Dielectric response of mixed-valent TmSe

Abstract

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 ( 0.5 eV) is attributed to the intermediate valence character of this compound, and is consistent with the model of $d$ 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 \ensuremath{\sim}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.