Hamiltonian reduction for the magnetic dynamics in antiferromagnetic crystals

The nonlinear spin dynamics in antiferromagnetic crystals is studied for the magnetic structures similar to that of hematite. For the case when only two magnetization vectors are non-zero and the Hamiltonian has an axial symmetry, a reduction to a Hamiltonian system with one degree of freedom is performed, based on the corresponding conservation law. The analysis of the phase portraits of this system provides tractable analytical and geometric descriptions of the regimes of nonlinear spin dynamics in the crystal.