Method to extracting the penetration field in superconductors from DC magnetization data

The lower critical field, B_c1, is one of the fundamental quantities of a superconductor that directly manifests the Cooper pair bulk density in the material. Although this field can be measured using several techniques, the most conventional method is to calculate this field from the experimentally measured DC penetration field, B_p, which is defined as the starting point of the deviation of the DC magnetization curve, M(B_appl), from a linear dependence. Surprisingly, we found no mathematical routine that describes how this starting point of deviation can be found. Here, we propose the extraction of B_p from the fit of the M(B_appl) dataset to the power law, where the threshold criterion M_c can be established by a convention. The advantage of this approach is that the procedure extracts one additional characteristic parameter: the power-law exponent. We demonstrated the applicability of this approach to polycrystalline ThIr₃, WB_4.2, BaTi₂Bi₂O, and Th₄H₁₅; thin films of Pb and MgB₂; and Nb single crystal. In most reports, B_c1(T) analysis is limited by the extraction of the London penetration depth. We advanced the analysis to extract primary thermodynamic superconducting parameters [i.e., the ground state superconducting energy gap, Δ(0); the relative jump in electronic specific heat at transition temperature, ΔCγT_c; and the gap-to-transition temperature ratio, 2Δ0k_BT_c] from B_c1(T) data. This extraction was performed for Nb, ThIr₃, TaRh₂B₂, and NbRh₂B₂.