Quantitative interpretation of magnetic force microscopy images from soft patterned elements

By combining a finite element tip model and numerical simulations of the tip–sample interaction, it is shown that magnetic force microscopy images of patterned soft elements may be quantitatively compared to experiments, even when performed at low lift heights, while preserving physically realistic tip characteristics. The analysis framework relies on variational principles. Assuming magnetically hard tips, the model is both exact and numerically more accurate than hitherto achieved.