Phonons Reflect Dynamic Spin-State Order in LaCoO_3

We investigate lattice dynamics in LaCoO_3 using inelastic neutron and x-ray scattering over T = 2650 K, spanning the spin-state crossover at T_1≈ 100 K and the insulator–metal transition at T_2≈ 550 K. Comparison with quasi-harmonic ab-initio lattice-dynamical calculations helps reveal anomalous softening of a ≈ 10 meV oxygen phonon, confined to the temperature interval T_1≤ T ≤ T_2 and localized in momentum space at q_SSO = ( 1/2,1/2,1/2)_c. This wave vector corresponds to the spin-state ordering originally proposed by Goodenough [J. Phys. Chem. Solids 6, 287-297 (1958)]. Our results therefore provide momentum-resolved evidence for dynamic correlations of high-spin and low-spin Co^3+ states in LaCoO_3, linking spin-state fluctuations to anomalous phonon renormalization.