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The magnetic penetration depth, $\lambda^{-2}(T)$, in the basal plane of amagnesium diboride (MgB$_2$) film was measured using a two-coil mutualinductance technique at 50 kHz. This film has $T_c\simeq 38$ K, $\Delta T_c\leq 1$ K, and $\lambda(0)\sim 1500$ \AA. At low temperatures,$\lambda^{-2}(T)$ shows a clear exponential temperature dependence, indicatings-wave superconducting order parameter symmetry. However, the data are notquantitatively well described by theory assuming a single gap. From the datafit by the full BCS calculation assuming a double gap, the values of the twodistinct gaps were obtained: $\Delta_S(0)=2.61\pm0.41$ meV and$\Delta_L(0)=6.50\pm0.33$ meV. The contributions of the small and the largegaps to the total superfluid density at T=0 were estimated to be 21% and 79%,respectively. Finally, we consider the effect of gap anisotropy on thepenetration depth measurements, and find that the anisotropy does not play asignificant role in determining the temperature dependence of the penetrationdepth.Comment: 8 pages, 5 figure

physical review. b, condensed matter

Reflection of a two-gap nature in penetration-depth measurements of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">MgB</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>film

Reflection of a two-gap nature in penetration-depth measurements ofMgB2film