Emergence of the local magnetic moments is one of the typical features of the systems with strong electronic correlations. Common in transition metal oxides at ambient conditions, the local moment formation competes with effects such as band broadening or crystal field splitting when pressure is applied. LaCoO$_3$ is a well known and much studied example of a system where two spin states S=0 and arguably S=2 are almost degenerate. This results in a strongly temperature dependent conductivity and magnetic susceptibility. We will present a dynamical mean-field study of a simple two-band Hubbard model, which mimics the electronic structure of LaCoO$_3$. We calculate the one-particle spectra and the local as well as uniform spin susceptibility, in qualitative agreement with experimental observations. Our main finding is the observation of a disproportionation into magnetic and non-magnetic sites at intermediate temperatures. We provide an explanation of this behavior in terms of a simplified spin model and discuss its implications for presence of a gap in the one-particle spectrum.
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