Dielectric response of mixed-valent TmSe

The optical reflectivity of TmS and of TmSe with varying degrees of valence mixing has been measured in the photon energy range from 30 meV (and partially from 1 meV) up to 12 eV. Intraband absorption below about 2 eV causes the metallic high reflectivity and the metallic lustrous color. The anomalous excitation spectrum of ${\mathrm{Tm}}_{1.0}$Se at low energy ($d$ electrons and holes scattered from partially occupied $f$ states at the Fermi level. The most striking result stems from the sum rule and spectral analysis of the collective mode of the conduction-band plasma: those electrons, whose partial $f$ character is responsible for the intermediate valence features in TmSe, appear to participate fully in the $d$ conduction-band plasma oscillation as if they had no $f$ character at all. The one-particle excitations above ∼2 eV are well explained in terms of transitions from the $p$-valence band and from highly correlated $4f$ states into the double-structured $5d$ conduction band. A comparison with x-ray photoelectron spectra reveals an apparent difference for the value of the effective $4f$ Coulomb correlation energy as determined by the two experiments and points to different final-state interactions.