Critical fields and vortex structure of ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ derived from reversible magnetization

The magnetic-field and temperature dependence of the Ginzburg-Landau order parameter 〈f〉 is derived from magnetization studies for grain-aligned ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ in the region of thermodynamic reversibility, based on the Hao-Clem model. The value of 〈f〉 at 5 T and 89 K is still 52.3% of the zero-field value. Fitting the magnetization data to the Hao-Clem theory reveals that ${\mathrm{\kappa }}_{\mathit{c}}$ is a slowly decreasing function of temperature near ${\mathit{T}}_{\mathit{c}}$. ${\mathit{H}}_{\mathit{c}}$(T) and ${\mathit{H}}_{\mathit{c}2}$(T) were determined with high precision along with the ${\mathrm{\kappa }}_{\mathit{c}}$(T) values. The detailed shape of the order parameter is derived from ${\mathrm{\kappa }}_{\mathit{c}}$(T) and ${\mathit{H}}_{\mathit{c}}$(T) data. Characteristic variables derived from the data are ${\mathit{H}}_{\mathit{c}}$(0)=1.18×${10}^4$ Oe, ${\lambda }_{\mathit{a}\mathit{b}}$(0)=1.31×${10}^3$ Å, and ${\xi }_{\mathit{a}\mathit{b}}$(0)=18 Å. The BCS fitting of ${\mathit{H}}_{\mathit{c}}$ reveals that the value of -${\mathit{dH}}_{\mathit{c}2}$/dT decreases from 2.25 T/K at T=82 to 1.9 T/K at ${\mathit{T}}_{\mathit{c}}$ of 92.4 K.