Journal of Nanoparticle Research

, Volume 13, Issue 12, pp 7115–7125 | Cite as

Energy contributions in magnetite nanoparticles: computation of magnetic phase diagram, theory, and simulation

  • J. Mejía-López
  • J. Mazo-Zuluaga
Research Paper


In this study, we present a theoretical analysis of magnetization processes by considering energy contributions in magnetite fine particles. The focus is on the K S-driven magnetic phase transition taking place between the low surface-anisotropy ferrimagnetic state and the hedgehog configuration obtained in the high surface-anisotropy limit. Analytical expressions of energy terms (exchange, magnetocrystalline anisotropy, surface-anisotropy) are presented and their magnitudes are computed for different particle sizes. Monte Carlo simulations were also carried out for comparison purposes. A core–shell model is implemented for simulating magnetite nanoparticles between 2 and 10 nm in diameter. Our simulation framework is based on a three-dimensional classical Heisenberg-like Hamiltonian with nearest magnetic neighbors interactions. It includes exchange coupling, cubic magnetocrystalline anisotropy for core ions, and single-ion site surface-anisotropy for those atoms belonging to the shell. The magnetic phase diagram and comparisons between analytical and numerical results are presented and discussed.


Ferrimagnetic nanoparticles Surface magnetism Magnetic anisotropy Magnetic phase transition Monte Carlo simulations Modeling and simulation 



This study was supported by several projects: the Chile-Colombia scientific exchange program CONICYT-COLCIENCIAS under contracts 2008-157, 279-2009; the FONDECYT grant 1100365, Millenium Science Nucleus “Basic and applied magnetism” P10-061-F; Financiamiento basal para centros científicos y tecnológicos de excelencia FB 0807; the CODI-UdeA projects IN576CE, IN578CE, and “Sostenibilidad” projects of the GES and GICM Groups at the Universidad de Antioquia. We are grateful to Dr. Johans Restrepo for helpful discussions. J.M-Z. wants to thank Universidad de Antioquia for a “Dedicación Exclusiva” program.


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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Facultad de FísicaPontificia Universidad Católica de ChileSantiago 22Chile
  2. 2.Center for the Development of Nanoscience and Nanotechnology-CEDENNASantiagoChile
  3. 3.Grupo de Estado Sólido, Grupo de Instrumentación Científica y Microelectrónica, Instituto de FísicaUniversidad de AntioquiaMedellínColombia

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