Domain-Enhanced Interlayer Coupling in Ferroelectric/Paraelectric Superlattices

We investigate the ferroelectric phase transition and domain formation in a periodic superlattice consisting of alternate ferroelectric (FE) and paraelectric (PE) layers of nanometric thickness. We find that the polarization domains formed in the different FE layers can interact with each other via the PE layers. By coupling the electrostatic equations with those obtained by minimizing the Ginzburg-Landau functional, we calculate the critical temperature of transition $T_c$ as a function of the FE/PE superlattice wavelength $\Lambda$ and quantitatively explain the recent experimental observation of a thickness dependence of the ferroelectric transition temperature in ${\mathrm{K}\mathrm{T}\mathrm{a}\mathrm{O}}_3/{\mathrm{K}\mathrm{N}\mathrm{b}\mathrm{O}}_3$ strained-layer superlattices.

Figure 1

Domains and depolarization field in weak (a) and strong (b) coupled ferroelectric layers in a FE/PE superlattice close to $T_c$.

Figure 2

Critical temperature $t_c=T_c/T_{c0}-1$ (a) and domain structure wave vector $q=\pi /d$ at $T=0$ and $T=T_c$ (b) as a function of superlattice wavelength $\Lambda =2a_f+2a_p$. Dotted line shows the asymptote (21). Circles show the experimental data for the ${\mathrm{K}\mathrm{T}\mathrm{a}\mathrm{O}}_3/{\mathrm{K}\mathrm{N}\mathrm{b}\mathrm{O}}_3$ superlattice [9]. The best fit parameters ${\epsilon }_{\parallel }=400$, ${\epsilon }_{\perp }=500$, ${\epsilon }_p=800$, $\lambda =0$, and $\lambda =0.01$ have been used. The length is scaled in units of ${\xi }_0\simeq 6\AA$.