Vortex Annihilation Research Articles

Optical vortex trapping and annihilation by means of nonlinear Bessel beams in nonlinear absorbing media

In nonlinear Kerr media at intensities such that multiphoton absorption is significant, a vortex of topological charge m in the center of a high-order nonlinear Bessel beam (NBB) can be stable and subsist endlessly. We show that the m-charged NBB is not only stable but is formed spontaneously from any other n-charged NBB and N "foreign" vortices of total charge s randomly nested in the beam cross section if n + s = m. All nested vortices merge in the center of the original NBB, which undergoes a mode conversion to the NBB that preserves the topological charge and the inward-directed power current that sustains the diffraction-free and attenuation-free propagation in the medium with nonlinear absorption. We foresee different applications such as the creation of stable, multiply charged vortices without tight alignment requirements but by spontaneous vortex combination, mixing waves or particles that the vortices can guide, fast annihilation of vortex dipoles, and cleaning of speckled beams by massive annihilation of vortices.

The Vortex State in Geologic Materials: A Micromagnetic Perspective

AbstractA wide variety of Earth and planetary materials are very good recorders of paleomagnetic information. However, most magnetic grains in these materials are not in the stable single domain grain size range but are larger and in nonuniform vortex magnetization states. We provide a detailed account of vortex phenomena in geologic materials by simulating first‐order reversal curves (FORCs) via finite‐element micromagnetic modeling of magnetite nanoparticles with realistic morphologies. The particles have been reconstructed from focused ion beam nanotomography of magnetite‐bearing obsidian and accommodate single and multiple vortex structures. Single vortex (SV) grains have fingerprints with contributions to both the transient and transient‐free zones of FORC diagrams. A fundamental feature of the SV fingerprint is a central ridge, representing a distribution of negative saturation vortex annihilation fields. SV irreversible events at multiple field values along different FORC branches determine the asymmetry in the upper and lower lobes of generic bulk FORC diagrams of natural materials with grains predominantly in the vortex state. Multivortex (MV) FORC signatures are modeled here for the first time. MV grains contribute mostly to the transient‐free zone of a FORC diagram, averaging out to create a broad central peak. The intensity of the central peak is higher than that of the lobes, implying that MV particles are more abundant than SV particles in geologic materials with vortex state fingerprints. The abundance of MV particles, as well as their single domain‐like properties point to MV grains being the main natural remanent magnetization carriers in geologic materials.

Magnetic vortex effects on first-order reversal curve (FORC) diagrams for greigite dispersions

First-order reversal curve (FORC) diagrams are used increasingly in geophysics for magnetic domain state identification. The domain state of a magnetic particle is highly sensitive to particle size, about which FORC diagrams provide valuable information. However, the FORC signal of particles with nonuniform magnetisations, which are the main carrier of natural remanent magnetisations in many systems, is still poorly understood. In this study, the properties of non-interacting, randomly oriented dispersions of greigite (Fe3S4) in the uniform single-domain (SD) to non-uniform single-vortex (SV) size range are investigated via micromagnetic calculations. Signals for SD particles (<50nm) are found to be in excellent agreement with previous SD coherent-rotation studies. A transitional range from ∼50nm to ∼80nm is identified for which a mixture of SD and SV behaviour produces complex FORC diagrams. Particles >∼80nm have purely SV behaviour with the remanent state for all particles in the ensemble in the SV state. It is found that for SV ensembles the FORC diagram provides a map of vortex nucleation and annihilation fields and that the FORC distribution peak should not be interpreted as the coercivity of the sample, but as a vortex annihilation field on the path to saturation.

Diffusion of quantum vortices

We determine the evolution of a cluster of quantum vortices initially placed at the centre of a larger vortex-free region. We find that the cluster spreads out spatially. This spreading motion consists of two effects: the rapid evaporation of vortex dipoles from the cluster and the slow expansion of the cluster itself. The latter is akin to a diffusion process controlled by the quantum of circulation. Numerical simulations of the Gross-Pitaevskii equation show that this phenomenon is qualitatively unaffected by the presence of sound waves, vortex annihilations, and boundaries, and it should be possible to create it in the laboratory.

Interacting Multiscale Acoustic Vortices as Coherent Excitations in Dust Acoustic Wave Turbulence.

In this work, using three-dimensional intermittent dust acoustic wave turbulence in a dusty plasma as a platform and multidimensional empirical mode decomposition into different-scale modes in the 2+1D spatiotemporal space, we demonstrate the experimental observation of the interacting multiscale acoustic vortices, winding around wormlike amplitude hole filaments coinciding with defect filaments, as the basic coherent excitations for acoustic-type wave turbulence. For different decomposed modes, the self-similar rescaled stretched exponential lifetime histograms of amplitude hole filaments, and the self-similar power spectra of dust density fluctuations, indicate that similar dynamical rules are followed over a wide range of scales. In addition to the intermode acoustic vortex pair generation, propagation, or annihilation, the intra- and intermode interactions of acoustic vortices with the same or opposite helicity, their entanglement and synchronization, are found to be the key dynamical processes in acoustic wave turbulence, akin to the interacting multiscale vortices around wormlike cores observed in hydrodynamic turbulence.

Decay of homogeneous two-dimensional quantum turbulence

We numerically simulate the free decay of two-dimensional quantum turbulence in a large, homogeneous Bose-Einstein condensate. The large number of vortices, the uniformity of the density profile and the absence of boundaries (where vortices can drift out of the condensate) isolate the annihilation of vortex-antivortex pairs as the only mechanism which reduces the number of vortices, $\Nv$, during the turbulence decay. The results clearly reveal that vortex annihilation is a four-vortex process, confirming the decay law $\Nv \sim t^{-1/3}$ where $t$ is time, which was inferred from experiments with relatively few vortices in small harmonically trapped condensates.

Defect-mediated vortex multiplication and annihilation in ferroelectrics and the feasibility of vortex switching by stress

The possibility of switching the direction of the dipole toroidal moment in ferroelectrics provides exciting opportunities for development of novel nanoscale memory and logic devices. However, a practical control of vortex chirality is rather challenging at present stage, not to mention via mechanical methods. In this paper, we performed the phase-field simulations to show that mechanical switching of vortex chirality can be achieved in ferroelectric nanoplatelet via defect engineering. After introducing a void defect in the nanoplatelet, relative stability of single-vortex state and multi-vortices state is found to be altered. Importantly, during stress-induced vortex multiplication process, the void is a favored nucleation core of new vortex; meanwhile, vortices tend to annihilate away from the void during a vortex annihilation process. As the favored regions of vortex nucleation and annihilation are not the same, a deterministic mechanical switching of vortex chirality can be achieved. The effects of temperature, shape of the nanoplatelet, void size, as well as void position, on the defect-mediated vortex switching behaviors are systematically revealed. Our study demonstrates the feasibility of vortex switching by mechanical loads and provides a route to control and develop electromechanical devices based on ferroic vortices.

Interplay between bulk and edge-bound topological defects in a square micromagnet

A field-driven transformation of a domain pattern in a square micromagnet, defined in a thin film of La0.7Sr0.3MnO3, is discussed in terms of creation and annihilation of bulk vortices and edge-bound topological defects with half-integer winding numbers. The evolution of the domain pattern was mapped with soft x-ray photoemission electron microscopy and magnetic force microscopy. Micromagnetic modeling, permitting detailed analysis of the spin texture, accurately reproduces the measured domain state transformation. The simulations also helped stipulate the energy barriers associated with the creation and annihilation of the topological charges and thus to assess the stability of the domain states in this magnetic microstructure.

Observation of dynamical vortices after quenches in a system with topology

Phase transitions are a fundamental concept in science describing diverse phenomena ranging from, e.g., the freezing of water to Bose-Einstein condensation. While the concept is well-established in equilibrium, similarly fundamental concepts for systems far from equilibrium are just being explored, such as the recently introduced dynamical phase transition (DPT). Here we report on the first observation of a DPT in the dynamics of a fermionic many-body state after a quench between two lattice Hamiltonians. With time-resolved state tomography in a system of ultracold atoms in optical lattices, we obtain full access to the evolution of the wave function. We observe the appearance, movement, and annihilation of vortices in reciprocal space. We identify their number as a dynamical topological order parameter, which suddenly changes its value at the critical times of the DPT. Our observation of a DPT is an important step towards a more comprehensive understanding of non-equilibrium dynamics in general.

Quantum criticality in photorefractive optics: Vortices in laser beams and antiferromagnets

We study vortex patterns in a prototype nonlinear optical system: counterpropagating laser beams in a photorefractive crystal, with or without the background photonic lattice. The vortices are effectively planar and have two ``flavors'' because there are two opposite directions of beam propagation. In a certain parameter range, the vortices form stable equilibrium configurations which we study using the methods of statistical field theory and generalize the Berezinsky-Kosterlitz-Thouless transition of the $\mathit{XY}$ model to the ``two-flavor'' case. In addition to the familiar conductor and insulator phases, we also have the perfect conductor (vortex proliferation in both beams or ``flavors'') and the frustrated insulator (energy costs of vortex proliferation and vortex annihilation balance each other). In the presence of disorder in the background lattice, a phase appears which shows long-range correlations and absence of long-range order, thus being analogous to glasses. An important benefit of this approach is that qualitative behavior of patterns can be known without intensive numerical work over large areas of the parameter space. The observed phases are analogous to those in magnetic systems, and make (classical) photorefractive optics a fruitful testing ground for (quantum) condensed matter systems. As an example, we map our system to a doped $\text{O}(3)$ antiferromagnet with ${\mathbb{Z}}_{2}$ defects, which has the same structure of the phase diagram.

The Influence of Edge Inhomogeneities on Vortex Hysteresis Curves in Magnetic Tunnel Junctions

Magnetoresistive sensors using a tunnel magnetoresistance (TMR) spin valve structure with CoFe and CoFeB free layer (FL) are investigated. Lateral dimension, thickness, and magnetic properties of the circular-shaped FL energetically favor the nucleation of a magnetic vortex. In the vortex configuration, the sensors show the expected hysteresis-free transfer curve. Distinct differences between CoFe and CoFeB in the vortex typical parameters are observed. The experimental results are compared to micromagnetic simulations. Influence of saturation magnetization ${M}_{s}$ on the vortex transfer curve is studied in order to reproduce the experimental data. However, only by adjusting ${M}_{s}$ iteratively the experimental data cannot be fully reproduced: The vortex annihilation ( ${H}_{\mathrm {an}}$ ) in CoFeB occurs at smaller fields than simulated. On the other hand, the change in TMR signal at ${H}_{\mathrm {an}}$ is significantly smaller in the experiment for CoFe. Discrepancies are most pronounced at ${H}_{\mathrm {an}}$ . This investigation focuses on the magnetic and electric properties at the edge of the FL structure. Reduction in ${H}_{\mathrm {an}}$ can be explained for 1.1 $\mu \text{m}$ FL diameters by introducing a magnetically disturbed edge. Reduced change in TMR signal at ${H}_{\mathrm {an}}$ can be understood by introducing an electrically inactive edge area. The analysis shows that for CoFe and CoFeB different edge inhomogeneity effects are present or edge inhomogeneities have different impacts.

Shape induced magnetic vortex state in hexagonal ordered cofe nanodot arrays using ultrathin alumina shadow mask

The magnetization reversal process of hexagonal ordered CoFe nanodot arrays was investigated as a function of nanodot thickness (td) varying from 10 to 30 nm with fixed diameter. For this purpose, ordered CoFe nanodots with a diameter of 80 ± 4 nm were grown by sputtering using ultra-thin alumina mask. The vortex annihilation and the dynamic spin configuration in the ordered CoFe nanodots were analyzed by means of magnetic hysteresis loops in complement with the micromagnetic simulation studies. A highly pinched hysteresis loop observed at 20 nm thickness suggests the occurrence of vortex state in these nanodots. With increase in dot thickness from 10 to 30 nm, the estimated coercivity values tend to increase from 80 to 175 Oe, indicating irreversible change in the nucleation/annihilation field of vortex state. The measured magnetic properties were then corroborated with the change in the shape of the nanodots from disk to hemisphere through micromagnetic simulation.

Magnetic vortex nucleation/annihilation in artificial-ferrimagnet microdisks

The topological nature of the magnetic-vortex state gives rise to peculiar magnetization reversal observed in magnetic microdisks. Interestingly, magnetostatic and exchange, energies which, drive this reversal can be effectively controlled in artificial ferrimagnet heterostructures composed of rare-earth and transition metals. [Py(t)/Gd(t)]25 (t = 1 or 2 nm) superlattices demonstrate a pronounced change of the magnetization and exchange stiffness in a 10–300 K temperature range as well as very small magnetic anisotropy. Due to these properties, the magnetization of cylindrical microdisks composed of these artificial ferrimagnets can be transformed from the vortex to uniformly magnetized states in a permanent magnetic field by changing the temperature. We explored the behavior of magnetization in 1.5-μm [Py(t)/Gd(t)]25 (t = 1 or 2 nm) disks at different temperatures and magnetic fields and observed that due to the energy barrier separating vortex and uniformly magnetized states, the vortex nucleation and annihilation occur at different temperatures. This causes the temperature dependences of the magnetization in these Py/Gd disks to demonstrate a unique hysteretic behavior in a narrow temperature range. It was discovered that for the [Py(2 nm)/Gd(2 nm)]25 microdisks, the vortex can be metastable within a certain temperature range.

Directed motion of vortices and annihilation of vortex–antivortex pairs in finite-gap superconductors via hot-lattice routes

Using finite gap, time-dependent Ginzburg–Landau equations, generalized to include non-thermal phonons, we report numerical simulations of vortex nucleation, propagation, and annihilation in thin, finite strips of magnetic-impurity free, perfectly homogeneous superconductors. When a steady electric current passes through the strip with either surface defects or nonequilibrium phonon sources (e.g., local “hotspots”), periodic vortex generation and annihilation is observed even in the absence of external magnetic fields. Local pulses of electric field are produced upon annihilation. The injected phonon lines steer the vortices during their motion within the strip, potentially allowing control of the annihilation site.

Dynamic evolution of circular edge dislocations in free space and atmospheric turbulence.

Based on the extended Huygens-Fresnel principle, the analytical expressions for the cross-spectral density function of circular edge dislocation beams propagating through atmospheric turbulence and free space have been derived, and used to study the dynamic evolution of circular edge dislocations. It is shown that the number of circular edge dislocations on propagation equals that at the source plane when propagating through free space. The radius of circular edge dislocations increases with increasing propagation distance z. n-circular edge dislocations vanish and transform to n pairs of optical vortices with the opposite topological charge when propagating through atmospheric turbulence, and the position of each pair of optical vortices are symmetric about the slanted axis y = x. All the optical vortices will annihilate as soon as the propagation distance becomes large enough. The smaller radius of circular edge dislocation corresponds with the sooner annihilation of optical vortices. The structure constant affects the annihilation distance of the pairs of optical vortices, and the annihilation distance of the pairs of optical vortices will increase with the decrement of the structure constant.

Dynamic structure of active nematic shells.

When a thin film of active, nematic microtubules and kinesin motor clusters is confined on the surface of a vesicle, four +1/2 topological defects oscillate in a periodic manner between tetrahedral and planar arrangements. Here a theoretical description of nematics, coupled to the relevant hydrodynamic equations, is presented here to explain the dynamics of active nematic shells. In extensile microtubule systems, the defects repel each other due to elasticity, and their collective motion leads to closed trajectories along the edges of a cube. That motion is accompanied by oscillations of their velocities, and the emergence and annihilation of vortices. When the activity increases, the system enters a chaotic regime. In contrast, for contractile systems, which are representative of some bacterial suspensions, a hitherto unknown static structure is predicted, where pairs of defects attract each other and flows arise spontaneously.

Vortex behavior of the Oldroyd-B fluid in the 4-1 planar contraction simulated with the streamfunction–log-conformation formulation

In this paper, we present numerical solutions of the Oldroyd-B fluid flowing through a 4:1 planar contraction, for Weissenberg numbers (Wi) up to 20. The incompressible viscoelastic flows are simulated with the streamfunction–log-conformation methodology. The log-conformation representation guarantees by construction the positive-definiteness of the conformation tensor, which circumvents the appearance of the high Weissenberg number problem. In addition, the streamfunction flow formulation removes the pressure variable from the governing equations and automatically satisfies the mass conservation. Thus, the streamfunction–log-conformation reformulation is beneficial for the accuracy and stability of the numerical algorithm. The resulting governing equations are solved with a high-resolution finite-volume method.Our numerical results for the reattachment length and the intensity of the recirculation vortices produced at the contraction plane are in excellent agreement with the benchmark solutions, available in the literature for Weissenberg numbers up to 3. For highly elastic flows, our results agree qualitatively well with the data of Afonso et al. (2011) [53]. Our simulations predict the reduction of the vortex size with increasing Wi, up to Wi≈5. Moreover, we observe a periodic third vortex growth and annihilation regime for Wi ≥ 15. The periodic vortex growth and annihilation is correlated with the accumulation of elastic strain in the cavity upstream of the contraction. This elastic instability is viewed as a mechanism that releases the elastic energy accumulated in the Oldroyd-B fluid at the fringe of the recirculation vortices. The dimensionless period of the third vortex annihilation appears to be independent on the Weissenberg number.

Nonlinear dynamics of domain walls with cross-ties

The dynamic behavior of a domain wall with cross-ties is analyzed on the basis of micromagnetic simulation with exact allowance for all main (exchange, magnetoanisotropic, and magnetostatic) interactions in thin magnetically uniaxial ferromagnetic films with planar anisotropy. It is found that the peculiarities of motion of such domain walls are closely related to the behavior of topological defects in the magnetization distribution (generation, motion, and annihilation of vortex–antivortex pairs on the film surface and Bloch points). We observe three different regimes of motion (stationary, periodic, and turbulent regimes), each of which is realized in a certain range of fields oriented along the easy magnetization axis. It is shown that the experimentally observed dynamic bends of the walls with cross-ties are determined by the type of motion of vortices and antivortices. The velocities of domain walls in different regimes are calculated, and the dynamic configurations of the magnetization and existing dynamic transitions between them are investigated.

Three-dimensional simulation of irregular dynamics of topological solitons in moving magnetic domain walls

A three-dimensional computer simulation of dynamic processes occurring in a domain wall moving in a soft-magnetic uniaxial film with in-plane anisotropy has been performed based on the micromagnetic approach. It has been shown that the domain wall motion is accompanied by topological transformations of the magnetization distribution, or, more specifically, by “fast” processes associated with the creation and annihilation of vortices, antivortices, and singular (Bloch) points. The method used for visualizing the topological structure of magnetization distributions is based on the numerical determination of topological charges of two types by means of the integration over the contours and surfaces with variable geometry. The obtained data indicate that the choice of the initial configuration predetermines the dynamic scenario of topological transformations.

Annihilation and Reanimation of a Tornado in the Improved Tornado Tube

Some new experiments using an improved version of the “tornado tube” are described here. The improved tornado tube consists of two plastic transparent bottles whose openings are connected with a ball valve, available at most hardware stores. After being filled with fluid and inverting, this tube allows demonstration of the generation, annihilation, and reanimation of vortices, or tornados.