Is MFM really useful?

Abstract

The ill-posed linear inverse problems, characterised by Fredholm integral equations of the first kind, are encountered in many areas of science and technology. This type of problems present some loss of information under the inversion process. The loss of information often makes the inversion process very difficult. Magnetic force microscopy (MFM) is a technique where problems related to loss of information occur. Work is presented here to understand what can be measured by the magnetic force microscope. A simple model is constructed, where the magnetic tip is approximated by a point dipole. Given the force F(r) acting on the dipole tip, we attempt to determine the magnetization distribution in a thin ferromagnetic film, M(r). This calculation should be interesting due to the rapidiy growing interest in magnetic thin films and magnetic multilayers.