Geodesic
Monte-Carlo modeling of magnetization kinetics of ferromagnetic nanoparticles
Matematičeskoe modelirovanie, Tome 24 (2012) no. 3, pp. 3-20.

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The Monte-Carlo method, being a powerful tool for finding the equilibrium states (and/or corresponding averaged characteristics) of diverse systems, in a number of situations can be successfully used also to describe the development of kinetic processes. In the present paper, the Monte-Carlo modeling is performed of the magnetic relaxation and the dynamics of forced magnetization of an ensemble of ferromagnet nanoparticles. By comparison with the exact solution, it is shown that in both cases the proportionality between the number of calculation steps and the physical duration of the transient or periodical process takes place. On this basis, the relations enabling one to quantify a single Monte-Carlo step in the real-time units are proposed. With respect to magnetic relaxation, the obtained result extends the well-known Nowak–Chantrell–Kennedy formula for the case of the nanoparticles with a finite magnetic anisotropy.
Keywords: Monte Carlo method, superparamagnetic media, magnetic hysteresis.
Mots-clés : magnetic nanoparticles 
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P. V. Melenev; Yu. L. Raikher; V. V. Rusakov; R. Perzynski. Monte-Carlo modeling of magnetization kinetics of ferromagnetic nanoparticles. Matematičeskoe modelirovanie, Tome 24 (2012) no. 3, pp. 3-20. http://geodesic.mathdoc.fr/item/MM_2012_24_3_a0/

[1] Landau D. P., Binder K., A Guide to Monte Carlo Simulations in Statistical Physics, 3${}^{\mathrm{rd}}$ edition, Cambridge University Press, New York, 2009, 488 pp. | MR | Zbl

[2] Garcia-Otero J., Porto M., Rivas J., Bunde A., “Influence of dipolar interaction on magnetic properties of ultrafine ferromagnetic particles”, Physical Review Letters, 84:1 (2000), 167–170 | DOI

[3] Ulrich M., Garcia-Otero J., Rivas J., Bunde A., “Slow relaxation in ferromagnetic nanoparticles: Indication of spin-glass behavior”, Physical Review B, 67 (2003), 024416, 4 pp. | DOI

[4] Serantes D., Baldomir D., Martinez-Boubeta C., Simeonidis K., Angelakeris M., Natividad E., Castro M., Mediano A., Chen D.-X., Sanchez A., Balcells L. I., Martinez B., “Influence of dipolar interactions on hyperthermia properties of ferromagnetic particles”, J. Applied Physics, 108 (2010), 073918, 5 pp. | DOI

[5] Sides S. W., Rikvold P. A., Novotny M. A., “Stochastic hysteresis and resonance in a kinetic Ising system”, Physical Review E, 57 (1998), 6512–6533 | DOI

[6] Brown G., Novotny M. A., Rikvold P. A., “Thermal and dynamic effects in Langevin simulation of hysteresis in nanoscale pillars”, Physica B, 306:1–4 (2001), 117–120 | DOI

[7] Nowak U., Chantrell R. W., Kennedy E. C., “Monte Carlo simulation with time step quantification in terms of Langevin dynamics”, Physical Review Letters, 84:1 (2000), 163–166 | DOI

[8] Gurevich A. G., Melkov G. A., Magnitnye kolebaniya i volny, Nauka, M., 1994, 451 pp. | Zbl

[9] Brown W. F. (Jr.), “Thermal fluctuations of a single-domain particle”, Physical Review, 130:5 (1963), 1677–1686 | DOI

[10] Coffey W. T., Kalmykov Yu. P., Waldron J. T., The Langevin Equation. With Applications in Physics, Chemistry and Electrical Engineering, 2${}^{\mathrm{nd}}$ edition, World Scientific, Singapore, 2004, 573 pp. | MR | Zbl

[11] Raikher Yu. L., Stepanov V. I., “Nonlinear dynamic susceptibilities and field-induced birefringence in magnetic fluids”, Advances in Chemical Physics, 129 (2004), 419–588 | DOI

[12] Smirnov-Rueda R., Chubykalo O., Nowak U., Chantrell R., Gonzalez J. M., “Real time quantification of Monte Carlo steps for different time scales”, J. Applied Physics, 87:9 (2000), 4798–4800 | DOI

[13] Chubykalo O., Nowak U., Smirnov-Rueda R., Wongsam M. A., Chantrell R. W., Gonzalez M., “Monte Carlo technique with a quantified time step: Application to the motion of magnetic moments”, Physical Review B, 67:6 (2003), 064422, 10 pp. | DOI

[14] Cheng X. Z., Jalil M. B. A., Lee H. K., Okabe Y., “Time-quantifiable Monte Carlo method for simulating a magnetization-reversal process”, Physical Review B, 72:9 (2005), 094420, 8 pp. | DOI

[15] Cheng X. Z., Jalil M. B. A., Lee H. K., Okabe Y., “Mapping the Monte Carlo scheme to Langevin dynamics: A Fokker–Planck approach”, Physical Review Letters, 96:6 (2006), 067208, 4 pp. | DOI

[16] Coffey W. T., Cregg P. J., Crothers D. S. F., Waldron J. T., Wickstead A. W., “Simple approximate formulae for the magnetic relaxation time of single domain ferromagnetic particles with uniaxial anisotropy”, J. Magnetism and Magnetic Materials, 131:3 (1994), L301–L303 | DOI

[17] Poperchny I. S., Raikher Yu. L., Stepanov V. I., “Dynamic magnetic hysteresis in single-domain particles with uniaxial anisotropy”, Physical Review B, 82:17 (2010), 174423, 14 pp. | DOI

[18] Melenev P. V., Raikher Yu. L., Rusakov V. V., Perzynski R., “Monte Carlo model for the dynamic magnetization of microspheres”, Physics Procedia, 9 (2010), 54–57 | DOI

[19] Aquino R., Depeyrot J., Sousa M. H., Tourinho F. A., Dubois E., Perzynski R., “Magnetization temperature dependence and freezing of surface spins in magnetic fluids based on ferrite nanoparticles”, Physical Review B, 72 (2005), 184435, 9 pp. | DOI