Features of incommensurate phases in multiferroics
  We present the results of a theoretical analysis of two-dimensionally modulated incommensurate phases in crystals and define the space distribution of magnetization and polarization vector in the incommensurate phase and demonstrate that their averaging in the incommensurate phase period equals zero. We apply symmetry arguments and show that despite the fact that the phase transition in the system is described by reducible representation of the space group high symmetry phase the superspace symmetry group of the in-commensurate phase contains all symmetry point groups of the high symmetry phase. We analyze the influence of the fractal distribu-tion of defects on the evolution of the incommensurate phase and show that a phase transition occurs in the incommensurate phase that is accompanied by the inversion loss. 
Bahruz Gadjiev