Quantitative MFM and Modelling
Determination of Magnetic Structures by Vector Magnetic Force Microscopy
The quantitative interpretation of Magnetic Force Microscopy (MFM) response of complex magnetization patterns is still difficult since this technique is not a direct measure of the magnetization. Therefore, the use of vector MFM in combination with MFM image simulation is suggested as a way to extract more information out of the MFM data. The vector MFM approach measures different components of the magnetic stray field derivative by magnetizing a hard magnetic tip in different directions.
A longitudinal recording media constitutes a good illustration for the principle contrast mechanisms measured with a perpendicular and a parallel magnetized tip (Fig.1).
Two basic contrast mechanisms can be observed for the perpendicular and parallel magnetized tips. The measurement - signal for the perpendicular magnetized tip has its maximum above the domain walls, while the signal for the parallel magnetized tip becomes zero there and has its maximum above the domains.
The MFM - image simulation is based on the so called point probe approximation (ppa). Within this approximation the tip is assumed to be homogeneously magnetized and the magnetization is represented by a single point dipole located inside the tip. The simulation consists of 2 parts (Fig. 2).
First the stray-field above the magnetic sample is calculated using a commercial magnetostatic solver . In the second part the contrast is calculated numerically from the modelled stray field data using the ppa.
Using this kind of MFM contrast simulation is very helpful for the fast interpretation of MFM images measured with tips magnetized in different directions. The MFM contrast modelling can be improved for example by using another tip model. The so called extended charge model  takes into account, that the tip is geometrically extended and describes the tip using magnetic charges.
The modelling and vector MFM measurements of the longitudinal recording media showed, that the reconstruction of the in-plane magnetization structure can be done by a signal ratio comparison of the in-plane components of the MFM signals. Based on the knowledge of the basic contrast mechanisms for the longitudinal recording media this interpretation method can be extended to more complex magnetization structures.
 U. Hartman: The point dipole approximation in magnetic force microscopy, Phys. Lett. A 137 (1989), 475.
 S. McVitie: R.P. Ferrier, J. Scott, G.S. White, A. Gallagher, Quantitative field measurements from magnetic force microscope tips and comparison with point and extended charge models, J. Appl. Phys. 89 (2001), 3656
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