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Two-band effect on the vortex dynamics and critical current density in an anisotropic MgB$_2$ thin film

We report the influence of intrinsic superconducting parameters on the vortex dynamics and the critical current densities of a MgB$_2$ thin film. The small magnetic penetration depth of λ= 50 nm at T=4 K is related to a clean π-band, and transport and magnetization data show an upper critical field similar to those reported in clean single crystals. We find a high self-field critical current density Jc, which is strongly reduced with applied magnetic field, and attribute this to suppression of the superconductivity in the π-band. The temperature dependence of the creep rate S(T) at low magnetic field can be explained by a simple Anderson-Kim mechanism. The system shows high pinning energies at low field that are strongly suppressed by high field, which is consistent with a two-band contribution.