Asymmetric ferroelectricity by design in atomic-layer superlattices with broken inversion symmetry

In atomic-layer superlattices constructed using three constituent phases, $\mathrm{CaTi}{\mathrm{O}}_3, \mathrm{SrTi}{\mathrm{O}}_3$, and $\mathrm{BaTi}{\mathrm{O}}_3$, the stacking sequence of the atomic layers is found to control the symmetry of the high-temperature dielectric response. In such a superlattice when a nanostructured asymmetric strain is programmed into the lattice via the stacking order, the natural symmetry at high temperatures is removed and a polarized sample is obtained in which the polarization increases as the temperature is lowered. In contrast to a ferroelectric characterized by a bistable ground state with two equal and opposite electronic polarizations, our experiments show evidence of asymmetric ferroelectric correlations that set in when such a sample becomes hysteretic below a temperature $T_x$, with two unequal polarization states. We further show that both the magnitude and direction of this ferroelectric asymmetry can be controlled by the engineered atomic-layer stacking order and periodicity of the superlattice.

Figure 1

Natural ferroelectricity and asymmetric ferroelectricity by design. (a) Centrosymmetric crystal structure of $\mathrm{BaTi}{\mathrm{O}}_3$ above the ferroelectric ordering temperature. (b) The characteristic free energy landscape for the ground state of a ferroelectric. (c) Schematic of an engineered free energy landscape for the ground state of an asymmetric ferroelectric: a noncentrosymmetric crystal that, at low temperatures, develops bistable correlations subject to a built-in asymmetric strain field. $F$($P$) shown here is consistent with a “–” stacking sequence. (d) A noncentrosymmetric crystal by design: bond valence sum calculations of the crystal structure for a 111− superlattice indicating distortions in the Ti-O octahedra along the stacking direction. (e) X-ray diffraction reciprocal space map of a 222+ superlattice around the substrate STO (103) peak indicating that the superlattice is clamped to the in-plane substrate lattice constant. Red dashed lines are a guide to the eye.

Figure 2

Sample architectures and imaging the commensurately strained sequenced superstructure. (a) Overall structure of capacitor devices that include a dielectric superlattice in between two conducting manganite layers. (b) STEM image of a 111− superlattice grown directly on an STO substrate. (c) Some of the supercell architectures we studied. (d) Electron diffraction pattern of a 111− superlattice on a logarithmic intensity scale. Sharp superlattice spots verify sequenced superstructure that is commensurately strained to the substrate: The asymmetric stacking sequence results in an asymmetric strain field along the stacking direction.

Figure 3

Evidence for sharp two-dimensional (2D) interfaces and octahedral distortions due to asymmetric strain. (a) Representative RHEED images at different stages of growth of a 222+ superlattice. (b) Self-organized oscillations of the RHEED specular intensity recorded in situ during deposition of a 222+ supercell. The plateaus in intensity at the end of each molecular layer correspond to a short (∼25 s) anneal. These plateaus suggest the lack of surface kinetics that could cause interface roughening. Inset shows an ex situ AFM image (1 μm square) of the surface of a 222+ superlattice. (c) Bright-field atomic-resolution STEM image of a 222+ superlattice shows the average lattice positions of all the atoms including oxygen. Asymmetric displacements of the oxygen sublattice with respect to the $A$-site sublattice can be observed. (d) Bond valence sum calculated atomic positions for a 222+ superlattice superimposed on the STEM image of (c) indicate qualitative agreement between calculated and observed lattice positions.

Figure 4

Field tuning of the dielectric susceptibility for different superlattices. These measurements were made at 77 Hz. (a) Data from the 222+, 1212, and 222− samples around room temperature showing the effect of structural symmetry on the symmetry of the electronic response. (b) Data from the asymmetric superlattices, 222+, 622+, and 111−, near the temperature which maximizes χ in each case. (c) χ($E$) for the 111− superlattice at different temperatures.

Figure 5

Asymmetric ferroelectric state in the 111− and 222+ samples. $P_0\left(T\right)$ for (a) 111− sample and (b) 222+ sample obtained by pyrocurrent measurements (solid lines). The remanent polarization levels at zero bias are also indicated (connected by dotted lines). $P$($E$) curves at different temperatures for (c) 111− sample and (d) 222+ sample. In both samples the $P$($E$) curves show a constant shift from the origin at all temperatures along the $E$-field axis and a strong temperature-dependent shift below $T_x$ along the polarization axis (indicated by an arrow). The locus of the symmetry point of the $P$($E$) curves for (e) 111− sample and (f) 222+ sample in the polarization-temperature plane showing the growth of $P_{\mathrm{static}}$. The error bars indicate an estimate of the overall uncertainty. The shifts in $P$($E$) and the sign of $P_0\left(T\right)$ and $P_{\mathrm{static}}\left(T\right)$ for the 222+ sample are opposite to that of the 111− sample.