Theoretical approach to magnetic force microscopy

This paper presents an analytical approach to magnetic force microscopy (MFM). Some features of a realistic magnetic tip, modeled by a truncated pyramid, have been studied theoretically. By use of analytical formulas to describe the magnetic field above a sample with periodic domains and perpendicular anisotropy, tip-sample interaction has been calculated as a function of tip geometry and tip-sample distance. Lateral resolution and sensitivity are related to the geometrical parameters that describe the shape of the tip, which leads to the surprising result that it is not the tip with the smallest tip radius that gives rise to the highest lateral resolution in MFM. Depending on the tip volume, the force sensitivity can vary by more than a factor of 3. The lateral resolution is shown to decrease, as expected, with increasing tip-sample separation. The theoretical results presented here are of relevance for the interpretation and comparison of experimental results. For a tip of given geometry and magnetization, the results of this paper allow the determination of the expected lateral resolution and sensitivity as a function of tip-sample separation