**Large scale excitations for multicomponent order parameter in the planar
magnetic with spin s=1**

**Abstract:**

In this work we use Heisenberg magnetic model with biquadratic exchange.
In the case of spin s=1 quadrupole operators together with spin operators
form algebra *su(3)*.
By means of mean field approximation we obtain motion
equations for so called magnetic coordinates. Remarkably, that the
motion equations are integrable in dimension one. Some of magnetic
coordinates serve as a multicomponent
order parameter. The construction is easily generalized to the planar case.

Examining geometry and topology of coadjoint orbits of complexified algebra
*sl(3,C)* we find the proper parameterization of all possible orbits (by means
of
stereographic projection) that gives variables convenient to calculate
topological charge and free energy. In terms of new variables we solve the
problem of minimization of free energy and obtain topologicaly stable
solutions
which are expansion of Belavin-Polyakov soliton in the case of group *SU(3)*.
It appears that
the solutions which we call topological excitations can
arise spontaneously and cause destruction of biquadratic order.

Joint work with *Petro Holod* (National University of "Kyiv-Mohyla Academy" and Bogolyubov Institute for Theoretical Physics,
Kyiv, Ukraine).