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The hysteretic properties of a nanosized monolayer on the square lattice have been studied based on the spin-1 Ising model, including a single-ion anisotropy (D) and dipolar-quadrupolar (or odd, L) interaction parameters using the pair approximation. The nanosized monolayer is divided into the core, core-surface, and surface parts as introduced in J. Magn. Magn. Mater. 373, 217 (2015). The dipolar (or magnetization M) and quadrupolar (Q) order parameters are calculated. We have investigated M vs. magnetic field H behaviors for different values of L, temperatures T, and monolayer sizes R. We also observed Q-D, M-D and Q-H hysteresis loops. These results are discussed in relation to other theoretical findings. [ABSTRACT FROM AUTHOR]

In this study, the pair approximation in the Kikuchi version is applied to study ferromagnetism of a nanosized bilayer system on a square lattice using the Ising model. Each layer is divided into the core, core-surface and surface parts as introduced for the monolayers by Özüm et al. (2015). Temperature, magnetic field and interlayer exchange energy variations of the long- and short-range order parameters are investigated. Some second-order phase transitions between ferromagnetic and paramagnetic phases with size effects are observed. By using the path probability method, the flow of the system towards some stable equilibrium states in the ferromagnetic phase is obtained via relaxation curves and flow diagrams. The results of the numerical calculations are in a fairly good agreement with the available theoretical works of other authors. [ABSTRACT FROM AUTHOR]