Khymyn R. Nonlinear dynamics for magnets with a strong spin reduction

We develop a consistent semiclassical theory of spin dynamics for an isotropic magnet with a spin S=1 taking into consideration both bilinear and biquadratic exchange interactions over spin operators. In all phase states of such magnet the presence of biquadratic exchange leads to the existence of the particular elementary soliton and magnon excitations, for which the quantum spin expectation value does not change in direction, but changes in length. Such "longitudinal" excitations do not exist in regular magnets, the dynamics of which is described in terms of the Landau-Lifshitz equation or by means of the spin Heisenberg Hamiltonian. The energy of such soliton at given value of its momentum is lower then the corresponding magnon-energy. It means that soliton is more energy benefical with the same momentum. Topologically non-trivial soliton states with finite energy exist in two-dimensional magnetic with S=1. They keep their topological charge on the phase transitions from collinear nematic to ferromagnetic and from orthogonal nematic to antiferromagnetic.