Topology and control of self-assembled domain patterns in low-dimensional ferroelectrics

We report on the dynamics of nonequilibrium phase transitions in low-dimensional ferroelectrics and find that self-patterned polar textures exhibit evolutive topology that can be fathomed through the picture of phase separation kinetics.

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Spinodal decomposition and nucleation processes in PZT thin film. Time evolution of the dipolar pattern within the middle layer of 80 × 80 × 5 film of Pb(Zr0.4Ti0.6)O3 under zero external field (a1–a6) and under 40 × 107 V/m applied along [001] pseudo-cubic direction (b1–b6), as obtained from molecular dynamics simulations. In each of the two cases, 1–6 correspond to 150, 250, 350, 450, 750, and 1500 fs after the quench from 650 K to 10 K, respectively. While a1–a6 indicate the onset of the spinodal instability and development of the labyrinthine pattern, b1–b6 show the nucleation process leading to the bubble domain pattern. Gray (red) dipoles are oriented along [001] ([001¯]) pseudo-cubic direction.

Nonequilibrium phase diagram of compressively strained low-dimensional PZT ferroelectric. a Temperature-electric field phase diagram of a Pb(Zr0.4Ti0.6)O3 ultra-thin film mimicked by a 80 × 80 × 5 supercell. Crosses correspond to transition field values calculated through the zeroth Betti number and lines interpolate between the data points obtained for 10 K and from 50 K to 350 K by steps of 50 K. Phases I and II correspond to connected and disconnected labyrinthine patterns, respectively, while phases III and IV denote the mixed bimerons-skyrmion phase and the skyrmions (or bubble) phase, respectively. Phase V corresponds to states where all dipoles are aligned along the applied field. The dashed line separating phases II from III marks the spinodal-like boundary, while the solid line separating phases IV from V marks the binodal-like boundary. b1–b4 provide dipolar configurations as obtained from simulations within each of phases I–IV in the middle layer of the 80 × 80 × 5 film at 10 K, where gray (red) dipoles are oriented along [001] ([001¯]) pseudo-cubic direction. c1, c2 show experimental PFM amplitude images of PZT films with 1 unit cells STO spacer and reveal labyrinthine and bubble-skyrmion morphologies, respectively. The labyrinth domain pattern was obtained after annealing the as-grown PZT films at 525 K for 10 min in air, and cooling it down to room temperature at cooling rate of 10–15 K/min. The bubble domains were then created by scanning the labyrinth domains using a SPM probe with an AC amplitude of 500 mV.

Topological transitional mechanisms and history dependence. Numerical onsets at 10 K of the disconnection processes of domains via the removal of a a fourfold junction, b threefold junction, and c the cleavage of an elongated bimeron into two skyrmions. For each division process, panels correspond to consecutive snapshots of the middle layer of Pb(Zr0.4Ti0.6)O3 80 × 80 × 5 thin film obtained upon increasing field magnitude at 10 K. de show the calculated structure factors at 10 K of the labyrinthine domain pattern (phase I) and of the skyrmion lattice (phase IV). f Experimental evidence at room temperature of the quasi-hexagonal arrangement of polar skyrmions as can be seen in PFM amplitude images of the PZT sandwich thin film. gh show experimental realizations of the pattern evolution involving fourfold and threefold, and bimeron, respectively, at room temperature. Figures correspond to PFM phase images where dark to bright contrast indicates a 180° phase difference, and were obtained through successive scans under a DC bias of 1.8 V. i Progressive depletion of the skyrmions lattice upon increasing of the field within the range of values triggering the transition from phases IV–V, i.e., the transition from the skyrmions lattice to the monodomain state at 10 K. Bright to dark colors correspond to increasing the out-of-plane component of local dipoles. j Electric field hysteresis of normalized tunneling conductance G/G0 at 10 K. The reference tunneling conductance G0 corresponds to the zero-field labyrinthine state.

Driven by complex relaxation dynamics, nonequilibrium phenomena such as self-assembly, pattern formation, and phase ordering kinetics endow phase-separating systems with incomparable richness of domain morphologies. This is particularly relevant in the case of ferroic materials, where complex domain wall arrangements primarily drive emergent phenomena. Understanding the intricate formation processes at play in the formation of modulated phases is thus pivotal for the development of future technologies, e.g., domain wall nanoelectronics, a field of research that has recently seen fiery surge of interest. So far, modulated phases of ferroelectric domains such as the dipolar maze or labyrinthine phase, and the nano-bubble or skyrmionic phase have been somewhat regarded as conceptually disparate. We here numerically predict and experimentally evidence that, depending on the magnitude of the external field, temperature and the kinetics of the phase separation, topologically non-trivial phases emerge upon sub-critically quenching tetragonal Pb(ZrxTi1 − x)O3 through either spinodal decomposition or nucleation processes. The resulting modulated phases are shown to harbor a variety of composite polar topological defects, such as the target skyrmion and the so-called bimeron, that emerge from different combinations of elementary defects. We also show that the self-assembled dipolar patterns, including the yet unreported disconnected labyrinthine and mixed bimerons-skyrmions phases, can be rationalized in their plurality through the unifying canvas of phase separation kinetics. This enables the treatment of chemically homogeneous low-dimensional and elastically constrained ferroelectrics as electrically manipulable phase-separating systems. We also show that the electric field control of skyrmions density elicits hysteretic behavior of conductance, a property that can be harnessed for solid-state neuromorphic computing. These results indicate that the coherent nanoscale intergrowth of topological orders leveraged thus far in diverse materials ranging from metallic alloys to liquid crystals and polymers, can be engineered in ferroic systems as well to enhance their functional topological-based properties.

For more information, please see our paper:   Topology and control of self-assembled domain patterns in low-dimensional ferroelectrics Y. Nahas, S. Prokhorenko, Q. Zhang, V. Govinden, N. Valanoor & L. Bellaiche Nature Communications volume 11, Article number: 5779 (2020)

Yousra Nahas

Research Assistant Professor, University of Arkansas