Helicity Of Vortices Research Articles

Machine learning estimation of magnetic parameters and classification of magnetic vortex states

Analysis of properties related to spin textures, such as the magnetic vortex state, is mainly based on spin configuration data, which is directly related to magnetic parameters involved in the system's Hamiltonian. Here, we focus on magnetic parameter estimation by implementing the machine learning (ML) approach, especially on magnetic force microscopy (MFM) images of vortex states within nanodots generated by micromagnetic simulation. The exchange constant Aex and saturation magnetization Ms as well as exchange length as a reduced parameter Lex(Aex, Ms) are estimated by different convolutional neural network (CNN) models. We also evaluated the CNN models, trained on simulated MFM images with non-zero temperature, on a reference experimental MFM image and found the performance to a satisfactory level of accuracy. Moreover, the same CNN models, trained for binary classification of vortex states based on helicity from MFM images, successfully identified the vortex helicity from simulated as well as experimental MFM images. These findings show the possible application of ML in magnetic parameter estimation and the analysis of magnetic vortex states simply with images obtained from this commonly used imaging technique that is significant in efficient investigation of material properties based on intrinsic parameters for spintronic device applications.

Helicity of magnetic vortices and skyrmions in soft ferromagnetic nanodots and films biased by stray radial fields

Static magnetization configurations of thin soft ferromagnetic films and nanodots, coupled to a hard antidot matrix with out-of-plane magnetization, are studied by micromagnetic simulations and analytical calculations. When the antidot matrix produces sufficient stray fields, having radial symmetry, these nanostructures support the formation of topologically nontrivial magnetic configurations---vortices and skyrmions in nanodots and films, respectively. It is demonstrated that the studied nanostructure reveals an additional degree of freedom---the helicity of the vortex or skyrmion---which can be tuned on demand by a variation of the material parameters and geometry. The variation of helicity $\ensuremath{\gamma}$ is not abrupt. In addition to Neel-like (radial) vortices and skyrmions $(\ensuremath{\gamma}=0,\ensuremath{\pi})$, it is possible to achieve unconventional configurations with an intermediate helicity $\ensuremath{\gamma}\ensuremath{\ne}0,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2,\ensuremath{\pi}$, which transform to common Bloch-like configurations $(\ensuremath{\gamma}=\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2)$ in the limit of negligible stray fields from the matrix. We present an analytical model, which allows us to calculate the stability region of pure Neel-like states, outside which unconventional magnetization states with intermediate helicity are realized.

Control of Vortex Helicity With a Quarter-Wave Plate in an Er:YAG Ceramic Solid State Laser

In this paper, we research the characteristics of the Laguerre-Gaussian (LG01) beams generated in an Er:YAG ceramic solid state laser pumped by an annular beam. The generated two LG01 beams (LG0,+1 and LG0,−1 modes) were found to have different thermally induced polarization behaviors and alternately existed in the resonator; then, a novel method was proposed and experimentally demonstrated to control the vortex helicity using a simple quarter-wave plate.

Topology of spin meron pairs in coupled Ni/Fe/Co/Cu(001) disks

The meron is a special topological object that carries only one-half of the topological charge unit. In condensed matter physics, a spin meron corresponds to one-half of a spin skyrmion. As compared to the many fascinating topological properties of skyrmion materials, little is known of the properties of spin merons especially about their formation. It was confirmed only recently that hedgehog merons could exist in pairs with opposite helicities via a spin flux closure. However, it is unclear whether a single hedgehog meron could ever exist by pairing with another type of meron. Using element-resolved magnetic imaging measurements on epitaxial trilayer disks, we show that a spin meron with a full range of helicity, including the hedgehog meron, can be stabilized by pairing with another vortex meron with a fine tuning of the magnetic coupling between the two merons. Furthermore, the meron divergence is fully controlled by the polarity of the vortex meron, independent of the vortex helicity.

Determination of an optical vortex topological charge using an astigmatic transform

It It is shown both theoretically and experimentally that if a cylindrical lens is placed into a laser beam, having an optical vortex with integer topological charge n and on-axis intensity null, then at the double focal distance behind the lens, the n-fold degenerate intensity null is split into n isolated intensity nulls. These intensity nulls lie on a straight line in the transverse plane at an angle of + 45 or – 45 degrees to the axis of the cylindrical lens, depending on the vortex helicity direction (i.e. sign of the topological charge). Experiments show that such a method can be used to determine higher-order topological charges up to n = 100.

Quantitative characterization of the energy circulation in helical beams by means of near-field diffraction

We present a method to measure the skew angle of the wave-fronts in an optical vortex, which is directly related with the energy flux. It is based on the analysis of the evolution on propagation of the near-field diffraction pattern generated by a single-slit, consisting of two main lobes that shift in opposite directions depending on the vortex helicity. The transverse displacement of each lobe as a function of the propagation distance allows to quantify the energy circulation. Analytical, numerical and experimental results are compared, showing good agreement. We illustrate the method for the case of Bessel beams, although we also discuss other types of helical beams, such as Laguerre-Gauss and Mathieu beams.

Angular momentum flux of nonparaxial acoustic vortex beams and torques on axisymmetric objects

An acoustic vortex in an inviscid fluid and its radiation torque on an axisymmetric absorbing object are analyzed beyond the paraxial approximation to clarify an analogy with an optical vortex. The angular momentum flux density tensor from the conservation of angular momentum is used as an efficient description of the transport of angular momentum. Analysis of a monochromatic nonparaxial acoustic vortex beam indicates that the local ratio of the axial (or radial) flux density of axial angular momentum to the axial (or radial) flux density of energy is exactly equal to the ratio of the beam's topological charge l to the acoustic frequency ω. The axial radiation torque exerted by the beam on an axisymmetric object centered on the beam's axis due to the transfer of angular momentum is proportional to the power absorbed by the object with a factor l/ω, which can be understood as a result of phonon absorption from the beam. Depending on the vortex's helicity, the torque is parallel or antiparallel to the beam's axis.

On the simulation of helical turbulence in an astrophysical nonmagnetic disk

The problem of the influence of vortex helicity on the synergic structuring of cosmic matter in it, as well as the appearance of the effect of negative viscosity in three-dimensional gyrotropic turbulence, were studied in the framework of the fundamental problem of simulating the evolution of a rotating astrophysical nonmagnetic disk—in particular, the accretion disk—surrounding the Sun at the early stage of its existence. The evolution equations for averaged vorticity and vortex helicity, as well as rheological relations for the turbulent flow of heat and asymmetrical tensor of the turbulent stress in helical turbulence, were obtained. The demonstrative dependence of helicity on the rotation velocity, density (temperature) gradients, and turbulent energy of the disk gas was established. The role of helicity in the appearance of the inverse Richardson-Kolmogorov energy cascade from small vortices to larger ones and the related process of the generation of the power-consuming macroscale coherent vortex formations appearing in gyrotropic turbulence at high Reynolds number were discussed. The results of the numerical experiments confirming the real existence of the inverse energy cascade in helical turbulence were analyzed. It was assumed that the relatively long-term decay of turbulence in the solar protoplanet cloud can be due to the absence of the reflective symmetry of the anisotropic field of the turbulent velocities with respect to its equatorial plane. As the concept of the inverse energy cascade in three-dimensional helical turbulence is more and more reliably confirmed in numerical experiments, accounting for this effect affecting the structure and dynamics of the astrophysical nonmagnetic disk becomes important during its simulation.

Aspect on vortex structure in noncentrosymmetric superconductors

Helicity of vortices is studied in a single order parameter Ginzburg–Landau model with n × B term. This unusual term changes the superconductor current, but does not change the quantum of magnetic flux, and the cross helicity of the probability density current in noncentrosymmetric superconductors. In this paper I compute the kinetic helicity and magnetic helicity of a superconductor and introduce a new helicity, i.e. a new topological invariant, to describe vortex phase.

Topological Structure of Vortices in Multicomponent Bose—Einstein Condensates

The structure of the vortex in a two-component Bose—Einstein condensate is studied by the method of Dirac δ function. The vortex can be characterized by the Brouwer degree and Hopf index, i.e., β1η1, β2η2. The circulation of the vortex can be a fraction, which is different from the usual result for a one-component condensate. The kinetic helicity of vortices is calculated.

Kinetic helicity of vortex in Bose-Einstein condensates

Kinetic helicity of vortex in Bose-Einstein condensates is studied and classified by Hopf index, linking number in geometry. A mechanism of generation and annihilation of vortex line is given by method of phase singularity theory. The dynamic behavior of vortex at the critical points is discussed detailly, and three kinds of length approximation relations at the neighborhood of singularity point are given.

3D-numerical simulations of the magnetic field evolution in a turbulent interstellar gas

Abstract A fully three-dimensional kinematic model is applied to simulate the evolution of the magnetic field in a small (120 pc in size) volume of the turbulent interstellar medium in the presence of the field diffusion. Turbulent motions are approximated by a sequence of non-overlapping in time vortices having the form of rotating gas columns much longer than the parcel size. A combined action of vertical vortices and those inclined at the angle of 30° to the galactic plane is considered. Due to the Coriolis force and density stratification their motions have a non-zero helicity. The magnetic field is found to evolve towards the structure resembling a fragment of a twisted flux tube, well-ordered over the volume analyzed. Its sense of twisting is determined by the vortex helicity.

Helicity, linkage and dynamo action

Abstract The pseudoscalar χu (flux helicity), which determines the number of linked flow lines in a simply-connected volume, and the scalar I Hv, which is proportional to the number of linkages of flow lines with magnetic field lines, are introduced. By these quantities a topological formulation of an antidynamo theorem is given. The conditions required for slow dynamo action are clarified. The relation of the flux helicity to the usual vortex helicity is discussed.