Controllability of vortex domain structure in ferroelectric nanodot: fruitful domain patterns and transformation paths

Theoretical Understanding of Polar Topological Phase Transitions in Functional Oxide Heterostructures: A Review

The exotic topological phase is attracting considerable attention in condensed matter physics and materials science over the past few decades due to intriguing physical insights. As a combination of "topology" and "ferroelectricity," the ferroelectric (polar) topological structures are a fertile playground for emergent phenomena and functionalities with various potential applications. Herein, the review starts with the universal concept of the polar topological phase and goes on to briefly discuss the important role of computational tools such as phase-field simulations in designing polar topological phases in oxide heterostructures. In particular, the history of the development of phase-field simulations for ferroelectric oxide heterostructures is highlighted. Then, the current research progress of polar topological phases and their emergent phenomena in ferroelectric functional oxide heterostructures is reviewed from a theoretical perspective, including the topological polar structures, the establishment of phase diagrams, their switching kinetics and interconnections, phonon dynamics, and various macroscopic properties. Finally, this review offers a perspective on the future directions for the discovery of novel topological phases in other ferroelectric systems and device design for next-generation electronic device applications.

Interplay of domain structure and phase transitions: theory, experiment and functionality

Domain walls and phase boundaries are fundamental ingredients of ferroelectrics and strongly influence their functional properties. Although both interfaces have been studied for decades, often only a phenomenological macroscopic understanding has been established. The recent developments in experiments and theory allow to address the relevant time and length scales and revisit nucleation, phase propagation and the coupling of domains and phase transitions. This review attempts to specify regularities of domain formation and evolution at ferroelectric transitions and give an overview on unusual polar topological structures that appear as transient states and at the nanoscale. We survey the benefits, validity, and limitations of experimental tools as well as simulation methods to study phase and domain interfaces. We focus on the recent success of these tools in joint scale-bridging studies to solve long lasting puzzles in the field and give an outlook on recent trends in superlattices.

Configurable topological textures in strain graded ferroelectric nanoplates

Topological defects in matter behave collectively to form highly non-trivial structures called topological textures that are characterised by conserved quantities such as the winding number. Here we show that an epitaxial ferroelectric square nanoplate of bismuth ferrite subjected to a large strain gradient (as much as 10⁵ m⁻¹) associated with misfit strain relaxation enables five discrete levels for the ferroelectric topological invariant of the entire system because of its peculiar radial quadrant domain texture and its inherent domain wall chirality. The total winding number of the topological texture can be configured from − 1 to 3 by selective non-local electric switching of the quadrant domains. By using angle-resolved piezoresponse force microscopy in conjunction with local winding number analysis, we directly identify the existence of vortices and anti-vortices, observe pair creation and annihilation and manipulate the net number of vortices. Our findings offer a useful concept for multi-level topological defect memory.

Exploring topological textures in ferroelectrics facilitates the understanding and application of topological features in matter. Here the authors demonstrate the strain field induced evolution of topological vortices in nanoplatelets of rhombohedral phase BiFeO3 using the angle-resolved piezoresponse force microscopy.

Characteristics and controllability of vortices in ferromagnetics, ferroelectrics, and multiferroics

Topological defects in condensed matter are attracting e significant attention due to their important role in phase transition and their fascinating characteristics. Among the various types of matter, ferroics which possess a switchable physical characteristic and form domain structure are ideal systems to form topological defects. In particular, a special class of topological defects-vortices-have been found to commonly exist in ferroics. They often manifest themselves as singular regions where domains merge in large systems, or stabilize as novel order states instead of forming domain structures in small enough systems. Understanding the characteristics and controllability of vortices in ferroics can provide us with deeper insight into the phase transition of condensed matter and also exciting opportunities in designing novel functional devices such as nano-memories, sensors, and transducers based on topological defects. In this review, we summarize the recent experimental and theoretical progress in ferroic vortices, with emphasis on those spin/dipole vortices formed in nanoscale ferromagnetics and ferroelectrics, and those structural domain vortices formed in multiferroic hexagonal manganites. We begin with an overview of this field. The fundamental concepts of ferroic vortices, followed by the theoretical simulation and experimental methods to explore ferroic vortices, are then introduced. The various characteristics of vortices (e.g. formation mechanisms, static/dynamic features, and electronic properties) and their controllability (e.g. by size, geometry, external thermal, electrical, magnetic, or mechanical fields) in ferromagnetics, ferroelectrics, and multiferroics are discussed in detail in individual sections. Finally, we conclude this review with an outlook on this rapidly developing field.

Charge screening strategy for domain pattern control in nano-scale ferroelectric systems

Strain engineering is a widespread strategy used to enhance performance of devices based on semiconductor thin films. In ferroelectrics strain engineering is used to control the domain pattern: When an epitaxial film is biaxially compressed, e.g. due to lattice mismatch with the substrate, the film displays out-of-plane, often strongly enhanced polarization, while stretching the film on the substrate results in in-plane polarization. However, this strategy is of a limited applicability in nanorods because of the small rod/substrate contact area. Here we demonstrate another strategy, in which the polar axis direction is controlled by charge screening. When charge screening is maintained by bottom and top metallization, the nanorods display an almost pure c-domain configuration (polarization perpendicular to the substrate); when the sidewalls of the nanorods are metallized too, a-domain formation prevails (polarization parallel to the substrate). Simulations of the depolarization fields under various boundary conditions support the experimental observations. The employed approach can be expanded to other low-dimensional nano-scale ferroelectric systems.

Stability of Polar Vortex Lattice in Ferroelectric Superlattices

A novel mesoscale state comprising of an ordered polar vortex lattice has been demonstrated in ferroelectric superlattices of PbTiO₃/SrTiO₃. Here, we employ phase-field simulations, analytical theory, and experimental observations to evaluate thermodynamic conditions and geometric length scales that are critical for the formation of such exotic vortex states. We show that the stability of these vortex lattices involves an intimate competition between long-range electrostatic, long-range elastic, and short-range polarization gradient-related interactions leading to both an upper and a lower bound to the length scale at which these states can be observed. We found that the critical length is related to the intrinsic domain wall width, which could serve as a simple intuitive design rule for the discovery of novel ultrafine topological structures in ferroic systems.

Size-dependent and distinguishing degenerated vortex states in ferroelectric nanodots under controllable surface charge conditions

Degenerated vortex states in ferroelectric nanodots are distinguished by characteristic short-circuit I–t curve under a controllable surface charge condition.

Hierarchical ferroelectric and ferrotoroidic polarizations coexistent in nano-metamaterials

Tailoring materials to obtain unique, or significantly enhanced material properties through rationally designed structures rather than chemical constituents is principle of metamaterial concept, which leads to the realization of remarkable optical and mechanical properties. Inspired by the recent progress in electromagnetic and mechanical metamaterials, here we introduce the concept of ferroelectric nano-metamaterials, and demonstrate through an experiment in silico with hierarchical nanostructures of ferroelectrics using sophisticated real-space phase-field techniques. This new concept enables variety of unusual and complex yet controllable domain patterns to be achieved, where the coexistence between hierarchical ferroelectric and ferrotoroidic polarizations establishes a new benchmark for exploration of complexity in spontaneous polarization ordering. The concept opens a novel route to effectively tailor domain configurations through the control of internal structure, facilitating access to stabilization and control of complex domain patterns that provide high potential for novel functionalities. A key design parameter to achieve such complex patterns is explored based on the parity of junctions that connect constituent nanostructures. We further highlight the variety of additional functionalities that are potentially obtained from ferroelectric nano-metamaterials, and provide promising perspectives for novel multifunctional devices. This study proposes an entirely new discipline of ferroelectric nano-metamaterials, further driving advances in metamaterials research.

Large and Tunable Polar-Toroidal Coupling in Ferroelectric Composite Nanowires toward Superior Electromechanical Responses

The collective dipole behaviors in (BaTiO₃)_m/(SrTiO₃)_n composite nanowires are investigated based on the first-principles-derived simulations. It demonstrates that such nanowire systems exhibit intriguing dipole orders, due to the combining effect of the anisotropic electrostatic interaction of the nanowire, the SrTiO₃-layer-modified electrostatic interaction and the multiphase ground state of BaTiO₃ layer. Particularly, a strong polar-toroidal coupling that is tunable by the SrTiO₃-layer thickness, temperature, external strains and electric fields is found to exist in the nanowires, with the appearance of fruitful dipole states (including those being purely polar, purely toroidal, both polar and toroidal, or distorted toroidal) and phase boundaries. As a consequence, an efficient cross control of the toroidal (polar) order by static (curled) electric field, and superior piezoelectric and piezotoroidal responses, can be achieved in the nanowires. The result provides new insights into the collective dipole behaviors in nanowire systems.

Unfolding grain size effects in barium titanate ferroelectric ceramics

Grain size effects on the physical properties of polycrystalline ferroelectrics have been extensively studied for decades; however there are still major controversies regarding the dependence of the piezoelectric and ferroelectric properties on the grain size. Dense BaTiO₃ ceramics with different grain sizes were fabricated by either conventional sintering or spark plasma sintering using micro- and nano-sized powders. The results show that the grain size effect on the dielectric permittivity is nearly independent of the sintering method and starting powder used. A peak in the permittivity is observed in all the ceramics with a grain size near 1 μm and can be attributed to a maximum domain wall density and mobility. The piezoelectric coefficient d₃₃ and remnant polarization P_r show diverse grain size effects depending on the particle size of the starting powder and sintering temperature. This suggests that besides domain wall density, other factors such as back fields and point defects, which influence the domain wall mobility, could be responsible for the different grain size dependence observed in the dielectric and piezoelectric/ferroelectric properties. In cases where point defects are not the dominant contributor, the piezoelectric constant d₃₃ and the remnant polarization P_r increase with increasing grain size.