Dielectric Anomalies in Ferroelectric Nanostructures

First-principles-based methods are used to determine the external dielectric susceptibility (i.e., the polarization response to the external electric field) and the internal susceptibility (i.e., the polarization response to the average internal field) in ferroelectric dots, wires, and films, as a function of the electrical boundary conditions. While the external susceptibility is obviously positive, we find that the internal one is negative over a wide range of boundary conditions for all kinds of nanostructures. A Landau-type phenomenological model provides a rationale for all of our findings.

Figure 1

External dielectric susceptibility ${\chi }_{\gamma \gamma }^{(\mathrm{ext})}$ of a PZT60 film [part (a)], wire [part (b)], and dot [part (c)] vs the screening parameter $\beta$. Left and right insets show the projections of the dipole patterns in the structures under OC-like and SC-like boundary conditions, respectively. The vertical lines characterize the transition from SC-like conditions to OC-like conditions.

Figure 2

Internal dielectric susceptibility ${\chi }_{\gamma \gamma }^{(\mathrm{int})}$ of a PZT60 film [part (a)], wire [part (b)], and dot [part (c)] vs the screening parameter $\beta$. The vertical lines characterize the transition from SC-like conditions to OC-like conditions. The insets emphasize that the ${\chi }_{\gamma \gamma }^{(\mathrm{int})}$ coefficients are slightly negative for $\beta =0$, and become more negative as $\beta$ increases. Note that ${\chi }_{xx}^{(\mathrm{int})}={\chi }_{xx}^{(\mathrm{ext})}$ and ${\chi }_{yy}^{(\mathrm{int})}={\chi }_{yy}^{(\mathrm{ext})}$ in the film, while ${\chi }_{zz}^{(\mathrm{int})}={\chi }_{zz}^{(\mathrm{ext})}$ in the wire—since no depolarizing field exists along these directions. These latter coefficients are already shown in Fig. 1.