Experimental evidence for the ω⁴ 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 shows 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).