Dynamic fluctuations and static speckle in critical X-ray scattering from SrTiO$_{3}$

We report a study of critical x-ray scattering from SrTiO$_{3}$ near the antiferrodistortive structural phase transition at $T_C \approx 105\mbox{K}$. A lineshape analysis of the thermal diffuse scattering results in the most precise experimental determination to date of the critical exponent $\gamma =1.38\pm 0.08$. The microscopic mechanism behind the anomalous ``central peak'' critical scattering component is clarified here by the first-ever observation of a static coherent diffraction pattern (speckle pattern) within the anomalous critical scattering of SrTiO$_{3}$. This observation allows us to directly attribute the origins of the central peak to Bragg diffraction from remnant static disorder above $T_C$.