In this study we address the role of surface anisotropy on the hysteretic properties of magnetite Fe3O4 nanoparticles and the circumstances yielding both horizontal and vertical shifts in the hysteresis loops. Our analysis involves temperature dependence and particle size effects. Different particle sizes ranging from 2 up to 7 nm were considered. Our theoretical framework is based on a three-dimensional classical Heisenberg model with nearest magnetic neighbor interactions involving tetrahedral (A) and octahedral (B) irons. Cubic magnetocrystalline anisotropy for core spins, single-ion site anisotropy for surface spins, and interaction with a uniform external magnetic field were considered. Our results revealed the onset of low temperature exchange bias field, which can be positive or negative at high enough values of the surface anisotropy constant (KS). Susceptibility data, computed separately for the core and the surface, suggest differences in the hard-soft magnetic character at the core-surface interface. Such differences are KS-driven and depend on the system size. Such a hard-soft interplay, via the surface anisotropy, is the proposed mechanism for explaining the observed exchange bias phenomenology. Our results indicate also that the strongly pinned spins at high enough surface anisotropy values are responsible for both the horizontal and vertical shifts in the hysteresis loops. The dependences of the switching and exchange bias fields with the surface anisotropy and temperature are finally discussed.
In this study we present results of electronic structure calculations for some iron oxide clusters of the form Fe n O m on the basis of the GGA+ U approximation. The cluster size ranged between 33 and 113 atoms corresponding to length scales between around 7 Å and 12 Å in diameter, respectively. Initial atomic configurations before relaxation were created by considering two different space groups corresponding to the cubic Fd3m and monoclinic P2 / c symmetries. The charge and the magnetization per atom were computed. In particular, the charge distribution of the cluster relaxed from cubic symmetry and containing 113 atoms reveals a well-defined periodic pattern of Fe pairs consistent with a partial charge-ordering scenario. Results evidence that the ground-state cohesive energy is smaller in the clusters originated from the P2 / c symmetry. This fact indicates that at least in the largest cluster, having more tendency to preserve the initial structure, the lowtemperature monoclinic phase is energetically more stable. Clusters starting from monoclinic symmetry are characterized by an insulating state, whereas those optimized from cubic symmetry exhibit a very small electronic gap. Finally, radial and angular distribution functions reveal strong modifications of the starting crystalline structures after relaxation with a tendency of forming cagelike structures.
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.
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