Magnetic Scanning Gate Microscopy of Graphene Hall Devices (Invited) R

Magnetic scanning gate microscopy of graphene Hall devices (invited) R. K. Rajkumar, A. Asenjo, V. Panchal, A. Manzin, Ó. Iglesias-Freire, and O. Kazakova

Citation: Journal of Applied Physics 115, 172606 (2014); doi: 10.1063/1.4870587 View online: http://dx.doi.org/10.1063/1.4870587 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/115/17?ver=pdfcov Published by the AIP Publishing

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[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP: 150.244.102.216 On: Mon, 01 Jun 2015 10:33:45 JOURNAL OF APPLIED PHYSICS 115, 172606 (2014)

Magnetic scanning gate microscopy of graphene Hall devices (invited) R. K. Rajkumar,1,2 A. Asenjo,3 V. Panchal,1 A. Manzin,4 O. Iglesias-Freire,3 and O. Kazakova1,a) 1National Physical Laboratory, Teddington TW11 0LW, United Kingdom 2University of Surrey, Guildford GU2 7XH, United Kingdom 3Instituto de Ciencia de Materiales de Madrid, Cantoblanco, 28049 Madrid, Spain 4Istituto Nazionale di Ricerca Metrologica, I-10135 Torino, Italy (Presented 7 November 2013; received 23 September 2013; accepted 9 December 2013; published online 14 April 2014) We have performed sensitivity mapping of graphene Hall devices with the width of 0.6–15 lm operating in the diffusive regime under non-uniform, local magnetic and electric fields induced by a scanning metallic magnetic probe. The transverse voltage was recorded, while tuning the magnitude and orientation of the bias current, the probe-sample distance, and orientation of the probe magnetization. A strong two-fold symmetry pattern has been observed, as a consequence of capacitive coupling between the probe and the sample. The effect is particularly pronounced in small devices (<1 lm), where the dominating electric field contribution significantly lowers the effective area of the magnetic sensor. We show that implementation of the Kelvin probe feedback loop in the standard scanning gate microscopy setup drastically reduces parasitic electric field effects and improves magnetic sensitivity. VC 2014 AIP Publishing LLC.[http://dx.doi.org/10.1063/1.4870587]

I. INTRODUCTION magnetic field contributions is crucial, though often difficult to implement. Electrostatic simulation was performed to Miniaturized Hall sensors made of two dimensional elec- study the effect of device geometry and allowed the tron gas (2DEG) semiconductor materials, and recently of improvement of device performances in terms of magnetic atomically thin graphene, have been increasingly used as high sensitivity and reduced impact of the electrostatic effects.9 sensitivity devices for detection of localized magnetic fields in In our earlier works, we employed SGM technique to biomedical applications1,2 and data storage.3,4 The behavior of study the local changes of the carrier concentration in epitax- such devices depends on many physical parameters, and a sig- ial graphene devices.10,11 In contrast to conventional 2DEG nificant effort has been made across a number of disciplines devices, where the sensing channel is often placed a few tens on optimization of the Hall sensor performance. Such optimi- of nanometers beneath the device surface due to the insertion zation becomes particularly relevant on a submicron scale, of cap layers, the carriers in the graphene channel can be eas- where it is often necessary to calibrate the Hall devices ily approached and influenced by the magnetic probe, ena- locally.5 One of the crucial intrinsic parameters is the distribu- bling a higher spatial resolution in scanning gate tion of the local carrier density (or potential landscape), which experiments. Additionally, graphene-based Hall sensors ben- determines the electron scattering and total electrical resist- efit from high sensitivity (Hall coefficient, R )12 and robust- ance of the sample. The necessity to understand and ideally H ness to large biasing currents (I ).13 The possibility to use visualize how this landscape changes when locally perturbed bias such devices for efficient and straightforward detection of a by electrical and magnetic fields has long been recognised.6 single magnetic bead was recently demonstrated.11 Previous research in the area, implementing a scanning In this paper, we report a detailed study into the charac- gate microscopy (SGM) technique was primarily focused on terization of graphene based Hall devices to local electric studies of 2DEG semiconductor devices. Baumgartner et al. and magnetic fields. It has been observed that these devices used local electric and uniform magnetic fields to demon- suffer from the same inherent problem as their semiconduc- strate that GaAs/AlGaAs Hall devices generally give differ- tor prototypes, namely, a superposition of local potential and ent responses to local electric perturbation in diffusive6 and magnetic responses. Depending on device dimensions, the ballistic7 regimes at low temperatures. This approach was contribution arising from the electrostatic forces between the significantly developed in room temperature experiments on current-biased device and metallically coated probe can sig- AlSb/InAs/AlSb near-surface quantum wells, where contri- nificantly dominate the magnetic signal, thus decreasing the butions of local magnetic and electrical fields to the total effectiveness of such devices for sensing applications. transverse voltage signal were first reported and transition Therefore, caution is to be stipulated when interpreting sen- from diffusive to quasi-ballistic transport was visualized.8 sor signal obtained in real world applications. These experiments demonstrated that proper separation of The paper consists of two sections. First, we perform a local electric (scanning probe or geometry induced) and detailed characterization of a range of epitaxial graphene devices in the classical Hall effect regime using local, non- a)Author to whom correspondence should be addressed. Electronic mail: uniform magnetic and electrical fields applied to the metallic [email protected]. magnetic scanning probe. We study the response of the

0021-8979/2014/115(17)/172606/6/$30.00 115, 172606-1 VC 2014 AIP Publishing LLC

graphene Hall device by varying parameters such as the bias current magnitude and direction, orientation of the probe magnetization, and distance between the probe and sensing surface. In the second part, we implement a combination of SGM with frequency-modulated Kelvin probe force microscopy (FM- KPFM) feedback loop.14 This completely eliminates the parasitic electric field contributions, allowing us to characterize the sensor to magnetic fields alone. The SGM-KPFM technique is particularly important for characterizing small graphene devi- FIG. 1. (a) Topography and (b) surface potential images of a 0.6-lm wide ces, which are greatly influenced by the parasitic electric field. device. For accurate interpretation of results, we demonstrate that it is necessary to perform the non-uniform field characterization to (i) Commercial probes (Bruker) with two different thick- calibrate the sensor prior to real world applications, such as nesses of Co/Cr coating, i.e., MESP (40 nm) and HM- magnetic bead detection. The experimental results are sup- MESP (>40 nm), with coercivity 400 Oe and moment ported with a finite element model that has been developed to (m)of1 1013 and >3 1013 emu, respectively.21 simulate the spatial distribution of the electric potential inside (ii) Customized probes, which were prepared by sputter- the graphene Hall bars in the presence of a probe that locally ing cobalt films with thicknesses of 15 and 20 nm induces magnetic and electric fields. onto one side of commercially available non-magnetic probes. II. EXPERIMENTAL SETUP Both types of probes have a resonance frequency of f0 75 The one-two layer epitaxial graphene (1LG and 2LG, kHz with a spring constant of 3 N/m. respectively) was grown on the Si-terminated face of a nomi- FM-KPFM is one of the most widely used surface nally on-axis 4H-SiC(0001) substrate at 2000 Cand1000 potential mapping techniques that utilize AC/DC voltages millibars argon gas pressure in a sublimation furnace.15–17 simultaneously, while scanning the sample’s topography The resulting material is n-doped, owing to charge transfer using dynamic mode AFM. The Kelvin feedback loop elimi- from the interfacial layer, with the measured electron concen- nates the electrostatic forces by applying a compensating DC 11 2 tration in the range ne ¼ 6–20 10 cm and mobility (l)of voltage to the probe at each pixel such that Vprobe equals 200–3000 cm2 V1 s1 at room temperatures.12,18 local potential at the sample surface.19,22 The surface poten- The fabrication process involves various steps of elec- tial of the sample is mapped by recording Vprobe at each tron beam lithography, oxygen plasma etching, and thermal pixel. deposition of Cr/Au (5/100 nm) electrical contact.19 Using Magnetic SGM is realized by scanning the device and these processes, symmetrical double-cross devices with measuring the voltage response to a localized magnetic field width (w) of 0.6–15 lm were fabricated (Fig. 1). Initial char- (Bprobe) produced by a magnetically coated probe. When acterization of devices was performed at room temperature scanning a DC current-biased Hall sensor with a magnetic 12 using magnetotransport and noise spectral measurements. force microscope (MFM) probe oscillating at f0, the sensor Results are summarized in Table I. experiences an oscillating magnetic field (dBprobe/dz), giving Scanning probe microscopy (SPM) measurements were rise to an oscillating transverse voltage (dVxy/dz). The volt- carried out using a Nanotec SPM system controlled by the age response is mapped at each pixel by measuring the sen- 20 WSxM software, using the amplitude modulation mode sor with an external lock-in amplifier referenced to f0.It with a phase-locked loop (PLL) that keeps the oscillation should be noted that f0 varies when PLL feedback is on, phase constant. Topography height images of the graphene making sure the relevant information on the in-phase channel device were recorded simultaneously with tapping phase and is recorded and avoiding frequency-shifts induced by scanning gate images, which were compiled either on their probe-sample interactions. own or with implementation of the FM-KPFM feedback. For The magnetic coating of an MFM probe is also electri- magnetic gating and calibration, the following probes were cally conductive; therefore, performing SGM on a current- used: biased device results in the probe-sample potential difference. In this experiment, a unipolar current source was used, which TABLE I. Summary of transport and noise measurements for epitaxial gra- effectively makes the potential of the sample always higher phene devices with the width w of 0.6–15 lm, where R is the 4-point resist- 4 than potential of the probe, i.e., Vsample > Vprobe, if the probe is ance, RH is the Hall coefficient, ne is the electron density, l is electron grounded. The response of the Hall sensor to the parasitic mobility, and B is the minimal detectable field. min electric field masks the magnetic field response, making accu-

Size R4 RH ne l Bmin at Ibias ¼ 60 lA rate measurements of the magnetic signal difﬁcult. However, (lm) (kX) (X/T) (cm2) (cm2/V s) (lT/ͱHz) the parasitic electric ﬁeld can be eliminated by using the FM- KPFM feedback loop, which applies a compensating voltage 0.6 29.5 296 2.1 1012 803 4.9 to the probe, such that the probe-sample potential difference is 1 33.6 838 7.5 1011 998 3.7 10 22.7 715 8.7 1011 170 3.7 zero at each pixel of the scan. Thus, performing SGM with in- 15 26.2 1022 6.1 1011 3124 1.3 situ FM-KPFM feedback (Fig. 2) allows effective separation of the electrostatic from magnetic responses.

FIG. 2. Schematics of the SGM-KPFM experimental setup.

III. MODELING OF THE HALL DEVICE RESPONSE TO LOCALIZED MAGNETIC AND ELECTRIC FIELDS A 2D finite element model has been developed to calcu- late the electric potential distribution and, thus, the transverse voltage in the graphene Hall device under the assumptions of diffusive transport regime and non-uniform 10 magnetic field Bprobe(r). In the electrostatic potential equa- tion, a spatially dependent conductivity tensor is introduced $ rðÞr 1 lB ðÞr rðÞr ¼ ÂÃ probe ; (1) 2 lB ðÞr 1 1 þ lBprobeðÞr probe FIG. 3. Vxy mapping of the 1-lm wide Hall cross at Ibias ¼þ70 lA obtained with a custom-made probe (20 nm Co coating). FM-KPFM feedback loop is where rðÞr ¼ lnðÞr e, with l being the electron mobility, (a) disabled and (b) enabled. Calculated maps of Vxy when the probe-sample n(r) being the local electron density, and e being the electron capacitive coupling is (c) included and (d) excluded. White lines outline the 8–10 contour of the device. (e) Line profiles obtained along the dashed lines as charge. The local magnetic field Bprobe(r) in Eq. (1) is indicated in (a) and (b). (f) Dependence of Vxy on the biased current as meas- the component of the probe stray field orthogonal to gra- ured at the device centre (point A in Fig. 3(b)). phene sheet, determined from Green integral formulation.9 The probe magnetic coating is modeled by introducing a 3D mappingwhentheprobeismagnetizeddownwardsand spatial distribution of dipoles with uniform magnetization scanned at 0 nm lift height with respect to the sensor surface. perpendicular to the sensor surface. For a finite electric field between the probe and sample, the The probe-sample capacitive coupling is handled by dominating features in V mapping are peaks at the corners of describing n(r) as a spatially dependent function xy the active sensing area (Fig. 3(a)). The image shows a two- ÂÃ Cprobe;max 2 2 fold symmetry, characterized by increase/decrease of the nðÞr ¼ n þ V VðÞr exp½ðÞrr0 =k ; (2) 0 e probe transverse voltage when the probe gates at the corners #1–3/#2–4, respectively. A maximal positive/negative signal

where n0 is the electron density in the absence of probe of 4.5 lV is measured at the respective corners (Figs. 3(a) induced doping effects, V(r) is the local voltage of the sam- and 3(e)). At the same time, a non-zero positive signal of ple, Cprobe,max is the maximum local value of the 2 lV is measured at the center of the cross (Figs. 3(b) and probe-sample capacitance per unit area at the considered lift 3(e)). The modeling approach described above (i.e., probe- height, and k is a characteristic length scale describing the sample capacitive coupling is included) confirms this behav- spatial decay of probe-sample capacitive coupling. ior, as demonstrated by the calculated map of Vxy reported in Fig. 3(c). Here, a maximum local area capacitance (Cprobe,max) IV. EXPERIMENTAL RESULTS AND DISCUSSION of 900 lF/m2 with a spatial decay length (k)of60 nm was estimated by fitting the experimental scanning gate images. A. Magnetic scanning gate microscopy When the current direction is reversed from 70 lAto First, we consider the case of standard SGM with a þ70 lA (from drain to source and vice versa), the voltage po- grounded metallic magnetic probe, i.e., FM-KPFM feedback larity flips at the corners, such that signal at the corners #1 and is disabled. We study the response of graphene Hall devices 3 changes from negative to positive (Figs. 4(a)–4(d)). The sig- to non-uniform magnetic fields introduced by a scanning nal at the center of the cross also changes its polarity with the custom-made probe with a 20-nm thick magnetic Co coating. bias current (Figs. 4(a) and 4(b)). Fig. 3(f) shows that the A bias current of Ibias ¼þ70 lA (from source to drain in Fig. transverse voltage at the center of the device (point A in Fig. 3(a)) is driven across the 1-lm device and the transverse 3(b)) increases almost linearly with the biased current. voltage Vxy ¼ VB VA is measured and mapped at each point The origin of the strong diagonal contrast can be under- of the probe position. Fig. 3(a) shows the transverse voltage stood by considering diversion of the flow of electrons

FIG. 4. SGM mapping of Vxy signal in 1-lm wide graphene Hall cross with bias current (Ibias) equal to (a) 70 lA and (b) þ70 lA. FM-KPFM feedback loop is disabled. White lines outline the contour of the device. (c) and (d) Line proﬁles obtained along the dashed lines indicated in (a) and (b), respectively. Schematic of the current distribution when the probe (Vprobe < Vsample) locally gates at corners #1 and 2 at bias current (e) and (f) Ibias < 0 and (g) and (h) Ibias > 0.

towards VA (VB) electrodes when the electrically biased to the probe stray magnetic field. It can be expected that the probe is scanned above corners #1 and 3 (#2 and 4) of the magnetic component of the Vxy should depend on the magni- sensor, which results in a rise (drop) in Vxy (see Fig. 3(a)). It tude and direction of the bias current, magnitude, and orien- should be noted that due to the use of a unipolar current tation of the probe magnetization and distance between source, the surface potential of the sample is always higher the probe and the device (as 1/z3 at large distances). than the grounded metallic probe, irrespective of the direc- Previously, it has been shown that magnitude of the mag- tion of the current. If we consider the case of Ibias < 0 (as netic response can be significantly lower than the electro- experimentally shown in Fig. 4(a)), the lower potential of the static signal.10,11 Moreover, in the case of small Hall probe (Vprobe < Vsample) repels electrons in the graphene; devices, the signal in the center has a more complex nature, therefore, the probe gating at corner #1 (#3) (Fig. 4(e)) being a superposition of magnetic and electrostatic compo- diverts the flow of electrons towards VB electrode connected nents (see Sec. IV C). Thus, prior any real magnetic sensing to the positive terminal of lock-in (Fig. 2), thus decreasing applications (e.g., on submicron and nanoscale), it becomes Vxy. Similarly, if the probe is gating at corner #2 (#4) (Fig. increasingly important to separate magnetic and parasitic 4(f)), the current flow is diverted towards VA electrode con- electrostatic components to understand the actual magnetic nected to the negative terminal of lock-in amplifier, increas- sensitivity of the device. ing Vxy as experimentally observed. Applying a positive bias current (I > 0) reverses the direction of the flow of elec- bias B. SGM with FM-KPFM feedback trons, thus, inverts the contrast (Figs. 4(g) and 4(h)), which is in agreement with experimental results (Fig. 4(b)). These Next, we perform magnetic SGM mapping of the device features are identical to those observed in electrical SGM with the FM-KPFM feedback loop turned on. As described experiments on classic semiconductor Hall devices.6,8 Thus, in Sec. II, the feedback loop eliminates the electrostatic the corner effect has a purely electrostatic nature originating forces by applying a compensating DC voltage to the probe 9,10 in probe-sample capacitive coupling. It should be noted at each pixel, such that Vprobe ¼ Vsample. When the electric that a strong bi-polar signal at the corners is also measured potential between the probe and sample is nullified at every when scanning graphene Hall devices with a non-magnetic point in the scan, the measured transverse voltage Vxy origi- metallic probe (i.e., Pt-Ir coated probe).23 Overall, the effect nates only from the local magnetic field of the probe oscillat- caused by the electrostatic interaction between the charged ing at f0. The result of the elimination of the electrostatic probe and biased graphene (or semiconductor) device should interaction by enabling the FM-KPFM feedback is shown in depend on the magnitude and direction of the biased current Fig. 3(b), which demonstrates a complete suppression of (as shown in Figs. 3(d), 4(a), and 4(b)), potential on the peaks at the corners of the Hall cross. This is also confirmed probe, vertical distance between the probe and the sample by the calculated map of Vxy, which has been computed (as 1/z2, where z is the vertical distance)24 and amplitude neglecting probe-sample capacitive effects. In this case, the of the probe oscillation. Moreover, graphene devices are map demonstrates a “bell-like behavior” with maximum val- expected to exhibit a higher capacitive coupling with the ues at the cross center, indicating that the signal at the center probe, since the carriers are on the surface of the sample. has a prevalent magnetic origin (Fig. 3(d)). It should be On the other hand, the signal at the center of the cross noted that the maximum magnitude of the output signal is has a magnetic origin and results from the Lorentz force due much lower after switching on the FM-KPFM feedback

FIG. 6. Transverse voltage as a function of the probe-sample separation, for a commercial HM-MESP. FM-KPFM feedback loop is on. Voltage was measured with probe positioned at the centre of the device, while lifting the probe vertically. Inset shows the schematics of the experiment.

In the next experiment, the dependence of the Hall volt- FIG. 5. SGM mapping of Vxy signal in 1-lm wide Hall cross. Images were age on the probe-sample distance has been studied. The AC taken using custom-made probe (20 nm coating) magnetized (a) downwards Hall voltage was measured, while the magnetic probe was (#) and (b) upwards ("). FM-KPFM feedback loop is on. The bias current is fixed at the center of the device in x, y plane and the probe- Ibias ¼70 lA and the probe-sample distance is 0 nm. White lines outline the contour of the device. (c) Line profiles obtained along the dashed lines sample separation in the z-direction was increased from 0 to are shown in (a) and (b). Smooth lines correspond to Gaussian fits. 1.25 lm. The FM-KPFM feedback loop was turned on to eliminate the electrostatic signal at that point. A HM-MESP compared to the initial experiment (Fig. 3(e)). The largest probe was used to characterize the 1 lm Hall device with value of Vxy is measured when the probe is at the center of the RH ¼ 848 X/T. A well-defined decrease in the Hall voltage sensing area, which is a result of its maximum coupling to the response is observed for separation distances up to 750 nm probe stray field (Fig. 3(b)). The signal at the cross center is (Fig. 6), before the signal becomes too weak to be detected notaffectedbytheinclusionoftheFM-KPFMfeedback. due to a significant decrease in the probe-sample coupling. As discussed above, magnetic and electrostatic forces have similar dependences on a number of experimental pa- C. Effect of device size rameters, i.e., current, probe oscillation amplitude, and vertical separation. Investigations into the orientation and Local distribution of the transverse voltage was mapped magnitude of the probe magnetization can provide unambigu- for Hall devices of different sizes, i.e., w ¼ 0.6–15 lm. In ous proof that carriers are affected by the Lorentz force. Thus, this case, the FM-KPFM feedback was kept disabled to bet- we perform mapping of the transverse voltage using an MFM ter illustrate the spatial distribution of the electrostatic signal. probe magnetized down (Fig. 5(a)) and up (Fig. 5(b))withthe Representative SGM images are shown in Fig. 7. It is note- FM-KPFM feedback on. The Ibias is fixed to 70 lA and the worthy that the images were obtained at different values of distance between the probe apex and the sensor surface is Ibias, as smaller devices are potentially unstable at larger cur- 0 nm, i.e., effectively the probe is above the surface at a dis- rents, whereas imaging of larger devices with low currents tance equal to the amplitude of probe oscillations. The results led to a small output signal. have been obtained using custom-made magnetic probes with As it can be seen from Figs. 7(c) and 7(d), small devices low magnetic moment (20-nm Co coating). The maps in Figs. (w ¼ 1 and 0.6 lm, respectively) are most affected by the 5(a) and 5(b) show that the polarity of the signal at the center electrostatic signal, as it becomes increasing difficult to dif- of the cross reverses as the probe magnetization has been ferentiate the electrostatic and magnetic signal, which is a changed by application of an external magnetic field of 61T result of the overlapping of two distributions with peaks at prior to the scan. The magnetic signal for different probe ori- the diagonal corners. As it has been previously shown for 1- entations can be fitted with a Gaussian response (Fig. 5(c)). It lm device the maximum response of the magnetic signal is should be noted that small peaks at the corners of the Hall de- typically a few times weaker than its electrostatic counterpart vice still can be observed (Figs. 5(a) and 5(b)). Moreover, the (Fig. 3(e)). This indicates that small devices are significantly polarity of these small peaks is not affected by the change of affected by electrostatic effects, which may notably decrease the probe magnetization, further proving the separate nature their performance as magnetic sensors. It is noteworthy, of electrostatic and magnetic signals. These peaks are a result however, that in practice any electrically charged object in of an incomplete nullification of the probe-sample electric the vicinity of the device can play the role of a metal probe field and could be further reduced by optimizing the FM- and affect the carrier flow in the device. KPFM feedback parameters. Thus, based on the results of this On the other hand, in large devices (w ¼ 10 and 15 lm) experiment, we can conclude that the voltage measured using the electrostatic component is relatively strongly localized at SGM-KPFM technique is the response to the Lorentz force the device corners (Figs. 7(a) and 7(b)), i.e., the decay length resulting from the probe stray magnetic field alone. of the electrostatic signal is much smaller than the device

probe magnetization. We demonstrate that the strong signal, with a two-fold symmetry observed at the device corners, has an electrostatic origin caused by capacitive coupling of the charged probe with a biased device, whereas the weaker response in the middle of the cross is mainly determined by the local magnetic ﬁeld of the probe. We show that the electrostatic effects are the most pronounced in small devices (<1 lm), where they affect the largest part of the sensor, thus decreasing the effective area of the sensor. Implementation of the FM-KPFM feedback loop in the standard magnetic SGM setup drastically reduces capacitive effects, improves magnetic sensitivity and expands the effective area of the device. The presented techniques provide a straightforward route for characterizing the device performance to non-uniform magnetic ﬁelds. Our results also demonstrate the necessity of considering the ideal device size, shape, and local magnetic and electrical environment for designing the optimal magnetic sensor performance, the most suitable for a particular application.

ACKNOWLEDGMENTS

This work has been funded by the IRD Graphene, FIG. 7. Vxy mapping of Hall crosses with width of (a) 15 lm, (b) 10 lm, (c) MetMgas, Concept Graphene and CSD2010-00024 projects 1 lm, and (d) 0.6 lm. FM-KPFM feedback loop is disabled. Line profiles obtained along the dashed lines for the devices with (e) w ¼ 10 lm and (f) as well as mobility program Salvadorde Madariaga. We are w ¼ 1 lm. very grateful to A. Tzalenchuk, R. Yakimova, A. Lartsev, and J. Gallop. width. However, it is worth mentioning that the magnetic output of these devices is negligible even after FM-KPFM 1K. Togawa et al., IEEE Trans. Magn. 41, 3661–3663 (2005). compensation (Fig. 7(e)). These results seem to be counterin- 2A. Sandhu et al., Nanotechnology 21, 442001 (2010). 3 tuitive, bearing in mind a larger Hall coefficient and corre- J. Heremans, J. Phys. D: Appl. Phys. 26, 1149–1168 (1993). 4S. A. Solin et al., Meas. Sci. Technol. 8, 1174–1181 (1997). spondently lower minimum detectable field (Table I). A 5T. Kebe, J. Appl. Phys. 95, 775 (2004). significant imbalance between the size of the sensor and 6A. Baumgartner et al., Phys. Rev. B 74, 165426 (2006). magnetic object leads to a poor magnetic coupling and sub- 7A. Baumgartner et al., Phys. Rev. B 76, 085316 (2007). 8 stantially decreases the output of the magnetic sensor. Ideal L. Folks et al., J. Phys.: Condens. Matter 21, 255802 (2009). 9V. Nabaei et al., J. Appl. Phys. 113, 064504 (2013). coupling is expected when the areas of the sensor and the 10R. K. Rajkumar et al., IEEE Trans. Magn. 49, 3445–3448 (2013). object are compatible.25 Thus, devices in this size range 11V. Panchal et al., IEEE Trans. Magn. 49, 3520–3523 (2013). (tens of microns), while ideal for detection of low uniform 12V. Panchal et al., J. Appl. Phys. 111, 07E509 (2012). 13J. Moser et al., Appl. Phys. Lett. 91, 163513 (2007). magnetic fields, are not particularly suitable for measure- 14U. Zerweck et al., Phys. Rev. B 71, 125424 (2005). ments of small localized fields, i.e., for single (or small num- 15C. Virojanadara et al., Phys. Rev. B 78, 245403 (2008). ber) magnetic particle detection in biomedical applications. 16K. V. Emtsev et al., Nature Mater. 8, 203–207 (2009). 17R. Yakimova et al., Mater. Sci. Forum 645–648, 565–568 (2010). 18 V. CONCLUSIONS A. Tzalenchuk et al., Nat. Nanotechnol. 5, 186–189 (2010). 19O. Kazakova et al., Crystals 3, 191–233 (2013). 20 Using magnetic SGM, we have mapped the distribution I. Horcas et al., Rev. Sci. Instrum. 78, 013705 (2007). 21See www.brukerafmprobes.com for data specification about MESP and of the transverse voltage response in epitaxial graphene devi- HM-MESP probes. ces with width of 0.6–15 lm. The local transverse voltage 22V. Panchal et al., Sci. Rep. 3, 2597 (2013). has been measured with dependence on the magnetic probe 23V. Panchal, Epitaxial Graphene Nanodevices and Their Applications for position, correlated to the sample topography and studied by Electronic and Magnetic Sensing (Royal Holloway, University of London, 2014). varying the magnitude and direction of the bias current as 24C. Barth et al., New J. Phys. 12, 093024 (2010). well as the probe-sample distance and orientation of the 25L. Di Michele et al., J. Appl. Phys. 110, 063916 (2011).