of spin-1/2 crystalline systems are well understood and presented in the literature [@ABP; @GM]. If one ignores the relativistic effects associated with the interaction of the electron magnetic moments, then the description is based on the Heisenberg model Hamiltonian and depending on the sign of the exchange integral, the system exhibits the ferromagnetic or antiferromagnetic ordering. The physical nature of the exchange interaction can be explained by considering the electrostatic interaction of two electrons between themselves and protons in a hydrogen molecule or by employing only the symmetry considerations which require the Hamiltonian to be invariant with respect to spatial rotations [@ABP]. The resulting Hamiltonian is expressed in terms of the Pauli matrices representing the generators of the SU(2) group. It takes into account purely quantum (exchange) effects originating from the Fermi-Dirac statistics for electrons.

The interaction in high-spin ($S>1/2$) crystalline systems has a more complicated character that goes beyond the usual Heisenberg model, while their phase diagram exhibits a more rich structure [@Nagaev]. In particular, for spin-1 systems with bilinear and biquadratic exchange interactions, the exotic orderings, such as nematic [@Nagaev; @Matveev; @Andreev; @Papa] and semi-ordered [@Papa] phases, may exist along with the traditional ferromagnetic and antiferromagnetic phases. Moreover, 