Acoustic collective excitations and static dielectric response in incommensurate crystals with real order parameter

Starting from the basic Landau model for the incommensurate-commensurate materials of the class II, we derive the spectrum of collective modes for all (meta)stable states from the corresponding phase diagram. It is shown that all incommensurate states posses Goldstone modes with acoustic dispersions. The representation in terms of collective modes is also used in the calculation and discussion of static dielectric response for systems with the commensurate wave number in the center of the Brillouin zone.Comment: 7 pages, 4 figures, REVTe

Collective modes in uniaxial incommensurate-commensurate systems with the real order parameter

The basic Landau model for uniaxial systems of the II class is nonintegrable, and allows for various stable and metastable periodic configurations, beside that representing the uniform (or dimerized) ordering. In the present paper we complete the analysis of this model by performing the second order variational procedure, and formulating the combined Floquet-Bloch approach to the ensuing nonstandard linear eigenvalue problem. This approach enables an analytic derivation of some general conclusions on the stability of particular states, and on the nature of accompanied collective excitations. Furthermore, we calculate numerically the spectra of collective modes for all states participating in the phase diagram, and analyze critical properties of Goldstone modes at all second order and first order transitions between disordered, uniform and periodic states. In particular it is shown that the Goldstone mode softens as the underlying soliton lattice becomes more and more dilute.Comment: 19 pages, 16 figures, REVTeX, to be published in Journal of Physics A: Mathematical and Genera

Landau Model for Commensurate-Commensurate Phase Transitions in Uniaxial Improper Ferroelectric Crystals

We propose the Landau model for lock-in phase transitions in uniaxially modulated improper ferroelectric incommensurate-commensurate systems of class I. It includes Umklapp terms of third and fourth order and secondary order parameter representing the local polarization. The corresponding phase diagram has the structure of harmless staircase, with the allowed wave numbers obeying the Farey tree algorithm. Among the stable commensurate phases only those with periods equal to odd number of lattice constants have finite macroscopic polarizations. These results are in excellent agreement with experimental findings in some A2BX4 compounds.Comment: 9 pages, 5 figures, revtex, to be published in Journal of Physics: Cond. Matter as a Letter to the Edito