On the influence of reference sample properties on magnetic force microscopy calibrations

Magnetic force microscopy (MFM) allows the characterization of magnetic stray field distributions with high sensitivity and spatial resolution. Based on a suitable calibration procedure, MFM can also yield quantitative magnetic field values. This process typically involves measuring a reference sample to determine the distribution of the tip's stray field or stray field gradient at the sample surface. This distribution is called the tip transfer function (TTF) and is derived through regularized deconvolution in Fourier space. The properties of the reference sample and the noise characteristics of the detection system significantly influence the derived TTF, thereby limiting its validity range. In a recent study, the tip stray field distribution, and hence the TTF, of an MFM tip was independently measured in real space using a nitrogen vacancy center as a quantum sensor, revealing considerable discrepancies with the reference-sample-based TTF. Here, we analyze the influence of the feature distribution of the reference sample and the MFM measurement parameters on the resulting TTF. We explain the observed differences between quantum-calibrated stray field distributions and the classical approach by attributing them to a loss of information due to missing or suppressed spectral components. Furthermore, we emphasize the importance of the spectral coverage of the TTF. Our findings indicate that for high-quality reconstruction of the stray field of a sample under test (SUT), it is more critical to ensure a strong overlap of frequency components between the reference sample and the SUT than to achieve an accurate real-space reconstruction of the tip stray field distribution.