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

Abstract

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.