Spin-crossover (SCO) and Prussian blue analogs (PBAs) materials are investigated in 2D with a three-state Blume–Emery–Griffiths (BEG) model where each spin interacts with its nearest neighbors (nn) and may be either in high-spin (HS) or low-spin (LS) state. The interactions through the system lattice are temperature-dependent to account for spin-phonon interactions. The system is also in contact with an oscillating magnetic field
energy. The generated numerical results by the dynamic mean field theory (DMFT) study approach are consistent with those derived by kinetic Monte Carlo (KMC) simulations with Glauber dynamics and Arrhenius transition rates. First-order transitions with thermally induced hysteresis phenomena have been observed. Near the hysteresis loops, the model exhibits throughout relaxation curves, some fluctuations in the LS phase, strengthened by increasing temperature where this phenomenon becomes temperature- and magnetic field-dependent.