Coexistence of antiferrodistortive and polar order in a superconducting $\mathrm{SrTi}{\mathrm{O}}_3$ film

Strontium titanate ($\mathrm{SrTi}{\mathrm{O}}_3$) can exhibit multiple orders, including superconductivity, an antiferrodistortive instability, and ferroelectricity. The cooperation or competition between these orders in samples that undergo all three transitions is of great fundamental interest. Here, we report scanning transmission electron microscopy imaging of the antiferrodistortive and ferroelectric structural distortions in a compressively strained $\mathrm{SrTi}{\mathrm{O}}_3$ film that was previously shown to become superconducting at ∼410 mK. The experiments are complemented by first-principles simulations. Unlike the polar ferroelectric phase, which is suppressed by dopants, the antiferrodistortive order is insensitive to the presence of the free carriers. The single-domain nature of the antiferrodistortive phase excludes any role of antiferrodistortive domain walls in the superconductivity. A previously reported low-temperature resistance anomaly is associated with the ferroelectric transition, not the antiferrodistortive transition.

Figure 1

Schematic showing the AFD structure (top left) and the planes parallel to which the TEM cross sections were prepared. The two planes, $\left(01\overline{1}\right)$ and $\left(\overline{1}10\right)$, respectively, are shaded in blue and red, respectively; while the $\left(\overline{1}10\right)$ is parallel to $\left[001\right]$, the $\left[01\overline{1}\right]$ is inclined by 45° against $\left[001\right].$

Figure 2

ABF imaging of the AFD domain structure using two cross sections along $\left[\overline{1}10\right]$ (a)–(d) and $\left[01\overline{1}\right]$ (e)–(h), respectively. (a) ABF-STEM image along $\left[\overline{1}10\right]$ and FFT (inset). (b) Magnified section of (a) with oxygen columns marked by red dots. (c) Schematic of the AFD structure along $\left[\overline{1}10\right]$. (d) Histogram of oxygen-oxygen distances. (e) ABF-STEM image along $\left[01\overline{1}\right]$. The FFT (inset) shows additional intensities indicated by the red arrows. Note the zigzag pattern of oxygen columns in this projection. (f) Magnified section of (a) with oxygen columns marked by red dots. (g) Schematic of the AFD structure along $\left[01\overline{1}\right]$, showing the zigzag pattern of oxygen columns and the resulting two distinct oxygen-oxygen distances, d1 and d2. (h) Histogram of the oxygen-oxygen distances, which has two peaks corresponding to d1 and d2.

Figure 3

Polar order quantified via the off-centering of Ti-O columns in HAADF-STEM images along $\left[100\right]$. (a) Polarization orientation maps. The color scale corresponds to 30° intervals of polarization directions. (b) Displacement vectors of the Ti-O column off-centering from the area outlined by the box in (a). The displacement vectors are depicted 12 times of their actual values. (c) Color contour map of Ti-O column off-centering for (a). (d) Histogram of the displacement vectors.

Figure 4

First-principles simulations of AFD and polar order. (a) Magnitude of ground-state Ti displacements (orange) and AFD rotation angles (blue) as a function of carrier concentration. (b) Imaginary phonon frequencies associated with the polar (orange) and AFD (blue) instabilities as a function of carrier concentration. (c)–(f) Representative snapshots calculated from Monte Carlo simulations at 300 K of the polarization (c), (d) and rotation (e), (f) order parameters for a 32 × 32 × 32 supercell with carrier density $1.4\times {10}^{20}\mathrm{c}{\mathrm{m}}^{-3}$. The polarization snapshots show small domains with opposite polarization (orange and purple patches), while the rotation snapshots show a large single domain.