Multigap Superconductivity in the Filled-Skutterudite Compound LaRu$_4$As$_{12}$ probed by muon spin rotation

Muon spin rotation ($\mu$SR) and inelastic X-ray scattering (IXS) were used to investigate the superconducting properties of the filled-skutterudite compound LaRu$_{4}$As$_{12}$. A two-gap isotropic ($s+s$)-wave model can explain the temperature dependence of the superfluid density. Zero field $\mu$SR measurements confirm that the time-reversal symmetry does not break upon entering the superconducting state. The measurements of lattice dynamics at 2, 20 and 300 K revealed temperature dependencies of the phonon modes that do not follow strictly a hardening of phonon frequencies upon cooling as expected within the quasi-harmonic picture. The 20~K data rather mark a turning point for the majority of the phonon frequencies. Indeed a hardening is observed approaching 20~K from above, while for a few branches a weak softening is visible upon further cooling to 2~K. The observed dispersion relations of phonon modes throughout the Brillouin zone matches with the DFT prediction quite closely. Our results point out that cubic LaRu$_{4}$As$_{12}$ is a good reference material for studying multiband superconductivity, including those with lower crystallographic symmetries such as iron arsenide-based superconductors.