Ferrielectric smectic phase with a layer-by-layer change of the two-component order parameter

One of the most remarkable properties of smectics is the wide variety of possible equilibrium structures. In this paper, based on the Landau theory of the phase transitions, the transitions between ferroelectric and antiferroelectric phases and the structure formed by smectic layers with different azimuthal and polar orientations of the molecules were calculated. This unique structure has been predicted P.V. Dolganov et al., JETP Lett. 76, 498 (2002)] using the minimization of the free energy with respect to the phase and modulus of the two-component order parameter, but never before detected. Recently, a nonresonant Bragg reflection, consistent with the predictions of the model, was found P. Fernandes et al., Eur. Phys. J. E 20, 81 (2006)] in the ferrielectric smectic C* _FI1(SmC* _FI1) phase. In the three-layer ferrielectric structure with a macroscopic helical pitch, the modulus of the order parameter is larger in anticlinic-like layers and smaller in layers with mixed ordering. The values of the interlayer interactions were determined for smectic liquid-crystalline materials forming different polar structures. The text was submitted by the authors in English.