Determination of the Magnetic Penetration Depth from Finite-Element Susceptibility Calculations of Spheroidal and Cylindrical Superconductors

Abstract

The magnetic penetration depth, $\lambda$, is a fundamental parameter of the superconducting state and is commonly determined from precision measurements of the magnetic susceptibility, $\chi$, in the Meissner state. However, extracting $\lambda$ 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, $\chi (\lambda )$, over a wide range of aspect ratios, we quantify the shape-dependent Meissner response and extract effective demagnetization factors in the $\lambda \to 0$ limit. For small but finite $\lambda$, we further determine effective sample dimensions from the initial variation of $\chi (\lambda )$ and propose an improved analytical expression for these. Our results provide a high-precision procedure for determining $\lambda$ from volume-exclusion based susceptibility measurements and should be directly applicable to the characterization of novel superconducting materials.

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