Ferroelectric nematic liquids with conics

Spontaneous electric polarization of solid ferroelectrics follows the direction of crystallographic axes. Domains of differently oriented polarization are divided by boundary defects, called domain walls (DWs), which are predominantly flat. Here we demonstrate that DWs are shaped as conic sections in a ferroelectric nematic (N_F) liquid crystal, which is a fluid with no crystallographic axes. The conics bisect the angle between two neighboring polarization fields to avoid electric charges. The remarkable bisecting properties of conic sections, known for millennia, find their material realization as intrinsic features of fluid ferroelectrics. The findings could be helpful in designing patterns of electric polarization and space charge.