An Inverse Problem for the ac Magnetic Force Microscopy of Superconductors

1999

Phys. Rev. Lett.

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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.

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confidence: 99%

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confidence: 99%

“…The issue of the inverse Laplace transform of a real-valued function was discussed and simple numerical examples were presented in Ref. [8].…”

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confidence: 99%

“…The functions R͑k͒ and T ͑k͒, respectively, specify the induced and penetration fields without and within the superconductor, by way of Hankel transforms [8],…”

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confidence: 99%

“…In Ref. [8] it was shown how Eq. (9) together with its initial conditions can be used to analytically construct the penetration depth profile from its Taylor series.…”

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confidence: 99%

See 3 more Smart Citations

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

1999

Phys. Rev. Lett.

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Theory for coil impedance of a conducting half space: Analytic results for eddy current analysis

Journal of Applied Physics

2001

The general formulation of the coil impedance of a conducting but nonmagnetic half space is examined. An intermediate kernel function is used to recast the theory in a form which gives a fuller physical interpretation and at the same time provides avenues for the solution of the ill-conditioned inverse conductivity problem. In particular, reflection and transmission coefficients depending upon the kernel function are introduced, which yield expressions for the induced and penetration fields, respectively. Correspondences between the forward and inverse conductivity problems, and problems in the London theory of superconductivity for the penetration depth, are established. The use of the kernel function aids in the development of analytic expressions for the single- and multiturn coil impedance and their instance for a half space of constant conductivity. Analytic results are obtained for various integral representations for both general and special impedance cases.

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

Journal of Applied Physics

1999

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.