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

Abstract

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 $d_s$ $m_z(\delta )$ versus temperature $T$ curves measured in different fields $\mathbf{H}=H(0,\sin (\delta ),\cos (\delta ))$ will cross at the critical temperature T_c of the slab. In contrast, in a 3D anisotropic bulk superconductor the crossing point occurs in the plot $m_z(\delta )/H_z^{1/2}$ versus $T$. The experimental facts that 2D crossing point features have been observed in ceramics and in single crystals for $\mathbf{H}$ close to $\mathbf{H}=H(0,0,1)$, but not for $\mathbf{H}=H(0,1,0)$, 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 $(d_s)$, 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 T_c and ${\lambda }_{\Vert }^2(T=0)$, plotted in terms of T_c versus $1/{\lambda }_{\Vert }^2(T=0)$ 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.

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