Direct evidence for ferroelectric polar distortion in ultrathin lead titanate perovskite films

X-ray photoelectron diffraction is used to directly probe the intracell polar atomic distortion and tetragonality associated with ferroelectricity in ultrathin epitaxial $\mathrm{Pb}\mathrm{Ti}{\mathrm{O}}_3$ films. Our measurements, combined with ab initio calculations, unambiguously demonstrate noncentrosymmetry in films a few unit cells thick, imply that films as thin as three unit cells still preserve a ferroelectric polar distortion, and also show that there is no thick paraelectric dead layer at the surface.

Figure 1

(Color online) (a) Schematic of the measurement setup. Core electrons have well-defined binding energies, and their photoemission spectra exhibit characteristic emission lines. By selecting a particular emission line, photoelectrons from a given emitter can be chosen, thus probing the local real-space environment of the emitter. The interpretation is facilitated by forward focusing of electron flux along the emitter-scatterer direction. The difference between two “forward-focusing” peak positions is directly related to a modified emitter-scatterer direction, illustrated here by the para-toward $\mathrm{up}-\mathrm{state}$-O shift. Above $490°\mathrm{C}$, bulk $\mathrm{Pb}\mathrm{Ti}{\mathrm{O}}_3$ has a cubic unit cell, with the O and Ti atoms centered in the Pb cage ($\mathrm{para}-\mathrm{state}$). (b) Below $490°\mathrm{C}$, bulk $\mathrm{Pb}\mathrm{Ti}{\mathrm{O}}_3$ has a tetragonal unit cell: two equivalent ferroelectric configurations corresponding to two opposite polarizations, $\mathrm{up}-\mathrm{state}$ and $\mathrm{down}-\mathrm{state}$. The displacements (in fractional units) from cubic phase sites are 0.111 and 0.037 for O and Ti, respectively (Ref. 16).

Figure 2

(Color online) Schematic view of the atomic displacements resulting from ferroelectric distortion and from surface and interface relaxation in the uppermost layers of a $\mathrm{Pb}\mathrm{Ti}{\mathrm{O}}_3$ film epitaxially grown on $\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_3$. In bulk $\mathrm{Pb}\mathrm{Ti}{\mathrm{O}}_3$, epitaxial strain produces a tetragonality at zero polarization that can be estimated from the macroscopic elasticity theory as $c_0∕a_{\mathrm{STO}}=1.03$. The ionic configuration resulting from the truncation of such a strained bulk paraelectric state (a) is considered as the reference structure. Freezing the bulk ferroelectric distortion (as reported in Ref. 16) into this reference structure results in the $\mathrm{up}-\mathrm{state}$ shown in (b). Additionally, the natural ionic relaxation at the surface in the paraelectric state has been computed from first-principles (see text) both for a thick $\mathrm{Pb}\mathrm{Ti}{\mathrm{O}}_3$ slab in vacuum (c) and a $\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_3$–(one unit cell) $\mathrm{Pb}\mathrm{Ti}{\mathrm{O}}_3$–vacuum stack (d). Numbers in black correspond to the change of interlayer distances. Numbers in gray (blue) corresponds to the atomic rumpling in each layer (cation-oxygen distance). All the values are in percent of $c_0$, except those in italic that concern $\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_3$ and are in percent of $a_{\mathrm{STO}}$.

Figure 3

(Color online) (a) Stereographic projection of experimental and theoretical O $1s$ emission line intensities on quarter hemispheres for four different cases: experimental data for a $20\mathrm{\AA }$ thin film and theoretical simulations taking into account up-, para-, and $\mathrm{down}-\mathrm{state}$ structures. Normal emission corresponds to the center of the plot and grazing emission $(\theta =70°)$ to the outer border. (b) $R-$factor calculation to quantify the agreement between experiment and simulations for different structures, where a low $R-$factor corresponds to good agreement. A cut in the (100)-plane containing Pb and O atoms is shown to facilitate the discussion. A downward shift of Pb and O atoms optimizes the fit.

Figure 4

(Color online) Tetragonality ($c∕a$ ratio) as a function of film thickness for $\mathrm{Pb}\mathrm{Ti}{\mathrm{O}}_3$ films (blue circles), for the $\mathrm{Nb}\text{−}\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_3$ substrate through $\mathrm{Pb}\mathrm{Ti}{\mathrm{O}}_3$ films of one and two unit cells (green squares) and the $\mathrm{Nb}\text{−}\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_3$ substrate surface (red triangle). Black open circles are x-ray-diffraction data and the black dotted curve is the result from model Hamiltonian calculations from Ref. 9. Ribbons, labeled 1 and 2, indicate regions as discussed in the text. The left scale indicates the $c∕a$ values extracted from the XPD experiment forward-focusing directions using $\theta$. The inset shows the crystallographic plane used to extract the $c∕a$ ratio. Pb-Pb scattering dominates compared to Pb-O scattering allowing $\theta$ to be determined via Pb-Pb forward focusing.