Mathematical Models and Computer Simulations

, Volume 4, Issue 5, pp 471–483 | Cite as

Modeling the magnetization kinetics of ferromagnetic particles by the Monte Carlo method

  • P. V. Melenev
  • Yu. L. Raikher
  • V. V. Rusakov
  • R. Perzynski


The Monte Carlo method, which is a powerful tool for finding equilibrium states (and/or their corresponding characteristics) in systems of a different nature in many cases allows one to also describe the course of kinetic processes. This work presents the Monte Carlo modeling of magnetic relaxation and dynamics of induced magnetization of an ensemble of ferromagnetic nanoparticles. It is shown by comparison with the exact solution that in both problems there is a proportionality between the number of calculation steps and the physical duration of the transition or periodic process. On this basis, relationships are proposed making it possible to estimate the time interval corresponding to a single Monte Carlo step. For the process of magnetic relaxation the obtained result is a generalization of the well-known Nowak-Chantrell-Kennedy formula for the case of particles with finite magnetic anisotropy.


Monte Carlo method magnetic nanoparticles superparamagnetism magnetic hysteresis 


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© Pleiades Publishing, Ltd. 2012

Authors and Affiliations

  • P. V. Melenev
    • 1
  • Yu. L. Raikher
    • 1
    • 2
  • V. V. Rusakov
    • 1
    • 2
  • R. Perzynski
    • 3
  1. 1.Institute of Continuous Media Mechanics, Ural BranchRussian Academy of SciencesPermRussia
  2. 2.Perm National Research Polytechnical UniversityPerm-GSPRussia
  3. 3.Laboratoire PECSA-CNRS-ESPCIUniversité Pierre et Marie CurieParisFrance

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