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≈2000 Oe by 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 multiband superconductors.