Abstract
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.
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