The superconducting pairing state of ${\mathrm{LaPt}}_4{\mathrm{Ge}}_{12}$ is studied by measuring the magnetic penetration depth $\lambda (T,B)$ and superfluid density ${\rho }_s\left(T\right)$ using a tunnel-diode-oscillator (TDO)-based method and transverse-field muon-spin rotation $\left(\mathrm{TF}\text{−}\mu \mathrm{SR}\right)$ spectroscopy. The penetration depth follows an exponential-type temperature dependence at $T\ll T_c$, but increases linearly with magnetic field at $T=1.5$ K. A detailed analysis demonstrates that both ${\lambda }_L\left(T\right)$ and ${\rho }_s^{\mathrm{TDO}}\left(T\right)$, measured in the Meissner state using the TDO method, are well described by a two-gap $\gamma$ model with gap sizes of ${\mathrm{\Delta }}_1\left(0\right)=1.31k_B{T}_c$ and ${\mathrm{\Delta }}_2\left(0\right)=1.80k_B{T}_c$, and weak interband coupling. In contrast, ${\rho }_s^{\mu \mathrm{SR}}\left(T\right)$, derived from the $\mu \mathrm{SR}$ data, can be fitted by a single-gap BCS model with a gap close to ${\mathrm{\Delta }}_2\left(0\right)$. We conclude that ${\mathrm{LaPt}}_4{\mathrm{Ge}}_{12}$ is a marginal two-gap superconductor and the small gap ${\mathrm{\Delta }}_1$ seems to be suppressed by a small magnetic field applied in the $\mu \mathrm{SR}$ experiments. In comparison, the $4f$ electrons in ${\mathrm{PrPt}}_4{\mathrm{Ge}}_{12}$ may enhance the interband coupling and, therefore, give rise to more robust multiband superconductivity.

• Received 23 April 2015

DOI:https://doi.org/10.1103/PhysRevB.92.220503