Electrostriction at the ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ Interface

We present a direct comparison between experimental data and ab initio calculations for the electrostrictive effect in the polar ${\mathrm{LaAlO}}_3$ layer grown on ${\mathrm{SrTiO}}_3$ substrates. From the structural data, a complete screening of the ${\mathrm{LaAlO}}_3$ dipole field is observed for film thicknesses between 6 and 20 uc. For thinner films, an expansion of the $c$ axis of 2% matching the theoretical predictions for an electrostrictive effect is observed experimentally.

Figure 1

(a) $l$ scan along 00 crystal truncation rod of an 8-uc-thick LAO film. (b) Finite size fringes around the $l=1$ reflection and (c) $l=6$ LAO reflection. Reciprocal lattice units (r.l.u.) are defined by the STO reflections.

Figure 2

LAO $a$- and $c$-axis parameters plotted as a function of the film thickness. The solid lines are a guide to the eye. The dashed horizontal line indicates the pseudocubic LAO bulk lattice constant. The inset shows in detail the expansion of the $c$ axis for low LAO thicknesses.

Figure 3

(a–b) Schematic view of the atomic layer sequence in LAO, showing the most relevant electrical quantities in the system: “built-in” polarization $P^0$ (small downward-pointing arrows), electric displacement field $D$ ($D_{\mathrm{LAO}}$ is equal to the interface charge ${\sigma }_S$), and internal electric field in LAO, $E$ (large upward-pointing arrow). The uncompensated (a) and fully compensated (b) limits are shown. (c) Calculated electrostrictive response of LAO bulk as a function of the electric displacement field $D$.

Figure 4

Evolution of (a) the electric field inside the LAO layer, (b) the surface charge at the LAO/STO interface, and (c) the LAO strain with the LAO layer thickness, according to ab initio calculations (red circles) and experiments (black squares). In (a), (b), and (c) the curves joining the points are explained in the text. Two $x$ scales are reported (top red for theory and bottom black for the experiment) to normalize at the same critical thickness (4 uc and 5 uc for experiment and theory, respectively). The green points (circled dots) show the calculated intermixed case.