An exponential-potential description for the guest-host interactions in rattler-containing cage materials

Anomalous low-energy excitations (ALEs) associated with the vibrations of atoms accommodated in a space with large freedom of motion are frequently observed in cage materials. Such ALEs have been of great interest for their important roles in large electron-phonon coupling targeting high-TC superconductivity as well as phonon-phonon scattering giving rise to low thermal conductivity to achieve high thermoelectric performance. In our previous work, we showed that van der Waals-like repulsive interactions between the atoms forming the host cage and the atoms accommodated inside the cage (rattler) play a crucial role in giving small force constants and consequently nearly dispersionless low-energy phonons. In the present work, we show that the exponential law derived from the revised Morse potential model that we used previously could provide a universal trend for the ALEs of three typical cage materials: clathrates, skutterudites, and pyrochlores. This not only confirms the effectiveness of the potential model but also provides a clear description for different types of rattler vibrational modes based on the deduced parameters from the potential model. In addition to the free space in which a rattler can move and the mass of the rattler, which we considered in our previous work, structural anisotropy, electronegativity of the component cage atoms, and the coordination number of the rattler are shown to be important factors for description of an ALE.