Determining the permeability of a half space of linear magnetic material by magnetic force microscopy

Abstract

A fundamental inversion problem for the magnetic force microscopy (MFM) of a semiinfinite linear magnetic material is formulated. The solution is developed for a general applied field in the upper half space. Static conditions are assumed so that a magnetic scalar potential can be employed. By specializing to a point-source model for the MFM tip, it is shown how the magnetic permeability μ(z) depending only upon the vertical coordinate can be recovered from one-dimensional force measurements. The inversion procedure uses a wave number-dependent kernel function K(k), which is analogous to a surface impedance ratio. A numerical example illustrates the process of obtaining μ(z) from the kernel function. The inversion results describe the use of MFM data to extract a material property as a function of depth.

Magnetic force images of nanomagnetic domains taken with platinum-coated tips

“…The tip/substrate interaction present during immersion of the Co-coated tip in the substrate film magnetic field was previously described; [13][14][15][16][17] the Pt-coated tip/substrate interaction is going to be discussed next. The tip was defined as having a sharpened conical shape with one flat end with area of r 2 .…”

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 .…”

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).…”