BEG spin-1 model with random exchange magnetic interactions for spin-crossover solids.

We have investigated magnetic phase diagrams of spin-crossover (SCO) solids throughout the Blume-Emery-Griffiths (BEG) spin-$1$ model where the spin states $\pm1$ and $0$ are associated to high-spin (HS) state and low-spin (LS) states respectively. In the present work, the quadrupolar interaction, $K$, parameter depends linearly on temperature and accounts for the role of the lattice phonons in the elastic interactions between the SCO units. Magnetic interactions are randomly distributed in the system and are controlled by a factor $\gamma=J_{ij}/K$ such that for $\gamma=0$ ($J_{ij}=0$), magnetic ordering is not expected. The crystal-field that acts on SCO sites depends both on the ligand-field strength and the degeneracy ratio between HS and LS states as in some previous works. The system is also under the effect of a random local magnetic field $h_i$ acting on each site $i$. The model is solved using a homogeneous mean field theory (MFT). Our investigations reveal the occurrence of thermally-induced gradual, and first-order spin-transitions by varying the model parameters. At vicinity of first-order transition, various types of isothermal magnetic hysteresis loops are obtained and their corresponding coercive field and loop patterns are discussed as function of temperature.