Ginzburg-Landau parameter in ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{6.95}$ below the irreversibility temperature as measured by ${\mathrm{\mu }}^{+}$SR in high magnetic fields

The vortex state of a type-II superconductor produces a distinctive ${\mathrm{\mu }}^{+}$SR line shape with features determined by the average internal field ${\mathit{B}}_{\mathit{o}}$, the magnetic penetration depth λ, the superconducting coherence length ξ, and the degree of disorder in the vortex lattice. Only in the high field regime (λ≫L>ξ, where L is the intervortex spacing) do the vortex cores (of radius ≊ξ) occupy a large enough area that they are observable in the line shape as a high field cutoff. Our ${\mathrm{\mu }}^{+}$SR measurements of the field distributions in a mosaic of single crystals of ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{6.95}$ in fields of 1.9, 4.1, 4.7, and 6.5 T (${\mathbf{B}}_{\mathit{o}}$≡c) are the measurements by μSR or NMR in a high-${\mathit{T}}_{\mathit{c}}$ superconductor which show all the features of the line shape. We find λ=0.15±0.01 μm at 10 K and the Ginzburg-Landau parameter κ≡λ/ξ=69.6±1.4 constant between 30 and 75 K; this is the only measurement to date of κ in ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{6.95}$ below the irreversibility temperature. Due to disorder in the vortex lattice, either from pinning or from vortex fluctuations that are quasistatic on the time scale of ${\mathrm{\mu }}^{+}$SR, the observed line shape is ‘‘smeared’’ relative to that predicted for a perfect lattice. From the degree of smearing, we estimate an upper limit of 5.5% for the rms deviation of individual vortices from their ideal positions.