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Crystalline compounds exhibiting low-frequency rattling phonons constitute animportant class of high-performance thermoelectrics owning to theirintrinsically very low lattice thermal conductivity ($\kappa_{l}$). Theoreticalapproach that is capable of revealing the physical origin and accuratelypredicting $\kappa_{l}$ is of particular interest, which, however, stillremains an outstanding challenge. In this study, we perform a case study oflattice dynamics and thermal transport properties of Ag$_{6}$Ge$_{10}$P$_{12}$,which has recently been identified as a high-performance thermoelectricphosphide due to low $\kappa_{l}$, arising from rattling vibrations associatedwith Ag$_{6}$ clusters. Analysis within a first-principles-basedlattice-dynamics framework based on self-consistent phonon theory reveals astrong temperature dependence of rattling phonons due to high-order anharmonicinteractions. Anharmonic hardening of the rattling optical modes has a strongeffect on the lifetimes of heat-carrying acoustic phonons by decreasing therate of three-phonon combination processes. This mechanism results in asignificant increase in $\kappa_l$ and changes its temperature dependence to$1/T^{0.64}$.

Impact of Temperature-Dependent Rattling Phonons on Lattice Dynamics and Thermal Transport in Ag$_{6}$Ge$_{10}$P$_{12}$