Crystal-field excitations and quadrupolar fluctuations of 4 f-electron systems studied by polarized light scattering

We present Raman-scattering results for three materials, CeB6, TbInO3, and YbRu2Ge2, to illustrate the essential aspects of crystal-field (CF) excitations and quadrupolar fluctuations of 4f-electron systems. For CF excitations, we illustrate how the 4f orbits are split by spin-orbit coupling and CF potential by presenting spectra for inter- and intra-multiplet excitations over a large energy range. We discuss identification of the CF ground state and establishment of low-energy CF level scheme from the symmetry and energy of measured CF excitations. In addition, we demonstrate that the CF linewidth is a sensitive probe of electron correlation by virtue of self-energy effect. For quadrupolar fluctuations, we discuss both ferroquadrupolar (FQ) and antiferroquadrupolar (AFQ) cases. Long-wavelength quadrupolar fluctuations of the same symmetry as the FQ order parameter persists well above the transition temperature, from which the strength of electronic intersite quadrupolar interaction can be evaluated. The tendency towards AFQ ordering induces ferromagnetic correlation between neighboring 4f-ion sites, leading to long-wavelength magnetic fluctuations.