Abnormally soft acoustic phonons in the Mg₃Sb₂ allomerisms

Softening modes in phonon dispersion are often indications of intriguing physical phenomena such as phase transition and exotic thermal conductance. The promising thermoelectric material Mg₃Sb₂ and its allomerisms including CaZn₂Sb₂, SrZn₂Sb₂, etc. are investigated for phonon dispersion variation in this study using density functional theory (DFT) calculations. Two different soft transverse acoustic (TA) modes are present in Mg₃Sb₂, one at the A point along the out-of-plane direction and the other at the in-plane M point with a lower frequency. In contrast, the in-plane TA modes of CaZn₂Sb₂ and SrZn₂Sb₂ exhibit much higher in energy, but they both have extremely soft TA modes at the A point instead. Here, we construct an oscillator model based on the projected interatomic force constant tensor along vibrational directions. Our results suggest that the disappearing shear interaction of the near-neighbor bond, tilted Mg–Sb plays a large role in the abnormally soft in-plane TA mode in Mg₃Sb₂. In contrast, the covalent vertical Zn–Sb bonds in CaZn₂Sb₂ and SrZn₂Sb₂ have also negligible shear interactions. In all cases, the “missing” nearest-neighbor interaction, combined with the weak next-neighbor interaction and repulsive long-range interaction result in the observed low-energy TA modes. Soft acoustic phonon is associated with lower thermal conductivity frequently. In general, we expect such in-depth analyses on the origin of these abnormally soft phonon modes in the Mg₃Sb₂ allomerisms would provide insights into seeking high-performance thermoelectric materials in the rich family of the Zintl phase compounds.