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Optical properties of bcc transition metals in the range 0–40 eV

By P. Romaniello, P.L. de Boeij, F. Carbone and D. van der Marel

Abstract

We present a systematic analysis of the optical properties of bcc transition metals in the groups VB: V, Nb, and Ta, and VIB: paramagnetic Cr, Mo, and W. For this we use our formulation of time-dependent current-density-functional theory for the linear response of metals. The calculated dielectric and electron energy-loss functions are compared with our ellipsometry measurements and with data reported in literature, showing an overall good agreement. The experimental data of the dielectric functions presented by Nestell and Christy and by Weaver et al. differ mostly in the low-frequency region. However, we found that their reflectivity data are in very good agreement up to about 3 eV. We attribute this apparent discrepancy to the Drude-like extrapolation model used by Weaver et al. in the Kramers-Kronig procedure to extract the optical constants from their reflectivity data. Our experiments are in good agreement with Nestell and Christy’s data. The calculated absorption spectra show some deviations from the experiments, in particular in the 3d metals. We assign the spectra in terms of transitions between pairs of bands and we analyze which parts of the Brillouin zone are mainly involved in the absorption. Our results suggest that the blueshift of some spectral features in our calculations can be attributed mainly to the incorrect description of the virtual d bands by the approximations used for the ground state exchange-correlation functional. These virtual bands are too weakly bound by the local density and generalized gradient approximations, in particular in the 3d metals. We calculate separately the inter- and intraband contributions to the absorption and we show using a k·p analysis that, within the scalar-relativistic approximation, interband transitions contribute to the absorption already at frequencies well below 0.5 eV. This finding makes questionable the Drude-like behavior normally assumed in the experimental analysis of the linear response.We find that the combination of the Drude model in which we use the calculated plasma frequency and an optimized relaxation time, and the calculated interband response can well describe the experimental spectra. The electron energy-loss spectra are very well reproduced by our calculations showing in each metal a dominant plasmon peak at about 22–24 eV, well above the corresponding Drude-like free-electron plasma frequency, and additional features in the range 10–15 eV. We show that the renormalization of the plasma frequency is due to the interplay between inter- and intraband processes, and that the additional features arise from the rich structure in the dielectric function caused by interband transitions.

Year: 2006
OAI identifier: oai:ub.rug.nl:dbi/49eedf2c3eb50
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