Metric for strong intrinsic fourth-order phonon anharmonicity

Under the framework of Taylor series expansion for potential energy, we propose a simple and robust metric, dubbed ``regular residual analysis,'' to measure the fourth-order phonon anharmonicity in crystals. The method is verified by studying the intrinsic strong higher-order anharmonic effects in ${\mathrm{UO}}_{2}$ and ${\mathrm{CeO}}_{2}$. Comparison of the thermal conductivity results, which calculated by the anharmonic lattice dynamics method coupled with the Boltzmann transport equation and the spectral energy density method coupled with ab initio molecular dynamics simulation further validates our analysis. Analysis of the bulk Si and Ge systems confirms that the fourth-order phonon anharmonicity is enhanced and cannot be neglected at high enough temperatures, which agrees with a previous study where the four-phonon scattering was explicitly determined. This metric will facilitate evaluating and interpreting the lattice thermal conductivity of crystals with strong fourth-order phonon anharmonicity.