A study with pair approximation of spin?1 ising model of noninteracting nanoparticles with quadratic and crystal field interactions

In this thesis; bilinear, quadratic and crystal field interactions of spin?1 Ising model was studied to investigate the magnetic properties of noninteracting monodomain nanoparticles. The Ising spins in three parts that are core, core-surface, and surface within the nanoparticle were incorporated. After the Hamiltonian which is used for Ising model was written genereally, it was written for three parts. Equations were solved for core-shell nanoparticle by using the pair approximation for bilinear, quadratic and crystal field interactions Hamiltonian of spin?1 Ising model. The free energy was calculated for core-shell nanoparticle. Magnetic properties were studied for bilinear, quadratic and crystal field interactions of homogeneous and composite nanoparticles for different values of temperature and diameter. Hysteresis loops of the homogeneous and composite system were plotted for different values of magnetic field and quadratic and crystal field values. The coercive field and its linear fit to the data were plotted as a function of radius of ferromagnetic nanoparticles.The Ising model is firstly used for ferromagnetism and then is advanced for different magnetic systems. The theoretical studies are show the way for these models before all else magnetic nanoparticle systems, nanomagnet, magnetic thin film, magnetic fluid etc. a lot of important technological experimental studies. This thesis is important because of the method which we used sets good example for other theorical studies. It provides opportunity to examine prior to magnetic properties of core-shell nanoparticles which are difficult to get by experimental studies. It offers the opportunity for magnetic nanoparticle systems to keep the DNA, detection and identification of harmful moleculs, in the bio-medical fields, so it gets an extremely convenient of their modellings.Keywords: Nanoparticle, Ising Models, Pair Approximation Methods, Nanomagnetism.