Coherence lengths and anisotropy in ${\mathrm{MgB}}_2$ 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 ${\xi }_{\mathrm{MF}}$ in the mixed state and a temperature-independent anisotropy ratio ${\gamma }_{\mathrm{MF}}={\xi }_{\mathrm{MF}}^{\mathrm{ab}}/{\xi }_{\mathrm{MF}}^c\approx 2.$ At the superconducting transition, the scaling of the fluctuation conductivity yields the Ginzburg-Landau coherence length with a different anisotropy ratio ${\gamma }_{\mathrm{GL}}=2.8,$ also temperature independent.