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Weak interband-coupling superconductivity in the filled skutterudite<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>LaPt</mml:mi><mml:mn>4</mml:mn></mml:msub><mml:msub><mml:mi>Ge</mml:mi><mml:mn>12</mml:mn></mml:msub></mml:mrow></mml:math>
The superconducting pairing state of ${\mathrm{LaPt}}_{4}{\mathrm{Ge}}_{12}$ is studied by measuring the magnetic penetration depth $\ensuremath{\lambda}(T,B)$ and superfluid density ${\ensuremath{\rho}}_{s}(T)$ using a tunnel-diode-oscillator (TDO)-based method and transverse-field muon-spin rotation $(\mathrm{TF}\text{\ensuremath{-}}\ensuremath{\mu}\mathrm{SR})$ spectroscopy. The penetration depth follows an exponential-type temperature dependence at $T\ensuremath{\ll}{T}_{c}$, but increases linearly with magnetic field at $T=1.5$ K. A …