Determination of the Magnetic Penetration Depth from Finite-Element Susceptibility Calculations of Spheroidal and Cylindrical Superconductors
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 $λ\rightarrow 0$ 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 novel superconducting materials.