Critical fields and critical currents of superconducting disks in transverse magnetic fields

The large nonuniform and field-dependent demagnetizing factors of superconducting disks in transverse magnetic fields complicates the determination of the lower critical field and critical current from magnetization. Correcting the applied field with a constant ellipsoidally approximated demagnetization correction D′ can result in significant errors. In this study of the magnetization characteristics of lead and Nb-Ti disks with various aspect ratios a, we find an empirical relation D′(a) that describes the scaling of the applied-field value ${\mathrm{H}}_{\mathrm{c}}^{\prime }$ (${\mathrm{H}}_{\mathrm{c}1\mathrm{}}^{\prime }$), at which flux penetration occurs, with respect to the intrinsic (lower) critical fields ${\mathrm{H}}_{\mathrm{c}}$ (${\mathrm{H}}_{\mathrm{c}1\mathrm{}}$). A model is described for determining ${\mathrm{H}}_{\mathrm{c}1\mathrm{}}$ and ${\mathrm{J}}_{\mathrm{c}}$ for such a geometry. The results have important implications for various magnetic measurements in high-${\mathrm{T}}_{\mathrm{c}}$ superconductors. The errors that can result in the measured values of ${\mathrm{H}}_{\mathrm{c}1\mathrm{}}$ and ${\mathrm{J}}_{\mathrm{c}}$, in the inferred penetration depths, and in the effective-mass anisotropies, are discussed.