Relaxor ferroeletric behavior inSr1−xPrxTiO3: Cooperation between polar and antiferrodistortive instabilities

Abstract

Chemical doping at the Sr and Ti sites is a feasible way to alter the quantum paraelectric state of $\mathrm{SrTi}{\mathrm{O}}_{3}$ perovskite. Doping with Pr is known to induce relaxor ferroelectricity at room temperature in the $\mathrm{S}{\mathrm{r}}_{1\ensuremath{-}x}\mathrm{P}{\mathrm{r}}_{x}\mathrm{Ti}{\mathrm{O}}_{3}$ solid solution. The relationship between its dielectric properties and structural phase transition has been debated, but no definitive structural argument has been proposed. Here we present a systematic structural study of $\mathrm{S}{\mathrm{r}}_{1\ensuremath{-}x}\mathrm{P}{\mathrm{r}}_{x}\mathrm{Ti}{\mathrm{O}}_{3}$ $(0.020\ensuremath{\le}x\ensuremath{\le}0.150)$. We establish the structural phase diagram using high-resolution x-ray powder diffraction by finding the antiferrodistortive structural phase transitions for all the compositions studied. By using pair distribution function analysis, we show the mismatch between local and long-range structures in terms of increased local order parameters. Finally, we propose a correlation between the local structural order parameters and the emergence of hard polar modes as found by Raman spectroscopy. Our results are quantitatively consistent with recent theoretical calculations showing that the increase of local tetragonality and local octahedral tilting above a critical value in fact underlie the polar instability. This confirms that structural orders involving both polar and antiferrodistortive characters compete and cooperate at different levels, promoting ferroelectricity in $\mathrm{S}{\mathrm{r}}_{1\ensuremath{-}x}\mathrm{P}{\mathrm{r}}_{x}\mathrm{Ti}{\mathrm{O}}_{3}$.