Ferrielectricity in smectic-C^{*} dechiralization-line lattices.

Recent experiments probing a new ferroelectric liquid crystal (CLF08) confined in cells with planar alignment have shown dielectric and optic anomalies suggesting the onset of ferrielectric ordering within the surface lattice of dechiralization lines. We present a phenomenological theory describing the corresponding phase transition sequence SmA→SmC^{*}→Ferri. Phase diagrams and thermodynamic, dielectric, and optic properties are worked out and compared with experiments.

Coupling of replicate order-parameters in incommensurate multiferroics.

The specific properties of incommensurate multiferroic phases resulting from the coupling of order-parameter replicates are worked out using the illustrative example of iron vanadate. The phase difference between the order-parameter copies induces an additional broken symmetry phase corresponding to the lowest symmetry of the system and varies critically at the transition to the multiferroic phase. It reflects the temperature dependence of the angle between paired spins in the antiferromagnetic spiral structure.

Directional magnetoelectric effects in MnWO4: magnetic sources of the electric polarization.

The ferroelectric order and magnetic field induced effects observed in the spiral phase of MnWO4 are described theoretically. It is demonstrated explicitly that the Dzyaloshinskii-Moriya antisymmetric interactions contribute to the correlation between spins and electric dipoles in the incommensurate and commensurate ferroelectric phases of magnetic multiferroics. However, other single-site symmetric interactions are shown to be involved in the magnetoelectric process, suggesting the possible existence of an electric polarization originating from purely symmetric effects.

Theory of two- and three-dimensional bent-core mesophases.

An extension of the vector-wave theory of antiferroelectric bent-core liquid crystals to columnar and soft-crystalline mesophases is presented. We enumerate and describe the phases resulting from the condensation of one, two, and three vector waves in the isotropic liquid of bent-core molecules. Beside the one-dimensional B2 and smectic- CP phases, 24 columnar and soft-crystalline orthorhombic, monoclinic, and triclinic phases can be stabilized when two or three waves have nonparallel wave vectors.

Macroscopic and molecular symmetries of unconventional nematic phases.

The effects of the molecular symmetry on macroscopic properties of conventional and unconventional nematic phases are investigated theoretically. These effects concern: (1) the form of the molecular orientation fluctuations, (2) the thermodynamic behavior and the list of stable ordered phases, (3) the effective symmetry of the molecules in the ordered phases. The order-parameter consists of tensors forming the main harmonics of the fluctuation distribution.