Two-Dimensional Classical Attractors in the Spin Phase Space of the S = 1 Easy-Axis Heisenberg Ferromagnet

  • V. G. Makhankov
  • A. V. Makhankov
  • A. T. Maksudov
  • Kh. Kh. Muminov
Conference paper
Part of the Research Reports in Physics book series (RESREPORTS)


The equations are derived which describe dynamics of small amplitude spin waves in the S=l easy-axis Heisenberg model. To proceed from quantum to quasiclassical description the generalized coherent states (CS) corresponding to the space CP2 =SU (3) /SU (2) ⊗U (1) are constructed and used as a trial functions. We find that classical vacuum states of the model lie in the SU (2) section of the total four-dimensional spin phase space. The latter is just a sphere, classical spins take their value on so spin dynamics is described by the well-known Landau-Lifshitz equation. It turns out, however, that nonlinear soliton-type solutions are captured in this cross-section too. Computer simulations also show that stationary solutions of the system is stable and lie in the SU (2) section. So the SU (2) cross- section in spin phase space can be considered as a two- dimensional classical attractor in this space.


Coherent State Trial Function Heisenberg Model Nonlinear Schrodinger Equation Exchange Anisotropy 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • V. G. Makhankov
    • 1
  • A. V. Makhankov
    • 1
  • A. T. Maksudov
    • 2
  • Kh. Kh. Muminov
    • 3
  1. 1.Joint Institute for Nuclear Research, DubnaMoscowUSSR
  2. 2.Leninabad Pedagogical InstituteLeninabadUSSR
  3. 3.Tajik State UniversityDushanbeUSSR

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