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Ordered States and Nonlinear Large-Scale Excitations in a Plane Magnet with Spin s=1

We study ordered states and topological excitations in a quasi-two-dimensional magnet, modeled by a square lattice with spins $s {=} 1$ at all sites, and the Hamiltonian with biquadratic exchange interaction between nearest neighbor sites. We propose two effective Hamiltonians for description of large-scale excitations in the two-dimensional case. They describe excitations of the mean field in a nematic phase and a mixed ferromagnetic-nematic phase. It is shown that the effective Hamiltonians are minimized on configurations with fixed topological charge. These topological excitations can arise at low temperatures and cause a destruction of a long-range order in the two-dimensional system.