  Engraving trenches on the surfaces of ultrathin ferroelectric (FE) films and
superlattices promises control over the orientation and direction of FE domain
walls (DWs). Through exploiting the phenomenon of DW-surface trench (ST)
parallel alignment, systems where DWs are known for becoming electrical
conductors could now become useful nanocircuits using only standard
lithographical techniques. Despite this clear application, the microscopic
mechanism responsible for the alignment phenomenon has remained elusive. Using
ultrathin PbTiO$_3$ films as a model system, we explore this mechanism with
large scale density functional theory simulations on as many as 5,136 atoms.
Although we expect multiple contributing factors, we show that parallel DW-ST
alignment can be well explained by this configuration giving rise to an
arrangement of electric dipole moments which best restore polar continuity to
the film. These moments preserve the polar texture of the pristine film, thus
minimizing ST-induced depolarizing fields. Given the generality of this
mechanism, we suggest that STs could be used to engineer other exotic polar
textures in a variety of FE nanostructures as supported by the appearance of
ST-induced polar cycloidal modulations in this letter. Our simulations also
support experimental observations of ST-induced negative strains which have
been suggested to play a role in the alignment mechanism.
