Thin-film-specific elastic effects in ferroelectric domain structures

Abstract

An essential feature of ferroelectric thin films is the presence in them of domain structures. In order to efficiently implement ferroelectric films into potential new ferroelectrics-based devices, it is of high interest to understand the behaviour of domain structures. Some properties of ferroelectric domain structures, such as internal structure of domain walls, orientation of domain walls, which were investigated and formulated for bulk systems, are typically believed to be applicable to thin films as well. In this work, importance of thin-film-specific effects on domain structure formation is discussed. It is shown that in thin films nonferroelastic domain walls may interact by elastic means on distances far exceeding the domain wall width, which is sometimes considered as the maximal range of their interaction. Theoretical study of films of practical interest shows that the force of elastic repulsion between the walls can be strong enough to be important during the polarization switching and for control of nonferroelastic domain structures. Further, this work discusses mechanisms of ferroelastic domain wall orientation specific to thin films. Typically, when a ferroelastic wall orients violating the condition of mechanical compatibility of the domains, macroscopic elastic fields appear leading to increase of the energy of the system restraining the deviation of the wall from the compatible state. It is shown that in thin films this increase of the energy can be small enough to allow competition with other contributions to the energy, such as domain wall self-energy, leading to large deviations of the wall orientation from its compatible state. Another investigated mechanism of ferroelastic domain wall orientation is interference of elastic fields generated by an incompatible wall with the film-substrate misfit stresses. A system is investigated where such interference, which leads to reduction of elastic energy of the structure, results in deviation of the wall from its compatible state, violating the domain wall electric neutrality as well. Using this result, the concept of elasticity-driven generation of charged conductive domain walls is developed; the concept is supported by reports of experimental observation of metallic-like domain wall conduction in Pb(Zr,Ti)O3 films. A theoretical description is provided for ferroelastic structures with narrow domain inclusions into dominant domain state. It is obtained that in sparse structures the domain periodicity follows linear dependence on the film thickness, not the classical Kittel-like square root dependence. Equilibrium parameters of the domain structure, such as periodicity of the structure, width of the narrow inclusions, are obtained; the results for Pb(Zr,Ti)O3 films are compared with experimental observations of the films. Finally, antiphase boundary with local ferroelectricity in antiferroelectric is investigated. The mechanical response of such boundary on external electric field is modelled. It is shown that the electric field gradient can be used as the driving force for displacement of the boundary. Conditions for displacement of the boundary sufficient for Scanning Probe Microscopy observations are formulated.