“…Theoretical methods that have proved successful in the study of quantum s = 1/2 magnets such as the spin wave theory [15], exact diagonalization [16,17,18], series expansion [19] large-N expansion [21], functional renormalization group [22], Green's function method [23], and projected entangled pair states [24], for the S = 1 spin systems face various difficulties and they need to be reconsidered. Sufficiently effective in this case is the Schwinger boson method [25], which was realized for different systems with spin S = 1 [26,27,28,29,30]. In our work, this method is generalized for more complicated pseudospin systems which take into account the effects of the biquadratic inter-site anisotropy.…”