A complex structure of the superconducting order parameter in $Ln_2$C$_3$ ($Ln$ = La, Y) is demonstrated by muon spin relaxation ($mu$SR) measurements in their mixed state. The muon depolarization rate [$sigma_{rm v}(T)$] exhibits a characteristic te
mperature dependence that can be perfectly described by a phenomenological double-gap model for nodeless superconductivity. While the magnitude of two gaps is similar between La$_2$C$_3$ and Y$_2$C$_3$, a significant difference in the interband coupling between those two cases is clearly observed in the behavior of $sigma_{rm v}(T)$.
Local magnetic field distribution B(r) in the mixed state of a boride superconductor, YB6, is studied by muon spin rotation (muSR). A comparative analysis using the modified London model and Ginzburg-Landau (GL) model indicates that the GL model exhi
bits better agreement with muSR data at higher fields, thereby demonstrating the importance of reproducing the field profile near the vortex cores when the intervortex distance becomes closer to the GL coherence length. The temperature and field dependence of magnetic penetration depth ($lambda$) does not show any hint of nonlocal effect nor of low-lying quasiparticle excitation. This suggests that the strong coupling of electrons to the rattling motion of Y ions in the boron cage suggested by bulk measurements gives rise to a conventional superconductivity with isotropic s-wave pairing. Taking account of the present result, a review is provided for probing the anisotropy of superconducting order parameters by the slope of $lambda$ against field.
