  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.
