Melting of excitonic dispersion in LaCoO$_3$: theory and experiment.

We present Co $L_3$-edge resonant inelastic x-ray scattering (RIXS) of bulk LaCoO$_3$ across the thermally-induced spin-state crossover around 100K. Owing to a high energy resolution of 25meV, we observe unambiguously the dispersion of the intermediate-spin (IS) excitations in the low temperature regime. Approaching the intermediate temperature regime, the IS excitations are damped and the bandwidth reduced. The observed behavior can be well described by a model of mobile IS excitons with strong attractive interaction, which we solve using dynamical mean-field theory for hard-core bosons. Our results provide a detailed mechanism of how HS and IS excitations interact to establish the physical properties of cobaltite perovskites.