Vortex Domain Research Articles

Mesoscale magnetic rings: Complex magnetization reversal uncovered by FORC

In this work, we investigate mesoscopic amorphous magnetic rings prepared by ion-implantation. The analysis is carried out combining conventional magnetization vs field measurements alongside MOKE microscopy imaging and, for the first time, first-order reversal curves (FORCs). With the information extracted from the FORC diagram, we can identify the presence of typical onion and vortex magnetic configurations, and also determine with high resolution the fields connected to their formation, stability, and annihilation. Furthermore, depending on the field and history, two different onion configurations exist, characterized by the presence of transverse or vortex domain walls. The FORC data reveal the different reversible/irreversible nature of the annihilation of the two onion configurations, and a signal peculiar of the presence of vortex domain walls. All these crucial information are not accessible with conventional M(H) loops, demonstrating that FORCs offer a unique perspective for the investigation of the physical phenomena of magnetic elements with complex geometries.

Hexagonal rare-earth manganites and ferrites: a review of improper ferroelectricity, magnetoelectric coupling, and unusual domain walls.

Hexagonal rare-earth manganites and ferrites are well-known improper ferroelectrics with low-temperature antiferromagnetism/weak ferromagnetism. In recent decades, new multi-functional device concepts and applications have provoked the exploration for multiferroics which simultaneously possess ferroelectric and magnetic orders. As a promising platform for multiferroicity, hexagonal manganites and ferrites are attracting great research interest among the fundamental scientific and technological communities. Moreover, the novel type of vortex-like ferroelectric domain walls are locked to the antiphase structural domain walls, providing an extra degree of freedom to tune the magnetoelectric coupling and other properties such as conductance. Here, we summarize the main experimental achievements and up-to-date theoretical understanding of the ferroelectric, magnetic, and magnetoelectric properties, as well as the intriguing domain patterns in hexagonal rare-earth manganites and ferrites. Recent work on non-stoichiometric compounds will also be briefly introduced.

Вклад силы присоединенных масс в формирование пропульсивной силы машущего профиля в вязкой жидкости

In the light of the recently proved general theorem on the added mass of bodies in a viscous incompressible fluid, the mechanism of the formation of the propulsive force of the flapping airfoil, which performs harmonic angular oscillations in the flow of a continuous medium, is investigated. The flow is described by the Navier-Stokes equations. The calculations were performed by a meshless numerical method of viscous vortex domains. The mechanism of the formation of a reversed vortex track in the wake behind the flapping profile in the positive traction mode is explained. The dominant contribution of the force of the added masses to the value of the propulsive force is revealed. The results obtained to some extent reveal the hydrodynamic mechanism of action of the caudal fin of underwater creatures.

Three-dimensional polarization vortex configuration evolution in compressed BaTiO3/SrTiO3 superlattice

The molecular dynamics method based on the shell model was used to investigate the polarization configuration evolution in a ferroelectric superlattice under a compressive strain that increases at a constant rate. The polarization curl was used to render the polarization configurations. The evolution of vortex domains in location, shape, and size as well as their relative movement and annihilation was observed in three dimensions. It was found that two clockwise-anticlockwise vortex arrays occur in different material layers simultaneously at a compressive strain of −0.05%. With increasing compressive strain, the vortexes continually change their locations, shapes, and sizes and possibly walk across the bimaterial interface. Their lengths could be shortened through being split in the middle or partially annihilating from both ends. Different from the single material case, there are three ways for polarization vortex annihilation to occur in ferroelectric superlattice structures. Vortexes neighboring the material interface or boundaries are inclined to annihilate first, and then the others inside the material annihilate by combining with their neighboring antivortexes. These observations are very helpful for extending applications of ferroelectric superlattices.

Crystal structure and magnetic properties of wafer-size Co nanostrip arrays self-organized on a step-bunched surface of Si(111)-5.55 × 5.55-Cu/(Cu, Cu2Si, W-O) buffers

Structure and magnetization reversal of Co nanostrips self-organized on a Si(111)-5.55 × 5.55-Cu step-bunched surface covered by Cu, Cu2Si and W-O buffer layers are systematically investigated and characterized in details. Optimal conditions for growth of well-ordered arrays of mm-long straight nanostrips with hexagonal close-packed and face-centered cubic crystal phases are defined. We find that the Co nanostrips with epitaxial and multiepitaxial structure grows on monocrystalline buffer layers of Cu and Cu2Si, respectively. The amorphous W-O buffer promotes the growth of polycrystalline Co nanostrips. We reveal the origin and compute the magnitude of magnetic anisotropy in Co nanostrips with different crystal phases. Structure-dependent magnetization reversal modes of nanostrip arrays are determined analytically using angular dependences of the coercive force. Our analysis of distributions of the switching and interaction fields by the first-order reversal curve diagram method specifies contributions of global and local interaction fields. Micromagnetic simulations considering the magnetostatic interaction between nanostrips demonstrate the crystal structure-dependent magnetization reversal mechanisms based on propagation of domain walls, whose type (symmetric or asymmetric transverse domain wall, vortex domain wall) and velocity are determined by the magnetic parameters, interaction fields and driving magnetic fields.

Microstructures and magnetic properties of Co-substituted Ce–Fe–B amorphous alloys

Compare with Ce–Fe–B crystalline magnets, the amorphous alloy exhibit interesting properties due to their domains, low anisotropy energy, and microstructure contribution. In order to investigate magnetic properties and microstructures of the amorphous Ce–Fe–B system with Co substituting for Fe, the ribbons with a nominal composition of Ce13.5(Fe79.5-xCox)B7 (x = 0, 3, 6, 9, 12) were prepared using vacuum melt spinner at a wheel speed of 50 m/s. The XRD and the corresponding SAED Pattern indicate the uniform amorphous microstructure is well maintained in each sample. These ribbons are magnetically soft and undergo a second order phase transition from ferromagnetic to paramagnetic state. With the increasing Co content, the Curie temperature almost linearly increases with temperature during 270 K and 410 K. Results from Lorentz Transmission Electron Microscopy (L-TEM) and micromagnetic simulation prove that the vortex domains can form spontaneously and stability in Ce–Fe–B amorphous materials no matter doping Co or not. The nontrivial topological domain structures found in experiments and numerical calculations have potential applications in the field of information storage, which is helpful to develop new applications of high abundance rare earth elements in functional materials.

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.

Characterization and control of vortex and antivortex domain defects in quadrilateral ferroelectric nanodots

Ferroelectric nanostructures have recently attracted considerable research interests for the discovery of novel topological dipole states. However, currently the preparation of high-quality nanodot arrays remains challenging, precluding the clear characterization of the dipole states in the nanodots. Combining pulsed laser deposition method with circular anodic aluminum oxide template, we reported an unexpected growth of high crystalline quality $\mathrm{PbZ}{\mathrm{r}}_{0.52}\mathrm{T}{\mathrm{i}}_{0.48}{\mathrm{O}}_{3}$ nanodot array in quadrilateral shape with size being \ensuremath{\sim}80 nm. Piezoresponse force microscopy measurement on various regions of the sample shows that the nanodots form rather diverse in-plane domain patterns, with the appearance of abundant topological domain defects including flux-closure vortices, center-divergent vortices, center-convergent vortices, and antivortices. A deterministic control of the domain structure of the nanodots via applying an electric field is further achieved. The nanodots were found to favor a center-divergent vortex pattern under negative tip bias, although the domain patterns of the nanodots at the as-grown state are different. Phase field simulations were performed to reproduce the experimental observation, and our results indicate that the screening condition of the nanodots is far from the ideal ones assumed in previous theoretical modellings. The nanodots are potentially useful in developing multi-state and reconfigurable electronic devices.

Strain-mediated electric manipulation of magnetic skyrmion and other topological states in geometric confined nanodiscs

Magnetic skyrmions in multilayer stack structures are promising magnetic memory bits for applications in race-track storage devices or random-access memories. For practical implementation in energy efficient memory devices, it is essential to achieve a deterministic switch of skyrmion states, e.g. nucleation and elimination, triggered by electric fields. In this work, by means of micromagnetic simulation, we demonstrate the strain-mediated electric field driven switching of magnetic skyrmion and other topological states without the presence of a magnetic field in a proposed device consisting of nanodiscs of trilayer Pt/Co/Ta stacks on a piezoelectric substrate. It is revealed that the multiple magnetic state switching behaviors, including the nucleation and elimination of skyrmion or labyrinth stripe domain states, as well as topological transitions between skyrmion, vortex, skyrmionium and vertical single domain states, can be triggered by applying an external electric field mediated by strains. The corresponding critical strains and their dependence on the geometric parameters of the nanodiscs (e.g. size and number of stacks) for triggering such magnetic switching are also explored. The stability of these topological domain states and possible switching behaviors (e.g. volatile and non-volatile) between the different states are discussed as well. The capability for controlled switching of these topological states provides a new pathway to energy efficient high-density magnetoelectric memory and logic devices.

Wave reversal mode: A new magnetization reversal mechanism in magnetic nanotubes

We have investigated the magnetic properties of 14 nm thick and 1 μm long nickel and permalloy nanotubes with external diameters of 40 and 100 nm as a function of the angle θ at which the external magnetic field is applied. Our results show that the coercivity of 40 nm diameter nickel nanotubes follows a non-monotonic behavior from θ = 0° up to θ = 60°, while that corresponding to permalloy displays an increasing monotonic trend at the same angular range. At θ = 90°, both materials evidence a sharp drop of the coercivity to zero, indicating that the reversal mechanism has changed to a pseudo-coherent rotation. On the other hand, nickel and permalloy nanotubes with 100 nm in diameter exhibit a similar angular dependence of the coercivity, reversing their magnetization through the nucleation and propagation of vortex domain walls for angles lower than 75°. For θ = 90°, a novel striking mechanism, the wave reversal mode (W), arises. This phenomenon leads to an unusual S-type shape in the hysteresis curves at those given parameters, which is until now an effect that has not been reported for these nanostructures.

Flow-induced oscillations of circular cylinder in a narrow channel

The problem of transverse auto-oscillations of a cylinder in a flow of a viscous incompressible fluid in a plane channel is considered. The fluid-structure interaction problem is solved in a complete conjugate formulation, in which a continuous medium and a moving rigid body are described as a general dynamical system without splitting into dynamic and hydrodynamic components. The mesh-free method is the most suitable for solving this problem, since the flow region changes not only the form but also the connectivity at the time when the body touches the wall. Another difficulty is connected with the need to construct an adequate model of elastic collisions of bodies in a liquid. Calculations are performed using the fully Lagrangian method of viscous vortex domains (VVD). A model has been developed for the elastic collision of a body with a fixed wall taking into account the influence of a liquid. The mechanism of self-oscillations is revealed. It is shown that the restitution coefficient characterizing the elastic interaction of colliding bodies is an important parameter of the problem under consideration.

Polyacrylamide Ferrogels with Ni Nanowires.

Nickel magnetic nanowires (NWs) have attracted significant attention due to their unique properties, which are useful for basic studies and technological applications, for example in biomedicine. Their structure and magnetic properties were systematically studied in the recent years. In this work, Ni NWs with high aspect ratios (length/diameter ~250) were fabricated by electrodeposition into commercial anodic aluminum oxide templates. The templates were then etched and the NWs were suspended in water, where their hydrodynamic size was evaluated by dynamic light scattering. The magnetic response of these NWs as a function of an external magnetic field indicates a dominant shape anisotropy with propagation of the vortex domain wall as the main magnetization reversal process. The suspension of Ni NWs was used in the synthesis of two types of polyacrylamide ferrogels (FGs) by free radical polymerization, with weight fractions of Ni NWs in FGs of 0.036% and 0.169%. The FGs were reasonably homogeneous. The magnetic response of these FGs (hysteresis loops) indicated that the NWs are randomly oriented inside the FG, and their magnetic response remains stable after embedding.

Bistability of magnetic states in Fe-Pd nanocap arrays

Magnetic bistability between vortex and single domain states in nanostructures are of great interest from both fundamental and technological perspectives. In soft magnetic nanostructures, the transition from a uniform collinear magnetic state to a vortex state (or vice versa) induced by a magnetic field involves an energy barrier. If the thermal energy is large enough for overcoming this energy barrier, magnetic bistability with a hysteresis-free switching occurs between the two magnetic states. In this work, we tune this energy barrier by tailoring the composition of FePd alloys, which were deposited onto self-assembled particle arrays forming magnetic vortex structures on top of the particles. The bifurcation temperature, where a hysteresis-free transition occurs, was extracted from the temperature dependence of the annihilation and nucleation field which increases almost linearly with Fe content of the magnetic alloy. This study provides insights into the magnetization reversal process associated with magnetic bistability, which allows adjusting the bifurcation temperature range by the material properties of the nanosystem.

Single-phase multiferroics: new materials, phenomena, and physics.

Multiferroics, where multiple ferroic orders coexist and are intimately coupled, promise novel applications in conceptually new devices on one hand, and on the other hand provide fascinating physics that is distinctly different from the physics of high-TC superconductors and colossal magnetoresistance manganites. In this mini-review, we highlight the recent progress of single-phase multiferroics in the exploration of new materials, efficient roadmaps for functionality enhancement, new phenomena beyond magnetoelectric coupling, and underlying novel physics. In the meantime, a slightly more detailed description is given of several multiferroics with ferrimagnetic orders and double-layered perovskite structure and also of recently emerging 2D multiferroics. Some emergent phenomena such as topological vortex domain structure, non-reciprocal response, and hybrid mechanisms for multiferroicity engineering and magnetoelectric coupling in various types of multiferroics will be briefly reviewed.

Strain anisotropy and magnetic domain structures in multiferroic heterostructures: High-throughput finite-element and phase-field studies

Understanding magnetic domain structures and their responses to electric fields in multiferroic heterostructures is critical to the design of electric-field-driven spintronic devices. High-throughput finite-element and phase-field simulations are performed to probe the piezoelectric strain anisotropy and its relaxation, magnetic domain structures and their responses to applied voltages as function of the in-plane dimensions and thickness of the magnetic Ni nanoislands grown on a Pb(Mg1/3Nb2/3)O3–PbTiO3 (PMN-PT) membrane. The piezoelectric strain anisotropy is found to increase with the in-plane aspect ratio, but it can be significantly relaxed, as large as >80%, in nanoislands of thickness larger than >15 nm. Magnetic domain diagrams are established to identify the domain structures for Ni nanoislands of different lengths of in-plane major and minor axis, as well as thickness. When a voltage is applied to the multiferroic heterostructure, the single-domain magnetic domain can be switched by the piezoelectric strain, whereas the vortex domain is not switched. However, for a multiferroic heterostructure with a thick nanoisland wherein most of the piezoelectric strain is relaxed, the single-domain magnetic domain shows a weak response to the voltage and cannot be switched. The effect of thickness variation in real magnets on the switching is also discussed. The present results are expected to provide guidance to the understanding and design of multiferroic nanostructures for achieving electric-field-modulated magnetic properties.

On the Effect of Magnetostatic Interaction on the Collective Motion of Vortex Domain Walls in a Pair of Nanostripes

The periodic motion of interacting vortex domain walls in a pair of nanostripes has been analytically and numerically investigated. A model consisting of two parallel nanostripes with the domain magnetization structure has been proposed, where domains are separated by vortex walls. The magnetic subsystems of the stripes magnetostatically interact, which causes the existence of normal magnetic vortex motion modes in the latter. Frequencies of the collective magnetization modes have been calculated using empirical expressions for the magnetic energy of interaction between vortex walls. It is shown that not any combinations of the polarity and chirality lead to the resonance magnetization behavior in ac fields.

Strain Anisotropy and Magnetic Domain Structures in Multiferroic Heterostructures: High-Throughput Finite-Element and Phase-Field Studies

Understanding magnetic domain structures and their responses to electric fields in multiferroic heterostructures is critical to the design of electric-field-driven spintronic devices. High-throughput finite-element and phase-field simulations are performed to probe the piezoelectric strain anisotropy and its relaxation, magnetic domain structures and their responses to applied voltages as function of the in-plane dimensions and thickness of the magnetic Ni nanoislands grown on a Pb(Mg1/3Nb2/3)O3-PbTiO3 (PMN-PT) membrane. The piezoelectric strain anisotropy is found to increase with the in-plane aspect ratio, but it can be significantly relaxed, as large as >80%, in nanoislands of thickness larger than >15 nm. Magnetic domain diagrams are established to identify the domain structures for Ni nanoislands of different lengths of in-plane major and minor axis, as well as thickness. For Ni nanoislands with a circular in-plane geometry, an analytical function describing the relationship between the critical thickness hcritical and the in-plane diameter is obtained based on high-throughput calculations. When a voltage is applied to the multiferroic heterostructure, the single-domain magnetic domain can be switched by the piezoelectric strain, whereas the vortex domain is not switched. However, for a multiferroic heterostructure with a thick nanoisland wherein most of the piezoelectric strain is relaxed, the single-domain magnetic domain shows a weak response to the voltage and cannot be switched by the voltage. The present results are expected to provide guidance to the understanding and design of multiferroic nanostructures for achieving electric-field-modulated magnetic properties.

Direct Observation of Vortex and Meissner Domains in a Ferromagnetic Superconductor EuFe2(As0.79P0.21)2 Single Crystal

A spontaneous vortex structure in magnetic domains (vortex domains) has been visualized by the decoration technique near the ferromagnetic transition temperature (TC = 18 K) in a ferromagnetic superconductor EuFe2(As0.79P0.21)2 single crystal with the superconducting transition temperature (TSC = 22 K). Meissner domains previously observed by magnetic force microscopy have also been observed in a narrow temperature range (ΔT ∼ 1 K) near TC. A domain structure with the alternating direction of the magnetic flux has been observed upon cooling below TC. Experimental results are in reasonable agreement with a theoretical estimate of the periods of domain structures and the temperature interval below TC in which they are observed.

Domain wall depinning in Ni80Fe20/Pt bilayer nanostrips under the combined action of magnetic field and spin-orbit torque

Abstract We study the domain wall depinning from a triangle-shaped notch in Ni80Fe20/Pt bilayer nanostrips using electrical detection technique. It is found that for the 630 nm wide strip, the depinning fields are distributed in a narrow range. While for the 300 nm wide strip, the depinning fields are distributed in two distinctly separated ranges. Micromagnetic simulations show that for the 630 nm wide strip, the depinning corresponds to vortex domain wall, while for 300 nm wide strip, the depinnings of both the vortex wall and the transverse wall are observed. The chirality of vortex wall and the polarity of transverse wall have strong influence on the depinning field. Electrical current has a clear impact on the depinning, but its influence is different for different wall configuration. It can decrease or slightly increase the depinning field of the vortex domain wall depending on the wall chirality and the current direction. The depinning field of the transverse domain wall exhibits an oscillation variation with the current density. Compared to the depinning process of the domain wall in a control sample Ni80Fe20/Au, it can be inferred the current influence on the domain wall depinning is caused mainly by the current-induced spin-orbit torque.

Motion of Coupled Magnetic Vortices in Parallel Nanostripes

The periodic motion of the interacting vortex domain walls in a pair of nanostripes has been theoretically investigated. As a model, two parallel nanostripes with magnetization inhomogeneities in the form of magnetic vortices have been examined. The magnetic subsystems of the stripes are magnetostatically coupled. The quasi-elastic coupling between vortices ensures the existence of normal modes of the periodic magnetization motion. The frequencies of these modes have been calculated. It is shown that not any combination of the vortex topological charge leads to the resonant behavior of magnetization in ac fields. The effect of the static component of a magnetic field on the frequency of the periodic motion of vortex domain walls is discussed.