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We show that the distinct differences of low-lying THz-frequency dynamicsbetween type-I clathrates with on-center and off-center guest ions naturallyfollow from a theoretical model taking into account essential features of thedynamics of rattling guest ions. Our model analysis demonstrates the drasticchange from the conventional dynamics shown by on-center systems to thepeculiar dynamics of off-center systems in a unified manner. We claim thatglass-like plateau thermal conductivities observed for off-center systems stemfrom the flattening of acoustic phonon dispersion in the regime |k|<|G|/4. Themechanism is applicable to other systems such as glasses or relaxers.

Significance of Off-Center Rattling for Emerging Low-lying THz Modes in type-I Clathrates