Journal of Experimental and Theoretical Physics

, Volume 88, Issue 1, pp 58–65

Longitudinal dynamic susceptibility of superparamagnetic particles with cubic anisotropy

  • Yu. P. Kalmykov
  • S. V. Titov
Solids

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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    L. Neel, Ann. Geophys. (C.N.R.S.) 5, 99 (1949).Google Scholar
  2. 2.
    W. F. Brown Jr., IEEE Trans. Magn. 15, 1196 (1979).Google Scholar
  3. 3.
    H. B. Braun and H. N. Bertram, J. Appl. Phys. 75, 4609 (1994).ADSGoogle Scholar
  4. 4.
    W. F. Brown Jr., J. Appl. Phys. 30, 130 (1959).Google Scholar
  5. 5.
    A. Aharoni, Phys. Rev. 177, 763 (1969).CrossRefADSGoogle Scholar
  6. 6.
    Yu. L. Raikher and M. I. Shliomis, Zh. Éksp. Teor. Fiz. 67, 1060 (1974) [Sov. Phys. JETP 40, 526 (1975)].Google Scholar
  7. 7.
    D. A. Garanin, V. V. Ishchenko, and L. V. Panina, Teor. Mat. Fiz. 82, 242 (1990).Google Scholar
  8. 8.
    Yu. L. Raikher and V. I. Stepanov, Zh. Éksp. Teor. Fiz. 102, 1409 (1992) [Sov. Phys. JETP 75, 764 (1992)].Google Scholar
  9. 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. 10.
    D. A. Garanin, Phys. Rev. E 54, 3250 (1996).CrossRefADSGoogle Scholar
  11. 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. 12.
    Yu. P. Kalmykov and W. T. Coffey, Phys. Rev. B 56, 3325 (1997).CrossRefADSGoogle Scholar
  13. 13.
    I. Klik and L. Gunther, J. Stat. Phys. 60, 473 (1990).CrossRefGoogle Scholar
  14. 14.
    A. Aharoni, Phys. Rev. B 7, 1103 (1973).CrossRefADSGoogle Scholar
  15. 15.
    D. A. Smith and F. A. de Rosario, J. Magn. Magn. Mater. 3, 219 (1976).CrossRefADSGoogle Scholar
  16. 16.
    I. Eisenstein and A. Aharoni, Phys. Rev. B 16, 1278 (1977).ADSGoogle Scholar
  17. 17.
    I. Eisenstein and A. Aharoni, Phys. Rev. B 16, 1285 (1977).ADSGoogle Scholar
  18. 18.
    I. Klik and L. Gunther, J. Appl. Phys. 67, 4509 (1990).CrossRefADSGoogle Scholar
  19. 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. 20.
    W. F. Brown Jr., Phys. Rev. 130, 1677 (1964).ADSGoogle Scholar
  21. 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. 22.
    H. Risken, The Fokker-Planck Equation. Method of Solution and Applications, 2nd ed., Springer, Berlin (1989).Google Scholar
  23. 23.
    W. T. Coffey, Yu. P. Kalmykov, and J. T. Waldron, The Langevin Equation, World Scientific, Singapore (1996).Google Scholar
  24. 24.
    T. L. Gilbert, Phys. Rev. 100, 1243 (1956).Google Scholar
  25. 25.
    R. L. Stratonovich of, Selected Problems on Fluctuation Theory in Radio Engineering [in Russian], Sovet-skoe Radio, Moscow (1961).Google Scholar
  26. 26.
    D. A. Varshalovich, A. N. Moskalev, and V. K. Khersonskii, Quantum Theory of Angular omentum, World Scientific, Singapore (1987).Google Scholar
  27. 27.
    Yu. P. Kalmykov, Khim. Fiz. 16, 130 (1997).Google Scholar
  28. 28.
    H. J. Breymayer, H. Risken, H. D. Vollmer, and W. Wonneberger, Appl. Phys. B 28, 335 (1982).CrossRefGoogle Scholar
  29. 29.
    T. Bitoh, K. Ohba, M. Takamatsu, T. Shirane, and S. Chikazawa, J. Phys. Soc. Jpn. 64, 1311 (1995).Google Scholar
  30. 30.
    T. Bitoh, K. Ohba, M. Takamatsu, T. Shirane, and S. Chikazawa, J. Magn. Magn. Mater. 154, 59 (1996).CrossRefADSGoogle Scholar

Copyright information

© American Institute of Physics 1999

Authors and Affiliations

  • Yu. P. Kalmykov
    • 1
  • S. V. Titov
    • 1
  1. 1.Institute of Radio Engineering and ElectronicsRussian Academy of SciencesFryazino, Moscow RegionRussia

Personalised recommendations