Determination of the crystal-field splitting of the 4f1 state in samarium-alloyed cerium hexaboride

The cerium hexaboride and its alloyed compounds are strongly correlated materials, hosting many-body hidden order or nontrivial band topology. The fine electronic structure of the Ce $4{f}^{1}$ state, derived from spin-orbit coupling and crystal electric field splitting (CEF), plays a vital role in forming the exotic quantum state in Ce-based compounds. By using the high-resolution resonant inelastic x-ray scattering technique, we determined the fine electronic excitation energies of the Ce $4{f}^{1}$ state in the Kondo material ${\mathrm{Ce}}_{0.3}{\mathrm{Sm}}_{0.7}{\mathrm{B}}_{6}$. The extracted energy levels show an overall consistency with other scattering techniques, except that CEF splitting in the total angular momentum $J=7/2$ state is identified to be $(89.5\ifmmode\pm\else\textpm\fi{}1)$ meV, clearly larger than the value of 82 meV drawn from Raman spectroscopy. A detailed discussion is made to reconcile the mismatch. This work provides key information on the Ce $4{f}^{1}$ orbital in ${\mathrm{CeB}}_{6}$, which would also put a constraint on the related theoretical model, helping to address the challenges for theoretical dealings with many-body correlations in Ce $4{f}^{1}$ compounds.