Defect stabilized periodic amplitude modulations in ferroelectrics

Theoretical analysis shows that the total free energy of a ferroelectric system with free boundary conditions increases with the number of the inhomogeneous regions, such as domain walls and other modulated structures. However, charged defects could lower the total energy of a ferroelectric system by interacting with charge density fluctuations in inhomogeneous regions. We discuss a special kind of inhomogeneous microstructure in a lanthanum doped lead titanate, the amplitude modulations, which can be stabilized by aliovalent dopants.