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Correlated oxides, such as BiMnO$_3$ and LaMnO$_3$, show complex interplay ofelectronic correlations and crystal structure exhibiting multiple first orderphase transitions, some without a clear order parameter. The quantitativetheoretical description of this temperature dependent electronic-structuralinterplay in the vicinity of a Mott transition is still a challenge. Here weaddress this issue by simultaneously considering both structural and electronicdegrees of freedom, within a self-consistent density functional theory withembedded dynamical mean field theory. Our results show the existence of novelelectronic states characterized by coexistence of insulating, semi-metallic andmetallic orbitals. This state is in agreement with resonant X-ray scattering.We also show that electronic entropy plays a decisive role in both electronicand structural phase transitions. By self-consistent determination of both, theelectronic state and the corresponding crystal structure, we show that thetemperature evolution of these phases can be quantitatively explained fromfirst principles, thus demonstrating the predictive power of the theoreticalmethod for both the structural and the electronic properties.

Role of orbital selectivity on crystal structures and electronic states in BiMnO$_3$ and LaMnO$_3$ perovskites