Strain-Driven Mixed-Phase Domain Architectures and Topological Transitions in Pb_{1- x} Sr_x TiO₃ Thin Films

The potential for creating hierarchical domain structures, or mixtures of energetically degenerate phases with distinct patterns that can be modified continually, in ferroelectric thin films offers a pathway to control their mesoscale structure beyond lattice-mismatch strain with a substrate. Here, it is demonstrated that varying the strontium content provides deterministic strain-driven control of hierarchical domain structures in Pb_{1- x} Sr_x TiO₃  solid-solution thin films wherein two types, c/a and a₁ /a₂ , of nanodomains can coexist. Combining phase-field simulations, epitaxial thin-film growth, detailed structural, domain, and physical-property characterization, it is observed that the system undergoes a gradual transformation (with increasing strontium content) from droplet-like a₁ /a₂  domains in a c/a domain matrix, to a connected-labyrinth geometry of c/a domains, to a disconnected labyrinth structure of the same, and, finally, to droplet-like c/a domains in an a₁ /a₂  domain matrix. A relationship between the different mixed-phase modulation patterns and its topological nature is established. Annealing the connected-labyrinth structure leads to domain coarsening forming distinctive regions of parallel c/a and a₁ /a₂  domain stripes, offering additional design flexibility. Finally, it is found that the connected-labyrinth domain patterns exhibit the highest dielectric permittivity.