We present a coherent x-ray diffraction study of the antiferrodistortive displacive transition of ${\mathrm{SrTiO}}_3$, a prototypical example of a phase transition for which the critical fluctuations exhibit two length scales and two time scales. From the microbeam x-ray coherent diffraction patterns, we show that the broad (short-length scale) and the narrow (long-length scale) components can be spatially disentangled, due to $100\mathrm{\text{−}}\mu \mathrm{m}$-scale spatial variations of the latter. Moreover, both components exhibit a speckle pattern, which is static on a $\sim 10\mathrm{mn}$ time scale. This gives evidence that the narrow component corresponds to static ordered domains. We interpret the speckles in the broad component as due to a very slow dynamical process, corresponding to the well-known central peak seen in inelastic neutron scattering.

• Received 10 November 2006

DOI:https://doi.org/10.1103/PhysRevLett.98.105501