Unification of the low-energy excitation peaks in the heat capacity that appears in clathrates

We report that anomalous low-energy excitation (ALE) peaks in the heat capacity emerging from single-crystal cage materials can be successfully rationalized in terms of a single unified exponential line for a variety of type-I clathrates by employing a parameter associated with the freedom of space and the modified radii of guest atoms estimated by band calculations. The origin of these low-energy excitations is interpreted in the framework of quasiharmonic van der Waals type guest-host interactions based on a unified picture with the help of first-principles calculations. It is shown that the influence of guest-host ionic and covalent bonding interactions on the phonon anharmonicity, which have so far been considered to play an important role, are not significant as long as high symmetry of the cage structure is preserved. The dominant van der Waals interactions explain the soft vibrational modes of the rattling, which suppress phonon transport and lead to the concept of ``phonon-glass electron-crystal'' (PGEC) for thermoelectric applications. A few exceptions existing in type-I clathrates, as indicated by deviations from the unified line, suggest that a quasiharmonic potential can become more asymmetric via lower symmetry of the cage structure, towards glasslike disordered states at even lower temperatures. Although the origin of the boson peaks appearing in disordered materials is still under debate due to incomplete information on the real structure, the understanding provided by the present paper for crystalline cage materials may provide information partly applicable to other disordered systems.