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=2-650  K, spanning the spin-state crossover at T_{1}≈100  K and the insulator-metal transition at T_{2}≈550  K. Comparison with quasiharmonic 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}=(½,½,½)_{c}. This wave vector is characteristic of the spin-state-ordering pattern originally proposed by Goodenough [An interpretation of the magnetic properties of the perovskite-type mixed crystals La_{1-x}Sr_{x}CoO_{3-λ}, J. Phys. Chem. Solids 6, 287 (1958)JPCSAW0022-369710.1016/0022-3697(58)90107-0]. Our results provide momentum-resolved evidence for dynamic correlations of high-spin and low-spin Co^{3+} states characterized by q_{SSO}=(½,½,½)_{c}, demonstrating that phonons are sensitive probes of fluctuating spin-state correlations in LaCoO_{3}.