Absolute cross sections for hyper-Raman scattering by soft modes in oxygen-octahedra ferroelectrics

We determine the order of magnitude of the normalized soft-mode hyper-Raman (HR) scattering efficiency S_HR/IL (differential cross section per unit volume and unit laser intensity) for oxygen-octahedra ferroelectrics in three ways. First, we deduce this quantity as well as the ratio of the HR tensor elements from known second-order susceptibilities by following the idea that soft-mode HR scattering merges into second-harmonic generation (SHG) when the soft mode becomes frozen. Second, we express the HR tensor in terms of the charges and coupling coefficients of the anharmonic shell model. The lack of data, however, does not yet allow a satisfying prediction of S_HR/IL. Only one HR tensor element of KTaO₃ can be estimated on the basis of the oxygen-nonlinear-polarizability model introduced by Migoni et al. Third, we determine the ratio of the HR tensor elements for SrTiO₃ and KTaO₃ from HR spectra measured under various scattering configurations. We also obtain S_HR/IL for SrTiO₃ and KI by comparing the intensities of simultaneously excited HR and second-order Raman (SOR) spectra and taking the SOR efficiency from the literature. Our experimental results are in accord with the estimations from known SHG coefficients and fit into the results on HR efficiencies published previously.