Soft phonon modes in tetragonal CeCoSi, which undergoes a structural transition at $T_0=12\mathrm{K}$ followed by antiferromagnetic order at $T_{\text{N}}=9.5\mathrm{K}$, have been investigated using high-resolution inelastic x-ray scattering. Pronounced softening was detected in the transverse acoustic modes corresponding to the $(yz+zx)$-type monoclinic distortion, consistent with the experimentally determined triclinic structure. Remarkably, the softening persists up to the zone boundary along $(0,0,q)$, indicating a short correlation length of the lattice instability. This instability, characterized by a Curie-type strain susceptibility, is interpreted as a consequence of the on-site $4f\text{−}5d$ hybridization, which is intrinsic to this crystal structure due to the lack of inversion symmetry at the two Ce sites.

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• Elastic modulus
• Lattice dynamics
• Orbital order
• Phonons
• Structural phase transition
• Antiferromagnets
• Rare-earth magnetic materials
• Nonresonant inelastic x-ray scattering