Surface anisotropy of a Fe 3O 4 nanoparticle: A simulation approach

Abstract

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 (Fe 3+ A, Fe 3+ B, Fe 2+ 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 J AA, J AB and J BB, 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.