National Physical Laboratory

Magnetic scanning probe calibration using graphene Hall sensors

We present a straightforward method for calibration of the stray magnetic field of magnetic force microscopy probes using epitaxial graphene Hall sensor and scanning gate microscopy in conjunction with Kelvin probe force microscopy feedback loop.

Magnetic force microscopy (MFM) is a well-established atomic force microscopy (AFM) based qualitative technique for imaging of magnetic domains. Quantitative measurements require careful calibration of the stray magnetic field (Bprobe) of the MFM probe. The high sensitivity of Hall sensors makes them ideal for measuring Bprobe. However, the surface potential difference between the current biased device and electrically conductive magnetic coating of the MFM probe gives rise to parasitic electric field, which leads to superposition of the electric and magnetic field, making it difficult to accurately determine Bprobe. We present a straightforward method of measuring only Bprobe using the frequency-modulated Kelvin probe force microscopy (FM-KPFM) feedback loop to eliminate the parasitic electric field (Figure 1). We call this method 'magnetic scanning gate microscopy' (M-SGM).

Figure 1: Schematic of the magnetic scanning gate microscopy experimental setup
Figure 1: Schematic of the magnetic scanning gate microscopy experimental setup

We performed Bprobe calibration using epitaxial graphene Hall sensors as they provide a high sensitivity to magnetic fields and robustness to large biasing currents. Moreover, the active layer in graphene is located at the surface, which leads to a significant increase in the vertical coupling as compared to a conventional 2DEG semiconductor. The device is scanned with the probe, while simultaneously measuring the transverse voltage at each pixel using a lock-in amplifier. The results of M-SGM with KPFM feedback disabled are shown in Figure 2a, where the map of the transverse voltage is dominated by the parasitic electric field (dark and bright contrasts in the corners of the Hall cross with a two-fold symmetry). However, with the KPFM enabled, the feedback loop compensates for any potential difference between the sample and probe. The map of the transverse voltage is now dominated by the MFM probe stray magnetic field with largest response at the centre of the Hall cross (Figure 2b). A 2D finite element model was developed to model the electric potential distribution and thus, the transverse voltage map of the Hall sensor (Figure 2c and 2d). The model takes into account the diffusive transport in graphene at room temperature and the non-uniform Bprobe, which was determined from Green integral formulation. The accuracy of Bprobe was insured by introducing a 3D spatial distribution of dipoles with uniform magnetisation perpendicular to the sensor surface.

Magnetic scanning probe calibration using graphene Hall sensors - Fig 2

Figure 2: (a) Transverse voltage map of the sensor dominated by the parasitic electric field. (b) Transverse voltage map of the sensor with KPFM feedback enabled, showing only the response to MFM probe stray magnetic field. Simulated transverse voltage map of the sensor from (c) parasitic electric field and (d) MFM probe stray magnetic field. (e) Line profiles of measured and simulated data, obtained along the dashed lines indicated in (a) and (b). (f) Dependence of the transverse voltage (Vxy) on the bias current as measured at the centre of the Hall cross (point A in panel b).

Thus, we successfully demonstrate calibration of Bprobe using FM-KPFM feedback loop in conjunction with M-SGM. These scanning probe microscopy methods provide a straightforward route for calibration of MFM probes when combined with accurate modelling of the MFM probe stray magnetic field.

See related publications for further details on magnetic scanning probe calibration.

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Last Updated: 13 Oct 2015
Created: 13 Oct 2015

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