Weak Interband-Coupling Superconductivity in the Filled Skutterudite LaPt4Ge12

The superconducting pairing state of LaPt${}_4$Ge${}_{12}$ is studied by measuring the magnetic penetration depth $\lambda (T,B)$ and the superfluid density ${\rho }_s(T)$ using a tunnel-diode-oscillator (TDO)-based method and by transverse field muon-spin rotation ($\mu$SR) spectroscopy. $\lambda (T)$ follows an exponential-type temperature dependence at $T\ll T_c$, but its zero-temperature value $\lambda (0)$ increases linearly with magnetic field. Detailed analyses demonstrate that both $\lambda (T)$ and the corresponding ${\rho }_s(T)$, measured in the Meissner state by the TDO method are well described by a two-gap $\gamma$ model with gap sizes of ${\mathrm{\Delta }}_1(0)=1.31k_B{T}_c$ and ${\mathrm{\Delta }}_2(0)=1.80k_B{T}_c$ and a very weak interband coupling. In contrast, ${\rho }_s(T)$, derived from the $\mu \mathrm{S}\mathrm{R}$ data taken in a small field, can be fitted by a single-gap BCS model with a gap close to ${\mathrm{\Delta }}_2(0)$. We conclude that LaPt${}_4$Ge${}_{12}$ is a marginal two-gap superconductor and the small gap ${\mathrm{\Delta }}_1$ seems to be destroyed by a small magnetic field. In comparison, in PrPt${}_4$Ge${}_{12}$ the $4f$-electrons may enhance the interband coupling and, therefore, give rise to more robust multiband superconductivity.