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

Abstract

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.