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

## TL;DR

This paper derives an effective Hamiltonian to study non-Heisenberg effects near spin crossover in correlated electron systems, revealing phase transitions, unusual susceptibility behavior, and pressure-temperature phase diagrams.

## Contribution

It introduces a low-energy Hamiltonian for the two-band Kanamori model that captures non-Heisenberg effects near spin crossover, including phase transitions and reentrant correlations.

## Key findings

- First-order magnetic phase transition near critical spin gap
- Anomalous Curie constant behavior in paramagnetic phase
- Reentrant spin-spin correlations at certain parameters

## Abstract

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 Heisenberg high-spin term proportional to exchange constant as well as low-spin term proportional to spin gap parameter $\varepsilon_s$. Using cluster mean field theory we obtain several non-Heisenberg effects. Near critical value of spin gap $\varepsilon^c_s$ there is a magnetic phase transition of first order. In the vicinity of $\varepsilon^c_s$ in the paramagnetic phase we observe non trivial 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 $\varepsilon_s > \varepsilon^c_s$. Finally, pressure-temperature magnetic phase diagram for ferroperriclase is obtained using the effective Hamiltonian.