Temperature dependence of lower critical fields in Y-Ba-Cu-O crystals

The temperature dependence of the anisotropic lower critical fields $H_{c1\mathrm{}}$ in single-crystal Y-Ba-Cu-O is determined from the onset of flux penetration in zero-field-cooled dc magnetization versus temperature from $T_c$ down to $0.5T_c$. An extended Bean-critical-state model is developed to define this onset consistently. The $H_{c1\mathrm{}}\text{'}\mathrm{s}$ are linear in temperature near $T_c$ as in Ginzburg-Landau theory and consistent with a clean local-limit BCS form with extrapolated $H_{c1\mathrm{}}\mathrm{}(T=0\mathrm{})=180\mathrm{}$ Oe for $\mathrm{H}\perp \hat{c}$ and 530 Oe for $\mathrm{H}\parallel \hat{c}$.