Specific features of the formation of phase states in a non-Heisenberg magnet with $S = 2$

Spin states of a non-Heisenberg magnet with a magnetic ion spin of $2$ have been determined. It has been shown that the inclusion of the higher-order spin invariants leads to realization of specific phases with the tensor order parameters whose realization is impossible in magnets with $S = 1$. The free energy of the system in different spin states has been studied. The geometric images of the tensor phases in the spin space have been determined.