Piezoelectricity in the Dielectric Component of Nanoscale Dielectric-Ferroelectric Superlattices

The origin of the functional properties of complex oxide superlattices can be resolved using time-resolved synchrotron x-ray diffraction into contributions from the component layers making up the repeating unit. The ${\mathrm{CaTiO}}_3$ layers of a ${\mathrm{CaTiO}}_3/{\mathrm{BaTiO}}_3$ superlattice have a piezoelectric response to an applied electric field, consistent with a large continuous polarization throughout the superlattice. The overall piezoelectric coefficient at large strains, $54\mathrm{pm}/\mathrm{V}$, agrees with first-principles predictions in which a tetragonal symmetry is imposed on the superlattice by the ${\mathrm{SrTiO}}_3$ substrate.

Figure 1

(a) One repeating unit of a superlattice consisting of 2 unit cells of ${\mathrm{BaTiO}}_3$ and 4 unit cells of ${\mathrm{CaTiO}}_3$. (b) Schematic x-ray diffraction pattern with superlattice reflections along the $q_z$ axis of reciprocal space for the steady state structure at $E=0$ and for the piezoelectrically distorted superlattice at nonzero $E$. (c) Time-dependent x-ray diffraction patterns for the $l=-3$, $-2$, $-1$, 0, and 1 reflections of the superlattice with $m=2$, and the (002) reflection of the ${\mathrm{SrTiO}}_3$ substrate. The time dependence of the applied electric field $E$ appears in the leftmost panel. The (002) reflection of the ${\mathrm{SrTiO}}_3$ substrate is unchanged by the applied electric field.

Figure 2

(a) Average piezoelectric strain $\epsilon$ as a function of applied electric field $E$, observed using the shift in $q_z$ of the superlattice reflection at $l=0$ $m=2$. (b) First-principles calculation of the layer-by-layer polarization $P$ in the ${\mathrm{TiO}}_2$ slabs within a single repeating unit of the superlattice. The polarization calculated for a strained ${\mathrm{BaTiO}}_3$ with an in-plane lattice parameter matching a ${\mathrm{SrTiO}}_3$ substrate (thin blue line) is only slightly larger than that of the ${\mathrm{BaTiO}}_3/{\mathrm{CaTiO}}_3$ superlattice [13].

Figure 3

(a) The intensity of superlattice reflections (red solid line) is determined by sampling the structure function of the repeating unit (black dashed line) at integer values of $l$. Electric-field dependence of the (b) $l=-1$ $m=2$ and (c) $l=+1$ $m=2$ reflections. The shaded regions represent the area integrated to obtain the integrated intensity.

Figure 4

Kinematic simulation of the change in the intensities of the (a) $l=-1$ $m=2$ and (b) $l=+1$ $m=2$ reflections, as a function of the average strain $\epsilon$ and the fraction $r$ of the strain occurring in ${\mathrm{BaTiO}}_3$. Symbols represent the intersection of the experimental strain and integrated intensity with the simulated intensity. The solid lines indicate the limits set by the statistical uncertainty in the integrated intensity. The experimental results are consistent with $r=1/3$, corresponding to equal strains in the ${\mathrm{BaTiO}}_3$ and ${\mathrm{CaTiO}}_3$ components. (c) DFT predictions of the fractional change in the Ca-Ca and Ba-Ba distances (symbols) are consistent with the sharing of strain according to $r=1/3$.