Torque magnetometry on single-crystal high-temperature superconductors near the critical temperature: A scaling approach

Abstract

Angular-dependent magnetic torque measurements performed near the critical temperature on single crystals of ${\mathrm{HgBa}}_{2}{\mathrm{CuO}}_{4+y},$ ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{CuO}}_{4},$ and ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{6.93}$ are scaled, following the three-dimensional (3D) $\mathrm{XY}$ model, in order to determine the scaling function ${\mathrm{dG}}^{\ifmmode\pm\else\textpm\fi{}}(z)/dz$ which describes the universal critical properties of high-${T}_{c}$ cuprates near ${T}_{c}.$ A systematic shift of the scaling function with increasing effective mass anisotropy $\ensuremath{\gamma}=\sqrt{{m}_{c}^{*}{/m}_{a}^{*}}$ is observed, which may be understood in terms of a 3D-2D crossover. Further evidence for a 3D-2D crossover is found from temperature-dependent torque measurements carried out in different magnetic fields at different field orientations $\ensuremath{\delta},$ which show a quasi-2D crossing region ${(M}^{*}{,T}^{*}).$ The occurrence of this crossing phenomenon is explained in a phenomenological way from the weak z dependence of the scaling function around a value ${z=z}^{*}.$ The crossing temperature ${T}^{*}$ is found to be angular dependent. Torque measurements above ${T}_{c}$ reveal that fluctuations are strongly enhanced in the underdoped regime where the anisotropy is large, whereas they are less important in the overdoped regime.