Exchange bias for core/shell magnetic nanoparticles

We study the properties of a finite magnetic system to model a magnetic nanoparticle, which is formed by a reduced number of magnetic dipole moments due to the spin of the atoms. The nanoparticle is of the type core/shell where the shell is formed by spins interacting through an antiferromagnetic exchange coupling while for the spins belonging to the core the coupling is ferromagnetic. The interaction between the spins at the interface core/shell can be either ferro or antiferromagnetic. To describe the states of the spins we used the XY model in which the spins are considered as continuous variables, free to point in any direction of the xy plane. We also consider a magnetocrystalline anisotropy, exchange anisotropy and the Zeeman effect. Our model is studied in a lattice with square symmetry, using the Monte Carlo method along with the Metropolis prescription. The results show that in the absence of an external magnetic field and exchange anisotropy, the system continuously goes to a disordered state from an ordered state at a well defined temperature. In the presence of external magnetic fields the system displays the exchange bias phenomenon, that is, the displacement of the hysteresis loops, due to the introduction of the exchange anisotropy term. However, this displacement depends on the core and shell sizes, as well as on the magnitude of the coupling between the shell and the core moments.