Fig. 1. Soft phonons from inelastic neutron scattering.

(A) Crystal structure of AMg₂X₂ and illustration of octahedral A-site and tetrahedral Mg(2) atoms. Red, orange, and blue represent A, Mg(2), and X, respectively. d₁ and d₂ are the nearest- and second-nearest-neighbor Mg(2)-X bonds. The nearest-neighbor A-X bond is d₃. Comparison of experimental neutron DOS E_i = 20 meV at 300 K of (B) Mg₃Bi₂ (blue) and YbMg₂Bi₂ (purple) and (C) Mg₃Sb₂ (red) and CaMg₂Sb₂ (orange). Significant stiffening is observed in ternary compounds despite a heavier mass of Ca or Yb than Mg. Extra shoulders at low energy are observed only in binary compounds. Neutron dynamical structure factor S(∣Q∣, ω) of (D) Mg₃Bi₂, (E) YbMg₂Bi₂, (F) Mg₃Sb₂, and (G) CaMg₂Sb₂, the same datasets as in (B) and (C). Total intensities are normalized to the value of Mg₃Bi₂. Much stronger intensities at the low-energy region can be observed in binary compared to ternary compounds.