Moving and Stationary Self-Localized Magnons as Spin-Wave Solitons in Heisenberg Ferromagnets

A theory of elementary excitations in Heisenberg ferromagnets with anisotropic exchange interactions is formulated without assuming the smallness of spin deviations from the ground state. This is done by using a path integral formalism in the SU(2) coherent state representation combined with the use of the stationary-phase approximation. Equations for spin-deviation field variables are solved in an approximate analytical form to show the existence by the intrinsic nonlinearity of mobile and immobile self-localized magnons in one- and d -dimensional cases, respectively. Discussions are given on their characteristic properties such as the energy eigenvalues lying below the linear spin-wave energy band, dispersion curves and localized-mode profiles. These intrinsic nonlinear modes can be considered as a natural extension of conventional (linear) spin waves to the nonlinear, soliton regime.