Magnetic force microscopy has unsurpassed capabilities in analysis of nanoscale and microscale magnetic samples and devices. Similar to other Scanning Probe Microscopy techniques, quantitative analysis remains a challenge. Despite large theoretical and practical progress in this area, present methods are seldom used due to their complexity and lack of systematic understanding of related uncertainties and recommended best practice. Use of the Tip Transfer Function (TTF) is a key concept in making Magnetic Force Microscopy measurements quantitative. We present a numerical study of several aspects of TTF reconstruction using multilayer samples with perpendicular magnetisation. We address the choice of numerical approach, impact of non-periodicity and windowing, suitable conventions for data normalisation and units, criteria for choice of regularisation parameter and experimental effects observed in real measurements. We present a simple regularisation parameter selection method based on TTF width and verify this approach via numerical experiments. Examples of TTF estimation are shown on both 2D and 3D experimental datasets. We give recommendations on best practices for robust TTF estimation, including the choice of windowing function, measurement strategy and dealing with experimental error sources. A method for synthetic MFM data generation, suitable for large scale numerical experiments is also presented.

CEITEC Brno University of Technology Brno 63800 Czech Republic

Czech Metrology Institute Brno 63800 Czech Republic

Department of Physical Electronics Faculty of Science Masaryk University Brno 61137 Czech Republic

IFW Dresden Dresden 01069 Germany

National Physical Laboratory Teddington TW11 0LW United Kingdom

Physics Department Royal Holloway University of London Egham TW20 0EX United Kingdom

Physikalisch Technische Bundesanstalt Braunschweig 38116 Germany

Plasma Technologies CEITEC Masaryk University Brno 62500 Czech Republic

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Synthetic Data in Quantitative Scanning Probe Microscopy