Order-Disorder Ferroelectric Transition of Strained ${\mathrm{SrTiO}}_3$

${\mathrm{SrTiO}}_3$ is an incipient ferroelectric that is believed to exhibit a prototype displacive, soft mode ferroelectric transition when subjected to mechanical stress or alloying. We use high-angle annular dark-field imaging in scanning transmission electron microscopy to reveal local polar regions in the room-temperature, paraelectric phase of strained ${\mathrm{SrTiO}}_3$ films, which undergo a ferroelectric transition at low temperatures. These films contain nanometer-sized domains in which the Ti columns are displaced. In contrast, these nanodomains are absent in unstrained films, which do not become ferroelectric. The results show that the ferroelectric transition of strained ${\mathrm{SrTiO}}_3$ is an order-disorder transition. We discuss the impact of the results on the nature of the ferroelectric transition of ${\mathrm{SrTiO}}_3$.

Figure 1

Cross-section HAADF-STEM images of ${\mathrm{SrTiO}}_3$ films grown on (a),(c) LSAT and (b) ${\mathrm{SrTiO}}_3$. (d) A schematic illustrating the polarization vector and its components.

Figure 2

Polarization vectors for ${\mathrm{SrTiO}}_3$ films grown on (a),(c) ${\mathrm{SrTiO}}_3$ and (b),(d) LSAT. The arrows in the figures in the top row indicate the magnitude (also indicated by the color scale) and orientation of the polarization vectors. The images in the bottom row display the direction of the polarization vectors overlaid on the HAADF image, with each color corresponding to a 30° interval of the polarization directions.

Figure 3

Additional regions of the film on LSAT showing nanodomains of different polarization orientations. The colors indicate the direction of the polarization vectors, with each color corresponding to a 30° interval of the polarization directions. The colored dots are overlaid on the actual HAADF-STEM images. The corresponding polarization vectors are shown in the Supplemental Material [47].

Figure 4

Magnitude of displacement vector components [defined in Fig. 1] acquired from multiple regions of films on (a) ${\mathrm{SrTiO}}_3$, (b) LSAT, and (c) on LSAT after oxygen annealing.