Two-dimensional nature of four-layer cuprate superconductors

Abstract

The magnetization of the four-layer superconductor ${\mathrm{CuBa}}_{2}{\mathrm{Ca}}_{3}{\mathrm{Cu}}_{4}{\mathrm{O}}_{12\ensuremath{-}\ensuremath{\delta}}$ with ${T}_{c}\ensuremath{\simeq}117\mathrm{K}$ is presented. The high-field magnetization around ${T}_{c}(H)$ follows the exact two-dimensional scaling function given by Te\ifmmode \check{s}\else \v{s}\fi{}anovi\ifmmode \acute{c}\else \'{c}\fi{} and Andreev. This feature is contrary to the inference that the interlayer coupling becomes strong if the number of ${\mathrm{CuO}}_{2}$ planes in a unit cell increases. Also, the fluctuation-induced susceptibility in the low-field region was analyzed by using the modified Lawrence-Doniach model. The effective number of independently fluctuating ${\mathrm{CuO}}_{2}$ layers per unit cell, ${g}_{\mathrm{eff}},$ turned out to be $\ensuremath{\simeq}2$ rather than 4, which indicated that two among the four ${\mathrm{CuO}}_{2}$ layers were in states far from their optimal doping levels. This result could explain why ${\mathrm{CuBa}}_{2}{\mathrm{Ca}}_{3}{\mathrm{Cu}}_{4}{\mathrm{O}}_{12\ensuremath{-}\ensuremath{\delta}}$ shows two-dimensional behavior.