Magnetic Field induced Dimensional Crossover Phenomena in Cuprate Superconductors and their Implications

We discuss the occurrence of crossing points in the magnetization temperature (m,T ) plane within the framework of critical phenomena. It is shown that in a two-dimensional superconducting slab of thickness ds mz (δ) versus temperature T curves measured in different fields H = H (0, sin (δ) , cos (δ)) will cross at the critical temperature Tc of the slab. In contrast, in a 3D anisotropic bulk superconductor the crossing point occurs in the plot mz (δ) /H 1/2 z versus T . The experimental facts that 2D crossing point features have been observed in ceramics and in single crystals for H close to H = H (0, 0, 1), but not for H = H (0, 1, 0), is explained in terms of an angle-dependent crossover field separating the regions where 2D or 3D thermal fluctuations dominate. The measured 2D-crossing point data are used to estimate one of the fundamental parameters of cuprate superconductors, the minimum thickness of the slab (ds), which remains superconducting. Our estimates, based on experimental 2D-crossing point data for single crystals, reveal that this length adopts material dependent values. Therefore, experimental data for Tc and λ‖ (T = 0), plotted in terms of Tc versus 1/λ 2 ‖ (T = 0) will not tend to a straight line with universal slope as the underdoped limit is approached. Implications for magnetic torque measurements are also worked out.