The microscopic mechanisms of heat transport in ${\mathrm{YAgTe}}_2$ are explored through advanced first-principles calculations combined with self-consistent phonon theory. The computed normal mode resolved residuals display a characteristic W-shaped profile, indicating significant quartic anharmonicity. Both cubic and quartic anharmonicities are thoroughly considered, including their contributions to phonon frequency renormalization and linewidth broadening. Furthermore, both diagonal and off-diagonal components of the heat flux operator are explicitly evaluated in the calculation of lattice thermal conductivity. The results are in excellent agreement with experimental values near room temperature. Our study identifies the primary cause of the low lattice thermal conductivity in ${\mathrm{YAgTe}}_2$ as strong anharmonicity from the rattling effect of Ag atoms, which leads to substantial three-phonon and four-phonon scattering. Notably, the competition between phonon hardening (described by the loop diagram) and phonon softening (due to the bubble diagram) plays a significant role in influencing particlelike propagation, particularly affecting group velocity and energy conservation. We also confirm that ${\mathrm{YAgTe}}_2$ with space group $P\overline{4}{2}_{1}m$ remains dynamically stable at elevated temperatures. There are minor discrepancies between our high-temperature theoretical predictions and experimental results, which may be attributed to the presence of mixed phases in the experiments, whereas our calculations assume a perfect lattice. A reassessment of the thermoelectric performance shows that, for $n$-type doping, the maximum $ZT$ of 2.11 is achieved at a carrier concentration of $9\times {10}^{19}{\text{cm}}^3$ at 700 K, while for $p$-type doping, the maximum $ZT$ is 1.34 at a carrier concentration of $4\times {10}^{19}{\text{cm}}^3$ at 700 K. These findings provide valuable insights for guiding future experimental studies.

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• Electrical conductivity
• Energy conversion technologies
• Thermal conductivity
• Thermoelectrics
• First-principles calculations