Effect of surface anisotropy on the magnetic properties of magnetite nanoparticles: A Heisenberg–Monte Carlo study

Abstract

In this study, we analyze the effect of surface anisotropy on the magnetic properties of magnetite Fe3O4 nanoparticles on the basis of a core-shell model. Magnetization, magnetic susceptibility, and specific heat are computed over a wide range of temperatures. In our model, we stress on magnetite nanoparticles of 5nm in diameter which consist of 6335 ions. Our theoretical framework is based on a three-dimensional classical Heisenberg Hamiltonian with the nearest magnetic neighbor interactions between iron ions involving tetrahedral (A) and octahedral (B) sites. Terms dealing with cubic magnetocrystalline anisotropy for core ions, a single-ion site surface anisotropy for those Fe ions belonging to the shell, and the interaction with a uniform external magnetic field are considered. To compute the equilibrium averages, a single-spin movement Monte Carlo–Metropolis dynamics was used. Results reveal the occurrence of low-temperature spin configurations different from those expected for a collinear single-domain ferrimagnetic state, depending on the magnitude and sign of the surface anisotropy constant. A transition to a spike state, with magnetization close to zero, is obtained beyond a certain critical positive surface anisotropy value. Such a transition is not observed for negative values. Moreover, a two-pole magnetic state is developed at sufficiently high negative values. Such differences are explained in terms of the interplay between the superexchange couplings and the easy directions imposed by the surface anisotropy vectors. Our results are summarized in a proposal of phase diagram for the different spin structures as a function of the surface-to-core anisotropy ratio. Lastly, hysteretic behavior is evaluated. Nanoparticles become magnetically harder as the surface anisotropy increases in magnitude, and the way in wich the coercive field changes with this quantity is explicitly shown.