Interplay between spin-crossover and magnetic interactions in a BEG model

A two-dimensional Blume-Emery-Griffiths spin-1 model with spin-phonon interaction is introduced to investigate the thermodynamic properties of Prussian Blue Analogs and Spin-crossover materials. The quadrupolar interaction parameter is assumed to depend on the temperature in the form K = α k <Subscript> B </Subscript> T while the crystal-field depends both on the ligand-field strength and the degeneracy ratio between high spin (HS) and low spin (LS) states as in some previous works. The model is solved by means of two statistical-mechanical methods: kinetic Monte Carlo simulations and corrective effective field theory calculations. Our calculations indicate that by tuning α, the spin-crossover transition changes to a sharp first order transition where the HS fraction, n <Subscript> HS </Subscript> changes discontinuously. Second order transitions are observed in the presence of magnetic ordering when the nearest-neighbor coupling constant J exceeds some critical value J <Subscript> c </Subscript> which depends on α and other model parameters. Below J <Subscript> c </Subscript>, simple spin-transition occurs at an equilibrium temperature T <Subscript> eq </Subscript> that is very sensitive to the values of the degenaracy ratio and the ligand-field. Competition between model parameters lead to interesting phase diagrams. Some of them are displayed for varying values of the coupling J and also in the specific case where J and K are of the same order of magnitude. Thermal hysteresis loops have been calculated by Monte Carlo simulations and also by using the self-consistent equations in the case of long-lived metastable states showing strong dependence on model parameters. Copyright EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2013