Magnetic force microscopy of layered superconductors

Abstract

The solution of a general problem in the magnetic force microscopy ͑MFM͒ of superconducting multilayers in the Meissner state is presented. We treat an arbitrary number of layers M with constant penetration depth j within each. The solution method is based upon a transfer matrix approach which provides semianalytic results. The technique is illustrated by numerical examples wherein the kernel function and lifting force are obtained. The ability to approximate continuous penetration depth profiles in half-space geometry by means of piecewise constant profiles is demonstrated. The utility of the piecewise constant representation for future application in the MFM inverse problem is discussed.

Application of magnetic force microscopy in nanomaterials characterization

“…The MFM continues to be mostly a qualitative tool, despite sophisticated modeling (Coffey, 1999(Coffey, , 2000Wadas, 1990). The basic problem is that MFM data consists of contours of equal force gradient, which in turn is proportional to the gradient of the magnetic field perpendicular to the sample (for a tip magnetized perpendicular to the sample surface).…”