The manner in which 90° ferroelectric-ferroelastic domains respond to changes in temperature has been mapped in BaTiO${}_3$ single crystals using atomic force microscopy. Domain periodicity remains unaltered until approximately 2 °C below the Curie temperature ($T_C$), whereupon domains coarsened dramatically. This behavior was successfully rationalized by considering the temperature dependence of the parameters associated with standard models of ferroelastic domain formation. However, while successful in describing the expected radical increase in equilibrium period with temperature, the model did not predict the unusual mechanism by which domain coarsening occurred; this was not continuous at a local level but instead involved discrete domain annihilation events. Subsequent insights from a combination of free energy analysis for the system and further experimental data from an analogous situation, in which domain period increases with increasing crystal thickness, suggested that domain annihilation is inevitable whenever a component of the relevant gradient that affects domain period is orientated parallel to the domain walls. Consistent with this thesis, we note that, for the observations presented herein, the thermal gradient possessed a significant component parallel to the domain walls. We suggest that domain annihilation is a general feature of domain structures in gradient fields.

• Received 1 December 2011

DOI:https://doi.org/10.1103/PhysRevB.85.054113