Three-dimensional superconducting behavior and thermodynamic parameters of $\mathrm{Hg}{\mathrm{Ba}}_2{\mathrm{Ca}}_{0.86}{\mathrm{Sr}}_{0.14}{\mathrm{Cu}}_2{\mathrm{O}}_{6-\delta }$

This study measures the temperature dependence of reversible magnetization of grain-aligned $\mathrm{Hg}{\mathrm{Ba}}_2{\mathrm{Ca}}_{0.86}{\mathrm{Sr}}_{0.14}{\mathrm{Cu}}_2{\mathrm{O}}_{6-\delta }$ high-$T_c$ superconductor with external magnetic fields parallel to the $c$ axis. The magnetization is field independent at $T^{*}=114.5\mathrm{}$ K, which indicates strong thermal vortex fluctuations. From the vortex fluctuation model, the lower limit of coherence length along the $c$ axis ${\xi }_c\mathrm{}\left(0\right)\mathrm{}\simeq 2$ and the anisotropy ratio $\gamma <~7.7$ has been obtained, which implies that this sample is anisotropic three-dimensional (3D) superconductor as ${\mathrm{Y}}_1{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$. These results are supported by good 3D scaling behavior of high-field magnetization around $T_c\mathrm{}\left(H\right)\mathrm{}$ as a function of $\frac{[T-T_c\mathrm{}(H\left)\right]}{{\mathrm{}\left(\mathrm{TH}\right)\mathrm{}}^{\frac{2}{3}}}$. The thermodynamic critical field $H_c\mathrm{}\left(T\right)\mathrm{}$ and the Ginzburg-Landau parameter $\kappa =114.8\mathrm{}$ were extracted from the model of Hao et al. Also, the various thermodynamic parameters were obtained: the penetration depth ${\lambda }_{\mathrm{ab}}\mathrm{}\left(0\right)=1913\mathrm{}$ Å, coherence length ${\xi }_{\mathrm{ab}}\mathrm{}\left(0\right)=13.9\mathrm{}$ Å, and the zero temperature upper critical field $H_{c2\mathrm{}}\mathrm{}\left(0\right)=170.4\mathrm{}$ T.