Thermodynamic parameters of ${\mathrm{HgBa}}_2$${\mathrm{Ca}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{8\mathrm{-}\mathit{x}}$ from high-field magnetization

We have measured the temperature dependence of reversible magnetization of grain-aligned ${\mathrm{HgBa}}_2$ ${\mathrm{Ca}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{8\mathrm{-}\mathit{x}}$ high-${\mathit{T}}_{\mathit{c}}$ superconductors with external magnetic field parallel to the c axis. Our data show the crossover of the magnetization below the superconducting onset temperature, which indicates a dominant vortex fluctuation. Except this vortex fluctuation region, reversible magnetization data could be described by using Hao and Clem’s model. From the analysis magnetization curve based on this model, the thermodynamic critical field ${\mathit{H}}_{\mathit{c}}$(T) and Ginzburg-Landau parameter κ=118 were extracted. Also, we obtained the superconducting parameters; the penetration depth ${\lambda }_{\mathit{a}\mathit{b}}$(0)=2060 Å, coherence length ${\xi }_{\mathit{a}\mathit{b}}$(0)=18 Å, and the zero-temperature upper critical field ${\mathit{H}}_{\mathit{c}2}$(0)=108 T.