Coherence lengths and anisotropy in MgB 2 superconductor

Field- and temperature-dependent microwave measurements have been carried out on ${\mathrm{MgB}}_{2}$ thin film grown on ${\mathrm{Al}}_{2}{\mathrm{O}}_{3}$ substrate. The analysis reveals the mean-field coherence length ${\ensuremath{\xi}}_{\mathrm{MF}}$ in the mixed state and a temperature-independent anisotropy ratio ${\ensuremath{\gamma}}_{\mathrm{MF}}={\ensuremath{\xi}}_{\mathrm{MF}}^{\mathrm{ab}}/{\ensuremath{\xi}}_{\mathrm{MF}}^{c}\ensuremath{\approx}2.$ At the superconducting transition, the scaling of the fluctuation conductivity yields the Ginzburg-Landau coherence length with a different anisotropy ratio ${\ensuremath{\gamma}}_{\mathrm{GL}}=2.8,$ also temperature independent.