Theory of hypothetical ferroelectric superlattices incorporating head-to-head and tail-to-tail 180° domain walls

While electrical compatibility constraints normally prevent head-to-head (HH) and tail-to-tail (TT) domain walls from forming in ferroelectric materials, we propose that such domain walls could be stabilized by intentional growth of atomic layers in which the cations are substituted from a neighboring column of the periodic table. In particular, we carry out predictive first-principles calculations of superlattices in which Sc, Nb, or other substitutional layers are inserted periodically into ${\mathrm{PbTiO}}_3$. We confirm that this gives rise to a domain structure with the longitudinal component of the polarization alternating from domain to domain, and with the substitutional layers serving as HH and TT domain walls. We also find that a substantial transverse component of the polarization can also be present.

Figure 1

(Color online) Sketch of ${\mathrm{PbTiO}}_3$-based ferroelectric superlattice in which head-to-head and tail-to-tail 180° domain walls coincide with acceptor (Sc) and donor (Nb) substitutional layers, respectively.

Figure 2

Density of states (DOS) of 40-atom ${\mathrm{PbTiO}}_3$ supercells considered in the text. (a) $P4∕mmm$ supercell of Fig. 1 containing HH and TT domain walls compensated by impurity layers. (b) Same, but with in-plane component of polarization ($Pmm2$ symmetry). (c) Reference structure in which polarization reverses as in Fig. 1, but no compensating impurity layers are present.

Figure 3

(Color online) Local polarization profile of the relaxed $Pmm2$ structure. The [001] component changes sign at the dopant layers, while the [100] component is roughly uniform throughout the supercell, giving rise to an overall polarization in the [100] direction. Dotted lines indicate the “ideal” value $0.5e∕a^2$; dashed lines represent the spontaneous polarization of bulk tetragonal ${\mathrm{PbTiO}}_3$.

Figure 4

DOS projected onto three different Ti atoms in the $Pmm2$ supercell. Ti(Sc) denotes the Ti atom in the ${\mathrm{TiO}}_2$ layer closest to the ${\mathrm{ScO}}_2$ layer; Ti(Nb) denotes the Ti atom in the ${\mathrm{TiO}}_2$ layer closest to the ${\mathrm{NbO}}_2$ layer; and Ti(Mid) denotes a Ti atom in the middle of the supercell, between the two dopant layers.