Microscopic foundation of the phenomenological few-level approach to coherent semiconductor optics

We present the results of inelastic neutron scattering experiments for Cr₂O₃ carried out using the single-crystal time-of-flight spectrometer PRISMA at ISIS (U.K.) as well as the three-axis spectrometer TAS-1 at JAERI(J). The collected data are analysed on the basis of phenomenological shell models showing convincing agreement between calculation and experiment both for the frequencies and intensities. All together the dispersion relations of 12 out of 20 phonon branches along the three-fold axis are determined. By a comparison with the Cr₂O₃ iso-type sapphire (Al₂O₃) it is found that the dynamical response of the oxygen ion is only little affected by the ionic substitution. The chromiumd electrons find their expression mainly in a strengthening of the metal-oxygen bonding. The problem of ionic polarizabilities is addressed in detail both for the oxygen and chromium ions.