Reverse modelling for magnetic force microscopy interpretation

Magnetic force microscopy (MFM) is a versatile technique that probes the magnetic field of samples with nanoscale resolution, but interpretation of a sample’s domain structure in the general case is challenging due to the large number of degrees of freedom in the sample. Often, this is overcome by assuming a magnetization perpendicular to the sample surface. We present a method to obtain possible solutions that does not require this strict assumption. We use the analytic relation between the magnetic moment density in a sample with repeating boundary conditions and the cantilever tip to generate both a basis of configurations that generate no measurable signal and candidate solutions that reproduce the measured signal. That basis is then combined with the candidate solutions to obtain an array of magnetic orientations that recreate the MFM signal while satisfying other user-defined criteria. If available, known material properties can be used to further discriminate among the resulting domain structures.