  Highly sophisticated synthesis methods and experimental techniques allow for
precise measurements of magnetic properties of nanoparticles that can be
reliably reproduced using theoretical models. Here, we investigate the magnetic
properties of ferrite nanoparticles by using theoretical techniques based on
Monte Carlo methods. We introduce three stages of sophistication in the
macromagnetic model. First, by using tailor-made hamiltonians we study single
nanoparticles. In a second stage, the internal structure of the nanoparticle is
taken into consideration by defining an internal (core) and external (shell)
region, respectively. In the last stage, an assembly of core/shell NPs are
considered. All internal magnetic couplings such as inter and intra-atomic
exchange interactions or magnetocrystalline anisotropies have been estimated.
Moreover, the hysteresis loops of the aforementioned three cases have been
calculated and compared with recent experimental measurements. In the case of
the assembly of nanoparticles, the hysteresis loops together with the
zero-field cooling and field cooling curves are shown to be in a very good
agreement with the experimental data. The current model provides an important
tool to understand the internal structure of the nanoparticles together with
the complex internal spin interactions of the core-shell ferrite nanoparticles.
