Flashing a look at the stability of the uniform ferroelectric nematic phase
Abstract
Recent discovery of the ferroelectric nematic phase NF resurrects a question about stability of the uniform NF state with respect to the formation of either standard for solid ferroelectrics domain structure, or often occurring in liquid crystals space modulation of the polarization vector P (and naturally coupled to P nematic director. In this work within Landau mean-field theory we investigate the linear stability of the minimal model admitting the conventional paraelectric nematic N and NF phases. Our minimal model, (besides the standard terms of the expansion over P and director gradients) includes, also standard for liquid crystals, director flexoelectric coupling term f and often overlooked in the literature (although similar by its symmetry to the director flexoelectric coupling) the flexo-dipolar coupling. We find that in the easy-plane anisotropy case the uniform NF state loses its stability with respect to one-dimensional or two-dimensional modulation. For non-zero f the 2D modulation threshold is always higher than its 1D counterpart. No any instability at all if one neglects the dipole-flexoelectric coupling. In the easy-axis case the both instability thresholds are the same, and the instability can occur even without flexo-dipolr coupling. We speculate that the phases with 1D or 2D modulations can be identified with discussed in the literature [see M.P.Rosseto, J.V.Selinger, Physical Review E, volume 101, page 052707 (2020)] single splay or double splay nematics.