Magnetic Transitions of Superconducting Thin Films and Foils. I. Lead

Abstract

The perpendicular and parallel magnetic transitions for pure Pb films and foils have been determined from transverse magnetization and ac susceptibility measurements as a function of thickness (400 Å to 35 μ) and temperature (1.4 to 4.2°K). The perpendicular critical field ($H_{\perp }$) for thicknesses less than a critical thickness, $d_c\approx 15$ kÅ, is in good agreement with the theory of Tinkham if it is assumed that the penetration depth is thickness-dependent. The data for thicknesses above $d_c$ follow a thickness dependence predicted from the effect of a positive surface energy on the free energy of the intermediate state. At $d_c$ there is a minimum in $H_{\perp }$. The parallel critical field ($H_{\parallel }$) up to $d_c$ is in good agreement with the theory of Saint James and de Gennes for a second-order transition. Above $d_c$, $H_{\parallel }$ agrees with the bulk value of $H_{c3\mathrm{}}$ for lead. In the vicinity of $d_c$ the magnetization curve starts to exhibit a reversible tail which persists to larger thicknesses and whose slope is in reasonable agreement with theory. From the data, the bulk values of $\kappa \mathrm{}\left(T\right)\mathrm{}$, $\lambda \mathrm{}\left(T\right)\mathrm{}$, ${\lambda }_L\mathrm{}\left(0\right)\mathrm{}$, and ${\xi }_0$, as well as the thickness dependence of these quantities, have been computed.