Properties of ferroelectric nanodots embedded in a polarizable medium: atomistic simulations

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.

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.

Polar Superhelices in Ferroelectric Chiral Nanosprings

Topological objects of nontrivial spin or dipolar field textures, such as skyrmions, merons, and vortices, interacting with applied external fields in ferroic materials are of great scientific interest as an intriguing playground of unique physical phenomena and novel technological paradigms. The quest for new topological configurations of such swirling field textures has primarily been done for magnets with Dzyaloshinskii-Moriya interactions, while the absence of such intrinsic chiral interactions among electric dipoles left ferroelectrics aside in this quest. Here, we demonstrate that a helical polarization coiled into another helix, namely a polar superhelix, can be extrinsically stabilized in ferroelectric nanosprings. The interplay between dipolar interactions confined in the chiral geometry and the complex strain field of mixed bending and twisting induces the superhelical configuration of electric polarization. The geometrical structure of the polar superhelix gives rise to electric chiralities at two different length scales and the coexistence of three order parameters, i.e., polarization, toroidization, and hypertoroidization, both of which can be manipulated by homogeneous electric and/or mechanical fields. Our work therefore provides a new geometrical configuration of swirling dipolar fields, which offers the possibility of multiple order-parameters, and electromechanically controllable dipolar chiralities and associated electro-optical responses.

Frustration and Self-Ordering of Topological Defects in Ferroelectrics

A first-principles-based effective Hamiltonian technique is used to investigate the interplay between geometrical frustration and the ordering of topological defects in a ferroelectric nanocomposite consisting of a square array of BaTiO_{3} nanowires embedded in a Ba_{0.15}Sr_{0.85}TiO_{3} matrix. Different arrangements of the wires' chiralities geometrically frustrate the matrix, which in response exhibits point topological defects featuring self-assembled ordered structures spatially fluctuating down to the lowest temperatures. These fluctuations thereby endow the system with residual configurational entropy from which many properties characteristic of geometric frustration, such as the ground state degeneracy and the broadness of the dielectric response, are further found to originate.

Discovery of stable skyrmionic state in ferroelectric nanocomposites

Non-coplanar swirling field textures, or skyrmions, are now widely recognized as objects of both fundamental interest and technological relevance. So far, skyrmions were amply investigated in magnets, where due to the presence of chiral interactions, these topological objects were found to be intrinsically stabilized. Ferroelectrics on the other hand, lacking such chiral interactions, were somewhat left aside in this quest. Here we demonstrate, via the use of a first-principles-based framework, that skyrmionic configuration of polarization can be extrinsically stabilized in ferroelectric nanocomposites. The interplay between the considered confined geometry and the dipolar interaction underlying the ferroelectric phase instability induces skyrmionic configurations. The topological structure of the obtained electrical skyrmion can be mapped onto the topology of domain-wall junctions. Furthermore, the stabilized electrical skyrmion can be as small as a few nanometers, thus revealing prospective skyrmion-based applications of ferroelectric nanocomposites.

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.

First-principles-based effective Hamiltonian simulations of bulks and films made of lead-free Ba(Zr,Ti)O3 relaxor ferroelectrics

A review of the recent development and application of a first-principles-derived effective Hamiltonian technique to the study of lead-free Ba(Zr,Ti)O3 (BZT) relaxor ferroelectrics is provided. In addition to the computation and analysis of macroscopic properties (such as different types of dielectric responses and electric polarization) and their connections to previous published works, particular emphasis is given to microscopic insights arising from this atomistic technique. These include (i) the numerically-found determination of the physical origin of the relaxor behavior in BZT; and (ii) the prediction of polar nanoregions and the evolution of their morphology as a response to temperature, electric fields and epitaxial misfit strain. Other striking phenomena that were predicted in BZT compounds, such as Fano resonance and field-driven percolation, are also documented and discussed. Finally, a brief perspective of possible remaining computational studies to be conducted in relaxor ferroelectrics, in order to further understand them, is attempted.

Novel complex phenomena in ferroelectric nanocomposites

A first-principles-based effective Hamiltonian is used to investigate finite-temperature properties of ferroelectric nanocomposites made of periodic arrays of ferroelectric nanowires embedded in a matrix formed by another ferroelectric material. Novel transitions and features related to flux-closure configurations are found. Examples include (i) a vortex core transition, that is characterized by the change of the vortex cores from being axisymmetric to exhibiting a 'broken symmetry'; (ii) translational mode of the vortex cores; (iii) striking zigzag dipolar chains along the vortex core axis; and (iv) phase-locking of ferroelectric vortices accompanied by ferroelectric antivortices. These complex phenomena are all found to coexist with a spontaneous electrical polarization aligned along the normal of the plane containing the vortices.

Finite-temperature properties of Ba(Zr,Ti)O3 relaxors from first principles

A first-principles-based technique is developed to investigate the properties of Ba(Zr,Ti)O(3) relaxor ferroelectrics as a function of temperature. The use of this scheme provides answers to important, unresolved and/or controversial questions such as the following. What do the different critical temperatures usually found in relaxors correspond to? Do polar nanoregions really exist in relaxors? If yes, do they only form inside chemically ordered regions? Is it necessary that antiferroelectricity develop in order for the relaxor behavior to occur? Are random fields and random strains really the mechanisms responsible for relaxor behavior? If not, what are these mechanisms? These ab initio based calculations also lead to deep microscopic insight into relaxors.

Exploring topological defects in epitaxial BiFeO3 thin films

Using a combination of piezoresponse force microscopy (PFM) and phase-field modeling, we demonstrate ubiquitous formation of center-type and possible ferroelectric closure domain arrangements during polarization switching near the ferroelastic domain walls in (100) oriented rhombohedral BiFeO(3). The formation of these topological defects is determined from the vertical and lateral PFM data and confirmed from the reversible changes in surface topography. These observations provide insight into the mechanisms of tip-induced ferroelastic domain control and suggest that formation of topological defect states under the action of local defect- and tip-induced fields is much more common than previously believed.

Control of vortices by homogeneous fields in asymmetric ferroelectric and ferromagnetic rings

Effective Hamiltonians have been used (i) to demonstrate that the shape asymmetry of ferromagnetic rings is essential to the recently discovered switching of the chirality of their vortices by homogeneous magnetic fields, via a transition into onion states; (ii) to reveal that an electric vortex can also be controlled by a homogeneous electric field in asymmetric ferroelectric nanorings, via the formation of antiferrotoroidic pair states rather than onion states; and (iii) to provide the fundamental reason that allows such control, namely, two new interaction energies involving a vector characterizing the asymmetry, the applied field, and the toroidal moment.