Inverse magnetic force microscopy of superconductors in half-space geometry

A key step in an inversion algorithm to recover the penetration depth lambda for a superconductor in the Meissner state from one-dimensional magnetic force microscopy (MFM) data is demonstrated numerically. The profile lambda(z) is found as a function of distance z into a superconducting half space. The algorithm reduces the inversion to the solution of a nonlinear system of ordinary differential equations of first order. A precursor inverse Laplace transformation of the MFM force data as a function of height gives a kernel function K which provides the initial conditions for integrating the nonlinear system. The results show that the penetration depth can be reconstructed to increasing distances within the sample as the size of the truncation of the nonlinear system is increased. Analytic results for the force function for the examples are also presented. (C) 2000 American Institute of Physics. [S0021-8979(00)01401-8].