In this study, we show that this counter-intuitive inverse phase sequence is ascribed to enhanced entropic contribution of domain walls, and that domain straightening and coarsening is predominantly driven by the relaxation and diffusion of topological defects.
Inverse transition simulations. a Temperature dependence of the orientational order parameter upon slowly heating the labyrinthine state of an 80 × 80 × 5 film of PZT. b–g, The evolution of the labyrinthine domain pattern in the middle layer of the film with increasing temperature: 10 K (b), 110 K (c), 185 K (d), 260 K (e), 335 K (f) and 410 K (g). Grey (red) dipoles are oriented along the  () pseudo-cubic direction.
The first-principles based effective Hamiltonian computational modeling in PZT and BFO, as well as the experimental observation via Piezoresponse force microscopy (PFM) and X-ray diffraction (XRD) measurements of the inverse dipolar transition in BFO, suggest the universality of the phenomenon in ferroelectric oxides.
Experimental observation and simulations of the inverse transition in BFO films. a, In-plane piezoresponse force microscopy phase images of a 95-nm-thick BFO film grown on a (110)-oriented orthorhombic DSO substrate, for the as-grown sample, and the same sample after annealing at 773 K, 1,023 K and 1,073 K. b, In-plane piezoresponse force microscopy image of a 30-nm-thick BFO film grown on SRO(10 nm)/DSO(110) (top left). Scale bar, 2 μm. Conducting atomic force microscopy (current mapping) images acquired with Vd.c. = 1.7 V applied on a SRO bottom electrode in periodic stripy areas (bottom left) and defected areas (red dashed lines) with high-conduction spots at three-fold junctions (top right) and endpoint (bottom right) topological defects. Scale bars, 500 nm. c, Distribution of the z component of polarization (red to green indicate negative to positive values) in a middle layer of BFO film at different temperatures, as obtained from 36 × 36 × 10 supercell effective-Hamiltonian-based Monte Carlo simulations under periodic boundary conditions with ideal short-circuit screening and isotropic misfit strain of −0.16%. The system was abruptly quenched from 2,000 K to 10 K and consequently progressively heated up with 40,000 relaxation sweeps at each temperature.
Conductive Atomic Force Microscopy (AFM) measurements further reveal that elementary point defects of the self-patterned labyrinthine phase are characterized by enhanced conduction that can be up to fifty times larger than the conduction at straight segments of domain walls.
Such findings may be put at use to leap beyond current domain and domain-wall-based technologies by enabling fundamentally new design principles and topologically enhanced functionalities within ferroelectric films.