Persistence of Ferroelectricity in ${\mathrm{BaTiO}}_3$ through the Insulator-Metal Transition

The ferroelectric ${\mathrm{BaTiO}}_3$ is a band-gap insulator. Itinerant electrons can be introduced in this material by doping, for example, with oxygen vacancies. Above a critical electron concentration of $n_c\approx 1\times {10}^{20}{\mathrm{cm}}^{-3}$, ${\mathrm{BaTiO}}_{3-\delta }$ becomes metallic. This immediately raises a question: Does metallic ${\mathrm{BaTiO}}_{3-\delta }$ still retain ferroelectricity? One may expect itinerant electrons to destroy ferroelectricity as they screen the long-range Coulomb interactions. We followed the phase transitions in ${\mathrm{BaTiO}}_{3-\delta }$ as a function of $n$ far into metallic phase. Although their stability range decreases with $n$, the low-symmetry phases in metallic ${\mathrm{BaTiO}}_{3-\delta }$ are still retained up to an estimated concentration of $n^{*}\approx 1.9\times {10}^{21}{\mathrm{cm}}^{-3}$. Moreover, it appears that the itinerant electrons partially stabilize the ferroelectric phases in metallic ${\mathrm{BaTiO}}_{3-\delta }$ by screening strong crystal field perturbations caused by oxygen vacancies.

Figure 1

(a) Temperature dependence of resistivity of ${\mathrm{BaTiO}}_{3-\delta }$ measured on both cooling and heating to reveal temperature hysteresis of the phase transitions. Electron concentration $n$ was determined from the Hall effect. Samples 1, 2, 3, 4, 5 correspond to $n=1.9\times {10}^{19}$, $3.1\times {10}^{19}$, $6.1\times {10}^{19}$, $1.6\times {10}^{20}$, and $3.5\times {10}^{20}{\mathrm{cm}}^{-3}$. Sample 6 is a ${\mathrm{BaTi}}_{0.875}{\mathrm{Nb}}_{0.125}{\mathrm{O}}_3$ polycrystal with $n\approx 2.0\times {10}^{21}{\mathrm{cm}}^{-3}$. The $\rho (T)$ dependence changes from insulating (curves 1 and 2) to metallic (curves 4 and 5). Structural phase transitions are manifested by pronounced $\rho (T)$ anomalies at corresponding temperatures. The inset shows an enlarged part of resistivity for metallic samples 4 and 5 in the region of the $O\mathrm{\text{−}}T$ and $T\mathrm{\text{−}}C$ phase transitions. The $O\mathrm{\text{−}}T$ and $T\mathrm{\text{−}}C$ phase transitions for sample 5 are indicated by arrows. (b) DSC of selected ${\mathrm{BaTiO}}_{3-\delta }$ samples. The samples’ labels correspond to those of (a). Sample 0 is undoped ${\mathrm{BaTiO}}_3$ with $n\le 1\times {10}^{12}{\mathrm{cm}}^{-3}$.

Figure 2

(a) Selected x-ray diffraction profiles for sample 5 at 100, 150, 200, 300, and 400 K. Lowering of the crystal symmetry can be noticed by visual changes in the profile of the $\{512\}$ reflection at $2\Theta \approx 39.8°$. (b) Temperature evolution of the lattice constants for sample 5 refined with the Rietveld method. For comparison, the data for stoichiometric ${\mathrm{BaTiO}}_3$ from Ref. 17 are shown as gray symbols. The lines are guides for the eye.

Figure 3

Real part of the optical conductivity of ${\mathrm{BaTiO}}_{3-\delta }$ that shows infrared active TO mode near $500{\mathrm{cm}}^{-1}$ for sample with $n=3.9\times {10}^{17}{\mathrm{cm}}^{-3}$ (a) and $n=2.0\times {10}^{20}{\mathrm{cm}}^{-3}$ (b). The insets show the temperature evolution of the mode frequency in $R$, $O$, and $T$ crystal phases. We fit the phonon mode with Lorentzians to obtain peak frequencies at given temperature.

Figure 4

Temperature-electron concentration phase diagram of ${\mathrm{BaTiO}}_{3-\delta }$. The phase transition temperatures for different electron concentrations were compiled from the resistivity and DSC data. Black triangles indicate the $C\mathrm{\text{−}}T$ phase transition temperature adopted from Ref. 13 for polycrystalline ${\mathrm{BaTiO}}_{3-\delta }$.