Inelastic electron scattering by intra- and interband plasmons in rhenium trioxide, tungsten trioxide, and some tungsten bronzes

Energy-loss spectra were measured by backscattering 500-eV electrons from films of WO₃ grown on single-crystal W(100), and from single crystals of Naₓ WO₃ ($0.35<x<0.86$) and ReO₃ which were cleaved in ultrahigh vacuum. The spectrum of a crystal with $x=0.61$ was nearly identical to the surface loss function Im[-(ε+1)^-1] calculated from ε measured by optical reflectivity on a crystal with $x=0.65$. For $x=0.61$, two plasmons are observed, ω_-=1.90 eV, and ω₊=6.5 eV. ω_- scales approximately as x1/2 and is assigned to the conduction-electron resonance. The plasmon lifetime τₚ=1.9×10^-15 sec determined from the observed linewidth agrees well with a value for the conduction-electron relaxation time τₑ=2.1×10^-15 sec we obtained from previously reported reflectivity data, but is shorter than a value τc=6.7×10^-15 sec we estimated from previously reported dc conductivity data. The higher-energy plasmon ω₊ is assigned to a screened longitudinal resonance of an interband excitation near 5 eV. ω₊ is essentially independent of x for 0≤x<0.9. By fitting ε between 0 and 10 eV with a model dielectric function, we found a value for the mean effective conduction electron mass m*=0.80 mₑ, the interband contribution to the static dielectric constant εₛ=4.35, and values for parameters characterizing the interband resonance. Taking these latter parameters to be independent of x, we calculated the bulk and surface loss functions for different x values. These calculations indicate that mode hybridization is unimportant for $x<1$ in the bronzes. The effects of damping or joint density-of-states width, screening, and mode interference on the plasmon spectra are discussed. It is shown that ReO₃ and Ag metal have dielectric and energy-loss functions which are similar to the tungsten bronzes. However, some of the assignments given in the literature as to the identities of the conduction-electron and interband plasmons are interchanged from those given above for the bronzes. We believe that the conduction-plasmon hybridization with interband resonances is less important in those materials than previously realized.