Evidence for three-dimensionalXYcritical properties in underdopedYBa2Cu3O7−δ

We perform a detailed analysis of the reversible magnetization data of Salem-Sugui et al. and Babíc et al. of underdoped and optimally doped $\mathrm{Y}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$ single crystals. Near the zero field transition temperature we observe extended consistency with the properties of the three-dimensional $XY$ universality class, even though the attained critical regime is limited by an inhomogeneity induced finite size effect. Nevertheless, as $T_c$ falls from $93.5\text{to}41.5\mathrm{K}$, the critical amplitude of the in-plane correlation length ${\xi }_{ab0}$, the anisotropy $\gamma ={\xi }_{ab0}∕{\xi }_{c0}$ and the critical amplitude of the in-plane penetration depth ${\lambda }_{ab0}$ increase substantially, while the critical amplitude of the $c$-axis correlation length ${\xi }_{c0}$ does not change much. As a consequence, the correlation volume $V_{\mathrm{corr}}^{-}$ increases and the critical amplitude of the specific heat singularity $A^{-}$ decreases dramatically, while the rise of ${\lambda }_{ab0}$ reflects the behavior of the zero temperature counterpart. Conversely, although ${\xi }_{ab0}$ and ${\lambda }_{ab0}$ increase with reduced $T_c$, the ratio ${\lambda }_{ab0}∕{\xi }_{ab0}^{-}$, corresponding to the Ginzburg-Landau parameter ${\kappa }_{ab}$, decreases substantially and $\mathrm{Y}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$ crosses over from an extreme to a weak type-II superconductor.