Experimental evidence for the <i>ω</i>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 DG(ω)∼ω4 at low frequencies ω. Yet, due to intrinsic difficulties in disentangling DG(ω) from the total VDoS D(ω), which is experimentally accessible through various scattering techniques, the ω4 tail of DG(ω) lacked direct experimental support. We develop a procedure to extract DG(ω) from the measured D(ω), based on recent advances in understanding low-frequency excitations in glasses, and apply it to available datasets for diverse glasses. The resulting analysis indicates that the ω4 tail of the nonphononic vibrational spectra of glasses is nontrivially consistent with a broad range of experimental observations. It also further supports that DG(ω) makes an additive contribution to D(ω).