  Charge manipulation and fabrication of stable domain patterns in
ferroelectric materials by scanning probe microscopy open up broad avenues for
the development of tunable electronics. Harnessing the polarization energy and
electrostatic forces with specific geometry of the system enables producing the
nanoscale domains by-design. Along with that, domain engineering requires
mastery of underlying physical mechanisms that govern the domain formation.
Here, we present a theoretical description of the domain formation by a
scanning probe microscopy tip in a ferroelectric film with strong in-plane
anisotropy of polarization. We demonstrate that local charge injection produces
wedge-shaped domains that propagate along the anisotropy axis, whereas the
tip-written lines of charge generate a comb-like domain structure. The results
of our calculations agree with earlier experimental observations and allow for
the optimization of the targeted domain structures.
