Acoustic phonon softening and lattice instability driven by on-site $f$-$d$ hybridization in CeCoSi

Soft phonon modes in tetragonal CeCoSi, which undergoes a structural transition at $T_0=12$ K followed by antiferromagnetic order at $T_{\text{N}}=9.5$ 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 $4f$-$5d$ hybridization, which is intrinsic to this crystal structure due to the lack of inversion symmetry at the two Ce sites.

💡 Research Summary

The authors investigate the lattice dynamics of tetragonal CeCoSi, a material that undergoes a non‑magnetic structural transition at T₀ = 12 K followed by antiferromagnetic order at T_N = 9.5 K. Using high‑resolution inelastic X‑ray scattering (IXS) at the SPring‑8 BL43LXU beamline, they measured phonon dispersions along the (q,0,0) and (0,0,q) directions with an energy resolution of about 1.4 meV. At 300 K the measured acoustic and optical branches are well reproduced by first‑principles calculations that treat the Ce 4f electrons as localized core states, confirming that the 4f electrons are essentially inert at high temperature.

When the temperature is lowered to 15 K, a pronounced softening appears in the transverse acoustic (TA) modes that correspond to the (yz + zx)‑type shear strain: the Δ₃,z mode propagating along