Origin of ultra-low thermal conductivity in unconventional clathrates: Strong scattering from extremely low-frequency rattling modes

Recent discoveries of materials with ultra-low thermal conductivity open a pathway to significant developments in the field of thermoelectricity. Here, we conduct a comparative study of three chemically similar antimonides to establish the root causes of their extraordinarily low thermal conductivity ($0.4-0.6$ Wm$^{-1}$K$^{-1}$ at 525 K). The materials of interest are: the unconventional type-XI clathrate K$_{58}$Zn$_{122}$Sb$_{207}$, the tunnel compound K$_{6.9}$Zn$_{21}$Sb$_{16}$, and the type-I clathrate K$_8$Zn$_{15.5}$Cu$_{2.5}$Sb$_{28}$ discovered herein. Calculations of the phonon dispersions show that the type-XI compound exhibits localized (i.e., rattling) phonon modes with unusually low frequencies that span the entire acoustic regime. In contrast, rattling in the type-I clathrate is observed only at higher frequencies, and no rattling modes are present in the tunnel structure. Modeling reveals that low-frequency rattling modes profoundly limit the acoustic scattering time; the scattering time of the type-XI clathrate is half that of the type-I clathrate and a quarter of the tunnel compound. For all three materials, the thermal conductivities are additionally suppressed by soft framework bonding that lowers the acoustic group velocities, and structural complexity that leads to diffusonic character of the optical modes. Understanding details of thermal transport in structurally complex materials will be crucial for developing the next generation of thermoelectrics.