Quantification of magnetic force microscopy images using combined electrostatic and magnetostatic imaging

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Abstract
A method for calibrating the force gradients and probe magnetic moment in phase-contrast magnetic force microscopy (MFM) is introduced. It is based upon the combined electrostatic force microscopy EFM and MFM images of a conducting non magnetic metal strip. The behavior of the phase contrast in EFM is analyzed and modeled as a finite area capacitor. This model is used in conjunction with the imaging data to derive the proportionality constant between the phase and the force gradient. This calibration is further used to relate the measured MFM images with the field gradient from the same conducting strip to derive the effective magnetic moment of the probe. The knowledge of the phase-force gradient proportionality constant and the probe’s effective moment is essential to directly quantify field derivatives in MFM images.