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We have investigated the local low-energy excitations in CeRu$_4$Sn$_6$, amaterial discussed recently in the framework of strongly correlated Weylsemimetals, by means of Ce $M_5$ resonant inelastic x-ray scattering (RIXS).The availability of both $^2$F$_\frac{5}{2}$ and $^2$F$_\frac{7}{2}$excitations of the Ce $4f^1$ configuration in the spectra allows for thedetermination of the crystal-electric field parameters that explainquantitatively the temperature dependence and anisotropy of the magneticsusceptibility. The absence of an azimuthal dependence in the spectra indicatesthat all crystal-electric field states are close to being rotational symmetric.We show further that the non-negligible impact of the $\check A_6^0$ parameteron the ground state of CeRu$_4$Sn$_6$ leads to a reduction of the magneticmoment due to multiplet intermixing. The RIXS results are consistent withinelastic neutron scattering (INS) data and are compared to the predictionsfrom \textsl{ab-initio} based electronic structure calculations.

Determining the local low-energy excitations in the Kondo semimetal CeRu$_4$Sn$_6$ using resonant inelastic x-ray scattering