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

The temperature dependence of the anisotropic lower critical fields Hc1 in single-crystal Y-Ba-Cu-O is determined from the onset of flux penetration in zero-field-cooled dc magnetization versus temperature from Tc down to 0.5Tc. An extended Bean-critical-state model is developed to define this onset consistently. The Hc1's are linear in temperature near Tc as in Ginzburg-Landau theory and consistent with a clean local-limit BCS form with extrapolated Hc1(T=0)=180 Oe for Hc^ and 530 Oe for Hc.