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Phonons reflect dynamic spin-state order in LaCoO$_3$
We investigate lattice dynamics in LaCoO$_3$ using inelastic neutron and x-ray scattering over $T = 2\mbox{-}650\,\mathrm{K}$, spanning the spin-state crossover at $T_{1} \approx 100\,\mathrm{K}$ and the insulator--metal transition at $T_{2} \approx 550\,\mathrm{K}$. Comparison with quasi-harmonic $
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