Onset of Ferrielectricity and the Hidden Nature of Nanoscale Polarization in Ferroelectric Thin Films

Using calculations from first principles and the concept of layer polarization, we have elucidated the nanoscale organization and local polarization in ferroelectric thin films between metallic contacts. The profile of the local polarization for different film thicknesses unveils a peculiar spatial pattern of atomic layers with uncompensated dipoles in what was originally thought to be a ferroelectric domain. This effectively ferrielectric behavior is induced by the dominant roles of the interfaces at such reduced dimensionality and can be interpreted using a simple classical model where the latter are explicitly taken into account.

Figure 1

(a) Rumpling [cation-oxygen perpendicular distance (in Å) within each atomic layer] profile for six unit cells ($m6$) of ${\mathrm{BaTiO}}_3$ sandwiched between Pt contacts. (On the horizontal axis Ti and Ba indicate the position of the individual ${\mathrm{TiO}}_2$ and BaO planes, and the orientation of the individual layer dipoles is displayed by arrows in the bottom of the panel.] (b) Solid (blue) circles: layer polarization (LP) profile for the same system $m6$ in units of ${10}^{-10}\mathrm{C}/\mathrm{m}$. The values for bulk ${\mathrm{BaTiO}}_3$ are shown with black triangles. (c)–(e) LP profiles for $m4$, $m2$, and $m1$, respectively.

Figure 2

Energy landscape $E^{\prime }(p_{{\mathrm{TiO}}_2},p_{\mathrm{BaO}})$ for different values of $\theta /M$ (film thickness). The interaction parameters for both interfaces were considered equal, ${\theta }_R={\theta }_L=\theta$, and were kept fixed as the film size $M$ is varied. The remaining parameters of the model have been derived from our ab initio calculations. (a) $\theta /M=0$, (b) $\theta /M=3$, (c) $\theta /M=5$. For (d) $\theta /M=10$ the system displays a ferrielectric dipole pattern.