Domains walls and patterns in hard and soft ferroelectric films

A spatially uniform polarization in thin films of ferroelectric material is typically unstable due to the creation of a depolarization field by the uncompensated bound charge, leading to domain formation. We examine polarization domains and their interfaces in both crystalline ferroelectric materials and the recently-discovered ferroelectric nematics (FNs). In crystalline materials, the interfaces are generally thin and Ising-like, spanning only a few crystal unit cells. By contrast, FNs exhibit solitonic walls, where the polarization continuously deforms between adjacent domains. Moreover, the arrangement of domains in FNs is influenced by the boundary (anchoring) conditions of the sample, unlike in hard materials, where domain patterns are governed by the internal crystalline structure. We show how the elastic and electrostatic energies conspire to yield domain patterns, including stripes and radial sectors, in the FN.