Oxide materials, particularly ternary and quaternary oxides, typically exhibit low thermal conductivities. However, a recent experiment revealed that the trirutile compound ${\mathrm{Ga}}_2{\mathrm{TeO}}_6$ possesses a relatively high lattice thermal conductivity of approximately $20{\mathrm{Wm}}^{-1}{\mathrm{K}}^{-1}$ at 323 K, significantly exceeding that of most ternary oxides. Here, we systematically investigate the lattice thermal conductivities of six trirutile materials using first-principles three-phonon calculations. For ${\mathrm{Ga}}_2{\mathrm{TeO}}_6$, the calculated room-temperature lattice thermal conductivities are 22.6 and $25.8{\mathrm{Wm}}^{-1}{\mathrm{K}}^{-1}$ along the $a$ and $c$ directions, respectively, in good agreement with the experimental data. By substituting lighter elements into ${\mathrm{Ga}}_2{\mathrm{TeO}}_6$, we predict that their lattice thermal conductivity can be further enhanced, potentially reaching $40{\mathrm{Wm}}^{-1}{\mathrm{K}}^{-1}$ at room temperatures. We show that the trirutile materials consistently exhibit higher lattice thermal conductivities than most other ternary oxides, despite their complex structures and the presence of heavy elements, primarily attributed to their high bulk moduli, reaching up to 240 GPa. This work provides valuable insights into the thermal and mechanical behavior of trirutile oxides, which may stimulate further theoretical and experimental investigations.

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• Elastic modulus
• Lattice thermal conductivity
• Phonons
• Oxides
• Boltzmann theory
• Density functional calculations