Excitonic order in strongly correlated systems with the spin crossover

Features of the formation of the magnetic structure and the exciton Bose–Einstein condensate phase of magnetic excitons in strongly correlated systems near the spin crossover have been considered with the effective Hamiltonian obtained from the two-band Hubbard–Kanamori model. The coexistence of antiferromagnetism and exciton condensate, as well as the appearance of the long-range excitonic antiferromagnetic order even in the absence of the interatomic exchange interaction, has been revealed. The role of the electron–phonon coupling has been considered.