Surface anisotropy of a Fe3O4 nanoparticle: A simulation approach

On the basis of a three-dimensional classical Heisenberg model with nearest magnetic neighbor interactions, and using a Monte Carlo–Metropolis dynamics, we study the magnetic behavior of a 5 nm diameter magnetite nanoparticle as a function of temperature. The nanoparticle is built by taken into account the inverse spinel structure of a stoichiometric magnetite, the valence of the iron ions (Fe3+A, Fe3+B, Fe2+B where A and B stand for tetrahedral and octahedral sites, respectively) as well as the different involved coordination numbers and superexchange integrals. The employed Hamiltonian includes coupling interactions between Fe ions through the integrals JAA, JAB and JBB, a Néel's surface anisotropy term applied to surface ions, and cubic magnetocrystalline anisotropy for those ions belonging to the core of the nanoparticle. Results reveal a strong influence of surface anisotropy, depending on its sign and magnitude, upon the total magnetization at low temperatures. Such results, which are summarized in a proposal of phase diagram, reveal the onset of spin structures different from a single-domain state. Differences in the thermal behavior respect to a bulk magnetite are also addressed and discussed.