Nonlinear dynamics of a quantum ferromagnetic chain: Spin-coherent-state approach

The spin evolution equation of an isotropic, quantum ferromagnetic Heisenberg chain is analyzed in the continuum approximation using spin-coherent states. The advantages of this approach are discussed. Magnetic solitary-wave solutions are found, and the expectation values of the energy, momentum, and angular momentum corresponding to these solutions are determined. The energy-momentum dispersion relation for the nonlinear excitations is derived. The semiclassical spectrum is shown to arise when quantum effects are neglected by using a random-phase approximation to calculate certain expectation values. On including the quantum effects, it is found that the spectrum comprises two branches: a lower-energy branch of spin-wave-like, small-amplitude solitary waves with small quantum corrections, and a higher branch of particlelike large-amplitude solitary waves subject to significant quantum corrections for small S values. A heuristic discussion of the stability of these excitations is presented. A physical interpretation of the dispersion relation obtained is given.