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

To study non-Heisenberg effects in the vicinity of spin crossover in strongly correlated electron systems we derive an effective low-energy Hamiltonian for the two-band Kanamori model. It contains a Heisenberg high-spin term proportional to exchange constant as well as a low-spin term proportional to spin gap parameter ${\varepsilon }_s$. Using cluster mean field theory we obtain several non-Heisenberg effects. Near the critical value of spin gap ${\varepsilon }_s^c$ there is a magnetic phase transition of first order. In the vicinity of ${\varepsilon }_s^c$ in the paramagnetic phase we observe nontrivial behavior of the Curie constant in the paramagnetic susceptibility in the wide range of temperature. Reentrant temperature behavior of nearest-neighbor spin-spin correlations is observed at ${\varepsilon }_s>{\varepsilon }_s^c$. Finally, the pressure-temperature magnetic phase diagram for ferroperriclase is obtained using the effective Hamiltonian.