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

Abstract

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.

Magnetic force microscopy of layered superconductors

“…However, there are technical avenues to overcome several of these complications. 2,17 The multilayer representation of a superconducting halfspace provides a suitable discrete description for an approximate solution of the MFM inverse problem. The set of unknowns to be determined could include the number of layers, M, the values ͕ j ͖ jϭ1 M , and the thicknesses ͕z j Ϫz jϪ1 ͖ jϭ2 M .…”

Theory of vortex force microscopy in superconducting layers

“…2 From the theoretical side, some remarkable advances refer to the still challenging inverse problem, i.e., recovering superconducting properties from observable quantities. In particular, the nondestructive evaluation of inhomogeneous penetration depth ͑r ជ͒, 3,4 and the concomitant difficulties related to finite-size effects, 5 have been dealt with. However, much of this work is only focused on Meissner state superconductors.…”