Experimental evidence for the $\omega^4$ tail of the nonphononic spectra of glasses

TL;DR

This study develops a method to extract the nonphononic vibrational density of states in glasses from experimental data, providing direct evidence that supports the universal $\, ext{omega}^4$ tail predicted by simulations.

Contribution

The paper introduces a new procedure to isolate the nonphononic vibrational spectrum from experimental measurements, confirming the $\, ext{omega}^4$ tail in glasses.

Findings

The $\, ext{omega}^4$ tail is consistent with experimental data.

The nonphononic spectrum adds additively to the total vibrational density of states.

The method bridges the gap between simulations and experiments.

Abstract

It is now established that glasses feature low-frequency, nonphononic excitations, in addition to phonons that follow Debye's vibrational density of state (VDoS). Extensive computer studies demonstrated that these nonphononic, glassy excitations follow a universal non-Debye VDoS ${\cal D}_{\rm G}(\omega)\!\sim\!\omega^4$, at low frequencies $\omega$. Yet, due to intrinsic difficulties in disentangling ${\cal D}_{\rm G}(\omega)$ from the total VDoS ${\cal D}(\omega)$, which is experimentally accessible through various scattering techniques, the $\omega^4$ tail of ${\cal D}_{\rm G}(\omega)$ lacked direct experimental support. We develop a procedure to extract ${\cal D}_{\rm G}(\omega)$ from the measured ${\cal D}(\omega)$, based on recent advances in understanding low-frequency excitations in glasses, and apply it to available datasets for diverse glasses. The resulting analysis shows that the $\omega^4$ tail of the nonphononic vibrational spectra of glasses is nontrivially consistent with a broad range of experimental observations. It also further supports that ${\cal D}_{\rm G}(\omega)$ makes an additive contribution to ${\cal D}(\omega)$.