Reversible magnetization, critical fields, and vortex structure in grain-aligned ${\mathrm{YBa}}_2$${\mathrm{Cu}}_4$${\mathrm{O}}_8$

Reversible-magnetization data have been studied for ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_4$ ${\mathrm{O}}_8$ in order to determine the thermodynamic properties and the magnetic-field dependence of the superfluid density. By fitting the Hao-Clem variational model to the reversible magnetization data below ${\mathit{T}}_{\mathit{c}}$, superconducting parameters such as the Ginzburg-Landau parameter κ, the thermodynamic critical field ${\mathit{H}}_{\mathit{c}}$, and the superconducting order parameter are determined. The upper and lower critical fields ${\mathit{H}}_{\mathit{c}2}$,${\mathit{H}}_{\mathit{c}1}$, the penetration depth λ, and the coherence length ξ are derived. Within the model there is a direct connection between the magnetization and the superfluid density, so the vortex structure, the behavior of the average order parameter in (H,T) plane, and the magnetic-field dependence of the superfluid density are obtained. In the high-field region, the evidence of strong vortex fluctuation effects is observed and explained by vortex fluctuation for a three-dimensional superconductor. The mean-field transition temperature ${\mathit{T}}_{\mathit{c}}$(H) and ${\mathit{dH}}_{\mathit{c}2}$/dT near ${\mathit{T}}_{\mathit{c}}$ derived from the analysis of vortex fluctuation effects are comparable with fitting results.