Lattice Thermal Conductivity in XMg₂Sb₂(X = Ca or Mg) Compounds: Temperature and High-Order Anharmonicity Effect

The binary compound Mg₃Sb₂ (also written as MgMg₂Sb₂) exhibits a much lower lattice thermal conductivity (κL) than its ternary analog CaMg₂Sb₂, despite its relatively low mass density and simple crystalline structure. Here, we perform a comparative first-principles study of the lattice dynamics in MgMg₂Sb₂ and CaMg₂Sb₂ based on the density functional theory, together with the self-consistent phonon theory and the Boltzmann transport theory. We show that the modest anharmonicity of CaMg₂Sb₂ renders the three-phonon processes dominant, and the temperature dependence of κ approximately follows the T-1 relationship. In contrast, the strong quartic anharmonicity of MgMg₂Sb₂ leads to the ultralow κ and weak temperature dependence, in agreement with the experimental observations. A comprehensive analysis reveals that the κLs in the two compounds are mainly carried by the acoustic phonons associated with the Sb atoms, and the different behaviors of κL result from the chemical bond changes around Sb atoms, which bond more covalently with the Mg atoms than the Ca atoms and thus lead to high-order anharmonicity in MgMg₂Sb₂. These results give us insights into the understanding of the anomalous thermal transport in thermoelectric materials.