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Engraving trenches on the surfaces of ultrathin ferroelectric (FE) films andsuperlattices promises control over the orientation and direction of FE domainwalls (DWs). Through exploiting the phenomenon of DW-surface trench (ST)parallel alignment, systems where DWs are known for becoming electricalconductors could now become useful nanocircuits using only standardlithographical techniques. Despite this clear application, the microscopicmechanism responsible for the alignment phenomenon has remained elusive. Usingultrathin PbTiO$_3$ films as a model system, we explore this mechanism withlarge scale density functional theory simulations on as many as 5,136 atoms.Although we expect multiple contributing factors, we show that parallel DW-STalignment can be well explained by this configuration giving rise to anarrangement of electric dipole moments which best restore polar continuity tothe film. These moments preserve the polar texture of the pristine film, thusminimizing ST-induced depolarizing fields. Given the generality of thismechanism, we suggest that STs could be used to engineer other exotic polartextures in a variety of FE nanostructures as supported by the appearance ofST-induced polar cycloidal modulations in this letter. Our simulations alsosupport experimental observations of ST-induced negative strains which havebeen suggested to play a role in the alignment mechanism.

Origin of ferroelectric domain wall alignment with surface trenches in ultrathin films