Temperature Dependent Phonon Spectra in Anharmonic Lattice with Cage-Like Structure

概要

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Temperature dependent phonon spectra are derived for an anharmonic lattice model using the self-consistent harmonic approximation. The lattice consists of cage and guest ions with anharmonic guest–cage interaction. By using a quasi-isotropic harmonic interaction that leads to polarization-independent dynamical matrix, renormalized phonon spectra are derived explicitly for the whole Brillouin zone and for all branches. The largest softening with decreasing temperature occurs in an Einstein-like mode corresponding to oscillation of guest ions. Cage oscillations also show slight softening since the cage–cage force is partly mediated via guest ions. In the high-temperature region, frequency of the Einstein mode is proportional to $T^{1/4}$ in agreement with the behavior derived previously for an impurity model. As temperature decreases below the Einstein frequency, the renormalized phonon frequency decreases through an inflection point, and finally tends to $T^{2}$ variation. The behavior compares favorably with recent neutron scattering results in PrOs4Sb12. The temperature dependence of the sound velocity is also calculated, which agrees qualitatively with that observed in Sr8Ga16Ge30.
2009-06-15