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Three-dimensional layered Mg$_3$Bi$_2$ has emerged as thermoelectric materialdue to its high cooling performance at ambient temperature, which benefits fromits low lattice thermal conductivity and semimetal character. However, thesemimetal character of Mg$_3$Bi$_2$ is sensitive to spin-orbit coupling (SOC).Thus, the underlying origin of low lattice thermal conductivity needs to beclarified in the presence of the SOC. In this work, the first-principlescalculations within the two-channel model are employed to investigate theeffects of the SOC on the phonon-phonon scattering on the phonon transport ofMg$_3$Bi$_2$. Our results show that the SOC strongly reduces the latticethermal conductivity (up to $\sim 35$ %). This reduction originates from theinfluence of the SOC on the transverse acoustic modes involving interlayershearing, leading to weak interlayer bonding and enhancement anharmonicityaround 50 cm$^{-1}$. Our results clarify the mechanism of low thermalconductivity in Mg$_3$Bi$_2$ and support the design of Mg$_3$Bi$_2$-basedmaterials for thermoelectric applications.

The role of spin-orbit interaction in low thermal conductivity of Mg$_3$Bi$_2$