Measurement of the magnetic penetration depth of a superconducting MgB$_{2}$ thin film with a large intraband diffusivity
We report the temperature dependent magnetic penetration depth $λ(T)$ and the superconducting critical field $H_{c2}(T)$ in a 500-nm MgB$_{2}$ film. Our analysis of the experimental results takes into account the two gap nature of the superconducting state and indicates larger intraband diffusivity in the three-dimensional (3D) $π$ band compared to that in the two-dimensional (2D) $σ$ band. Direct comparison of our results with those reported previously for single crystals indicates that larger intraband scattering in the 3D $π$ band leads to an increase of $λ$. We calculated $λ$ and the thermodynamic critical field $H_{c}\approx$2000 Oe employing the gap equations for two-band superconductors. Good agreement between the measured and calculated $λ$ value indicates the two independent measurements, such as magnetic force microscopy and transport, provide a venue for investigating superconducting properties in multi-band superconductors.