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

TL;DR

This paper investigates how magnetic field orientation affects the dimensional crossover phenomena in cuprate superconductors, revealing the significance of slab thickness and anisotropy in their critical behavior and experimental measurements.

Contribution

It introduces a framework explaining 2D and 3D crossing points in magnetization data and estimates the minimum superconducting slab thickness in cuprates based on experimental crossing point data.

Findings

2D crossing points occur at the critical temperature in specific field orientations.

The minimum superconducting slab thickness varies with material and influences critical parameters.

Experimental T_c versus λ² plots do not follow a universal linear trend near the underdoped limit.

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.