Terahertz dielectric response of cubic $\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3$

A first-principles-based approach is developed to study the dielectric response of paraelectric $\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3$, as a function of frequency and temperature. Two different overdamped modes of comparable strengths are found to contribute to such response, in the $\simeq 1–150{\mathrm{cm}}^{-1}$ frequency range for temperatures up to $\simeq 750\mathrm{K}$. The lower frequency mode softens toward the Curie point, while the higher-frequency mode stays in the $60–100{\mathrm{cm}}^{-1}$ range and is associated with temperature-independent short-range correlations. Our far-infrared reflectivity measurements confirm the existence of these two modes, and yield a very good agreement with calculations.

Figure 1

Complex dielectric response of cubic $\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3$ versus frequency at $T=440$ (bold lines) and $470\mathrm{K}$ (thin lines). Panels (a) and (b) display the ${\epsilon }^{\prime }$ real and ${\epsilon }^{″}$ imaginary parts, respectively. The solid lines show our predictions, while the dashed lines report our measurements. The arrows emphasize the frequencies of the two peaks of ${\epsilon }^{″}$ associated with Eq. (2).

Figure 2

(Color online) Temperature evolution of the ${\nu }_1^{\prime }$ and ${\nu }_2^{\prime }$ frequencies [panel (a)], and of the ${\nu }_1$ and ${\nu }_2$ frequencies [panel (b)]. Our first-principles-based data are shown in open symbols, while the solid symbols display experimental results. The solid circles and squares report our own measurements, while the solid diamonds and triangles indicate the observations of Refs. 4, 7, respectively.

Figure 3

(Color online) Real-space decomposition, ${\chi }^{″}(\nu ={\nu }_i^{\prime },x,y,z=0)∕({\epsilon }^{″}(\nu ={\nu }_i^{\prime })-1)$ (for $i=1$ and 2, expressed in percent and for three different temperatures), of the two peaks of the imaginary part of the dielectric constant. The $x$, $y$, and $z$ axes are chosen along the [100], [010], and [001] directions, respectively, and their coordinates are expressed in terms of the five-atom unit cell lattice’s constant (that is, $a=3.9\mathrm{\AA })$.