Vortex Domain Research Articles

Unveiling Frequency-Dependent Electromechanical Dynamics in Ferroelectric BaTiO3 Nanofilm with a Core-Shell Structure

Diverse domain patterns significantly influence the nonlinear electromechanical behaviors of ferroelectric nanomaterials, with polarization switching under strong electric fields being inherently a frequency-dependent phenomenon. Nevertheless, research in this area remains limited. In this study, we present a phase-field investigation of frequency-dependent electromechanical dynamics of a polycrystalline BaTiO3 nanofilm with a core-shell structure, subjected to applied frequencies ranging from 1 to 80 kHz. Our findings elucidate the microstructural mechanisms underlying the electromechanical behaviors observed in these materials. The effect of the grain size and the strains effect are also taken into account. Hysteresis and butterfly loops exhibit a marked change in shape as the frequency changes. We discuss the underlying domain-switching dynamics as a basis for evaluating such frequency-dependent properties. In addition, we examine the scaling behaviors of the dynamic hysteresis and the influence of grain boundaries on the domain structure. We can also observe from hysteresis loops that the remnant polarization and coercive field significantly diminish when grain sizes decrease from 60 to 5 nm. A smaller grain size of the nanofilm yields a larger percentage of the dielectric grain boundary, which “dilutes” the overall ferroelectricity of the film. A vortex domain structure is more likely to form at low frequency and a small grain size.

Quasi-2D and 3D phase-field simulation studies of polar vortex domain structures for high-density domain engineering.

Phase-field simulations were performed on the polar vortex array structure appearing in the SrTiO3/PbTiO3/SrTiO3 heterostructure to investigate the Kittel law relationship (w ∝ d1/2) between the vortex array period (w) and the PbTiO3 ferroelectric layer thickness (d). Quasi-two-dimensional simulation results show that the equilibrium period can be determined from the relationship between the size of the simulation box and the total free energy density and that the obtained period obeys the Kittel law. However, three-dimensional simulation results show that the polar vortex arrays are not homogeneous in the direction perpendicular to the vortex plane. In the pure vortex state, no obvious correlation exists between the simulation size and energy because of the dislocations caused by the vortex period mismatch. However, in the mixed state with ferroelectric a1/a2, the vortex domains exhibit equilibrium periods that satisfy the Kittel law relationship because of the confinement effect caused by phase separation. Further study of the confined vortex domains in these mixed states and the vortex domains of finite size due to mismatched dislocations are expected to enable domain engineering of higher domain densities.

Effect of grain size and grain boundary on the energy storage performance of polycrystalline ferroelectrics

Dielectric capacitors based on polycrystalline ferroelectrics have attracted much attention due to their significant power density and fast charge–discharge speed. The energy storage performance of polycrystalline ferroelectrics is highly dependent on the grain size and grain boundary. Here, the effect of grain size and grain boundary on the domain structures and polarization–electric field (P–E) hysteresis loops of polycrystalline ferroelectrics are investigated by using a phase-field model based on the time dependent Ginzburg–Landau (TDGL) equation. It is found that the depolarization field in the grain boundary induces the vortex domain when the grain size is reduced or the grain boundary thickness increases in certain extent, resulting in slender P–E loops, which contributes to an improvement in the energy storage efficiency and density. However, as the grain size further decreases or the grain boundary thickness further increases, the energy storage density decreases, which is attributed to the concurrent reduction in both the remnant and saturation polarizations. This study provides a considerable insight for optimizing the energy storage performance by carefully adjusting the grain size and grain boundary thickness in polycrystalline ferroelectrics.

Vortex Domain Wall Thermal Pinning and Depinning in a Constricted Magnetic Nanowire for Storage Memory Nanodevices.

In this study, we investigate the thermal pinning and depinning behaviors of vortex domain walls (VDWs) in constricted magnetic nanowires, with a focus on potential applications in storage memory nanodevices. Using micromagnetic simulations and spin transfer torque, we examine the impacts of device temperature on VDW transformation into a transverse domain wall (TDW), mobility, and thermal strength pinning at the constricted area. We explore how thermal fluctuations influence the stability and mobility of domain walls within stepped nanowires. The thermal structural stability of VDWs and their pinning were investigated considering the effects of the stepped area depth (d) and its length (λ). Our findings indicate that the thermal stability of VDWs in magnetic stepped nanowires increases with decreasing the depth of the stepped area (d) and increasing nanowire thickness (th). For th ≥ 50 nm, the stability is maintained at temperatures ≥ 1200 K. In the stepped area, VDW thermal pinning strength increases with increasing d and decreasing λ. For values of d ≥ 100 nm, VDWs depin from the stepped area at temperatures ≥ 1000 K. Our results reveal that thermal effects significantly influence the pinning strength at constricted sites, impacting the overall performance and reliability of magnetic memory devices. These insights are crucial for optimizing the design and functionality of next-generation nanodevices. The stepped design offers numerous advantages, including simple fabrication using a single electron beam lithography exposure step on the resist. Additionally, adjusting λ and d allows for precise control over the pinning strength by modifying the dimensions of the stepped areas.

The effect of diameter on hysteresis loop squareness in iron nanowires array by micromagnetic simulation

Utilization of micromagnetic simulation is a very attractive subject to understand the magnetic behavior of nanowire arrays that tune their geometrical features and magnetic properties. Here, the micromagnetic simulations utilize to investigation of the single, and a 3 × 3 array of iron nanowires with diameters from 30 to 60 nm. The diameter size and the distance between the wires are selected according to the fabrication of iron nanowires grown in alumina templates. The simulation indicated that an increase in diameter led to a decrease in the coercive field and squareness ratio in both single nanowires and nanowire arrays. Besides, the simulation discloses that the magnetization reversal process of the nanowires with diameters more than 42 nm occurs through the nucleation and propagation of vortex domain walls. In the nanowires array, an increase in wire diameter increases the number of jumps in the hysteresis loop, indicating a more magnetic interaction between the nanowires.

Electric Field-Manipulated Optical Chirality in Ferroelectric Vortex Domains.

Manipulating optical chirality via electric fields has garnered considerable attention in the realm of both fundamental physics and practical applications. Chiral ferroelectrics, characterized by their inherent optical chirality and switchable spontaneous polarization, are emerging as a promising platform for electronic-photonic integrated circuits applications. Unlike organics with chiral carbon centers, integrating chirality into technologically mature inorganic ferroelectrics has posed a long-standing challenge. Here, the successful introduction of chirality is reported into self-assembly La-doped BiFeO3 nanoislands, which exhibit ferroelectric vortex domains. By employing synergistic experimental techniques with piezoresponse force microscopy and nonlinear optical second-harmonic generation probes, a clear correlation between chirality and polarization configuration within these ferroelectric nanoislands is established. Furthermore, the deterministic control of ferroelectric vortex domains and chirality is demonstrated by applying electric fields, enabling reversible and nonvolatile generation and elimination of optically chiral signals. These findings significantly expand the repertoire of field-controllable chiral systems and lay the groundwork for the development of innovative ferroelectric optoelectronic devices.

Electric properties of the twelve-fold vortex structure in hexagonal manganites

Hexagonal manganites, as a functional ferroelectric (FE) material, receive considerable attention due to their improper ferroelectricity and topological vortex structures. This family exhibits three low-symmetry states accompanied by distinct vortex domain structures. In addition to the FE P63 cm and anti-FE (AFE) P-3c1 states accompanied by dual six-fold vortex structures, there is another FE P3c1 state accompanied by a twelve-fold vortex structure. The responses of FE materials to external stimuli, such as external electric fields, are the core ingredients in the physics of FEs and are significant for technological applications. Under external electric fields, the responses of FE materials are determined by special FE domain structures. The electric properties of the FE P63 cm and AFE P-3c1 states are very different. However, the electric properties of the FE P3c1 state, which only stabilizes in Ga-substituted In(Mn, Ga)O3, are unclear. The present work studies the electric properties of the FE P3c1 state. The electric-field-driven transition of the FE P3c1 state is found to follow two sequences, i.e. (1) twelve-fold P3c1 → nine-fold P3c1 + P63 cm → three-fold P63 cm, and (2) twelve-fold P3c1 → six-fold P3c1 → three-fold P63 cm. The variation of average polarization with E for the FE P3c1 state with the second transition sequence manifests as an unusual triple-hysteresis loop, different from the usual single-hysteresis loop of FE materials. The results are related to the coexistence of the FE and non-FE domain walls in the FE P3c1 state. Furthermore, it is found that the FE P3c1 state at substitution concentration 0.39 exhibits the highest dielectric response. The results advance our understanding of topological vortex structures in hexagonal manganites.

Topological domain characteristics during the transition from ferroelectric to antiferroelectric in hexagonal manganites

Hexagonal manganites can exhibit the low-symmetry ferroelectric (FE) P63cm and partially undistorted anti-ferroelectric (PUA) P-3c1 states. The two states are accompanied by distinct sixfold vortex domain structures. The transition from the FE P63cm and PUA P-3c1 states (FE-PUA transition) is an effective means to control domain structures with distinct FE properties, which is of rich physical properties and potential applications. The FE-PUA transition can only be achieved by doping Ga on the Mn site of InMnO3, but the actual transition path and the associated domain structure evolution are still unclear. Namely, whether this transition goes through an intermediate P3c1 state remains an issue. In this work, we start from the Landau phenomenological theory to investigate the FE-PUA transition by directly tracking the domain structure evolution. The emerging 12-fold vortex domain structure at the intermediate stage of this transition indicates that this transition is not direct, and its actual path follows the P63cm → P3c1 → P-3c1 sequence, demonstrating the essential role of the intermediate P3c1 state. Besides, a pinning effect as a by-product is also discussed. This work comprehensively illustrates the characteristics of domain structure evolution during the FE-PUA transition, refining our understanding of the whole phase transition and topological physics associated with vortex domain structures in hexagonal manganites.

A phase-field simulation of easily switchable vortex structure for multilevel low-power ferroelectric memory

Ferroelectric materials with multi-directional polarization orders can form a variety of special domain structures, which have a wide range of applications. In this work, lead-free potassium sodium niobate ferroelectric thin films were simulated by solving the Time-Dependent-Landau-Ginzburg (TDLG) equation. Based on vortex topological structure characteristic of perovskite-type ferroelectric, domain types are simplified from 26 to 9 through virtual polarization vectors. By temperature selection, we accomplished a large easily switchable vortex structure with 20% side length. Based on this, as low as 0.04V/nm electric-field pulse was applied to explore vortex domain structures change. Under different low external electric-field pulses, conductance states change in vortex have been calculated and discussed systematically. Free energy computation results reveal that the domain wall (DW) conductance states primarily originate from the competition between electrostatic energy, gradient energy, and elastic energy. Finally, we propose the multilevel data ferroelectric memory through easily switchable vortex topological structures for the first time. Under electric-field pulses, diverse storage states were presented through 0/1 measurement of 8 positions. By achieving an easy-to-distinguish and robust-to-switch data map at the vortex structure, this work might provide a significant idea of vortex structure on low-power ferroelectric memory applications.

Simulation of two-dimensional flow around an elliptical cylinder at high Reynolds numbers

The modified viscous vortex domains method is used for direct numerical simulation of two-dimensional flow around an elliptical cylinder at the Reynolds number up to Re = 106. The modified method is based on the use of a conformal mapping from the outer region of an ellipse to the outer region of a circle. Transformed Navier–Stokes equations under an arbitrary conformal mapping are derived. These equations are solved in the mapped plane. An efficient algorithm for calculating boundary elements, previously developed to calculate the flow around a circular cylinder, is applied. The application of this algorithm makes it possible to reduce the calculation time by orders of magnitude and significantly expands the possibilities of flow simulation at high values of the Reynolds number. The method developed in this work can be implemented in other vortex methods.

Magnetization reversal and domain wall pinning in nanowires with nonlinear modulation of diameter

Micromagnetic simulation of magnetization reversal is studied on cylindrical tapered nanowire with radii 50nm and 10nm at wider and narrower end respectively. The radius decreases from wider end to the narrower end non-linearly as R-βzδ where δ is the degree of non-linearity. Value of δ is either an integer (n) or reciprocal of integer (1/n). At remanence, a vortex and flower state at the wider and narrower extremes respectively are exhibited combined with ferromagnetic ordering in the majority of volume. When δ is below 1/2, pinning and depinning of domain wall drives the hysteresis following a Modified Kondorsky model. Otherwise, the magnetization reversal proceeds with nucleation and propagation of vortex domain wall according to Kondorsky model. The propagation of domain wall is dependent upon the value of δ which suggests tunability of magnetic characteristics with modulation of diameter. For instance, large values of coercivity is observed for wires that have strong domain wall pinning which is considerably reduced when depinning and propagation of domain wall takes over. A large range (20kA/m to 130kA/m) of coercivity can be obtained by changing the modulation.

Topological Vortex Domain Engineering for High Dielectric Energy Storage Performance

AbstractEnhancing the energy storage performance of dielectric material through the adoption of a novel domain strategy is highly desirable. In this study, Bi0.5Na0.5TiO3‐based thin films are fabricated with topological vortex domains (VDs) by controlling the grain size and investigated the correlation between these VDs and the macroscopic polarization response, which is crucial for the energy storage performance. The emergence of VDs, in contrast to conventional ferroelectric domains, promotes polarization reversal in dielectric materials. Additionally, in contrast to the severely reduced saturation polarization typically noted in conventional relaxor ferroelectrics (RFE), the presence of VDs in RFE leads to only a slight reduction in saturation polarization. These two advantages contribute to the superior energy storage performance of the films with VDs. This approach offers a novel and promising direction for developing dielectrics with high‐energy storage capabilities.

Effect of Aspect Ratio of Ferroelectric Nanofilms on Polarization Vortex Stability under Uniaxial Tension or Compression.

Mastering the variations in the stability of a polarization vortex is fundamental for the development of ferroelectric devices based on polarization vortex domain structures. Some phase field simulations were conducted on PbTiO3 nanofilms with an initial polarization vortex under uniaxial tension or compression to investigate the conditions of vortex instability and the effects of aspect ratio of nanofilms and temperature on them. The instability of a polarization vortex is strongly dependent on aspect ratio and temperature. The critical compressive stress increases with decreasing aspect ratio under the action of compressive stress. However, the critical tensile stress first decreases and then increases with decreasing aspect ratio, then continues to decrease. There are two inflection points in the curve. In addition, an elevated temperature makes both the critical tensile and compressive stresses decline, and will also cause the aspect ratio corresponding to the inflection point to decrease. These are very important for the design of promising nano-ferroelectric devices based on polarization vortices to improve their performance while maintaining storage density.

Manipulation of BiFeO3 nanostructure by substrate terrace morphology

Topological domain structures, such as vortex and center domain have been found in BiFeO3 nanoislands fabricated by self-assemble approaches, which exhibit great application potential in nonvolatile storage. However, how to control the self-assembled nanostructure during preparation process is still an open question. Here, we successfully grew BiFeO3 films with nano-stripe, nano-maze and dense nanoisland structures on LaAlO3 (001) substrate by pulsed laser deposition. We found the formation of different nanostructures is related to the terrace morphology of the substrate. Nano-stripe structure with strip domain and high conduction tail-to-tail domain wall preferred to form on wide terrace, nano-maze structure with three-fold or four-fold center-type domain usually form on bunched terrace, while dense nanoisland structure with two/three-fold domain preferred to from on the narrow or rough terrace LaAlO3 substrate. These findings provide guidance for manipulating the ferroelectric topological domain structure during film preparation process.

Angular first-order reversal curve analysis of FeNi/Cu multilayered nanowire arrays with different diameters

The main goal of the emerging field of spintronics is the shrinkage of materials and devices while improving their magnetic performance for a variety of applications, especially three-dimensional information storage. This stipulates the understanding of fundamental magnetic mechanisms such as magnetization reversal and switching events in multilayer systems with tunable size. Here, a porous anodic alumina membrane-assisted electrochemical deposition method is employed to fabricate FeNi/Cu multilayered nanowire arrays (MNWAs) with diameters in the range of D = 35–80 nm. Angular magnetic properties of these MNWAs are investigated via hysteresis loop and first-order reversal curve (FORC) measurements for angle fields of 0° ≤ θ ≤ 90°. While the former indicates the existence of different contributions of vortex domain wall propagation for smaller (D ≤50 nm) and larger (D >50 nm) diameters, the latter reveals the occurrence of single vortex states, depending on θ and D. Moreover, at θ = 0°, a transition from single domain to multidomain-like behavior appears to occur with increasing D from 35 to 80 nm based on FORC diagrams, significantly influencing magnetization reversibility of magnetic FeNi segments with relatively high aspect ratios (>5). The variation of magnetostatic interactions with respect to θ is discussed and compared at each diameter as an effective factor in determining angular magnetic properties. Also, the axial variation behavior of coercivity as a function of D is correlated with changes in the reversible percentage, shedding light on the expectations from the vortex domain wall propagation.

Non-Fickian solute transport in three-dimensional crossed shear rock fractures at different contact ratios

Solute transport in fractured rocks plays a crucial role in many subsurface processes, such as geothermal resource extraction and carbon capture and storage. This study conducted simulations of non-Fickian solute transport at varying contact ratios and voids in crossed shear fractures. Results indicated that increasing the contact ratio of the crossed fractures intensified the “tailing” phenomenon of non-Fickian solute transport, and has a negative relationship with the solute outflow concentration. Additionally, the anisotropy of intersections and the variations in their void structure both influence the redistribution and mixing of fluid and solute, therefore, we propose a method to determine the solute mixing patterns at the intersection. Ultimately, while the volume and magnitude of the separated vortex domain in the flow field can influence the non-Fickian solute transport, the “tailing” phenomenon is more significantly affected by its magnitude.

Phase-field simulations of topological conservation in multi-vortex induced by surface charge in BiFeO3 thin films

The creations and manipulations of vortexes in ferroelectric materials with external stimuli are expected to be used in the design and fabrication of sensing materials and multifunctional electronic devices. In this work, we investigated the surface charge-induced multi-vortex evolution using the phase-field simulations in BiFeO3. A combination of domain morphology, polarization distribution and winding number calculation was considered. The results show that vortex and anti-vortex exist simultaneously in pairs, and the total value of winding numbers is always 0. In addition, the minimum distance [Formula: see text] between the surface charge regions is 9[Formula: see text]nm when the vortex domains are independent of each other. This work provides a reference for the manipulation of ferroelectric vortex induced by surface charges, which lays a theoretical foundation for the design and fabrication of high-density vortex memories.

Phase field study on the flexoelectric response of dielectric–ferroelectric multilayers

We report a theoretical modeling of the flexoelectric response of dielectric–ferroelectric (DE–FE) multilayers based on phase field simulations in the framework of the Landau–Ginzburg–Devonshire (LGD) theory. The correlation between negative capacitance and flexoelectric response is revealed, and the single-domain and multi-domain models are compared. It shows that the dielectric layers drive the ferroelectric layer into a negative capacitance regime, and the flexoelectric response of the multilayer is maximal when the negative capacitance of the ferroelectric layer has a minimal absolute value. Moreover, the flexoelectric response peak will be shifted to a lower temperature by increasing the thickness of dielectric layer, indicating a possibility of achieving a stronger flexoelectric response at room temperature compared with that of pure ferroelectric. However, while the single-domain model shows that the flexoelectric response peak is simply shifted to a lower temperature with near constant peak value and width, the multi-domain model reveals a significant suppressing of the flexoelectric peak by the dielectric layer. This is attributed to the formation of the vortex domain state, which eases the depolarization effect and leads to large absolute value of negative capacitance of the ferroelectric layer. Our work provides new insights into flexoelectricity in ferroelectric heterostructures.

Confined magnetic vortex motion from metal-organic frameworks derived Ni@C microspheres boosts electromagnetic wave energy dissipation

Magnetic domain structure plays an important role in regulating the electromagnetic properties, which dominates the magnetic response behaviors. Herein, unique magnetic vortex domain is firstly obtained in the Ni nanoparticles (NPs) reduced from the Ni-based metal-organic frameworks (MOFs) precursor. Due to both the high symmetry spheres and boundary restriction of graphited carbon shell, confined magnetic vortex structure is generated in the nanoscale Ni core during the annealing process. Meanwhile, MOFs-derived [email protected] assembly powders construct special magnetic flux distribution and electron migration routes. MOFs-derived [email protected] microspheres exhibit outstanding electromagnetic (EM) wave absorption performance. The minimum reflection loss value of [email protected]–V microspheres with vortex domain can reach −54.6 ​dB at only 2.5 ​mm thickness, and the efficient absorption bandwidth up to 5.0 ​GHz at only 2.0 ​mm. Significantly, configuration evolution of magnetic vortex driven by the orientation and reversion of polarity core boosts EM wave energy dissipation. Magnetic coupling effect among neighboring [email protected] microspheres significantly enhances the magnetic reaction intensity. Graphitized carbon matrix and heterojunction Ni–C interfaces further offer the conduction loss and interfacial polarization. As result, MOFs-derived [email protected]–V powders display unique magnetic vortex, electronic migration network, and high-performance EM wave energy dissipation.

Dynamics and Reversible Control of the Bloch-Point Vortex Domain Wall in Short Cylindrical Magnetic Nanowires

Fast and efficient switching of nanomagnets is one of the main challenges in the development of future magnetic memories. We numerically investigate the evolution of static and dynamic spin-wave (SW) magnetization in short (50--400 nm in length and 120 nm in diameter) cylindrical ferromagnetic nanowires, where competing magnetization configurations of a single vortex (SV) and a Bloch-point vortex domain wall (BP-DW) can be formed. For a limited nanowire length range (between 150 and 300 nm), we demonstrate reversible transitions induced by a microwave field (forwards) and by opposite spin currents (backwards) between topologically different SV and BP-DW states. By tuning the nanowire length, the excitation frequency, the microwave pulse duration, and the spin-current value, we show that the optimum (low-power) manipulation of the BP-DW can be achieved with a microwave excitation tuned to the main SW mode for nanowire lengths around 230--250 nm, where single-vortex domain-wall magnetization reversal via nucleation and propagation of a SV-DW transition takes place. An analytical model of the dynamics of the Bloch point provides an estimate of the gyrotropic mode frequency close to that obtained via micromagnetic simulations. A practical implementation of the method in a device is proposed, involving microwave excitation and the generation of opposite spin currents via the spin-orbit torque. Our findings open up an alternative pathway for the creation of topological magnetic memories.