Bethe lattice approach and relaxation dynamics study of spin-crossover materials

Dynamical properties of Prussian blue analogs and spin-crossover materials are investigated in the framework of a Blume–Emery–Griffiths (BEG) spin-1 model, where states ±1 and 0 represent the high-spin (HS) state and the low-spin state, respectively. The quadrupolar interaction depends on the temperature in the form K=α k_BT . Magnetic interactions are controlled by a factor γ =J/K such that for γ =0 ( J=0 ), magnetic ordering is not expected. The model is exactly solved using the Bethe lattice approach for the equilibrium properties. The results are closer to those calculated by numerical simulations with suitable Arrhenius-type transition rates. The study of relaxation processes of non-equilibrium HS states revealed one-step nonlinear sigmoidal relaxation curves of the HS fraction at low temperatures. We found that increasing the magnetic interactions leads to the appearance of a plateau in the thermal hysteresis as well as in the relaxation curves of the HS fraction at low temperature.