The influence of chirality on the macroscopic behavior of multiferroic smectic phases

We study the influence of chirality on various types of multiferroic phases, which show simultaneously liquid crystalline order, as well as long range electric or magnetic order, including the possibilities of ferro, antiferro, and conical forms. The main focus is on the chiral ferroelectric smectic CF* phase. This includes a discussion of possible ground states, including defect phases not considered before. We present the macroscopic dynamics of the simplest possible ground state, namely a helix superposed on the ferroelectric structure of smectic CF with C1h symmetry, thus leading to triclinic C1 symmetry. A combination of linear irreversible thermodynamics and symmetry arguments is used to derive the resulting dynamic equations applicable at sufficiently low frequencies and long wavelengths. Specific for smectic CF*, when compared to CF, are, for example, static cross-coupling terms between layer compressions and spatial variations of the in-plane director. Correspondingly, we find in the dissipative domain several chiral contributions specific for CF*, when compared to nonchiral CF, including cross-coupling terms between layer compressions and gradients of the in-plane director. For various other types of chiral multiferroic smectic phases, we concentrate on the differences to their nonchiral analogs, including the McMillan phase, smectic CM, and the antiferroelectric smectic ZA phase. We point out that the chiralization of a ferromagnetic smectic A phase could lead to conical magnetism, a topic that is also of high current interest in solid state physics. Finally, we elucidate the significance of mesoscopic aspects in the dynamic equation for the displacement field across various multiferroic smectic phases.