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We applied Monte Carlo simulation to investigate the thermodynamic properties and hysteresis loops of the hexagonal core-shell nanoparticle described by a ferrimagnetic mixed-spin (3/2, 5/2) Ising model. The results revealed the significance of the single-ion anisotropy, exchange coupling, external magnetic field in dominating various thermodynamic quantities and hysteresis loops. We obtained the variation of the critical temperature with various parameters. Under certain parameter conditions, the system may exhibit rich multiple-loop hysteresis behaviors, depending on the competition among the physical parameters. An Ising model of nanoparticle with hexagonal core-shell structure is proposed. The multiple profiles and saturation values of the magnetization are discovered in the system. [Display omitted] • A ferrimagnetic hexagonal core-shell nanoparticle was proposed under an external magnetic field. • Magnetization, susceptibility, and internal energy were discussed by Monte Carlo simulation. • The compensation temperature was found under the effect of single-ion anisotropy. • Multiple-loop hysteresis behaviors were discovered due to the competition among different physical parameters. [ABSTRACT FROM AUTHOR]

• A ferrimagnetic double-layer core–shell Ising graphene nanoisland was studied in an oscillating magnetic field. • The dynamic order parameter, the susceptibility and the internal energy were discussed by Monte Carlo simulation. • The phase diagrams as well as the multiple-loop hysteresis behaviors were exhibited. • The behaviors of the coercivity and remanence under the influence of various parameters were investigated. By using Monte Carlo simulations, we discuss the dynamic magnetic properties of a double-layer core–shell graphene nanoisland with mixed-spin (2, 5/2) configuration in an oscillating magnetic field. We investigate the influence of exchange couplings, oscillating magnetic field, and temperature on the dynamic magnetic and thermodynamic properties of the system. We obtain the various characteristic curves of the dynamic order parameter, susceptibility, and internal energy as well as hysteresis loops. To better understand the impact of these physical parameters on the phase transition of the system, the phase diagrams are depicted. It should be noticed that the system can exhibit multiple-loop hysteresis behaviors under certain conditions. Besides, we plot the coercivity and remanence of the system under the influence of various parameters. [ABSTRACT FROM AUTHOR]