Polar correlations and defect-induced ferroelectricity in cryogenic ${\mathrm{KTaO}}_3$

${\mathrm{KTaO}}_3$ is an incipient ferroelectric material with an extrapolated transition temperature below 0 K. It contains a small number of “unavoidable defects” which are randomly distributed. Some of these defects are polar and their interaction leads to macroscopic coherent polar structures at low temperatures. In this article it is shown that freezing of local defect dipoles coincides with elastic stiffening and damping of ultrasonic waves in ${\mathrm{KTaO}}_3$. The elastic freezing anomalies are accompanied by stepwise increases of piezoelectricity, forming a thermal polar staircase below ca. 120 K and a gigantic enhancement below 50 K. A small spontaneous polarization also emerges below this temperature, gradually increasing to a value of $0.045 \mu \mathrm{C} \mathrm{cm}{}^{-2}$ at 5 K with increasing coherency of defect dipoles. The orientation of this spontaneous polarization depends on a weak strain-induced anisotropy of the macroscopic sample. Defect-induced ferroelectricity, as demonstrated for ${\mathrm{KTaO}}_3$, may be a possible way forward to develop functional device materials based on the switching of coherently interacting defects.

Figure 1

Dielectric constant of single crystal ${\mathrm{KTaO}}_3$ as a function of temperature. (a) The inverse dielectric constant measured at 1.3 kHz extrapolates to a temperature below 0 K, indicating the incipient ferroelectric nature of ${\mathrm{KTaO}}_3$. (b) Dielectric constant measured at 1.3 kHz (continuous line) and $tan\delta$ measured at 1.3 kHz, 100 kHz, and 820 kHz (represented by red, blue, and black dashed lines, respectively), between 5 K and 300 K. The inset is an Arrhenius plot where $f$ is the measuring frequency and $T$ the temperature at which $tan\delta$ shows a maximum. This shows a good fit to $\tau ={\tau }_{0}exp(E_a/k_{\mathrm{B}}T)$, where $\tau$ is the relaxation time, $k_{\mathrm{B}}$ is the Boltzmann constant, the activation energy, $E_a$, is 81 meV, and $1/{\tau }_0=2.2\times {10}^{12} \mathrm{s}{}^{-1}$.

Figure 2

Image of the ${\mathrm{KTaO}}_3$ single crystal sample taken with a polarizing microscope, indicating the existence of weak birefringence due to defects. The white region is one of the edges of the sample. The scale bar is shown on the top right corner of the figure.

Figure 3

Segments of (a) RPS and (b) RUS spectra collected between 7 K and 160 K in a heating sequence. For these measurements 25 V was applied across the sample or the emitter transducer, for RPS and RUS, respectively. In both panels, the left vertical axis corresponds to amplitude and the right vertical axis is temperature. The spectra have been translated up the $y$ axis in proportion to the temperature at which they were collected and the right vertical axis has been labeled accordingly.

Figure 4

(a) Peak area of the resonance mode at $f\sim 820$ kHz as a function of temperature obtained from RPS (red plus signs) and RUS (blue circles) spectra displayed in Fig. 3. Numbers with black arrows show where the peak area displays stepwise changes at certain temperatures, indicating an enhanced piezoelectric coupling with falling temperature. Panel (b) shows a plot of peak area/dielectric constant against temperature, which represents the qualitative temperature evolution of the piezoelectric charge coefficient $g=d/\epsilon$.

Figure 5

Polarization-electric field loops of single crystal ${\mathrm{KTaO}}_3$ obtained at 1 Hz using a $540 \mu \mathrm{m}$ thick sample: (a) 5 K; (b) 15 K; (c) 20 K; (d) 50 K.

Figure 6

Polarization and pyroelectric coefficient $\left(dP/dT\right)$ of ${\mathrm{KTaO}}_3$ obtained by the application of 440 V across a $540 \mu \mathrm{m}$ thick sample in a heating sequence.

Figure 7

(a) Nominal spontaneous polarization evaluated using “PUND” $P\left(E\right)$ loops. (b)–(e) Specimen PUND loops from the data set used to compile (a).

Figure 8

Mechanical damping, expressed in terms of $Q^{-1}$, associated with individual peaks from the RUS spectra of ${\mathrm{KTaO}}_3$. (a) Temperature evolution of $Q^{-1}$ between 8 K and 300 K obtained using the RUS spectra presented in Fig. 11 (see Appendix). From the upper curve to the lowest, mode frequencies at 10 K are approximately 84 kHz, 150 kHz, 370 kHz, 425 kHz, 500 kHz, 592 kHz, 740 kHz, 880 kHz, 1140 kHz, and 1180 kHz. See caption of Fig. 4 and text for the description of numbers I, II, III, IV, V, and VI. (b) A peak in $Q^{-1}$ located at $\sim 60$ K (II) for the mode at 740 kHz and the fit using Eq. (1) (red line), for which the baseline (blue line) was also taken into account gives $E_a=86$ meV. (c) A peak at 320 K (VI) in $Q^{-1}$ for the mode located at 500 kHz obtained using the spectra presented in Figs. 11 and 12. The fit using Eq. (1), the red line, yields $E_a=0.51$ eV.

Figure 9

Temperature evolution of the squared frequency of a resonance mode ($f\sim 150$ kHz) between 10 K and 300 K. Plus signs correspond to the data, which deviate from the linear regime near 170 K, as indicated by the red line. The lower inset shows that a deviation from the linear temperature dependence, indicated by dotted black lines, has also been observed in the dielectric constant in the same temperature range. The blue line is the baseline $f^2=m+n{\theta }_{s}coth{\theta }_s/T$, where $m$ and $n$ are constants and ${\theta }_s=40$ K is the quantum saturation temperature. Upper inset in panel (a) shows the temperature evolution of the lattice constant extracted from Abe et al. [54] and a fit using $a=m+n{\theta }_{s}coth{\theta }_s/T$ with ${\theta }_s=196$ K. For the baseline ${\theta }_s=40$ K was determined using the resonance mode at 500 K shown in (b). (c) A plot of $\Delta f^2=f^2-f_{\mathrm{baseline}}^2$ for the mode presented in panel (a). Numbers II, III, IV, and V correspond to those presented in Fig. 4 and are used to indicate anomalies in the frequency.

Figure 10

Temperature evolution of the squared frequency of an elastic resonance mode ($f\sim 740$ kHz) of single crystal ${\mathrm{KTaO}}_3$ obtained using RPS (red plus signs) and RUS measurements, where the latter were performed both with (blue circles) and without (black triangles) [see Fig. 1 and Fig. 4]. The inset shows the temperature dependence of another resonance mode located around 820 kHz.

Figure 11

Stack of RUS spectra collected between 305 K and 8 K on a ${\mathrm{KTaO}}_3$ single crystal. These measurements were performed after the removal of silver electrodes from the sample. The left vertical axis is amplitude and right vertical axis represents temperature. The spectra have been translated up the $y$ axis in proportion to the temperature at which they were collected and the right axis has been labeled accordingly.

Figure 12

Segments of RUS spectra of ${\mathrm{KTaO}}_3$ collected between 300 K and 650 K, showing the temperature evolution of a resonance mode from the sample at $\sim 500$ kHz. Spectra shown in red correspond to heating data, whereas those in blue were collected in a cooling sequence.