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

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 ${\mathcal{D}}_{\mathrm{G}}(\omega )\text{\hspace{0.17em}⁣}\sim \text{\hspace{0.17em}⁣}{\omega }^4$, at low frequencies $\omega$. Yet, due to intrinsic difficulties in disentangling ${\mathcal{D}}_{\mathrm{G}}(\omega )$ from the total VDoS $\mathcal{D}(\omega )$, which is experimentally accessible through various scattering techniques, the ${\omega }^4$ tail of ${\mathcal{D}}_{\mathrm{G}}(\omega )$ lacked direct experimental support. We develop a procedure to extract ${\mathcal{D}}_{\mathrm{G}}(\omega )$ from the measured $\mathcal{D}(\omega )$, 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 ${\mathcal{D}}_{\mathrm{G}}(\omega )$ makes an additive contribution to $\mathcal{D}(\omega )$.