Cooperative phenomena in spin crossover systems

Within the framework of a realistic multiband $p-d$ 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 the single-ion mechanism of spin crossover under the change in 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 Mott's insulators with $d^6$ ions.