The soliton wavenumber cut-off and the excitation spectrum of the 1-D Heisenberg ferromagnet in the semiclassical continuum approximation

The scheme for the semiclassical quantisation of the solitons of the 1-D continuum Heisenberg ferromagnet is examined. A parameter that can be interpreted as the intrinsic wavenumber Q of a classical soliton is identified. The cut-off restriction that Q lies within the first Brillouin zone has to be added to the continuum model if its results are to be consistently interpreted in terms of an underlying spin S lattice model.