Magnon-Phonon Localization and Quasielastic Spectral Response in Quasi-One-Dimensional Heisenberg Ferromagnets

Abstract

Localized soliton excitations in a quasi-one-dimensional isotropic Heisenberg ferromagnet are investigated by explicitly accounting for coupling between the magnetic subsystem and longitudinal lattice vibrations. In the low-temperature regime, spin operators are bosonized using the Holstein-Primakoff transformation. In the continuum limit, the coupled dynamics of the magnetic excitation and lattice deformation reduces to a nonlinear Schrödinger equation. A complete set of working expressions is given for the spin-phonon Hamiltonian, phonon energy, continuum equation, one-soliton solution, localization width, energy, 
momentum, effective mass, and dynamic structure factor. The analysis shows that magnon-phonon coupling produces self-consistent spatial localization of the spin excitation over a finite length scale. As the coupling tends to zero, the localization width diverges and the excitation continuously approaches an extended spin wave. In the low-temperature, low-velocity regime, a dilute soliton subsystem generates a quasielastic central component in the scattering spectrum. Its width and integrated intensity depend on temperature, wave vector, localization length, and effective mass. This central component provides an experimentally accessible signature of nonlinear localized modes in quasi-one-imensional magnetic systems and can be probed by neutron scattering and, where applicable, infrared spectroscopy.