Exact nonlinear spin waves in some models of interacting classical spins on a one-dimensional lattice

Abstract

We present exact finite-amplitude spin wave solutions for the nonlinear differential-difference equations describing the dynamics of spin vectors in a ferromagnetic (FM) and an antiferromagnetic (AFM) classical Heisenberg model of interacting spins on a one-dimensional lattice. We find that the dispersion relation between the frequency and wave vector of the FM nonlinear spin wave has the same form as that of the well-known low-amplitude spin wave, but with a prefactor which is explicitly dependent on its amplitude. This is in contrast with the AFM nonlinear spin wave, where we obtain the following intriguing results: Both the frequency and the wave vector acquire complicated dependences on the sublattice spin wave amplitudes. However, the dispersion relation between them is identical to that of the usual low-amplitude AFM spin wave, with no explicit dependence on the amplitudes. We outline how such solutions can also be supported in certain variants of the above models.