Nonlinear dynamics and two-dimensional solitons for spin-1 ferromagnets with biquadratic exchange

We develop a consistent semiclassical theory of spin dynamics for an isotropic ferromagnet with a spin S=1 taking into consideration both bilinear and biquadratic exchange interactions over spin operators. For such non-Heisenberg magnets, a peculiar class of spin oscillations and waves, for which the quantum spin expectation value does not change in direction, but changes in length, is presented. 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. We demonstrate the presence of nonlinear uniform oscillations and waves as well as self-localized dynamical excitations (solitons) with finite energy. The possibility of excitation of such oscillations by ultrafast laser pulse is discussed.