Picosecond view of microscopic-scale polarization clusters in paraelectric BaTiO3

The polarization clusters existing in both the ferroelectric and the paraelectric phase of BaTiO3 are directly observed and characterized for the first time by a picosecond soft x-ray laser speckle technique. These dynamic clusters appear continuously across the Curie temperature T(c). The clusters' distance increases approximately linearly with temperature, while their mean size does not change significantly. The polarization exhibits a maximum at a temperature about 5 degrees C above T(c). The clusters' short-range correlation strength diverges as (T-T(c))(-0.41+/-0.02) as temperature decreases toward T(c).