Damping of spinful excitons in LaCoO$_3$ by thermal fluctuations: 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 100~K. Owing to a high energy resolution of 25~meV, 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 is 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 high-spin (HS) and IS excitations interact to establish the physical properties of cobaltite perovskites.