Theory of domain patterns in ferroelectric nematic liquid crystal films

Spontaneous electric polarization in a material creates a depolarization field which can destabilize a uniform polarization ground state. In films of the newly-discovered ferroelectric nematic (N_F) materials, mitigation of the depolarization field is hindered by the nematic elasticity and depends on anchoring conditions. We show that in N_F films with in-plane anchoring, the depolarization field creates domains with alternating polarization directions. A wide variety of domain patterns is possible, including uniform stripes and radial sectors. These patterns depend on the anchoring and ionic conditions of the N_F sample. Beyond a certain critical film thickness, the domains additionally develop a 180^○ twist perpendicular to the film surface. We develop the theoretical description of the domain patterns, demonstrating the competition between electrostatics, anchoring, and nematic elasticity.