Atomistic simulations of the incipient ferroelectric $\mathrm{K}\mathrm{Ta}{\mathrm{O}}_3$

A parameterized effective Hamiltonian approach is used to investigate $\mathrm{K}\mathrm{Ta}{\mathrm{O}}_3$. We find that the experimentally observed anomalous dielectric response of this incipient ferroelectric is well reproduced by this approach, once quantum effects are accounted for. Quantum fluctuations suppress the paraelectric-to-ferroelectric phase transition; it is unnecessary to introduce defects to explain the dielectric behavior. The resulting quantum-induced local structure exhibits off-center atomic displacements that display longitudinal, needle-like correlations extending a few lattice constants.

Figure 1

(Color online) ${\chi }_{33}$ dielectric susceptibility of $\mathrm{K}\mathrm{Ta}{\mathrm{O}}_3$ as a function of temperature $T$. (a) Results for the LDA-fitted $H_{\mathrm{eff}}$ parameters. (b) Results for the modified set of parameters. Solid circles and stars correspond to PI-QMC and CMC results, respectively. Dashed and dotted lines represent experimental data from Refs. 2, 3, respectively. Solid line shows the fit of the PI-QMC results by a Barrett relation, $A∕[(T_1∕2)\text{coth}(T_1∕2T)-T_0]$ (in Ref. 26), with $A=\mathrm{27\hspace{0.17em}000}$, $T_1=72\mathrm{K}$ and $T_0=29\mathrm{K}$. Note that our CMC simulations yield a paraelectric-to-ferroelectric transition around $30\mathrm{K}$, which provides a numerical proof for the concept of classical Curie temperature given to $T_0$ in the Barrett relation.

Figure 2

Magnitude of local modes of $\mathrm{K}\mathrm{Ta}{\mathrm{O}}_3$ at $\mathrm{T}=3\mathrm{K}$ vs the angle that these modes make with respect to the [100] pseudocubic direction. The modified set of $H_{\mathrm{eff}}$ parameters is used.

Figure 3

(Color) Correlation function ${\theta }_x\left(\mathbf{r}\right)$ of Eq. (1) for $\mathrm{K}\mathrm{Ta}{\mathrm{O}}_3$ plotted in the $x\text{‐}y$ plane for a $12\times 12\times 12$ simulation at $T=3\mathrm{K}$. (a) CMC results; (b) PI-QMC results. Each small square represents one lattice B site; the origin lies at the center. The modified set of $H_{\mathrm{eff}}$ parameters is used. Note that the color scales are different in the two panels.