Direct Observation of the Critical Relaxation of Polarization Clusters in ${\mathrm{BaTiO}}_3$ Using a Pulsed X-Ray Laser Technique

We have developed a new method to investigate the relaxation time of the dipole moment in polarization clusters in ${\mathrm{BaTiO}}_3$. Time correlation of speckle intensities was measured by the use of a double pulsed soft x-ray laser. The evolution of the relaxation time of the dipole moment near the Curie temperature ($T_C$) was investigated. The maximum relaxation time ($\sim 90\mathrm{ps}$) is shown to appear at a temperature of 4.5 K above the $T_C$, being coincident with the one where the maximum polarization takes place. This method is widely applicable to any other critical decay processes at phase transitions.

Figure 1

Schematic set up of x-ray intensity correlation measurements by use of a Michelson type delay pulse generator, and an x-ray streak camera. The delay pulse generator consists of a beam splitter (BS), and two $\mathrm{Mo}/\mathrm{Si}$ multilayer mirrors $M1$ and $M2$, and two optical shutters OS1 and OS2.

Figure 2

(a) A streak camera image of the two speckle intensities separated by a delay time 25 ps, (b) intensity profiles of the speckle images in the horizontal direction, (c) a $q$ dependence of the $g^{(2)}$ in the vicinity of the specular reflection, where $q$ is the value relative to the center of specular reflection.

Figure 3

Decay curves of $g^{(2)}$ as a function of delay time at several sample temperatures (a) from 2 K below the $T_C$ up to 10 K above the $T_C$ by 2 K step: results due to the 1st experiment, and (b) from 4 K above the $T_C$ up to 8 K above the $T_C$ by 0.5 K step: results due to the 2nd experiment.

Figure 4

Temperature dependence of the relaxation time ${\tau }_0$ and the polarization of the cluster. A maximum that takes place at 4.5 K above the $T_C$ coincides with the maximum of the polarization of the clusters. Solid and broken lines are just guide to the eye.