. 2015, 15, 7893.[41] M. Rief, F. Oesterhelt, B. Heymann, H. E. Gaub, Science 1997, 275,1295.[42] Z. Zhang, G. Chen, K. Gu, S. Koizumi, M. Liao, Functional Diamond2023, 3, 2221280.Adv. Mater. Technol. 2025, 2500470 2500470 (10 of 10) © 2025 The Author(s). Advanced Materials Technologies published by Wiley-VCH GmbH 2365709x, 0, Downloaded from https://advanced.onlinelibrary.wiley.com/doi/10.1002/admt.202500470 by Meiyong Liao - National Institute For , Wiley Online Library on [10/07/2025]. 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