Glassy anomalies in the lattice heat capacity of a crystalline solid caused by ferroelectric fluctuation

Amorphous solids are known to exhibit excess heat capacity that shows a hump near 10 K and diverges from the Debye $T^3$ law at low temperature below 1 K. Here we report that these glassy features are also observed in an insulating crystalline solid. Substitutional chemical suppression of the structural phase transition temperature ($T_{\mathrm{C}}$) of the ferroelectric oxide ${\mathrm{Ba}}_{1-x}{\mathrm{Sr}}_x{\mathrm{Al}}_2{\mathrm{O}}_4$ results in the disappearance of the $T_{\mathrm{C}}$ at $x=0.07$. For the compositional window of $x=0.2$–0.5, the lattice heat capacity shows a large hump below 10 K and diverges from the $T^3$ law below approximately 2.5 K. Synchrotron x-ray diffraction experiments on single crystals reveal the short-range correlation in the crystal structure that survives down to low temperature; this short-range correlation is responsible for the observed glasslike features in its lattice heat capacity.

Figure 1

(a) Crystal structure of ${\mathrm{BaAl}}_2{\mathrm{O}}_4$ of the $P{6}_{3}22$ phase. (b) Phase diagram of ${\mathrm{Ba}}_{1-x}{\mathrm{Sr}}_x{\mathrm{Al}}_2{\mathrm{O}}_4$. The $T_{\mathrm{C}}$ is rapidly suppressed by increasing $x$ [28, 29, 31]. At $x=0.07$, the three distinct instabilities, namely, those at the M and K points and along the $\mathrm{\Gamma }$-A line in reciprocal space, emerge simultaneously and form superstructures. The $\sqrt{3}a$ structure, which is the ordered phase of the ${\mathrm{K}}_2$ mode [33], exists in a narrow compositional window shaded light blue. In the region below $T^{*}$, short-range correlation is dominant. The $T^{*}$ values are indicated by blue diamonds.

Figure 2

Synchrotron x-ray diffraction patterns at (a) 300 K and (b) 100 K of a ${\mathrm{Ba}}_{1-x}{\mathrm{Sr}}_x{\mathrm{Al}}_2{\mathrm{O}}_4$ ($x=0.07$) single crystal. The white arrows indicate the superlattice reflections at the K point. At 100 K, satellite reflections are visible along the $\mathrm{\Gamma }-\text{A}$ line, as marked by blue arrows. The superlattice reflection at the M point is marked by a yellow arrow. The weak reflections found just above and below the K points come from surface microcrystallites and therefore are not important. (c) The first Brillouin zone of the hexagonal crystal.

Figure 3

Integrated intensity profiles of $x=0.07$–0.40 plotted along the [110] direction at 300 K (left) and 100 K (right). $\eta =0$ and 1 correspond to reciprocal points of the lower and upper fundamental reflections, respectively. They are fitted using several Lorentzian functions shown by green and blue lines. Gray lines show backgrounds. Fitting results for other temperatures are shown in the Supplemental Material [34].

Figure 4

(a) Normalized peak intensity ($I_{\mathrm{p}}/I_{\mathrm{Bragg}}$) and (b) FWHM at the K points plotted against temperature. For $x\ge 0.25$, each plot shows a maximum at approximately 300 K, as denoted by $T^{*}$. The open and solid symbols represent the data obtained upon heating and cooling, respectively. Solid lines are guides for the eye.

Figure 5

(a) The lattice heat capacity ($C_{\mathrm{p}}$) divided by $T^3$ is plotted against temperature. Enhanced lattice heat capacity near 10 K is observed for $x\ge 0.07$. In addition, the $x=0.2$–0.5 samples show an upturn below $\approx 2.5$ K, which is typical behavior in amorphous solids. (b) Enlarged view of $T\le 8$ K plotted on a linear scale. (c) Debye temperature (${\mathrm{\Theta }}_{\mathrm{D}}$) obtained by using the coefficient of $C/T^3$. For $x=0.2$–0.5, the coefficient of $C/T^3$ was determined by using the local minimum value, as indicated by broken lines in (a).