Finite-size and surface effects in maghemite nanoparticles:  Monte Carlo simulations

Abstract

Finite-size and surface effects in fine particle systems are investigated by Monte Carlo simulation of a model of a ␥-Fe 2 O 3 ͑maghemite͒ single particle. Periodic boundary conditions for a large enough system have been used to simulate the bulk properties and the results compared with those for a spherical shaped particle with free boundaries to evidence the role played by the surface on the anomalous magnetic properties displayed by these systems at low temperatures. Several outcomes of the model are in qualitative agreement with the experimental findings. A reduction of the magnetic ordering temperature, spontaneous magnetization, and coercive field is observed as the particle size is decreased. Moreover, the hysteresis loops become elongated with high values of the differential susceptibility, resembling those from frustrated or disordered systems. These facts are a consequence of the formation of a surface layer with higher degree of magnetic disorder than the core, which, for small sizes, dominates the magnetization processes of the particle. However, in contradiction with the assumptions of some authors, our model does not predict the freezing of the surface layer into a spin-glass-like state. The results indicate that magnetic disorder at the surface simply facilitates the thermal demagnetization of the particle at zero field, while the magnetization is increased at moderate fields, since surface disorder diminishes ferrimagnetic correlations within the particle. The change in shape of the hysteresis loops with the particle size demonstrates that the reversal mode is strongly influenced by the reduced atomic coordination and disorder at the surface.

Role of surface disorder on the magnetic properties and hysteresis of nanoparticles

“…However now, due to the dominant AF intersublattice coupling, there is a tendency to achieve antiparallel alignment among spins in different sublattices that causes a greater degree of disorder at the surface with respect to the FM case. Notice also that, even for small k S , M z does not approach 1 as T tends to zero as in the FM case, but instead tends to the value of magnetization of the noncompensated spins (M U nc = (N O − N T )/N T otal ), that for a particle of diameter D = 3 is M U nc = 0.285(0.412) for surface (core) spins [11]. Moreover, for the ferrimagnetic particle, there is a change in the magnetic order at low T as the k S /k C ratio increases.…”

“…which is an extension of our previous study with Ising spins [11]. Here, S i are three dimensional classical vector spins placed on a discrete lattice and H is the magnetic field, that in the following will be given in temperature units as h = µ H/k B , with µ the moment of the magnetic ion.…”

“…The model considered is an extension to Heisenberg spins of our previous MC simulations for an Ising spin model of a γ-Fe 2 O 3 particle [11,12]. The particles considered are spheres of diameter D (in units of the linear unit cell size a).…”

Influence of surface anisotropy on the hysteresis of magnetic nanoparticles

“…Moreover, current experimental techniques do not allow to probe sur-face microscopic structure in geometries such as those of a nanoparticle, a fact that forces to assume phenomenological models for surface anisotropy. Monte Carlo (MC) simulations constitute a benchmark to probe different models since, by modeling magnetic ions as classical [5,6,7,8] or Ising spins [9,10,11], the interatomic interactions, the local magnetic anisotropy directions and the values of anisotropy constants can be easily varied while taking into account the exact geometry of the underlying lattice of magnetic ions. Here, we will present results of MC simulations aimed to understand the influence of surface anisotropy on the magnetic properties and hysteresis of a single nanoparticle, neglecting the effects of interactions with other particles.…”

Thermodynamic properties of small magnetic particles

“…As we note, these curves characterize a ferromagnetic behavior with a critical temperature T c = (1.29 ± 0.02)J/k B . As we can see in Fig.2, the critical temperature (actually the pseudocritical temperature [10]) increases with the size of the particle [10,19] up to reach the thermodynamic limit. In our case this limit is easily found for a particle with nine shells, where we obtain T c = (1.44±0.02)J/k B , which is very close to the value obtained for a ferromagnetic system [20].…”