Theory for anisotropic local ferroelectric switching

Theoretical modeling of polarization switching around a biased tip contact is important for fundamental understanding and advanced applications of ferroelectrics. Here we propose a simple in-plane two-dimensional model that considers surface charge transport and the associated evolution of the electric field driving domain growth. The model reproduces peculiar domain shapes ranging from round to faceted in KTiOPO₄(C_2vsymmetry) and LiNbO₃(C_3vsymmetry). This is done through modulation of dielectric permittivity, which mimics domain wall pinning on the lattice. In contrast to previous works, which attempted to justify domain anisotropy by means of point symmetry invariants, here we illustrate the necessity of taking translational symmetry into account. The results are pertinent to ferroelectric racetrack memories and other applications requiring domain tailoring.