Skip to main content
Log in

Longitudinal dynamic susceptibility of superparamagnetic particles with cubic anisotropy

  • Solids
  • Published:
Journal of Experimental and Theoretical Physics Aims and scope Submit manuscript

Abstract

We study the linear response of a system of single-domain ferromagnetic particles with cubic magnetic anisotropy to a weak external a.c. magnetic field. By averaging the Gilbert equation with a fluctuating field for the magnetization of an individual particle we derive a system of recurrence equations for the spectra of equilibrium correlation functions describing the longitudinal relaxation of the system. We find the solution of this system by using matrix continued fractions. We also evaluate the longitudinal relaxation time and the spectrum of the complex-valued magnetic susceptibility. Finally, we show that the nature of susceptibility dispersion is determined by the anisotropy and dissipation 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. Neel, Ann. Geophys. (C.N.R.S.) 5, 99 (1949).

    Google Scholar 

  2. W. F. Brown Jr., IEEE Trans. Magn. 15, 1196 (1979).

    Google Scholar 

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

    ADS  Google Scholar 

  4. W. F. Brown Jr., J. Appl. Phys. 30, 130 (1959).

    Google Scholar 

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

    Article  ADS  Google Scholar 

  6. Yu. L. Raikher and M. I. Shliomis, Zh. Éksp. Teor. Fiz. 67, 1060 (1974) [Sov. Phys. JETP 40, 526 (1975)].

    Google Scholar 

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

    Google Scholar 

  8. Yu. L. Raikher and V. I. Stepanov, Zh. Éksp. Teor. Fiz. 102, 1409 (1992) [Sov. Phys. JETP 75, 764 (1992)].

    Google Scholar 

  9. W. T. Coffey, D. S. F. Crothers, Yu. P. Kalmykov, and J. T. Waldron, Phys. Rev. B 51, 15 947 (1995).

    Google Scholar 

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

    Article  ADS  Google Scholar 

  11. É. K. Sadykov and A. G. Isavnin, Fiz. Tverd. Tela (St. Petersburg) 38, 2104 (1997) [Phys. Solid State 38, 1160 (1996)].

    Google Scholar 

  12. Yu. P. Kalmykov and W. T. Coffey, Phys. Rev. B 56, 3325 (1997).

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

  14. A. Aharoni, Phys. Rev. B 7, 1103 (1973).

    Article  ADS  Google Scholar 

  15. D. A. Smith and F. A. de Rosario, J. Magn. Magn. Mater. 3, 219 (1976).

    Article  ADS  Google Scholar 

  16. I. Eisenstein and A. Aharoni, Phys. Rev. B 16, 1278 (1977).

    ADS  Google Scholar 

  17. I. Eisenstein and A. Aharoni, Phys. Rev. B 16, 1285 (1977).

    ADS  Google Scholar 

  18. I. Klik and L. Gunther, J. Appl. Phys. 67, 4509 (1990).

    Article  ADS  Google Scholar 

  19. L. J. Geoghegan, W. T. Coffey, and B. Mulligan, in Advances in Chemical Physics, Vol. 100, I. Prigogine and S. A. Rice (Eds.), Wiley, New York (1997), p. 475.

    Google Scholar 

  20. W. F. Brown Jr., Phys. Rev. 130, 1677 (1964).

    ADS  Google Scholar 

  21. Yu. L. Raikher and M. I. Shliomis, in Advances in Chemical Physics, Vol. 87, W. T. Coffey (Ed.), Wiley, New York (1994), p. 595.

    Google Scholar 

  22. H. Risken, The Fokker-Planck Equation. Method of Solution and Applications, 2nd ed., Springer, Berlin (1989).

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  25. R. L. Stratonovich of, Selected Problems on Fluctuation Theory in Radio Engineering [in Russian], Sovet-skoe Radio, Moscow (1961).

    Google Scholar 

  26. D. A. Varshalovich, A. N. Moskalev, and V. K. Khersonskii, Quantum Theory of Angular omentum, World Scientific, Singapore (1987).

    Google Scholar 

  27. Yu. P. Kalmykov, Khim. Fiz. 16, 130 (1997).

    Google Scholar 

  28. H. J. Breymayer, H. Risken, H. D. Vollmer, and W. Wonneberger, Appl. Phys. B 28, 335 (1982).

    Article  Google Scholar 

  29. T. Bitoh, K. Ohba, M. Takamatsu, T. Shirane, and S. Chikazawa, J. Phys. Soc. Jpn. 64, 1311 (1995).

    Google Scholar 

  30. T. Bitoh, K. Ohba, M. Takamatsu, T. Shirane, and S. Chikazawa, J. Magn. Magn. Mater. 154, 59 (1996).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Zh. Éksp. Teor. Fiz. 115, 101–114 (January 1999)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kalmykov, Y.P., Titov, S.V. Longitudinal dynamic susceptibility of superparamagnetic particles with cubic anisotropy. J. Exp. Theor. Phys. 88, 58–65 (1999). https://doi.org/10.1134/1.558764

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1134/1.558764

Keywords

Navigation