A group-theoretical approach for studying localized periodic and quasiperiodic vibrations in two- and three-dimensional lattice dynamical models is developed. This approach is demonstrated for the scalar models on the plane square lattice. The symmetry-determined invariant manifolds admitting existence of localized vibrations are found, and some types of discrete breathers are constructed on these manifolds. A general method using the apparatus of matrix representations of symmetry groups to simplify the standard linear stability analysis is discussed. This method allows one to decompose the corresponding system of linear differential equations with time-dependent coefficients into a number of independent subsystems whose dimensions are less than the full dimension of the considered system.

Abstract. Two prominent magnetoelectrics MnWO 4 and CuO possess lowtemperature commensurate paraelectric magnetically ordered phase. Here using Monte Carlo simulations we show that the walls between the domains of this phase are ferroelectric with the same electric polarization direction and value as those in the magnetoelectric phases of these compounds. We also suggest that experimental observation of electric polarization of domain walls in MnWO 4 should help to determine the macroscopic interactions responsible for its magnetoelectric properties.

No abstract