In this work, we investigate the hysteresis behavior of a bilayer graphene system composed of mixed spins S = 7/2 and σ = 1/2 interacting through ferrimagnetic coupling. The system is described by a modified Blume–Capel Hamiltonian that incorporates both intra-layer and inter-layer exchange interactions (J1, J2, J3), as well as a uniaxial crystal field D and an external magnetic field. To analyze the magnetic properties, we employ Monte Carlo simulations based on the Metropolis algorithm, which allows us to explore the thermal and magnetic responses of the system in detail.

Particular attention is given to the effects of key physical parameters, including exchange interactions, crystal field, and temperature, on the hysteresis behavior. The obtained results reveal that the shape, size, and nature of the hysteresis loops are strongly dependent on these parameters. In particular, increasing temperature leads to enhanced thermal fluctuations, resulting in a gradual reduction in the hysteresis loop area. Above a certain critical temperature, the loops completely disappear, indicating a transition from a ferrimagnetic ordered phase to a paramagnetic state.

Moreover, variations in exchange interactions and crystal field significantly influence important magnetic characteristics such as coercivity, remanent magnetization, and loop symmetry. These findings are in good agreement with previous studies on multilayer magnetic systems and demonstrate the crucial role of competing interactions in determining the magnetic behavior.

Overall, this study provides valuable insights into the tunability of hysteresis properties in bilayer graphene systems, which could be useful for future applications in spintronics, particularly in the design of multistate magnetic memory devices.