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Determination of the magnetic penetration depth from finite-element susceptibility calculations of spheroidal and cylindrical superconductors

M. J. Grant and A. Carrington

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Phys. Rev. B 114, 194507 – Published 13 October, 2026

DOI: https://doi.org/10.1103/rvkn-1sm8

Abstract

The magnetic penetration depth, λ, is a fundamental parameter of the superconducting state and is commonly determined from precision measurements of the magnetic susceptibility, χ, in the Meissner state. However, extracting λ from such measurements requires an accurate treatment of geometry-dependent demagnetization effects, for which analytic results are only available in a limited number of cases. Here we present a finite-element analysis of the magnetic response of three-dimensional superconducting spheroids and cylinders with finite penetration depth. By calculating the magnetic moment and susceptibility, χ(λ), over a wide range of aspect ratios, we quantify the shape-dependent Meissner response and extract effective demagnetization factors in the λ→0 limit. For small but finite λ, we further determine effective sample dimensions from the initial variation of χ(λ) and propose an improved analytical expression for these. Our results provide a high-precision procedure for determining λ from volume-exclusion based susceptibility measurements and should be directly applicable to the characterization of superconducting materials.

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Phys. Rev. B 114, 194507– Published 13 October, 2026
  • Received 23 June 2026
  • Revised 21 August 2026
  • Accepted 29 September 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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