Origin of Ferroelectric Domain Wall Alignment with Surface Trenches in Ultrathin Films

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 ${\mathrm{PbTiO}}_3$ 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.

Figure 1

(a)–(c) Bird’s eye views of ST configurations. $+\mathrm{AFD}$ is bracketed in (a) and (b) as they are treated with and without AFD modes. (a) Parallel to a domain wall, positioned over a domain wall: ${\parallel }^{\mathrm{DW}}$. (b) Parallel to a domain wall, positioned over a domain centroid: ${\parallel }^{\mathrm{DC}}$. (c) Perpendicular to a domain wall: $\perp +\mathrm{AFD}$. (d) Looking down the axis (the [010] direction) of the $d=1$ ${\parallel }^{\mathrm{DW}}$ film.

Figure 2

Local polarization vector fields calculated using the linear approximation first noted by Resta [48]. Atom coloring is shared with Fig. 1 but O is removed for clarity. (a) At the DC of the pristine film. The Pb site in the grey box is used in the scale bar positioned below (d). (b) At the DC of the $d=1{\parallel }^{\mathrm{DC}}$ film. The purple dashed box is discussed in the text. (c) At the DW of the pristine film. (d) At the DW of the $d=1{\parallel }^{\mathrm{DW}}$ film. The orange dashed box is discussed in the text. (e) A single polar vortex of the $d=2\perp +\mathrm{AFD}$ film from the region colored on (f). (g),(h) depict strings of Ti-centered local polarizations along the [010] direction from the color-matched dashed circles on (e).

Figure 3

Out-of-plane surface strain ${\epsilon }_{33}^{\mathrm{surf}}$ along [100] for (a) the $d=1$, ${\parallel }_{4\mathrm{\Lambda }}^{\mathrm{DC}}$ film and (b) the $d=1$, ${\parallel }_{4\mathrm{\Lambda }}^{\mathrm{DW}}$ film. Pristine film strain is shown for means of comparison. Up domains are colored light grey, down domains are colored a darker grey and the trench site is colored in red.