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To study non-Heisenberg effects in the vicinity of spin crossover in stronglycorrelated electron systems we derive an effective low-energy Hamiltonian forthe two-band Kanamori model. It contains Heisenberg high-spin term proportionalto exchange constant as well as low-spin term proportional to spin gapparameter $\varepsilon_s$. Using cluster mean field theory we obtain severalnon-Heisenberg effects. Near critical value of spin gap $\varepsilon^c_s$ thereis a magnetic phase transition of first order. In the vicinity of$\varepsilon^c_s$ in the paramagnetic phase we observe non trivial behavior ofthe Curie constant in the paramagnetic susceptibility in the wide range oftemperature. Reentrant temperature behavior of nearest-neighbor spin-spincorrelations is observed at $\varepsilon_s > \varepsilon^c_s$. Finally,pressure-temperature magnetic phase diagram for ferroperriclase is obtainedusing the effective Hamiltonian.

Magnetism in spin crossover systems: short-range order and effects beyond the Heisenberg model