Excess of low-energy excitations in glasses

Abstract

Low-frequency Raman spectra of metaphosphate glasses (${\mathrm{Sm}}_2$ ${\mathrm{O}}_3$ ${)}_{\mathit{x}}$(${\mathrm{P}}_2$ ${\mathrm{O}}_5$ ${)}_{1\mathrm{-}\mathit{x}}$, (${\mathrm{Eu}}_2$ ${\mathrm{O}}_3$ ${)}_{\mathit{x}}$(${\mathrm{P}}_2$ ${\mathrm{O}}_5$ ${)}_{1\mathrm{-}\mathit{x}}$, (${\mathrm{Gd}}_2$ ${\mathrm{O}}_3$ ${)}_{\mathit{x}}$(${\mathrm{P}}_2$ ${\mathrm{O}}_5$ ${)}_{1\mathrm{-}\mathit{x}}$, and ${\mathrm{GeO}}_2$ have been measured in a wide temperature range from T≊10 K to the respective glass transition temperatures T≊1000 K. Analysis of the Raman data in comparison with complementary low-temperature specific heat, and ultrasonic measurements reveals that the temperature and frequency dependences of the quasielastic scattering and boson peak, as well as anomalous low-temperature specific heat, are in qualitative agreement with the predictions of soft potential model (SPM). In the case of the spectral density of ‘‘excess’’ soft modes, which are assumed to coexist and interact with ordinary phonons, the agreement can even be made quantitative under the restricted assumptions that the low-frequency Raman scattering reflects the total (phonon + excess) density of states, and the photon-vibration coupling constant is approximately linearly dependent upon frequency. However neither of these assumptions are compatible with recent formulations of SPM.