Grain size influence upon magnetic behavior at nanoscale. A computational approach

Abstract

In this work, a study of magnetic properties of nanogranular films constructed with different grain sizes is presented. The total energy of the system is proposed by mean a Hamiltonian with four contributions, which was solved using the Monte Carlo Method. The proposed terms include: (i) The exchange interactions, which consider the stress at grain boundaries. (ii) Three anisotropy contributions: cubic magnetocrystallinity in the grain cores, the Neel’s approximation in the film surface and the cubic magnetoelastic distortion at the grain boundaries. (iii) The dipolar interactions with a cutoff radius of five replicas and (iv) the energy contribution from the external magnetic field. Hysteresis loops and the temperature dependence of the magnetization under the zero-field-cooled (ZFC) and field-cooled (FC) conditions were computed. The used parameters, such as grain size, grain polydispersity, exchange values among others were chosen considering typical values reported from experimental works. The ZFC magnetization curve shows a broader maximum of which determines the blocking temperature. This maximum moves towards higher temperatures as the grain volume increases, fact related to greater stability of the ferromagnetic (FM) coupling on those grains with larger sizes, being a direct consequence of the decrease in the number of atoms located at the boundaries and of the reduction in the surface disorder. The hysteresis loops features, as well as the trend of some parameters (e.g., coercive field and remanence magnetization) as function of grain size, are in acceptable agreement with the experimental data tendencies. Local anisotropy in boundaries observed around coercive field explains grain size dependence of coercive field at nanoscale.