Uncertainty Analysis of Stray Field Measurements by Quantitative Magnetic Force Microscopy

Magnetic force microscopy (MFM) measurements generally provide phase images that represent the signature of domain structures on the surface of nanomaterials. To quantitatively determine stray magnetic fields based on an MFM image requires calibrated properties of the magnetic tip. In this article, an approach is employed for calibrating a magnetic tip using a Co/Pt multilayered film as a reference sample that shows stable well-known magnetic properties and well-defined perpendicular band domains. The approach is based on a regularized deconvolution process in the Fourier domain with a Wiener filter and the L-curve method for determining a suitable regularization parameter to get a physically reasonable result. The calibrated tip is applied for a traceable quantitative determination of the stray fields of a test sample, which has a spatial frequency spectrum covered by that of the reference sample. According to the “guide to the expression of uncertainty in measurement,” uncertainties of the processing algorithm are estimated considering the fact that the regularization influences the quantitative analysis significantly. We discuss relevant uncertainty components and their propagations between the real domain and the Fourier domain for both, the tip calibration procedure and the stray field calculation, and propose an uncertainty evaluation procedure for quantitative MFM.