Distance dependence of the phase signal in eddy current microscopy

Atomic force microscopy using a magnetic tip is a promising tool for investigating conductivity on the nano-scale. By the oscillating magnetic tip eddy currents are induced in the conducting parts of the sample which can be detected in the phase signal of the cantilever. However, the origin of the phase signal is still controversial because theoretical calculations using a monopole appoximation for taking the electromagnetic forces acting on the tip into account yield an effect which is too small by more than two orders of magnitude. In order to determine the origin of the signal we used especially prepared gold nano patterns embedded in a non-conducting polycarbonate matrix and measured the distance dependence of the phase signal. Our data clearly shows that the interacting forces are long ranged and therefore, are likely due to the electromagnetic interaction between the magnetic tip and the conducting parts of the surface. Due to the long range character of the interaction a change in conductivity of $\Delta\sigma=4,5\cdot10^{7} (\Omega$m$)^{-1}$ can be detected far away from the surface without any interference from the topography

Quantitative Measurement of the Magnetic Moment of Individual Magnetic Nanoparticles by Magnetic Force Microscopy

The quantitative measurement of the magnetization of individual magnetic nanoparticles (MNPs) using magnetic force microscopy (MFM) is described. Quantitative measurement is realized by calibration of the MFM signal using an MNP reference sample with traceably determined magnetization. A resolution of the magnetic moment of the order of 10-18 A m2 under ambient conditions is demonstrated, which is presently limited by the tip's magnetic moment and the noise level of the instrument. The calibration scheme can be applied to practically any magnetic force microscope and tip, thus allowing a wide range of future applications, for example in nanomagnetism and biotechnology

Calibration of multi-layered probes with low/high magnetic moments

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