Magnetite thin films: A simulational approach
Introduction
Parallel to the development of films growth techniques, a great interest on thin-film magnetism has recently arisen. Several works deal with properties of Ising-type films [1] and more recently the interest has been focused on iron oxides like maghemite [2]. However, to our knowledge, simulations of magnetite (Fe3O4) thin films have not been reported. In consequence and due to the technological importance of these systems at nanometric scale, we stress on the magnetic properties and critical behavior of magnetite thin films using the Monte Carlo method and the Ising model.
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Model and simulation
As is well known, magnetic crystallizes in the Fd3m inverse spinel structure, with 8 Fe3+ ions located in tetrahedral sites plus (8 Fe3+ and 8 Fe2+) ions distributed into octahedral sites, per unit cell. In our model, magnetic ions FeA3+, FeB3+, and FeB2+ are represented by Ising spins where labels A and B refer to tetrahedral and octahedral sites respectively, while oxygen ions are consider as non magnetic. The Ising Hamiltonian describing our system reads as follows:The
Results and discussion
Fig. 1 shows the temperature dependence of the specific heat per spin c for different film thicknesses. Hence, a well-defined lambda-type behavior is observed in agreement with a thermal-driven ferrimagnetic to paramagnetic phase transition occurring at some TC where c tends to diverge. Furthermore, as the film thickness decreases, TC becomes smaller. Such reduction is ascribed to the breaking of symmetry at the surface having a smaller coordination number and consequently a lower density of
Conclusion
From our results, a remarkable reduction of TC as the film thickness becomes smaller is concluded. This fact is attributable to the breaking of symmetry at the surface and consequently to a lower density of magnetic bonds. Such dependence is ruled out by finite-size scaling theory and well characterized by an exponent . Compared to what happens in nanoparticles, results suggest a different class of universality depending on topological features.
Acknowledgements
This work was supported by Univ. de Antioquia Mediana Cuantía GICM 2005, Project SIU24-1-28 and COLCIENCIAS Project no. 1115-05-17603. Simulations were performed on the Hercules cluster (University of Antioquia) http://urania.udea.edu.co/facom/index.
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