Exploring the role of four-phonon scattering in the lattice thermal transport of LaMoN$_3$

Abstract: In this work, we systematically investigate the lattice thermal conductivity ($\kappa_L$) of LaMoN$_3$ in the $C$2/$c$ and $R$3$c$ phases using first-principles calculations combined with the Boltzmann transport equation. In the $C$2/$c$ phase, $\kappa_L$ exhibits strong anisotropy, with values of 0.75 W/mK, 1.89 W/mK, and 0.82 W/mK along the a, b, and c axes, respectively, at 300 K. In contrast, the $R$3$c$ phase shows nearly isotropic thermal conductivity, with values of 6.28 W/mK, 7.05 W/mK, and 7.31 W/mK along the a, b, and c directions. In both phases, acoustic phonons dominate thermal transport. However, in the $C$2/$c$ phase, the absence of an acoustic-optical gap results in increased three-phonon scattering leading to smaller values of $\kappa_L$. Additionally, four-phonon scattering plays a dominant role in the C2/c phase, reducing $\kappa_L$ by approximately 96\%, whereas in the $R3c$ phase, it leads to a smaller but still significant reduction of ~50\%. These results highlight the critical role of four-phonon interactions in determining the thermal transport properties of LaMoN$_3$ and reveal the stark contrast in thermal conductivity between its two structural phases.