Raman spectroscopy of $f$-electron metals: an example of CeB$_{6}$
We performed an optical spectroscopy study of electronic and magnetic excitations for a rare-earth system with a single electron quasi-localized in the f-shell on an ion at high-symmetry crystallographic site in application to CeB$_{6}$ heavy-fermion metal. We carried out group-theoretical classification of the electronic crystal field (CF) transitions and assessed their coupling to light cross-sections for polarization resolved Raman scattering processes. We discuss applicability of symmetrized Raman susceptibility to studies of exotic charge and spin high multiplet ordering phases in f-electron systems. We study temperature effects on intra- and inter-multiplet CF transitions and also on the coupling between the CF excitations with the lattice vibrations. We acquired temperature dependence of the low-frequency polarization resolved Raman response and obtained the static Raman susceptibility for all Raman-allowed symmetry channels: A$_{1g}$, E$_{g}$, T$_{1g}$, and T$_{2g}$ of the cubic O$_{h}$ point group. We demonstrate that for CeB$_{6}$ system only T$_{1g}$-symmetry static Raman susceptibility shows an anomalous temperature dependence which is consistent with the magnetic susceptibility data measured by other techniques. This anomalous behavior in the T$_{1g}$-channel signifies the presence of long wavelength magnetic fluctuations, while the lack of susceptibility enhancement for all the remaining symmetry channels indicates that long wavelength charge quadrupole fluctuations at low-temperature are weak.