Ferroelectric dead layer driven by a polar interface

Based on first-principles and model calculations we investigate the effect of polar interfaces on the ferroelectric stability of thin-film ferroelectrics. As a representative model, we consider a ${\text{TiO}}_2$-terminated ${\text{BaTiO}}_3$ film with LaO monolayers at the two interfaces that serve as doping layers. We find that the polar interfaces create an intrinsic electric field that is screened by the electron charge leaking into the ${\text{BaTiO}}_3$ layer. The amount of the leaking charge is controlled by the boundary conditions which are different for three heterostructures considered, namely, vacuum/$\text{LaO}/{\text{BaTiO}}_3/\text{LaO}$, $\text{LaO}/{\text{BaTiO}}_3$, and ${\text{SrRuO}}_3/\text{LaO}/{\text{BaTiO}}_3/\text{LaO}$. The intrinsic electric field forces ionic displacements in ${\text{BaTiO}}_3$ to produce the electric polarization directed into the interior of the ${\text{BaTiO}}_3$ layer. This creates a ferroelectric dead layer near the interfaces that is nonswitchable and thus detrimental to ferroelectricity. Our first-principles and model calculations demonstrate that the effect is stronger for a larger effective ionic charge at the interface and longer screening length due to a stronger intrinsic electric field that penetrates deeper into the ferroelectric. The predicted mechanism for a ferroelectric dead layer at the interface controls the critical thickness for ferroelectricity in systems with polar interfaces.

Figure 1

(Color online) Charge distribution and the intrinsic electric field in a ${\text{BaTiO}}_3$ film terminated with positively charged ${\left(\text{LaO}\right)}^{+}$ monolayers at the left and right interfaces. A gradient shadow region indicates the screening charge penetrating into ${\text{BaTiO}}_3$. Arrows indicate the intrinsic electric field that has a tendency to pin the local polarization along the field direction.

Figure 2

(Color online) DOS projected onto the $3d$ states of Ti atoms located at the left and right interfaces (solid lines) and in the middle of the ${\text{BaTiO}}_3$ layer (shaded area) for (a) vacuum/$\text{LaO}/{\left({\text{BaTiO}}_3\right)}_{8.5}/\text{LaO}$, (b) $\text{LaO}/{\left({\text{BaTiO}}_3\right)}_{8.5}$, and (c) ${\left({\text{SrRuO}}_3\right)}_{5.5}/\text{LaO}/{\left({\text{BaTiO}}_3\right)}_{8.5}/\text{LaO}$ heterostructures. The Fermi level lies at zero energy and denoted by the dashed line. The insets show the VBM with respect to the Fermi energy within the ${\text{BaTiO}}_3$ layer as a function of $z$.

Figure 3

(Color online) [(a)–(c)] Displacements $\left(D\right)$ of cations (Ba and Ti) with respect to oxygen anions and [(d)–(f)] local polarizations $\left(P\right)$ across a ${\text{BaTiO}}_3$ layer in [(a) and (d)] vacuum/$\text{LaO}/{\left({\text{BaTiO}}_3\right)}_8/\text{LaO}$, [(b) and (e)] $\text{LaO}/{\left({\text{BaTiO}}_3\right)}_{8.5}$, and [(c) and (f)] ${\left({\text{SrRuO}}_3\right)}_{5.5}/\text{LaO}/{\left({\text{BaTiO}}_3\right)}_{8.5}/\text{LaO}$ heterostructures. Solid squares and open circles in (a)–(c) denote Ba-O and Ti-O displacements, respectively. In figures (d)–(f) the local polarizations are obtained using the displacements calculated from first-principles in conjunctions with the Born effective charges (squares) and from the phenomenological model (solid lines).

Figure 4

(Color online) [(a)–(c)] Displacements $\left(D\right)$ of cations (Ba and Ti) with respect to oxygen anions and [(d)–(f)] local polarizations $\left(P\right)$ across the ${\text{BaTiO}}_3$ layer in $\text{LaO}/{\left({\text{BaTiO}}_3\right)}_n$ heterostructures containing [(a) and (d)] $n=8.5$, [(b) and (e)] 14.5, or [(c) and (f)] 21.5 unit cells of ${\text{BaTiO}}_3$. Solid squares and open circles in (a)–(c) denote Ba-O and Ti-O displacements, respectively. In figures (d)–(f) the local polarizations are obtained using the displacements calculated from first principles in conjunctions with the Born effective charges (squares) and from the phenomenological model (solid lines).

Figure 5

(Color online) Average polarization $\overline{P}$ of a ${\text{BaTiO}}_3$ film (a) as a function of the decay length $\lambda$ for three film thicknesses $t$ and (b) as a function of the film thickness $t$ for two values of $\lambda$ calculated within the phenomenological model (solid symbols) and using first-principles calculations and the Born charge model (open symbols). The inset in (a) shows $\overline{P}$ for $E_i=0$.

Figure 6

(Color online) Band alignment in $\text{LaO}/{\left({\text{BaTiO}}_3\right)}_{21.5}$ system. (a) Local DOS on ${\text{TiO}}_2$ monolayers $\left(l\right)$ as a function of the energy. The curved line to the left (right) indicates the position of the valence-band maxima (conduction-band minima) and the vertical solid line denotes the Fermi energy $E_F$; (b) planar-averaged electrostatic potential across ${\text{BaTiO}}_3$ (thin line) and the macroscopic electrostatic potential (thick line); (c) position of the corelike $\text{O}2s$ states for different ${\text{TiO}}_2$ layers (squares) and the macroscopic electrostatic potential shifted by $-18.2\text{eV}$ (solid line).