Features of incommensurate phases in K2SeO4, K2ZnCl4, and Rb2ZnCl4

Among the A2BX4 family, features of incommensurate phases in K2SeO4, K2ZnCl4, and Rb2ZnCl4 have been examined using a Ginzburg-Landau theory with complex amplitudes of the first- and higher-order lattice distortions as an order parameter. Characteristic features of the present theory are that the theory is based on an extended-zone scheme and only higher-order distortions with wave vectors close to a vector of the first-order one are taken into account. Free energies of incommensurate and commensurate phases then have the third-order umklapp and lock-in terms, respectively, from an invariance of the translational symmetry. Note that neither a polarization wave in the incommensurate phase nor a macroscopic polarization in the commensurate one is considered. In spite of this neglection, the present theory can sufficiently reproduce incommensurate features such as a change in an incommensurability and a phase modulation. That is, the incommensurate features in these materials are understood to originate mainly from the phase modulation of the first-order distortion by means of the higher-order ones.