  The effects associated with exciton Bose condensate formation in strongly
correlated spin crossover systems are considered within the effective
Hamiltonian obtained from the two-orbital Hubbard-Kanamori model. The
collective excitations spectrum at various points of the temperature-crystal
field phase diagram is calculated. The role of the electron-phonon interaction
is discussed. The exciton and magnetic order photoenhancement (induction) in
strongly correlated spin crossover systems a new mechanism based on the
cooperative effect of electron-phonon and interatomic exchange interactions and
the appearance of a massive collective phase mode is demonstrated.
