Nonlinear dynamics of the classical isotropic Heisenberg antiferromagnetic chain: The sigma model sector and the kink sector

We identify two distinct low-energy sectors in the classical isotropic antiferromagnetic Heisenberg spin-S chain, in the continuum limit. We show that two types of rotation generators arise for the field in each sector. Using these, the Lagrangian for sector I is shown to be that of the nonlinear sigma model. Sector II has a null Lagrangian. Its Hamiltonian density is just the Pontryagin term. Exact solutions are found in the form of magnons and precessing pulses in I and moving kinks in II. The kink has 'spin' S. Sector I has a higher minimum energy than II