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


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.


Magnetisation dynamics Dipolar interaction Hyper-chaos 



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.


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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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