In-Plane and Out-of-Plane Ferroelectric Instabilities in Epitaxial ${\mathrm{SrTiO}}_3$ Films

The in-plane and out-of-plane ferroelectric instabilities in compressed (100)-epitaxial ${\mathrm{SrTiO}}_3$ films were examined by infrared reflection spectroscopy. The strongly stiffened in-plane soft mode frequency softened very slowly on cooling. On the other hand, the silent mode appeared at around 150 K, indicating an out-of-plane ferroelectric transition. This behavior points to a split of in-plane and out-of-plane ferroelectric instability temperatures due to the lowered symmetry of the ${\mathrm{SrTiO}}_3$ lattice caused by mechanical misfit strain. Infrared spectroscopy provides a possibility to detect such an effect in the strained epitaxial ferroelectric films.

Figure 1

XRD pattern and RHEED image (inset) of a 50-nm-thick STO film on a NGO substrate. The incident electron beam axis is parallel to $\mathrm{STO}⟨110⟩$.

Figure 2

(a) IR reflectance of the STO $\mathrm{\text{film}}+\mathrm{NGO}$ substrate system (solid line) and bare substrate (open circle). (b) Ratio of both reflectances. Arrows with numbers indicate the three fitted STO polar phonon frequencies.

Figure 3

${\mathrm{TO}}_1$ frequency of STO film on a NGO (open circles) and bulk STO (open squares) [26].

Figure 4

Temperature dependence of the strength of a stiffened silent $F_{2u}$ mode in a STO film.

Figure 5

Theoretically predicted temperature dependence of reciprocal permittivity of STO film (hatched areas) for each in-plane (${\epsilon }_{\parallel }^{-1}$) and out-of-plane (${\epsilon }_{\perp }^{-1}$) direction, considering the spread in reported coefficients for STO [20]. The reciprocal in-plane permittivity of the film estimated from the ${\mathrm{TO}}_1$ frequency (open circles) and that of a similar film measured by an LCR meter (open squares with error bar) [24] are also shown. The arrow shows the appearance temperature of the silent mode in the film (see Fig. 4).