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Journal of Low Temperature Physics

, Volume 181, Issue 5–6, pp 211–222 | Cite as

Hyper-chaotic Magnetisation Dynamics of Two Interacting Dipoles

  • D. Urzagasti
  • D. Becerra-Alonso
  • L. M. Pérez
  • H. L. Mancini
  • D. LarozeEmail author
Article

Abstract

The present work is a numerical study of the deterministic spin dynamics of two interacting anisotropic magnetic particles in the presence of a time-dependent external magnetic field using the Landau–Lifshitz equation. Particles are coupled through the dipole–dipole interaction. The applied magnetic field is made of a constant longitudinal amplitude component and a time-dependent transversal amplitude component. Dynamical states obtained are represented by their Lyapunov exponents and bifurcation diagrams. The dependence on the largest and the second largest Lyapunov exponents, as a function of the magnitude and frequency of the applied magnetic field, and the relative distance between particles, is studied. The system presents multiple transitions between regular and chaotic behaviour depending on the control parameters. In particular, the system presents consistent hyper-chaotic states.

Keywords

Magnetisation dynamics Dipolar interaction Hyper-chaos 

Notes

Acknowledgments

We thank R. L. Stamps (University of Glasgow, UK) for invaluable discussions. DU acknowledges the PhD fellowship from the Performance Agreement Project UTA/Mineduc (Universidad de Tarapacá). DBA was supported in part by the Spanish Inter-Ministerial Commission of Science and Technology under Project TIN2014-54583-C2-1-R, the European Regional Development fund, and the “Junta de Andalucía” (Spain), under Project P2011-TIC-7508. LMP and HLM acknowledge partial financial support from the Spanish Ministry of Science and Technology under Contract Nos. FIS2011-24642 and FIS2014-54101-P. DL acknowledges partial financial support from FONDECYT 1120764, Basal Program Center for Development of Nanoscience and Nanotechnology (CEDENNA) FB0807, UTA-Project 8750-12 and Engineering and Physical Sciences Research Council Grant No. EP/L002922/1.

References

  1. 1.
    M.C. Cross, P.C. Hohenberg, Rev. Mod. Phys. 65, 851 (1993)CrossRefADSGoogle Scholar
  2. 2.
    E.N. Lorenz, J. Atmos. Sci. 20, 130 (1963)CrossRefADSGoogle Scholar
  3. 3.
    C. Sparrow, The Lorenz Equations: Bifurcations, Chaos and Strange Attractors (Springer, New York, 1982)zbMATHCrossRefGoogle Scholar
  4. 4.
    E. Ott, Chaos in Dynamical Systems (Cambridge University Press, Cambridge, 2002)zbMATHCrossRefGoogle Scholar
  5. 5.
    G. Gibson, C. Jeffries, Phys. Rev. A 29, 811 (1984)CrossRefADSGoogle Scholar
  6. 6.
    F.M. de Aguiar, A. Azevedo, S.M. Rezende, Phys. Rev. B 39, 9448 (1989)CrossRefADSGoogle Scholar
  7. 7.
    J. Becker, F. Rodelsperger, Th Weyrauch, H. Benner, W. Just, A. Cenys, Phys. Rev. E 59, 1622 (1999)CrossRefADSGoogle Scholar
  8. 8.
    J. Cai, Y. Kato, A. Ogawa, Y. Harada, M. Chiba, T. Hirata, J. Phys. Soc. Jpn. 71, 3087 (2002)CrossRefADSGoogle Scholar
  9. 9.
    M.G. Cottam (ed.), Linear and Nonlinear Spin Waves in Magnetic Films and Superlattices (World Scientific, Singapore, 1992)Google Scholar
  10. 10.
    P.E. Wigen (ed.), Nonlinear Phenomena and Chaos in Magnetic Materials (World Scientific, Singapore, 1994)Google Scholar
  11. 11.
    L. Landau, Collected Papers of Landau (Pergamon, New York, 1965)Google Scholar
  12. 12.
    L.F. Alvarez, O. Pla, O. Chubykalo, Phys. Rev. B 61, 11613 (2000)CrossRefADSGoogle Scholar
  13. 13.
    Z. Li, Y.C. Li, S. Zhang, Phys. Rev. B 74, 054417 (2006)CrossRefADSGoogle Scholar
  14. 14.
    Z. Li, Y.C. Li, S. Zhang, Phys. Rev. Lett. 99, 134101 (2007)CrossRefADSGoogle Scholar
  15. 15.
    H.Z. Xu, X. Chen, J.M. Liu, J. App. Phys. 104, 093919 (2008)CrossRefADSGoogle Scholar
  16. 16.
    Y. Lan, Y.C. Li, Nonlinearity 21, 2801 (2008)zbMATHMathSciNetCrossRefADSGoogle Scholar
  17. 17.
    D. Laroze, L.M. Perez, Physica B 403, 473 (2008)CrossRefADSGoogle Scholar
  18. 18.
    D.V. Vagin, P. Polyakov, J. Appl. Phys. 105, 033914 (2009)CrossRefADSGoogle Scholar
  19. 19.
    R.K. Smith, M. Grabowski, R.E. Camley, J. Magn. Magn. Mater. 322, 2127 (2010)CrossRefADSGoogle Scholar
  20. 20.
    J. Bragard, H. Pleiner, O.J. Suarez, P. Vargas, J.A.C. Gallas, D. Laroze, Phys. Rev. E 84, 037202 (2011)CrossRefADSGoogle Scholar
  21. 21.
    D. Laroze, J. Bragard, O.J. Suarez, H. Pleiner, IEEE Trans. Mag. 47, 10 (2011)CrossRefGoogle Scholar
  22. 22.
    D. Laroze, D. Becerra-Alonso, J.A.C. Gallas, H. Pleiner, IEEE Trans. Magn. 48, 3567 (2012)CrossRefADSGoogle Scholar
  23. 23.
    L.M. Pérez, J. Bragard, H.L. Mancini, J.A.C. Gallas, A.M. Cabanas, O.J. Suarez, D. Laroze, Netw. Heterog. Media 10, 209 (2015)MathSciNetCrossRefGoogle Scholar
  24. 24.
    T. Shinbrot, C. Grebogi, J.A. Yorke, E. Ott, Nature 363, 411 (1993)CrossRefADSGoogle Scholar
  25. 25.
    S. Boccaletti, C. Grebogi, Y.-C. Lai, H. Mancini, D. Maza, Phys. Rep. 329, 103 (2000)MathSciNetCrossRefADSGoogle Scholar
  26. 26.
    D. Mentrup, J. Schnack, M. Luban, Physica A 272, 153 (1999)CrossRefADSGoogle Scholar
  27. 27.
    D.V. Efremov, R.A. Klemm, Phys. Rev. B 66, 174427 (2002)CrossRefADSGoogle Scholar
  28. 28.
    D. Laroze, P. Vargas, Physica B 372, 332 (2006)CrossRefADSGoogle Scholar
  29. 29.
    L.M. Pérez, O.J. Suarez, D. Laroze, H.L. Mancini, Cent. Eur. J. Phys. 11, 1629 (2013)Google Scholar
  30. 30.
    D. Laroze, P. Vargas, C. Cortes, G. Gutierrez, J. Magn. Magn. Mater. 320, 1440 (2008)CrossRefADSGoogle Scholar
  31. 31.
    G. Möller, R. Moessner, Phys. Rev. Lett. 96, 237202 (2006)CrossRefADSGoogle Scholar
  32. 32.
    R.F. Wang, C. Nisoli, R.S. Freitas, J. Li, W. McConville, B.J. Cooley, M.S. Lund, N. Samarth, C. Leighton, V.H. Crespi, P. Schiffer, Nature (Lond.) 439, 303 (2006)CrossRefADSGoogle Scholar
  33. 33.
    I.D. Mayergoyz, G. Bertotti, C. Serpico, Nonlinear Magnetization Dynamics in Nanosystems (Elsevier, Dordrecht, 2009)zbMATHGoogle Scholar
  34. 34.
    R.C. O’Handley, Modern Magnetic Materials: Principles and Applications (Wiley, New York, 1999)Google Scholar
  35. 35.
    W.F. Brown Jr, J. Appl. Phys. 30, 130s (1959)CrossRefADSGoogle Scholar
  36. 36.
    J.L. García-Palacios, F.J. Lázaro, Phys. Rev. B 58, 14937 (1998)CrossRefADSGoogle Scholar
  37. 37.
    A. Wolf, J.B. Swift, H.L. Swinney, J.A. Vastano, Physica D 16, 285 (1985)zbMATHMathSciNetCrossRefADSGoogle Scholar
  38. 38.
    J.A.C. Gallas, Int. J. Bifurc. Chaos 20, 197 (2010). and references thereinzbMATHMathSciNetCrossRefGoogle Scholar
  39. 39.
    D. Laroze, H. Pleiner, Commun. Nonlinear Sci. Numer. Simul. 26, 167 (2015)MathSciNetCrossRefADSGoogle Scholar
  40. 40.
    J.A.C. Gallas, Phys. Rev. Lett. 70, 2714 (1993)CrossRefADSGoogle Scholar
  41. 41.
    C. Bonatto, J.C. Garreau, J.A.C. Gallas, Phys. Rev. Lett. 95, 143905 (2005)CrossRefADSGoogle Scholar
  42. 42.
    D. Laroze, P.G. Siddheshwar, H. Pleiner, Commun. Nonlinear Sci. Numer. Simul. 18, 2436 (2013)zbMATHMathSciNetCrossRefADSGoogle Scholar
  43. 43.
    W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery, Numerical Recipes in Fortran (Cambridge University Press, Cambridge, 1992)zbMATHGoogle Scholar
  44. 44.
    X. Batlle, A. Labarta, J. Phys. D 35, R15 (2002)CrossRefADSGoogle Scholar
  45. 45.
    P. Landeros, J. Escrig, D. Altbir, D. Laroze, J. d’Albuquerque e Castro, P. Vargas, Phys. Rev. B 65, 094435 (2005)CrossRefADSGoogle Scholar
  46. 46.
    H. Brune, M. Giovannini, K. Bromann, K. Kern, Nature (Lond.) 394, 451 (1998)CrossRefADSGoogle Scholar
  47. 47.
    Y. Khivintsev, B. Kuanr, T.J. Fal, M. Haftel, R.E. Camley, Z. Celinski, D.L. Mills, Phys. Rev. B 81, 054436 (2010)CrossRefADSGoogle Scholar
  48. 48.
    Y. Khivintsev, J. Marsh, V. Zagorodnii, I. Harward, J. Lovejoy, P. Krivosik, R.E. Camley, Z. Celinski, Appl. Phys. Lett. 98, 042505 (2011)CrossRefADSGoogle Scholar
  49. 49.
    C. Cheng, W.E. Bailey, Appl. Phys. Lett. 103, 242402 (2013)CrossRefADSGoogle Scholar
  50. 50.
    M.G. Phelps, K.L. Livesey, A.M. Ferona, R.E. Camley, EPL 109, 37007 (2015)CrossRefADSGoogle Scholar
  51. 51.
    R. Gilmore, M. Lefranc, The Topology of Chaos, Alice in Stretch and Squeeze Land (Wiley, New York, 2002)Google Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • D. Urzagasti
    • 1
  • D. Becerra-Alonso
    • 2
  • L. M. Pérez
    • 3
  • H. L. Mancini
    • 3
  • D. Laroze
    • 4
    • 5
    Email author
  1. 1.Instituto de Investigaciones FísicasUMSALa PazBolivia
  2. 2.Universidad Loyola AndalucíaCórdobaSpain
  3. 3.Departamento de Física y Matemática AplicadaUniversidad de NavarraPamplonaSpain
  4. 4.SUPA School of Physics and AstronomyUniversity of GlasgowGlasgowUK
  5. 5.Instituto de Alta de InvestigaciónUniversidad de TarapacáAricaChile

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