Debye to non-Debye scaling of the Boson peak dynamics: critical behavior and local disorder in vitreous germania

We report on the observation of a significant softening of the Boson peak (BP) frequency of vitreous GeO2 above the glass transition temperature. The softening reminds a critical trend, with a transition temperature intermediate between the glass transition temperature, Tg, and the melting point. The softening of the BP frequency corresponds to a transition from a region dominated by Debye scaling to a non-Debye one. Below Tg the density of vibrational states varies according to the modification of the elastic continuum medium. Above Tg the relevant softening of the BP modes can be explained by a broadening of the distribution of elastic constants between neighboring atoms, induced by the structural rearrangement. These findings are discussed together with recent experimental and theoretical results on the low frequency vibrations in glasses.