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 on 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 regions. The coercive field and its linear fit to the data were plotted as a function of radius of ferromagnetic nanoparticles.