Skip to main content
Log in

Nonlinear response of superparamagnetic particles to a sudden change of a high constant magnetic field

  • Magnetism and Ferroelectricity
  • Published:
Physics of the Solid State Aims and scope Submit manuscript

Abstract

For a system of superparamagnetic particles in a high external constant magnetic field, a technique for calculating the nonlinear response to a sudden change in the field direction and magnitude is proposed. A set of momentary equations for the averaged spherical harmonics, which is derived from the Fokker-Planck equation for the magnetization-orientation distribution function is the basis of this technique. As an example, the nonlinear response of a system of particles with anisotropy of the easy-axis type is examined. For this case, a solution to the momentary equations is obtained by using matrix continued fractions. The magnetization relaxation time and the spectrum of the relaxation function are calculated for typical values of anisotropy, dissipation, and nonlinearity parameters. It is shown that the magnetization kinetics is essentially dependent on these parameters.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. L. Néel, Ann. Geophys. 5, 99 (1949).

    Google Scholar 

  2. H. B. Braun and H. N. Bertram, J. Appl. Phys. 75, 4609 (1994).

    ADS  Google Scholar 

  3. C. P. Bean and J. D. Livingston, Suppl. J. Appl. Phys. 30, 1205 (1959).

    Google Scholar 

  4. W. F. Brown, Jr., Phys. Rev. 130, 1677 (1963).

    ADS  Google Scholar 

  5. T. L. Gilbert, Phys. Rev. 100, 1243 (1956).

    Google Scholar 

  6. W. F. Brown, Jr., IEEE Trans. Mag. 15, 1196 (1979).

    Google Scholar 

  7. Yu. L. Raikher and M. I. Shliomis, Adv. Chem. Phys. 87, 595 (1994).

    Google Scholar 

  8. L. J. Geoghegan, W. T. Coffey, and B. Mulligan, Adv. Chem. Phys. 100, 475 (1997).

    Google Scholar 

  9. L. M. Blinov, Electro-and Magnetooptics of Liquid Crystals (Nauka, Moscow, 1982).

    Google Scholar 

  10. G. Moro and P. L. Nordio, Z. Phys. B.: Condens. Matter 64, 217 (1986).

    Article  Google Scholar 

  11. J. L. Dejardin, Dynamic Kerr Effect (World Scientific, Singapour, 1996).

    Google Scholar 

  12. A. Aharoni, Phys. Rev. 177, 763 (1969).

    Article  ADS  Google Scholar 

  13. D. A. Garanin, V. V. Ishchenko, and L. V. Panina, Zh. Teor. Mat. Fiz. 82, 242 (1990).

    Google Scholar 

  14. W. T. Coffey, D. S. F. Crothers, Yu. P. Kalmykov, et al., Phys. Rev. B 51, 15947 (1995).

    Google Scholar 

  15. É. K. Sadykov and A. G. Isavnin, Fiz. Tverd. Tela 38, 2104 (1996) [Phys. Solid State 38, 1160 (1996)].

    Google Scholar 

  16. Yu. L. Raikher and V. I. Stepanov, Phys. Rev. B 55, 15005 (1997).

    Google Scholar 

  17. Yu. L. Raikher, V. I. Stepanov, A. N. Grigirenko, et al., Phys. Rev. E 56, 6400 (1997).

    Article  ADS  Google Scholar 

  18. I. Klik and L. Gunther, J. Stat. Phys. 60, 473 (1990).

    Article  Google Scholar 

  19. Yu. P. Kalmykov and S. V. Titov, Fiz. Tverd. Tela 41, 2020 (1999) [Phys. Solid State 41, 1854 (1999)].

    Google Scholar 

  20. Yu. P. Kalmykov and S. V. Titov, Phys. Rev. Lett. 82, 2967 (1999).

    Article  ADS  Google Scholar 

  21. R. N. Zare, Angular Momentum: Understanding Spacial Aspects in Chemistry and Physics (Wiley, New York, 1988; Mir, Moscow, 1993).

    Google Scholar 

  22. Yu. P. Kalmykov, S. V. Titov, and W. T. Coffey, Phys. Rev. B 58, 3267 (1998).

    Article  ADS  Google Scholar 

  23. Yu. P. Kalmykov and S. V. Titov, Fiz. Tverd. Tela 40, 1642 (1998) [Phys. Solid State 40, 1492 (1998)].

    Google Scholar 

  24. Yu. P. Kalmykov and S. V. Titov, Zh. Éksp. Teor. Fiz. 115, 101 (1999) [JETP 88, 58 (1999)].

    Google Scholar 

  25. H. Risken, The Fokker-Planck Equation (Springer, Berlin, 1989).

    Google Scholar 

  26. W. T. Coffey, Yu. P. Kalmykov, and J. T. Waldron, The Langevin Equation (World Scientific, Singapore, 1996).

    Google Scholar 

  27. Yu. P. Kalmykov, J. L. Dejardin, and W. T. Coffey, Phys. Rev. E 55, 2509 (1997).

    Article  ADS  Google Scholar 

  28. W. T. Coffey, D. S. F. Crothers, J. L. Dormann, et al., Phys. Rev. B 58, 3249 (1998).

    Article  ADS  Google Scholar 

  29. W. T. Coffey, D. S. F. Crothers, J. L. Dormann, et al., Phys. Rev. Lett. 80, 5655 (1998).

    Article  ADS  Google Scholar 

  30. D. A. Garanin, Phys. Rev. E 54, 3250 (1996).

    ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

__________

Translated from Fizika Tverdogo Tela, Vol. 42, No. 5, 2000, pp. 893–898.

Original Russian Text Copyright © 2000 by Kalmykov, Titov.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kalmykov, Y.P., Titov, S.V. Nonlinear response of superparamagnetic particles to a sudden change of a high constant magnetic field. Phys. Solid State 42, 918–924 (2000). https://doi.org/10.1134/1.1131312

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1134/1.1131312

Keywords

Navigation