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

Control of vortex chirality in a symmetric ferromagnetic ring using a ferromagnetic nanoelement

Controlling the vortex chirality in ferromagnetic nanodots and nanorings has been a topic of investigation for the last few years. Many control methods have been proposed and it has been found that the control is related to the breaking of the circular symmetry of the ring. In this paper, we present a theoretical study demonstrating the control of chirality in a symmetrical ferromagnetic nanoring by breaking the circular symmetry of the system by placing an elongated ferromagnetic nanoelement inside the ring. Here, the stray magnetostatic field exerted by the asymmetrically placed nanoelement determines the movement of the domain walls upon re-magnetization of the nanoring and the resulting chirality in remanence. Thus, the use of a nanoelement not only allows control of the chirality of the vortex state in an isolated ring, but also offers an opportunity to control magnetization in denser nanoring systems, as well as for spintronic and magnonic applications.

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.

Ferroelectric nematic liquid crystal thermomotor

A thermal gradient-induced circular motion of particles placed on ferroelectric nematic liquid crystal sessile drops is demonstrated and explained. Unlike hurricanes and tornadoes that are the prime examples for thermal motors and where turbulent flows are apparent, here the texture without tracer particles appears completely steady indicating laminar flow. We provide a simple model showing that the tangential arrangement of the ferroelectric polarization combined with the vertical thermal gradient and the pyroelectricity of the fluid drives the rotation of the tracer particles that become electrically charged in the fluid. These observations provide a fascinating example of the unique nature of fluid ferroelectric liquid crystals.

Vortex Domain Walls in Ferroelectrics

Controlling the domain formation in ferroelectric materials at the nanoscale is a fertile ground to explore emergent phenomena and their technological prospects. For example, charged ferroelectric domain walls in BiFeO₃ and ErMnO₃ exhibit significantly enhanced conductivity which could serve as the foundation for next-generation circuits (Estévez and Laurson, Phys. Rev. B 2015, 91, 054407). Here, we describe a concept in which polar vortices perform the same role as a ferroelectric domain wall in classical domain structures with the key difference being that the polar vortices can accommodate charged (i.e., head-to-head and tail-to-tail) domains, for example, in ferroelectric PbTiO₃/dielectric SrTiO₃ superlattices. Such a vortex domain wall structure can be manipulated in a reversible fashion under an external applied field.

Exotic Quad-Domain Textures and Transport Characteristics of Self-Assembled BiFeO3 Nanoislands on Nb-Doped SrTiO3

Topological quad-domain textures with interesting cross-shaped buffer domains (walls) have been recently observed in BiFeO₃ (BFO) nanoislands, indicating a new platform for exploring topological defects and multilevel memories. Such domain textures have nevertheless only been limited in BFO nanoislands grown on LaAlO₃ substrates with a large lattice mismatch of ∼-4.4%. Here, we report that such exotic domain textures could also form in BFO nanoislands directly grown on a conductive substrate with a much smaller lattice mismatch and the local transport characteristics of the BFO nanoislands are distinct from the previously reported ones. The angle-resolved piezoresponse force images verify that the domain textures consist of center-divergent quad-domains with upward polarizations and cross-shaped buffer domains with downward polarizations. Interestingly, textures with multiple crosses are also observed in nanoislands of larger sizes, besides the previously reported ones with a single cross. The nanoislands exhibit strong diodelike rectifying characteristics and the quad-domains show a higher average conductance than the cross-shaped buffer domains, indicating that there is a certain correlation between the local conductance of the nanoislands and the domain textures. This transport behavior is attributed to the effect of the depolarization field on the Schottky barriers at both the substrate/BFO interface and the tip/BFO junction. Our findings extend the current understanding of the exotic quad-domain textures of ferroelectric nanoislands and shed light on their potential applications for configurable electronic devices.

Atomic imaging of mechanically induced topological transition of ferroelectric vortices

Ferroelectric vortices formed through complex lattice–charge interactions have great potential in applications for future nanoelectronics such as memories. For practical applications, it is crucial to manipulate these topological states under external stimuli. Here, we apply mechanical loads to locally manipulate the vortices in a PbTiO₃/SrTiO₃ superlattice via atomically resolved in-situ scanning transmission electron microscopy. The vortices undergo a transition to the a-domain with in-plane polarization under external compressive stress and spontaneously recover after removal of the stress. We reveal the detailed transition process at the atomic scale and reproduce this numerically using phase-field simulations. These findings provide new pathways to control the exotic topological ferroelectric structures for future nanoelectronics and also valuable insights into understanding of lattice-charge interactions at nanoscale.

Controlling topological polar vortices promises to open up new applications for ferroelectric materials. Here, the authors proposed a method to mechanically manipulate polar vortices and monitored the transition between vortex and ferroelectric phase by in-situ scanning transmission electron microscopy.

Mechanical writing of in-plane ferroelectric vortices by tip-force and their coupled chirality

Recent experiments have demonstrated the existence of vortex or flux-closure domains in ferroelectric nanostructures, which are attractive to develop high-density data storage and novel configurable electronic devices. However, it remains challenging to stabilize in-plane vortex or flux-closure domains in ferroelectric film for the absence of a lateral geometry confinement. Based on a 3D phase field model, here we show that stabilization of isolated or interacting in-plane vortices in ferroelectric film can be achieved via applying a mechanical tip-force. The formation of such dipole vortices is caused by a conjoint effect of the tip-force-induced depolarization effect and in-plane strain. The effects of factors like film thickness, misfit strain, tip force and temperature on the vortex formation are systematically revealed and summarized as phase diagrams. The interaction between tip-induced vortices is also investigated. It is found that as the two tips get closer than the critical distance, the two initially isolated vortices become coupled, with identical or opposite chirality, depending on the distance between the two tips. A maximum data storage density of isolated in-plane vortices in ferroelectric thin film is estimated to be ~1 Tb in^-2. Our work thus demonstrates a mechanical strategy to stabilize dipole vortices, and provides a comprehensive insight into the characteristics of ferroelectric film under a mechanical tip force.

Intrinsic and extrinsic effects on the electrotoroidic switching in a ferroelectric notched nanodot by a homogeneous electric field

The control of topological defects in ferroelectrics, in particular by a homogeneous electric field, has emerged as an active research direction. A polarization vortex, which is a fundamental topological defect formed in ferroelectric nanodots, has recently been demonstrated to be switchable by a homogeneous electric field through the control of the built-in electrical distribution using low-symmetry nanodots. Such electrotoroidic switching is investigated for nearly ideal systems, e.g., free-standing nanodots. However, the electrotoroidic switching may be impacted by several factors, for instance, the nanoscale effect of flexoelectricity (intrinsic effect), epitaxial strain and the frequency of the applied field (extrinsic effects). In the present study, the switching of the polarization vortex in a notched nanodot under a homogeneous electric field is investigated. The emphasis is put on a comparison between intrinsic and extrinsic effects on the vortex switching. The results show that the vortex switching takes place through alternate vortex-to-polar and polar-to-vortex transformations due to the appearance of the notch. Although the flexoelectricity breaks the symmetry of the polarization field in the notched nanodot during the polarization transformation and gives rise to an unusual behavior of the vortex core, which departs from the symmetry axis of the notched nanodot, this intrinsic effect plays a relatively insignificant role in the switching behavior of the polarization vortex. In comparison to the intrinsic effect, interestingly, the extrinsic effects strongly influence the vortex switching behavior. Specifically, the frequency of the applied electric field can alter both the shape of the toroidal hysteresis loop and the domain transformation process of the vortex switching. In addition, under substrate constraints, the magnitude of the coercive electric fields at which the vortex-to-polar and polar-to-vortex transformations occur linearly decreases with the increase of strain. The present study provides instructive information on the efficient control of a polarization vortex, which is dominated by extrinsic factors rather than intrinsic ones.

Torsion-induced vortex switching and skyrmion-like state in ferroelectric nanodisks

The controllability of vortex state in ferroelectric nanodisks under the effect of external torsion is investigated in this work based on phase-field simulation. We discover a novel Bloch skyrmion-like state in ferroelectric nanodisks due to the combining effect of the torsion and the depolarization field. Moreover, a new strategy is proposed to achieve deterministic switching of the vortex chirality in the ferroelectric nanodisks. On the one hand, if a fixed external electric field is applied to the nanodisk, the vortex chirality can be switched by the torsion force. On the other hand, if we apply a fixed torsion force to the nanodisk, the vortex chirality can be readily switched by an external electric field. The feasibility of both mechanical and electrical switching of the vortex in the ferroelectric nanodisks is based on the trilinear coupling between the toroidization, polarization and shear strain of the system. The influences of temperature, electric field, torsion, and size of the nanodisk on the control of the vortex state are further revealed. Our findings shed light on the practical control and application of ferroelectric dipole vortices.

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.

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.

Morphogenesis mechanisms in the solvothermal synthesis of BaTiO3 from titanate nanorods and nanotubes

A rich variety of single crystalline BaTiO3 (BT) nanostructures have been synthesized by two different routes using titanate nanorods and nanotubes as precursors. Free standing, mixed or agglomerated nanotori, solid or hollow nanospheres and nanocubes were obtained. A careful analysis of the shape evolution of the resulting BT nano-objects obtained with both types of precursors and different parameters (precursor composition and shape, temperature, Ba/Ti molar ratio) allowed an improved understanding of the nanostructure formation. The morphogenesis models at play such as Ostwald ripening and the Kirkendall effect have been identified. Other mechanisms hereafter called the self and merging rebuilding processes and a tentative Turing-reaction-diffusion-model are proposed to explain the formation of these obtained nanoparticles.

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

Ferroelectric vortex domain structure which exists in low-dimensional ferroelectrics is being intensively researched for future applications in functional nanodevices. Here we demonstrate that adjusting surface charge screening in combination with temperature can provide an efficient way to gain control of vortex domain structure in ferroelectric nanodot. Systematical simulating experiments have been conducted to reveal the stability and evolution mechanisms of domain structure in ferroelectric nanodot under various conditions, including processes of cooling-down/heating-up under different surface charge screening conditions, and increasing/decreasing surface charge screening at different temperatures. Fruitful phase diagrams as functions of surface screening and temperature are presented, together with evolution paths of various domain patterns. Calculations discover up to 25 different kinds of domain patterns and 22 typical evolution paths of phase transitions. The fruitful controllability of vortex domain structure by surface charge screening in combination with temperature should shed light on prospective nanodevice applications of low-dimensional ferroelectric nanostructures.

Predicted coupling of the electromagnetic angular momentum density with magnetic moments

Analytical derivations are developed to demonstrate that (i) the angular moment density associated with an electromagnetic field can directly couple with magnetic moments to produce a physical energy, (ii) this direct coupling explains known, subtle phenomena, including some recently predicted in magnetoelectric materials, and (iii) this coupling also results in novel effects, such as the occurrence of a magnetic anisotropy that is driven by antiferroelectricity.

Vortex domain structure in ferroelectric nanoplatelets and control of its transformation by mechanical load

Vortex domain patterns in low-dimensional ferroelectrics and multiferroics have been extensively studied with the aim of developing nanoscale functional devices. However, control of the vortex domain structure has not been investigated systematically. Taking into account effects of inhomogeneous electromechanical fields, ambient temperature, surface and size, we demonstrate significant influence of mechanical load on the vortex domain structure in ferroelectric nanoplatelets. Our analysis shows that the size and number of dipole vortices can be controlled by mechanical load, and yields rich temperature-stress (T-S) phase diagrams. Simulations also reveal that transformations between “vortex states” induced by the mechanical load are possible, which is totally different from the conventional way controlled on the vortex domain by the electric field. These results are relevant to application of vortex domain structures in ferroelectric nanodevices, and suggest a novel route to applications including memories, mechanical sensors and transducers.

Prediction of the magnetotoroidic effect from atomistic simulations

An effective Hamiltonian technique is used to investigate the effect of applying curled electric fields on physical properties of stress-free BiFeO(3) dots being under open-circuit electrical boundary conditions. It is discovered that such fields can lead to a control of not only the magnitude but also the direction of the magnetization. Such control originates from the field-induced transformation or switching of electrical vortices and their couplings with oxygen octahedral tilts and magnetic dipoles. This control involves striking intermediate states and constitutes a novel phenomenon that can be termed a "magnetotoroidic" effect.

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.

Electric field induced by dynamical change of dipolar configurations in ferromagnets

An analytical expression for the electric field, Eint, induced by any dynamical change of dipolar configuration is derived for ferromagnets. Effective Hamiltonian simulations are further conducted to realistically compute such field in an asymmetric permalloy ring. It is found that Eint mostly consists of short pulses that are correlated with the rapid temporal change of the magnetic toroidal moment in this low-dimensional ferromagnet, thus providing macroscopic information about the dynamical change of magnetic vortices. Discussion about the connection between Eint and some electric fields recently mentioned in the literature is also provided.

Nature of dynamical coupling between polarization and strain in nanoscale ferroelectrics from first principles

A first-principle-based technique is used to investigate dynamical coupling between polarization and picosecond time-scale strain pulses in ferroelectric nanolayers. Two different dynamical mechanisms are found. The first mechanism concerns homogeneous dipole patterns, is governed by the ultrafast soft-mode dynamics, mostly consists in the modification of the dipoles' magnitude, and leads to a polarization only weakly changing and following the strain pulse via an "usual" coupling law. On the other hand, the second mechanism occurs in highly inhomogeneous dipole patterns, is characterized by a large change in polarization and by a time delay between polarization and strain, and is governed by the "slower breathing" of dipolar inhomogeneities. This second mechanism provides a successful explanation of puzzling experimental data.

Controlling double vortex states in low-dimensional dipolar systems

The reversal process of the chirality of each opposite vortex belonging to a double vortex state in ferromagnetic hysterons, via the application of in-plane magnetic fields, is reported. Simulations reveal that such a process involves the formation of four intermediate states, including original ones. Hysteresis loops can occur only in a counterclockwise fashion because of one of these intermediate states. Double vortex states can also be controlled by electric fields in ferroelectric nanostructures of different shapes, but with some key differences with respect to the ferromagnetic case.