Figure 1

Experiment setup. The TCE soft x-ray laser at $139\AA$ came from the Ag slab target pumped by a $\sim 10\mathrm{J}$, picosecond glass laser. The grazing angle was $10°$. The coordinates, $x$ and $q$, are in the horizontal direction. All the components were set in a vacuum ($\sim {10}^{-5}\mathrm{T}\mathrm{o}\mathrm{r}\mathrm{r}$), where the temperature of the ${\mathrm{B}\mathrm{a}\mathrm{T}\mathrm{i}\mathrm{O}}_3$ can be controlled from room temperature to $500°\mathrm{C}$. The image in (a) is a photograph of the domains taken by an optical polarization microscopy at room temperature. M: $\mathrm{M}\mathrm{o}/\mathrm{S}\mathrm{i}$ multiplayer; slit: $80\mu \mathrm{m}(\mathrm{\text{horizontal}})\times 200\mu \mathrm{m}(\mathrm{\text{vertical}})$.Reuse & Permissions

Figure 2

Speckle patterns measured by a single exposure of 7 ps with the TCE soft x-ray laser. (a) The direct probing beam pattern; (b) diffraction patterns via the $a/c$ domain region at room temperature $24°\mathrm{C}$; (c), (d), (e), (f), (g), and (h) correspond to the diffraction pattern from the same region of the sample at temperature $106°\mathrm{C}$, $118°\mathrm{C}$, $119°\mathrm{C}$, $120°\mathrm{C}$, $121°\mathrm{C}$, and $130°\mathrm{C}$, respectively. The Curie temperature of the sample is $122°\mathrm{C}$. The scattering took place along the horizontal direction $q$, since the domain walls were set vertically. All these pictures are shown in a same scale for comparison.Reuse & Permissions

Figure 3

The spatial power spectrum of the complex transmittance function projected on the slit. The spatial frequency is along the $x$ direction shown in Fig. 1. (a) was calculated from the left-hand-side group and (b) was from the right-hand-side group of the speckles shown in Fig. 2b; (c)–(f) were calculated from the speckles shown in Figs. 2d, 2e, 2f, 2g, respectively. The data shown in Fig. 2h were used as the apparatus function (specular reflection of the sample) in calculating the power spectrum from the speckles, as described in the text. The sharp peaks in these figures indicate a quasiperiodic distribution of the domains. The high-frequency oscillation has clearly been shown to evolve from $0.85\mu {\mathrm{m}}^{-1}$ for room temperature to $0.25\mu {\mathrm{m}}^{-1}$ for $121°\mathrm{C}$, $1°\mathrm{C}$ lower than the Curie temperature.Reuse & Permissions

Figure 4

The reduced temperature [$\mu =(T_c-T)/T_c$] dependence of the average correlated domain size ${\sigma }_s$ at thermal equilibrium near the Curie temperature on a logarithmic scale. The solid line is the least-square fitting with ${\sigma }_s\propto {\mu }^{\kappa }$, which gives the exponent $\kappa =0.37\pm 0.02$.Reuse & Permissions