Classical Planar Heisenberg Ferromagnet, Complex Scalar Field and Nonlinear Excitations

Abstract

Nonlinear excitations in a classical planar Heisenberg ferromagnet in an external field (CPHFF) are studied. Taking a classical counterpart of the spin-raising operator as a relevant field variable, we establish a close correspondence between the CPHFF and a complex scalar field (CSF) in which each atom in a complex lattice field, while coupled with its neighbours, sits on ψ4-like on-site potential with saturable nonlinearity; In their static form CPHFF equations and CSF equations are identical to each other. In the continuum limit the CSF takes a semi-classical form of a Bose liquid with nonlinearity, however, characteristic of classical spin system. Solutions to the field equations are studied by using the continuum approximation. In one-dimensional case moving domain-wall solutions associated with symmetry-breaking states are obtained for the CPHFF and the CSF. In two- and three-dimensional cases static solutions to the field equations are obtained in the form of vortex solutions in close analogy to the case of the Ginzburg-Pitaevskii equation in the theory of superfluidity.