  Within the framework of a realistic multi-band p-d-model, we derived an
effective Hamiltonian to describe the exchange interaction effects near the
spin crossover in magnetic Mott-Hubbard insulators under pressure. It is shown
that single-ion mechanism of spin crossover under change of the crystal field
does not lead to a thermodynamic phase transition, however, at T = 0 a quantum
phase transition appears. It has been found that the cooperativity leads to a
modification of the quantum phase transition to a first-order phase transition
and the appearance of metastable states of the system. The pressure -
temperature phase diagram has been obtained to describe the magnetization and
high-spin population near the spin crossover of the Motts dielectrics with
d6-ions.
