Electronic characterization of polar nanoregions in relaxor-type ferroelectricNaNbO3films

Strained ${\mathrm{NaNbO}}₃$ films of different thicknesses are epitaxially grown on (110) ${\mathrm{NdGaO}}₃$ substrates. A detailed analysis of the permittivity of these films demonstrates that strain not only leads to a modification of the permittivity and the ferroelectric transition temperature, it also results in a pronounced relaxor-type behavior and allows a direct estimation of the size and mobility of the polar nanoregions (PNRs). The compressive strain reduces the transition temperature to 125 K and enhances the corresponding permittivity up to ${\ensuremath{\varepsilon}}^{\ensuremath{'}}\ensuremath{\approx}1500$ for the thinnest film. Since the strain relaxes with increasing film thickness, both effects, reduction of phase transition temperature and enhancement of ${\ensuremath{\varepsilon}}^{\ensuremath{'}}$, depend on the thickness of the film. The films show a characteristic frequency and electric field dependence of ${\ensuremath{\varepsilon}}^{\ensuremath{'}}$, which is discussed in terms of the Vogel-Fulcher equation and Rayleigh law, respectively. Using the electric field dependence of the resulting freezing temperature ${T}_{\mathrm{VF}}$, allows a direct estimation of the volume of the PNRs at the freezing temperature, i.e. from 70 to $270\phantom{\rule{0.16em}{0ex}}\mathrm{n}{\mathrm{m}}³$. Assuming an idealized spherical shape of the PNRs, diameters of a few nanometers (5.2--8 nm) are determined that depend on the applied ac electric field. The irreversible part of the polarization seems to be dominated by the presence and mobility of the PNRs. It shows a characteristic peak at low temperature around ${T}_{\mathrm{VF}}$, vanishes at a temperature where the activation energy of the PRNs extrapolates to zero, and shows a frequency dispersion that is characteristic for relaxor-type behavior.