Incommensurate phase transitions under the existence of the lifshitz invariant

The fundamental features of successive transitions from the prototype to the incommensurate phase and then to the commensurate phase, induced by the instability of an irreducible representation from which the Lifshitz invariant can be constructed, are clarified, and discussed in the relationship with the incommensurate phase transitions actually observed in ammonium fluoroberyllate and potassium selenate. Detection of two soft modes in potassium selenate in the incommensurate and the commensurate phases, by means of the Raman scattering experiments, will be mentioned.