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

Emergent Mechanics of Magnetic Skyrmions Deformed by Defects

While magnetic skyrmions are often modeled as rigid particles, both experiments and micromagnetic simulations indicate their easy-to-deform characteristic, especially when their motion is restricted by defects. Here we establish a theoretical framework for the dynamics of magnetic skyrmions by incorporating the degrees of freedom related to deformation and predict well the current-driven dynamics of deformable skyrmions in the presence of line defects without any parameter fitting, where classical theories based on rigid-particle assumption deviate significantly. Further, we define an emergent property of magnetic skyrmions-flexibility and show that this property strongly modulates the depinning dynamics of skyrmions along a line defect with breaches. Our work explores the emergent mechanics of magnetic skyrmions and extends the current understanding on the dynamics of skyrmions interacted with defects.

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.

Acoustic Waves Induced by Einstein-de Haas Effect in the Ultrafast Core Reversal of Magnetic Vortex

The interaction between acoustic wave and magnetization in ferromagnetic thin films has attracted great attention due to its interesting physics and potential applications. However, up to now, the magneto-acoustic interaction has mainly been studied on the basis of magnetostriction. In this Letter, we develop a phase field model of magneto-acoustic interaction based on the Einstein-de Haas effect, and predict the acoustic wave during the ultrafast core reversal of magnetic vortex in a ferromagnetic disk. Because of the Einstein-de Haas effect, the ultrafast change of magnetization at the vortex core leads to a large mechanical angular momentum, which induces a body couple at the vortex core and excites a high-frequency acoustic wave. Moreover, the displacement amplitude of the acoustic wave is highly dependent on the gyromagnetic ratio. The smaller the gyromagnetic ratio is, the larger the displacement amplitude is. The present work not only provides a new mechanism for dynamic magnetoelastic coupling but also sheds new insights on the magneto-acoustic interaction.

Hexagonal Close-Packed Polar-Skyrmion Lattice in Ultrathin Ferroelectric PbTiO_{3} Films

Polar skyrmions are topologically stable, swirling polarization textures with particlelike characteristics, which hold promise for next-generation, nanoscale logic and memory. However, the understanding of how to create ordered polar skyrmion lattice structures and how such structures respond to applied electric fields, temperature, and film thickness remains elusive. Here, using phase-field simulations, the evolution of polar topology and the emergence of a phase transition to a hexagonal close-packed skyrmion lattice is explored through the construction of a temperature-electric field phase diagram for ultrathin ferroelectric PbTiO_{3} films. The hexagonal-lattice skyrmion crystal can be stabilized under application of an external, out-of-plane electric field which carefully adjusts the delicate interplay of elastic, electrostatic, and gradient energies. In addition, the lattice constants of the polar skyrmion crystals are found to increase with film thickness, consistent with expectation from Kittel's law. Our studies pave the way for the development of novel ordered condensed matter phases assembled from topological polar textures and related emergent properties in nanoscale ferroelectrics.

High-pressure single crystal growth and magnetoelectric properties of CdMn7O12

The concurrent presence of large electric polarization and strong magnetoelectric coupling is quite desirable for potential applications of multiferroics. In this paper, we report the growth of CdMn₇O₁₂single crystals by flux method under a high pressure of 8 GPa for the first time. An antiferromagnetic (AFM) order with a polar magnetic point group is found to occur at the onset temperature ofT_N1= 88 K (AFM1 phase). As a consequence, the pyroelectric current emerges atT_N1and gradually increases and reaches its maximum atT_set= 63 K, at which the AFM1 phase finally settles down. BelowT_set, CdMn₇O₁₂single crystal exhibits a large ferroelectric polarization up to 2640µC m^-2. Moreover, the spin-induced electric polarization can be readily tuned by applying magnetic fields, giving rise to considerable magnetoelectric coupling effects. Thus, the current CdMn₇O₁₂single crystal acts as a rare multiferroic system where both large polarization and strong magnetoelectric coupling merge concurrently.

Flexoresponses of Synthetic Antiferromagnetic Systems Hosting Skyrmions

While strain gradients break lattice centrosymmetry, ferromagnetism is a time-reversal symmetry breaking product. Flexomagnetic effect in ferromagnets is usually indirect and weak. In this Letter, we reveal a topologically enhanced flexomagnetic effect in synthetic antiferromagnetic systems based on Dzyaloshinskii-Moriya interaction and the large deformability of skyrmion. Moreover, the synthetic antiferromagnetic skyrmion exhibits an unexpected Hall effect under strain gradient. We propose that this flexo-Hall effect originates from a geometric Magnus force related to the asymmetric deformation of skyrmion. Our results shed new insights into the flexoresponses in systems hosting topological structures and may open up a new field-"flexoskyrmionics".

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.

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.

Microdynamic Study of Spin-Lattice Coupling Effects on Skyrmion Transport

Skyrmion transport fundamentally determines the speed, energy consumption, and functionality of skyrmion-based spintronic devices, attracting considerable attention. Recent experimental studies found there is a migration barrier for the thermal activated transport of a skyrmion, which is speculated to be induced by the pinning effects of crystalline defects. In this Letter, we propose an alternative source of migration barrier for skyrmion transport, i.e., a local lattice distortion field due to spin-lattice coupling, which can lead to the same Arrhenius diffusion behavior in defect-free skyrmion materials. By performing spin-lattice dynamics simulations, we study the microdynamic insight into the influence of local lattice distortion field, which refreshes the mechanistic understanding on skyrmion transport.

PFM (piezoresponse force microscopy)-aided design for molecular ferroelectrics

With prosperity, decay, and another spring, molecular ferroelectrics have passed a hundred years since Valasek first discovered ferroelectricity in the molecular compound Rochelle salt. Recently, the proposal of ferroelectrochemistry has injected new vigor into this century-old research field. It should be highlighted that piezoresponse force microscopy (PFM) technique, as a non-destructive imaging and manipulation method for ferroelectric domains at the nanoscale, can significantly speed up the design rate of molecular ferroelectrics as well as enhance the ferroelectric and piezoelectric performances relying on domain engineering. Herein, we provide a brief review of the contribution of the PFM technique toward assisting the design and performance optimization of molecular ferroelectrics. Relying on the relationship between ferroelectric domains and crystallography, together with other physical characteristics such as domain switching and piezoelectricity, we believe that the PFM technique can be effectively applied to assist the design of high-performance molecular ferroelectrics equipped with multifunctionality, and thereby facilitate their practical utilization in optics, electronics, magnetics, thermotics, and mechanics among others.

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.

Quasi-one-dimensional metallic conduction channels in exotic ferroelectric topological defects

Ferroelectric topological objects provide a fertile ground for exploring emerging physical properties that could potentially be utilized in future nanoelectronic devices. Here, we demonstrate quasi-one-dimensional metallic high conduction channels associated with the topological cores of quadrant vortex domain and center domain (monopole-like) states confined in high quality BiFeO3 nanoislands, abbreviated as the vortex core and the center core. We unveil via the phase-field simulation that the superfine metallic conduction channels along the center cores arise from the screening charge carriers confined at the core region, whereas the high conductance of vortex cores results from a field-induced twisted state. These conducting channels can be reversibly created and deleted by manipulating the two topological states via electric field, leading to an apparent electroresistance effect with an on/off ratio higher than 103. These results open up the possibility of utilizing these functional one-dimensional topological objects in high-density nanoelectronic devices, e.g. nonvolatile memory.

Organic Ferroelectric Vortex-Antivortex Domain Structure

Organic ferroelectrics are attracting tremendous interest because of their mechanical flexibility, ease of fabrication, and low acoustical impedance. Although great advances have been made in recent years, topological defects such as vortices remain relatively unexplored in the organic ferroelectric system. Here, from [quinuclidinium]ReO₄ ([Q]ReO₄), we applied the molecular design strategy of H/F substitution to successfully synthesize the organic ferroelectric [4-fluoroquinuclidinium]ReO₄ ([4-F-Q]ReO₄). Through H/F substitution, the Curie temperature and spontaneous polarization are respectively increased from 367 K and 5.83 μC/cm² in [Q]ReO₄ to 466 K and 11.37 μC/cm² in [4-F-Q]ReO₄. Moreover, under mechanical stress fields, three kinds of stripelike domains with various polarization directions emerge to form a windmill-like domain pattern in the thin film of [4-F-Q]ReO₄, in which intriguing vortex-antivortex topological configurations can exist stably. This work provides an efficient strategy for optimizing the properties of organic ferroelectrics and exploring emergent phenomena.

Observation of Vortex Domains in a Two-Dimensional Lead Iodide Perovskite Ferroelectric

Topological defects, such as vortices and skyrmions, provide a wealth of splendid possibilities for new nanoscale devices because of their marvelous electronic, magnetic, and mechanical behaviors. Recently, great advances have been made in the study of the ferroelectric vortex in conventional perovskite oxides, such as BaTiO₃ and BiFeO₃. Despite extensive interest, however, no intriguing ferroelectric vortex structures have yet been found in organic-inorganic hybrid perovskites (OIHPs), which are desirable for their mechanical flexibility, ease of fabrication, and low acoustical impedance. We observed the robust vortex-antivortex topological configurations in a two-dimensional (2D) layered OIHP ferroelectric (4,4-DFPD)₂PbI₄ (4,4-DFPD is 4,4-difluoropiperidinium). This provides future directions for the study of perovskites and makes it a promising alternative for nanoscale ferroelectric devices in medical, micromechanical, and biomechanical applications.

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.

Topological domain states and magnetoelectric properties in multiferroic nanostructures

Multiferroic nanostructures have been attracting tremendous attention over the past decade, due to their rich cross-coupling effects and prospective electronic applications. In particular, the emergence of some exotic phenomena in size-confined multiferroic systems, including topological domain states such as vortices, center domains, and skyrmion bubble domains, has opened a new avenue to a number of intriguing physical properties and functionalities, and thus underpins a wide range of applications in future nanoelectronic devices. It is also highly appreciated that nano-domain engineering provides a pathway to control the magnetoelectric properties, which is promising for future energy-efficient spintronic devices. In recent years, this field, still in its infancy, has witnessed a rapid development and a number of challenges too. In this article, we shall review the recent advances in the emergent domain-related exotic phenomena in multiferroic nanostructures. Specific attention is paid to the topological domain structures and related novel physical behaviors as well as the electric-field-driven magnetic switching via domain engineering. This review will end with a discussion of future challenges and potential directions.

Poling of an artificial magneto-toroidal crystal

Although ferromagnetism is known to be of enormous importance, the exploitation of materials with a compensated (for example, antiferromagnetic) arrangement of long-range ordered magnetic moments is still in its infancy. Antiferromagnetism is more robust against external perturbations, exhibits ultrafast responses of the spin system¹ and is key to phenomena such as exchange bias^2,3, magnetically induced ferroelectricity⁴ or certain magnetoresistance phenomena⁵. However, there is no conjugate field for the manipulation of antiferromagnetic order, hindering both its observation and direct manipulation. Only recently, direct poling of a particular antiferromagnet was achieved with spintronic approaches⁶. An interesting alternative to antiferromagnetism is ferrotoroidicity-a recently established fourth form of ferroic order^7,8. This is defined as a vortex-like magnetic state with zero net magnetization, yet with a spontaneously occurring toroidal moment⁹. As a hallmark of ferroic order, there must be a conjugate field that can manipulate the order parameter. For ferrotoroidic materials, this is a toroidal field-a magnetic vortex field violating both space-inversion and time-reversal symmetry analogous to the toroidal moment¹⁰. However, the nature and generation of the toroidal field remain elusive for conventional crystalline systems. Here, we demonstrate the creation of an artificial crystal^11,12 consisting of mesoscopic planar nanomagnets with a magneto-toroidal-ordered ground state. Effective toroidal fields of either sign are applied by scanning a magnetic tip over the crystal. Thus, we achieve local control over the orientation of the toroidal moment despite its zero net magnetization.

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.

Observation of magnetic vortex pairs at room temperature in a planar α-Fe2O3/Co heterostructure

Vortices, occurring whenever a flow field 'whirls' around a one-dimensional core, are among the simplest topological structures, ubiquitous to many branches of physics. In the crystalline state, vortex formation is rare, since it is generally hampered by long-range interactions: in ferroic materials (ferromagnetic and ferroelectric), vortices are observed only when the effects of the dipole-dipole interaction are modified by confinement at the nanoscale^1-3, or when the parameter associated with the vorticity does not couple directly with strain ⁴ . Here, we observe an unprecedented form of vortices in antiferromagnetic haematite (α-Fe₂O₃) epitaxial films, in which the primary whirling parameter is the staggered magnetization. Remarkably, ferromagnetic topological objects with the same vorticity and winding number as the α-Fe₂O₃ vortices are imprinted onto an ultra-thin Co ferromagnetic over-layer by interfacial exchange. Our data suggest that the ferromagnetic vortices may be merons (half-skyrmions, carrying an out-of plane core magnetization), and indicate that the vortex/meron pairs can be manipulated by the application of an in-plane magnetic field, giving rise to large-scale vortex-antivortex annihilation.