Modified Mean-Field Theory of One-Dimensional Spin Models with Anisotropy and Long-Range Dipolar Interactions

  • P. J. Camp School of Chemistry, University of Edinburgh, Department of Theoretical and Mathematical Physics, Institute of Natural Sciences and Mathematics, Ural Federal University
  • A. O. Ivanov Department of Theoretical and Mathematical Physics, Institute of Natural Sciences and Mathematics, Ural Federal University, M.N. Mikheev Institute of Metal Physics, UB of the RAS
Keywords: Heisenberg model, Ising model, dipolar interactions, magnetization, magnetic susceptibility, modified mean-field theory, Monte Carlo simulations

Abstract

The effects of interactions and anisotropy on the magnetic properties of linear chains of superparamagnetic nanoparticles are studied theoretically by mapping the problem onto spin models. With zero anisotropy, the magnetic dipole moments are free to rotate, and the system resembles a classical ferromagnetic Heisenberg model with long-range dipolar interactions. With strong anisotropy, they are constrained to align with the chain, and the system resembles the classical ferromagnetic Ising model with long-range interactions. Using a modified mean-field theory, expressions for the magnetization curve and initial magnetic susceptibility are derived from the response of a single particle subject to an effective field arising from the applied field and the interactions with the other particles. Various approximations for the effective field are tested against results from Monte Carlo simulations. It is shown that, for physically relevant interaction strengths, reliable theoretical predictions for both the zero-anisotropy and strong-anisotropy cases can be derived in a simple closed form.

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Published
2020-07-30
How to Cite
Camp, P., & Ivanov, A. (2020). Modified Mean-Field Theory of One-Dimensional Spin Models with Anisotropy and Long-Range Dipolar Interactions. Ukrainian Journal of Physics, 65(8), 691. https://doi.org/10.15407/ujpe65.8.691
Section
Physics of magnetic phenomena and physics of ferroics