Theory of Inverse Magnetic Force Microscopy of Superconductors in Half-Space Geometry

Recent advances in the theory of the inversion of magnetic force microscopy (MFM) force data describe the recovery of the penetration depth for a superconductor in the Meissner state. The algorithm reduces the inversion to the solution of a nonlinear system of ordinary differential equations of first order. Given a precursor inverse Laplace transformation of the MFM force data as a function of height, the penetration depth can be reconstructed to increasing distances within the sample as the size of the integrated truncation of the nonlinear system is increased. With the inclusion of an appropriate shape factor, problems with a spatially extended MFM tip can be treated.