Abstract
We present a comprehensive method for visualisation and quantification of the magnetic stray field of magnetic force microscopy (MFM) probes, applied to the particular case of custom-made multi-layered probes with controllable high/low magnetic moment states. The probes consist of two decoupled magnetic layers separated by a non-magnetic interlayer, which results in four stable magnetic states: ±ferromagnetic (FM) and ±antiferromagnetic (A-FM). Direct visualisation of the stray field surrounding the probe apex using electron holography convincingly demonstrates a striking difference in the spatial distribution and strength of the magnetic flux in FM and A-FM states. In situ MFM studies of reference samples are used to determine the probe switching fields and spatial resolution. Furthermore, quantitative values of the probe magnetic moments are obtained by determining their real space tip transfer function (RSTTF). We also map the local Hall voltage in graphene Hall nanosensors induced by the probes in different states. The measured transport properties of nanosensors and RSTTF outcomes are introduced as an input in a numerical model of Hall devices to verify the probe magnetic moments. The modelling results fully match the experimental measurements, outlining an all-inclusive method for the calibration of complex magnetic probes with a controllable low/high magnetic moment.
Highlights
Magnetic force microscopy (MFM) is a specific mode of scanning probe microscopy, which allows the acquisition of magnetisation distribution on a sample surface with spatial resolution down to a few tens of nanometres[1, 2]
We perform Hall voltage mapping of 200 nm-wide single layer epitaxial graphene Hall sensors using magnetic scanning gate microscopy (mSGM) with frequency-modulated Kelvin probe force microscopy (FM-KPFM) feedback for different magnetic states and orientations of the magnetisation for both commercial and ML-magnetic force microscopy (MFM) probes. These maps were compared to a numerical model that uses the double point dipole approximation of the probes to calculate the electric potential in the Hall sensor and, to reconstruct the Hall voltage maps, including the effects of localised magnetic fields and capacitive coupling that can arise from a partial compensation of the probe-sensor electric potential difference via FM-KPFM20, 27. With these experimental and modelling techniques, we demonstrate that the ML-MFM probes can be reliably and controllably switched to any one of the four ±FM and ±A-FM states by applying ad hoc magnetic field pulses
Using a number of experimental (EH, in situ MFM, mSGM and quantitative MFM (qMFM)) and modelling (RSTTF, finite element model) techniques, we have presented a method for visualising and quantifying the magnetic stray field of MFM probes and used it to study custom-made ML-MFM probes of two thicknesses in multiple magnetic states
Summary
Magnetic force microscopy (MFM) is a specific mode of scanning probe microscopy, which allows the acquisition of magnetisation distribution on a sample surface with spatial resolution down to a few tens of nanometres[1, 2]. Quantitative measurements require a precise characterisation of the probe’s properties and a subsequent ‘subtraction’ of the probe-sample coupling contribution from the measured MFM data[3, 8] Another shortcoming of standard MFM is uncontrollable switching of magnetisation in soft magnetic structures due to strong interaction with the relatively hard magnetic coating of MFM probes[9, 10] or, vice versa[9,10,11,12,13]. This technique can be used to predict the response of the probe given a magnetic charge map[18], it applies a number of assumptions about probe – sample interaction and cannot be used in cases where the presence of the probe modifies the properties of the sample
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