Orientation-dependent structural phase diagrams and dielectric properties of ${\mathrm{PbZr}}_{1-x}{\mathrm{Ti}}_x{\mathrm{O}}_3$ polydomain thin films

The orientation-dependent equilibrium ferroelectric domain structures and dielectric properties of polydomain ${\mathrm{PbZr}}_1{}_{-}{}_x{\mathrm{Ti}}_x{\mathrm{O}}_3$ thin films are investigated using a phenomenological Ginzburg-Landau-Devonshire thermodynamic model. We develop and describe three-dimensional polydomain models for (001)-, (101)-, and (111)-oriented films and explore the evolution of the structure and dielectric permittivity of the system as a function of epitaxial strain across the composition range $0.5\le x\le 1.0$. Our studies reveal that the film orientation, epitaxial strain, and composition can combine in unexpected ways to drive exotic phase stability and transformations which have intriguing implications for the properties. In particular, in (101)- and (111)-oriented films, the application of epitaxial strains along non-$\langle 001\rangle$-type crystallographic directions significantly reduces the stability range of the parent tetragonal phase [which is dominant in (001)-oriented films] and results in a variety of new symmetries. We also observe that the film orientation can be used to tune the relative fraction of intrinsic (i.e., within a domain) and extrinsic (i.e., from domain wall motion) contributions to the dielectric permittivity. Ultimately these studies reveal how composition, epitaxial strain, and film orientation provide for comprehensive control of the structure and properties of ferroelectrics.

Figure 1

(a) The composition-strain monodomain phase diagram, (b) a schematic illustration of possible monodomain components in the polydomain structure, and (c) the composition-strain polydomain phase diagram for (001)-oriented films.

Figure 2

(a) The composition-strain monodomain phase diagram, (b) a schematic illustration of possible monodomain components in the polydomain structure, and (c) the composition-strain polydomain phase diagram for (101)-oriented films.

Figure 3

(a) The composition-strain monodomain phase diagram, (b) a schematic illustration of possible monodomain components in the polydomain structure, and (c) the composition-strain polydomain phase diagram for (111)-oriented films.

Figure 4

The composition-strain map for (a) the intrinsic and (b) the total (intrinsic plus extrinsic contribution) dielectric response in (001)-oriented films.

Figure 5

The composition-strain map for (a) the intrinsic and (b) the total (intrinsic plus extrinsic contribution) dielectric response in (101)-oriented films.

Figure 6

The composition-strain map for the total (intrinsic plus extrinsic contribution) dielectric response in (111)-oriented films.