Emergence of a fluctuating state in the stuffed tridymite-type oxides Ba1−xSrxAl2O4

Abstract

We investigated the crystal structures and dielectric properties of an improper ferroelectric ${\mathrm{Ba}}_{1\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{Al}}_{2}{\mathrm{O}}_{4} (x\ensuremath{\le}0.1)$ and revealed that suppressing the condensation of the $M$-point soft mode involves the emergence of a ``fluctuating'' state. In the low-Sr-concentration region of $x\ensuremath{\le}0.06$, crystals exhibit a ferroelectric phase transition at ${T}_{\mathrm{C}}$ from a paraelectric phase with a space group $P{6}_{3}22$ (PE phase) to a low-temperature ferroelectric phase with a $P{6}_{3}$ structure with doubled $a$ and $b$ axes (FE phase). Additionally, the temperature dependence of the dielectric constant ${\ensuremath{\varepsilon}}^{\ensuremath{'}}$ exhibits a peak at ${T}_{\mathrm{C}}$. As $x$ increases, ${T}_{\mathrm{C}}$ decreases substantially, and the peak at ${T}_{\mathrm{C}}$ becomes small. For $x\ensuremath{\ge}0.07$, the peak is barely noticeable and becomes an anomaly at ${T}^{*}\ensuremath{\approx}200$ K, indicating that the system possesses another state (FL state) below the ${T}^{*}$. The PE phase has been reported to possess two energetically competing soft modes at the $M$ and $K$ points. Electron diffraction (ED) experiments revealed that the superlattice reflections of the FE phase become diffuse scatterings originating from the $M$-point soft mode as the FE-FL boundary is approached. The $K$-point soft mode disappears in the FL state, whereas the $M$-point soft mode survives and fluctuates without condensation. Dark-field (DF) images revealed that the $M$-point soft mode exhibits coherent motion in nanodomains with sizes of approximately 10 nm in the FL state. The emergence of the FL state is ascribed to enhanced vibration of the ${\mathrm{AlO}}_{4}$ tetrahedra resulting from the substitution of Sr, which has a smaller ionic radius than Ba.