Significant four-phonon scattering and its heat transfer implications in crystalline Ge$_2$Sb$_2$Te$_5$

We systematically demonstrate the temperature-dependent thermal transport properties in crystalline Ge$_2$Sb$_2$Te$_5$via first-principles density functional theory-informed linearized Boltzmann transport equation. The investigation, covering a wide temperature range (30 K-600 K), reports the emergence of an unusual optical phonon-dominated thermal transport in crystalline Ge$_2$Sb$_2$Te$_5$. Further, a significant contribution of four-phonon scattering is recorded which markedly alters the lattice thermal conductivity. Therefore, the combined effect of cubic and quartic phonon anharmonicity is seen to navigate the underlying physical mechanism and open up intriguing phononic interactions in Ge$_2$Sb$_2$Te$_5$ at high temperature. Irrespective of three and four-phonon processes, Umklapp is seen to prevail over normal scattering events. Consequently, four-phonon scattering is found to notably reduce the lattice thermal conductivity of Ge$_2$Sb$_2$Te$_5$ to 28 $\%$ at room temperature and 42 $\%$ at higher temperature. This quartic anharmonicity further manifests in the breakdown of T$^{-1}$ scaling of thermal conductivity and challenges the idea of a universal lower bound to phononic thermal diffusivity at high temperature. The faster decay of thermal diffusivity compared to T$^{-1}$ is rationalized encompassing the quartic anharmonicity via a modified time scale. These results invoke better understanding and precision to the theoretical prediction of thermal transport properties of Ge$_2$Sb$_2$Te$_5$. Concomitantly, this also triggers the possibility to explore the manifestations of the lower bound of thermal diffusivity in materials possessing pronounced four-phonon scattering.