Anharmonic lattice dynamics and the origin of intrinsic ultralow thermal conductivity in AgI materials

Ionic conductors such as AgI with ultralow thermal conductivities $({\ensuremath{\kappa}}_{l})$ are of increasing interest because of their excellent thermoelectric properties. However, the origin of their intrinsic low ${\ensuremath{\kappa}}_{l}$ values remain elusive. In this study, comprehensive theoretical calculations of the lattice dynamics and the thermal transport properties of $\ensuremath{\gamma}\text{\ensuremath{-}}\mathrm{AgI}$ (zinc-blende structure) and $\ensuremath{\beta}\text{\ensuremath{-}}\mathrm{AgI}$ (wurtzite structure) as functions of temperature were carried out based on many-body perturbation theory and phonon Boltzmann transport theory. First, the mean-squared displacements (MSDs) of ${\mathrm{Ag}}^{+}$ were significantly larger than those of ${\mathrm{I}}^{\ensuremath{-}}$ in both $\ensuremath{\gamma}\text{\ensuremath{-}}$ and \ensuremath{\beta}-phases below the order-disorder phase transition temperature $({T}_{\mathrm{c}})$, which led to a characteristic ``rattling'' feature and low-frequency, nearly flat local phonon vibrations. According to our previous work [Xie et al., Phys. Rev. Lett. 125, 245901 (2020)], such nondispersive flat phonon band structures are expected to give rise to four-phonon resonance and result in a dramatic increase in the four-phonon scattering over the conventional three-phonon scattering. For $\ensuremath{\gamma}\text{\ensuremath{-}}\mathrm{AgI}$, similar four-phonon resonance behavior was also discovered for the low-lying transverse acoustic phonon branches, and it was found that their four-phonon scattering rates were an order of magnitude larger than the corresponding three-phonon scattering rates. Considering the four-phonon scattering, the theoretical ${\ensuremath{\kappa}}_{l}$ of $\ensuremath{\gamma}\text{\ensuremath{-}}\mathrm{AgI}$ was predicted to be $\ensuremath{\sim}0.32$ W/m K at 300 K, which was in good agreement with the value deduced from our experiments ($\ensuremath{\sim}0.36$ W/m K at 300 K). Compared to $\ensuremath{\gamma}\text{\ensuremath{-}}\mathrm{AgI}$, the acoustic phonons in $\ensuremath{\beta}\text{\ensuremath{-}}\mathrm{AgI}$ were more dispersive, and they intertwined with low-energy optical phonons at the zone boundaries. It was found that three-phonon resonance became as important as four-phonon resonance for the nearly flat longitudinal phonon band. The theoretical ${\ensuremath{\kappa}}_{l}$ for $\ensuremath{\beta}\text{\ensuremath{-}}\mathrm{AgI}$ was determined to be around $\ensuremath{\sim}0.32$ W/m K at room temperature, closely reproducing our measurement value $\ensuremath{\sim}0.29$ W/m K. Our results for AgI demonstrate the strong quartic anharmonicity in materials characterized by the rattling of weak bonding atoms as well as dispersionless phonon band structures. It is believed that this intimate relationship between the low-${\ensuremath{\kappa}}_{l}$ and flat phonon dispersion can be employed as a good indicator when searching for material systems with ultralow ${\ensuremath{\kappa}}_{l}$ values, e.g., cagelike rattling structures, quasi-two-dimensional structures, and chainlike structures.