In the figure above, we show the eigenenergies and eigenstates derived from the model Hamiltonian calculation. (a) Evolution of the 4f-orbital energy with CF potential and SOC strength. [from left to center] Increasing CF potential in the absence of SOC (a1), and then increasing SOC strength in the existence of full CF potential (a2); [from left to center] increasing SOC in the absence of CF potential (a3), and then increasing CF potential in the existence of full SOC (a4). In this panel, the full SOC strength is ξ=610 cm−1 , and the full CF potential strengths are B4=-0.758 cm−1 and B6=-0.0165 cm−1 . (b) The wavefunctions and the angular electron-cloud distribution of the eigenstates. [left] The wavefunctions of the eigenstates when only CF potential is present. Red denotes positive value while blue denotes negative value; [middle] the angular electron-cloud distribution of the eigenstates when both SOC and CF potential are present; [right] the angular electron-cloud distribution of the eigenstates when only SOC is present.Long-range order of multipoles, namely high-rank electric or magnetic moments, has been attracting great interest. For example, second-rank quadrupolar moments could lead to novel phenomena including quadrupolar Kondo effect and quadrupole-fluctuation-mediated superconductivity. f-electron systems are suitable choices to study multipolar interactions and ordering phenomena by virtue of the interplay of the spin and orbital degrees of freedom. CeB6, with its simple chemical composition, lattice structure, and electronic configuration, is considered a prototypical example of heavy-fermion metals with quadrupolar ordering. Additionally, CeB6 serves as stable electron-emitting cathodes due to its low work function. This material has found broad applications in surface analysis, metrology, X-ray sources and free electron lasers. Therefore, a study of CeB6 , which illustrates the rich physics of this compound in a detailed and transparent way, contributes to both academia and industry.
In this work, we report a comprehensive spectroscopic study of CeB6 to explore its electronic, phononic and magnetic excitations. We identify an intense photo-luminescence feature resulting from the resonant optical transition between Ce 4f and 5d bands. We preform a detailed temperature-dependent study of both intra- and inter-multiplet crystal-field (CF) excitations, and illustrate the interaction between light and CF states by a model Hamiltonian calculation. By studying lattice dynamics, we show the electron-phonon interaction dominates phonon-lineshape broadening, and moreover induces a summation mode of CF transition and lattice vibration. We observe quasi-elastic magnetic fluctuations developing below 20K. The temperature dependence of the corresponding Raman susceptibility is consistent with the magnetic susceptibility data. By comparing our data with those measured by other techniques, we identify this magnetic feature as a manifestation of ferromagnetic correlations induced by tendency towards quadrupolar ordering.
This systematic study of CeB6 will serve as basis for future study of this model system. Especially, we demonstrate two virtues of Raman scattering which have not been generally appreciated: 1, temperature dependence of the parameters of CF excitations reveals the interaction between f-electrons and itinerant electrons; 2, low-energy Raman response probes dynamical fluctuations related to exotic multipolar ordering. More importantly, this work demonstrates the spectroscopic approaches and theoretical analyses of studying rare-earth systems with localized f-electrons, especially systems with a single f-electron or hole localized on an rare-earth ion at high-symmetry crystallographic site, by secondary-emission spectroscopy. The same method has direct applicability to f-electron systems consisting of Ce or Yb ions, and can be further applied to a range of rare-earth materials.
