Defect-induced hyper-Raman spectra in cubic zirconia

Hyper-Raman scattering of cubic zirconia and CaF₂ is measured at room temperature. For a CaF₂ crystal, the frequencies of the TO and LO modes with T₁ᵤ symmetry are determined to be 260 and 480 cm^-1, which are in good accord with the results of infrared measurements. In a fluorite-type cubic zirconia, the defect-induced hyper-Raman spectra due to the oxygen vacancies are observed. The structures of the hyper-Raman spectra are reasonably explained by the frequency distribution of hyper-Raman-active modes in the whole Brillouin zone, which is estimated from the imaginary part of the simple projections of the phonon displacement-displacement Green's functions onto a defect space consisting of an O₆ molecule. From the analysis of the mode vectors for the O₆ molecule, the attempt frequency of oxygen ions is found to correspond to the 690-cm^-1 band in the observed hyper-Raman spectra with T₁ᵤ symmetry.