Spin-1 model of noninteracting nanoparticles

In this work, we presented a spin-1 model to investigate the magnetic properties of noninteracting monodomain nanoparticles based oil the pair approximation. Nearest-neighbor pair interactions are incorporated between the Ising spins in three parts that are core, core-surface, and surface within the nanoparticle. Using the spin-1 Ising model of magnetization in the pair approximation, we calculated the free energy and minimized with respect to pair variables to obtain the field-cooled magnetization. Hysteresis loops of the system were plotted for various values of exchange coupling constants and axial anisotropy of strength which Couples, the Core, core-surface, and surface re-ions. The coercive field and its linear fit to the data were plotted as a function of radius of ferromagnetic nanoparticles.