Curling Mode Research Articles

Spherical bispectrum expansion and quadratic estimators

We describe a general expansion of spherical (full-sky) bispectra into a set of orthogonal modes. For squeezed shapes, the basis separates physically-distinct signals and is dominated by the lowest moments. In terms of reduced bispectra, we identify a set of discrete polynomials that are pairwise orthogonal with respect to the relevant Wigner 3j symbol, and reduce to Chebyshev polynomials in the flat-sky (high-momentum) limit for both parity-even and parity-odd cases. For squeezed shapes, the flat-sky limit is equivalent to previous moment expansions used for CMB bispectra and quadratic estimators, but in general reduces to a distinct expansion in the angular dependence of triangles at fixed total side length (momentum).We use the full-sky expansion to construct a tower of orthogonal CMB lensing quadratic estimators and construct estimators that are immune to foregrounds like point sources or noise inhomogeneities. In parity-even combinations (such as the lensing gradient mode from TT, or the lensing curl mode from EB) the leading two modes can be identified with information from the magnification and shear respectively, whereas the parity-odd combinations are shear-only. Although not directly separable, we show that these estimators can nonetheless be evaluated numerically sufficiently easily.

Effects of ferromagnetic branch structures on coercivity of alnico permanent magnets

The effects of various branches geometry and dimensions such as length, thickness, and width for H-, U-, O-, YH- and YU-shaped alnico structures on coercivity (Hci) using micromagnetic simulation for coherent rotation and curling modes are investigated. The simulation results suggest that the H-shaped structure needs long and short branch length for the coherent rotation and curling, respectively, regardless of branch thickness and width to realize high Hci. Short branch length with thin thickness and short width are recommended for both rotations for the U- and O-shaped structures. Lastly, both Y-shaped structures need branch with long length, thin thickness, and mid-long width for the coherent rotation, but short width for the YH-shaped and mid-long width for the YU-shaped regardless of length and thickness for curling are desired. Furthermore, among the five studied structures, H- or YH-shaped structure for coherent rotation and O-shaped structure for curling are highly recommended for fabrication to realize a high Hci.

Time-domain imaging of curling modes in a confined magnetic vortex and a micromagnetic study exploring the role of spiral spin waves emitted by the core

The curling spin wave modes of a ferromagnetic vortex confined to a microscale disc have been directly imaged in response to a microwave field excitation using time-resolved scanning Kerr microscopy. Micromagnetic simulations have been used to explore the interaction of gyrotropic vortex core dynamics with the curling modes observed in the region of circulating in-plane magnetization. Hybridization of the fundamental gyrotropic mode with the degenerate, lowest-frequency, azimuthal modes has previously been reported to lead to their splitting and counter propagating motion, as we observe in our spectra and measured images. The curling nature of the modes can be ascribed to asymmetry in the static and dynamic magnetization across the disc thickness, but here we also present evidence that spiral spin waves emitted by the core can influence the spatial character of higher frequency curling modes for which hybridization is only permitted with gyrotropic modes of the same sense of azimuthal motion. While it is challenging to identify if such modes are truly hybridized from the mode dispersion in a confined disc, our simulations reveal that spiral spin waves from the core may act as mediators of the interaction between the core dynamics and azimuthal modes. At higher frequency, modes with radial character only do not exhibit marked curling, but instead show evidence of interaction with spin waves generated at the edge of the disc. The measured spatio-temporal character of the observed curling modes is accurately reproduced by our simulations, which reveal the emission of propagating short-wavelength spiral spin waves from both core and edge regions of the disc. Our simulations suggest that the propagating modes are not inconsequential, but may play a role in the dynamic overlap required for hybridization of modes of the core and in-plane magnetised regions.

Dynamic collapse of circular metal foam core sandwich tubes in splitting and curling mode

This paper investigates the dynamic collapse of circular metal foam core sandwich tubes in splitting and curling mode subjected to low-velocity impact. The splitting and curling modes occur along the prefabricated cracks on sandwich tubes. The deformation modes, i.e. crack propagation along the prefabricated crack, new crack initiation, merging old cracks are observed in experiments. It is found that the number of strips in the sandwich tube tends to develop from the number of prefabricated cracks to the number of steady strips. Based on the principle of minimum energy, the method for predicting the number of steady cracks in the inner and outer tubes of the sandwich tubes is established. The quasi-static analytical model is approximately used to predict experimental results, and analytical results capture experimental ones reasonably. It is demonstrated the better energy absorption characteristics can be obtained by the proper thickness of metal foam core.

Preparation and magnetic properties of gradient diameter FeCoNi alloys nanowires arrays

FeCoNi MNWs with uniform and gradient diameter are successfully prepared by three-electrode constant potential deposition in AAO template. The deposition time of FeCoNi MNWs overgrow in the AAO template are investigated. The morphology and structure of FeCoNi MNWs are characterized by TEM, EDS, SAED and XRD. The effects of magnetization reversal mechanism, magnetic interaction, magnetic domain states and reversibility of FeCoNi MNWs are studied by FORCs technology. The results show that the magnetization reversal mechanism of UDNWs-20 present coherent mode, while UDNWs-60 and UDNWs-100 present curling mode as well as coherent mode. There is a transition of curling inverse to coherent inverse in magnetic reversal of GDNWs-20~100. When the UDNWs diameter increase from 20 nm to 60 nm and 100 nm, the domain state change from SD to MD state and the irreversible component reduce from about 100% to 71.3% and 60.2%. The SD GDNWs-20~100 contains 72.8% irreversible and 27.2% reversible components. The magnetic interaction, magnetic domain states and reversibility of FeCoNi GDNWs are different from those of UDNWs.

Magnetic properties of Sr0.95Nd0.05Fe12-xScxO19 hexaferrite nanoparticles

Sr0.95Nd0.05Fe12-xScxO19 (0 ≤ x ≤ 1.56) nanocrystallites, 50–100 nm thick, were obtained by citric sol-gel method. Single P63/mmc phase with lattice parameters increasing continuously with x was proved by X-ray diffraction. Scanning electron microscope control of the microstructure shows a decrease in particle size with increasing x from 1000 to ∼250 nm. Saturated hysteresis loops were obtained in field of 5 T and magnetization switching via curling mode was observed for crystallites with sizes from 1000 to ∼600 nm. For smaller particles magnetization was switched via coherent reorientation. The effect of doping on magnetic properties was apparent in samples containing more than one Sc3+ ion substituting Fe3+ pro one unit cell (x ≥ 0.60). The saturation magnetization was found to increase on cooling from 300 K and for samples with x ≥ 0.60 exhibits local maximum at Tcone temperatures considerably lower in comparison with those of bulk counterparts. The appearance of conical magnetic order is reflected in temperature dependences of extrinsic magnetic properties, coercivity and remanence, which decrease also on doping. Temperature variation of magnetization in zero field cooling/field cooling modes shows that Tcone is shifted downwards with increasing field.

Wide-Band Electromagnetic Wave Propagation and Resonance in Long Cobalt Nanoprisms

Electromagnetic wave interaction with confined metallic magnetic structures is complex due to the excitation of nonuniform electromagnetic fields and magnetic precession and spin-wave modes over length scales that are dependent on the geometric, electromagnetic, and micromagnetic properties of the magnetic structures. Here, we solve the coupled system of Maxwell's equations and the Landau-Lifshitz-Gilbert equation using a stable algorithm based on the finite-difference time-domain method to study the transient wide-band electromagnetic propagation and resonance in infinitely long cobalt nanoprisms with a square cross section of side lengths 50--1000 nm. In particular, we identify the resonance mechanisms through studying the local transient and spectral distributions of magnetization in the prisms. The nanoprisms are excited by an axially polarized plane wave at normal incidence with a 70 GHz Gaussian pulse profile. For this incident wave condition, the simulations confirm that resonance in the cobalt prisms is excited mainly by the current-induced magnetic fields and indicate a magnetization curling resonance mode for prism side lengths less than 100 nm. The eigenfrequencies for the curling mode are confirmed theoretically using a model for an equivalent long circular cylinder with radial spin-wave modes. For prism side lengths longer than 100 nm (but less than the nonmagnetic skin depth), the magnetic response is confined to thin regions along the prism edges due to resonance-induced skin effects. The simulations indicate predominately uniform magnetization precession in the confined edge regions with increased pinning in the corners. The uniform resonance mode in the central part of the edge regions increases in intensity with prism size, with frequency described using Kittel's ferromagnetic resonance frequency of a thin planar structure. A higher-frequency size-independent uniform resonance mode is observed in the corner regions with frequency determined by the local demagnetizing factors. Local and integrated power absorption spectra are calculated using the simulated transient magnetization and fields, and confirm the resonance modes and frequencies in the cobalt prisms and their size dependence. The profile of the local power absorption spectra is also used to estimate the thickness of the confined edge regions or magnetic skin depth in the cobalt prisms at the fundamental resonance mode and is found to be approximately 50 nm. The outcomes of this work would benefit the design and engineering of lightweight and compact materials and devices incorporating metallic magnetic nanostructures. This work also provides a foundation for further modeling and understanding of electromagnetic transmission and propagation in more complex metallic ferromagnetic structures and composites excited by different electromagnetic wave conditions.

Probing magnetism of individual nano-structures using Nb [formula omitted]-SQUIDs in hysteresis free mode

The magnetization reversal of an individual magnetic nano-structure has been best studied using a μ-SQUID. An optimum inductive shunt helps in eliminating the hysteresis in μ-SQUID’s current voltage characteristics, giving thus a direct voltage readout of magnetic flux with high bandwidth and sensitivity. Here we report on a new μ-SQUID magnetometry setup for studying the magnetism of individual magnetic nano-structures. The switching field anisotropy of Permalloy nano-needles was studied using both hysteretic and non–hysteretic μ-SQUID modes. The observed anisotropy fits well the magnetization reversal through curling mode under the Néel-Brown model as well as micromagnetic simulations. The latter show a reversal through vortex nucleation and annihilation whose signatures we observe through minor hysteresis loops in experiments. Some preliminary magnetization reversal studies on Fe3O4 nano-particles using a non–hysteretic μ-SQUID mode are also briefly discussed.

The bispectrum of polarized galactic foregrounds

Understanding the properties of the galactic emission at millimetre wavelengths is important for studies of the cosmic microwave background (CMB). In this work we explore the bispectrum, the harmonic equivalent of the three point function, from galactic dust and synchrotron emission. We investigate these effects across a broad range of frequencies using the synchrotron dominated S-band Polarization All Sky Survey (SPASS) maps at 2.3 GHz, the Planck satellite maps (30-857 GHz) and dust dominated Infrared Astronomical Satellite (IRAS) maps at 3 THz. We measure bispectra of total intensity fields, T, as well as the gradient, E, and curl modes, B, of the polarization field. We find that the synchrotron and galactic dust have strong temperature bispectra with significant contributions in the squeezed limit, which probes the correlations between two small scale modes with a large scale mode. Additionally, we find that the dust also has strong polarised bispectra that also peak in the squeezed configuration. We explore parity odd bispectra, such as BTT bispectra, and find strong parity odd bispectra for the galactic dust notably in BTT, BTE and BEE configurations. After masking bright sources, we find no evidence for polarised synchrotron bispectra and no evidence for cross bispectra between the dust and synchrotron emission. The strong foreground bispectra discussed here need to be carefully controlled to avoid biasing measurements of primordial non-Gaussianity. Finally we use these bispectra tools to test for residual foregrounds in the component separated Planck maps and find no evidence of residual foregrounds. These tools will be useful for characterizing residual foregrounds in component separated maps, particularly for experiments with less frequency coverage than the Planck satellite.

Uniaxial magnetization reversal process in electrodeposited high-density iron nanowire arrays with ultra-large aspect ratio

In this study, magnetization reversal modes of iron nanowire arrays with large aspect ratios were investigated by Shtrikman’s micromagnetic theory. The iron nanowire arrays were potentiostatically electrodeposited into anodized aluminum oxide nanochannels with average diameters, Dp, of ca. 33 nm, 52 nm, 67 nm, and 85 nm. The growth rate of the iron nanowires was ca. 105 nm s−1 at the cathode potential of −1.2 V (vs. an Ag/AgCl reference), and the axial length, Lw, reached up to ca. 60 µm. Maximum aspect ratio, Lw/Dw of the iron nanowires was found to be ca. 1800, and the axial direction coincided with 〈1 1 0〉 direction of the bcc-Fe crystal structure. The effect of the average diameter size on the coercivity of iron nanowire arrays corresponded well to the theoretical estimate, which was calculated by the magnetization curling mode in Shtrikman’s micromagnetic theory. As the average diameter of the iron nanowires was decreased, coercivity and squareness of the nanowire arrays increased up to 1.63 kOe and 0.87, respectively.

Structural and Uniaxial Magnetic Anisotropy of Co1-XMgX(X = 0.04–0.12) Nanowires in Alumina Templates

The nanoporous anodized aluminum oxide (AAO) templates were synthesized by two-step anodization in a solution of 0.5 M phosphoric acid at 60 V and temperature T ~ 0 °C. The CoMg nanowires were synthesized by template-based AC Electrodeposition technique at different voltages by AC source 13–17 V at room temperature. These CoMg nanowires were investigated via different characterization techniques such as scanning electron microscopy (SEM), energy-dispersive X-ray (EDX) spectroscopy, X-ray diffraction (XRD), Fourier transform infrared spectroscopy (FTIR), and vibrating sample magnetometer (VSM). The SEM result shows that nanowires have average diameter about 150 nm and length about 23 μm. The EDX reveals that nanowires only consisted of Mg and Co atoms, and atomic ratio of Mg/(Co + Mg) showed increasing tendency with deposition voltage which depicts that higher AC electrodeposition voltage is more suitable for Mg-rich deposition. The XRD results show that CoMg nanowires have hexagonal crystal structure with polycrystalline nature. The MH loops confirm that nanowires are soft ferromagnetic with uniaxial magnetic anisotropy. It is observed from angular dependence of coercivity that magnetization reversal mechanism occurs by a combination of curling and nucleation mode. The squareness (Mr/Ms) is found to be 0.24 along nanowires and 0.16 perpendicular to nanowire axis suggesting that easy magnetization direction lies along the nanowires. The effective anisotropy is observed along the nanowire axis due to dominance of shape anisotropy and suppression of dipole-dipole interactions among nanowires.

Magnetoresistance of a single polycrystalline nickel nanowire

We report the magnetoresistance study of an individual polycrystalline nickel nanowire at temperature T=10K. Transport measurements have indicated a large coercive field of the nanowire, justified by the polycrystalline structure of the studied sample, where both magnetocrystalline anisotropy of randomly oriented grains and effective uniaxial anisotropy at the grain boundaries enhance the coercive field. Magnetization reversal studied with micromagnetic simulations occurs via the curling mode when vortices are nucleated and propagate along the nanowire, and propagation is inhibited at grain boundaries. The applicability of micromagnetic simulations is confirmed by a good agreement between experimental and simulated magnetoresistance curves.

Anhysteretic remanent magnetization: model of grain size distribution of spherical magnetite grains

A phenomenological model based on a linear relationship between the magnetic coercivity field and the reciprocal of the grain diameter is applied to explain the anhysteretic remanent magnetization (ARM) imparted to artificial samples with different concentrations of a very well characterized magnetite powder. By analyses of scanning electron microscopy images, the spherically shaped single domain synthetic magnetite is found to follow a lognormal grain size distribution with ~86 nm of mean diameter. The proposed model, fitted to ARM measurements up to a peak alternating field of 100 mT, yields a very good agreement. The coercivity behaviour predicted by micromagnetism theory disagrees with the experimental results of this work. A likely explanation for the discrepancy is that the magnetite particles, which consist of a mixture of grains in coherent rotation and curling modes, produce similar observations as domain processes.

The Exchange Energy Term and the Curling Reversal Mode in Hard Magnetic Materials Manufactured by Powder Metallurgy

The curling reversal mode is discussed, with emphasis on the assumptions of the model, many of them unrealistic. The curling mode assumes the Bloch approximation, where a cosine function is approximated by a polynomial of second order. It is argued that if the curling model takes place, this could affect the anisotropy field, and then the anisotropy field would be function of the grain size, but this is not observed. Exchange effects may affect hysteresis curve, as discussed in the SW-CLC model.

Fabrication and magnetic investigations of highly uniform CoNiGa alloy nanowires

CoNiGa ternary alloy nanowire arrays were successfully fabricated by simple DC electrodeposition into the anodized aluminum oxide (AAO) templates. A systematic study of the potential and components of the electrolyte were conducted to obtain different components of CoNiGa nanowires. The largest Ga content in the prepared alloy nanowires was about 17%, while for Co and Ni contents which can be controlled in a wide range by adjusting the composition and pH value of the electrolyte appropriately. X-ray diffraction analysis confirmed that the as-grown CoNiGa nanowire arrays were polycrystal with fcc phase of Co where Co atoms partially substituted by Ni and Ga. Magnetization curves of samples with different composition were measured at room temperature as well as low temperature. The results showed that the components of the alloy nanowires have a great impact on its magnetic properties. For Co55Ni28Ga17 nanowires, the magnetization reversal mode changes from curling mode to coherent rotation as the angle increases, and the temperature dependence of coercivity can be well described by the thermal activation effect.

PRIMORDIAL GRAVITATIONAL WAVES AND RESCATTERED ELECTROMAGNETIC RADIATION IN THE COSMIC MICROWAVE BACKGROUND

ABSTRACT Understanding the interaction of primordial gravitational waves (GWs) with the Cosmic Microwave Background (CMB) plasma is important for observational cosmology. In this article, we provide an analysis of an apparently as-yet-overlooked effect. We consider a single free electric charge and suppose that it can be agitated by primordial GWs propagating through the CMB plasma, resulting in periodic, regular motion along particular directions. Light reflected by the charge will be partially polarized, and this will imprint a characteristic pattern on the CMB. We study this effect by considering a simple model in which anisotropic incident electromagnetic (EM) radiation is rescattered by a charge sitting in spacetime perturbed by GWs, and becomes polarized. As the charge is driven to move along particular directions, we calculate its dipole moment to determine the leading-order rescattered EM radiation. The Stokes parameters of the rescattered radiation exhibit a net linear polarization. We investigate how this polarization effect can be schematically represented out of the Stokes parameters. We work out the representations of gradient modes (E-modes) and curl modes (B-modes) to produce polarization maps. Although the polarization effect results from GWs, we find that its representations, the E- and B-modes, do not practically reflect the GW properties such as strain amplitude, frequency, and polarization states.

Observable cosmological vector mode in the dark ages

The second-order vector mode is inevitably induced from the coupling of first-order scalar modes in cosmological perturbation theory and might hinder a possible detection of primordial gravitational waves from inflation through 21cm lensing observations. Here, we investigate the weak lensing signal in 21cm photons emitted by neutral hydrogen atoms in the dark ages induced by the second-order vector mode by decomposing the deflection angle of the 21cm lensing signal into the gradient and curl modes. The curl mode is a good tracer of the cosmological vector and tensor modes since the scalar mode does not induce the curl one. By comparing angular power spectra of the 21cm lensing curl mode induced by the second-order vector mode and primordial gravitational waves whose amplitude is parametrized by the tensor-to-scalar ratio $r$, we find that the 21cm curl mode from the second-order vector mode dominates over that from primordial gravitational waves on almost all scales if $r \lesssim 10^{-5}$. If we use the multipoles of the power spectrum up to $\ell_{\rm max} = 10^{5}$ and $10^{6}$ in reconstructing the curl mode from 21cm temperature maps, the signal-to-noise ratios of the 21cm curl mode from the second-order vector mode achieve ${\rm S/N} \approx 0.46$ and $73$, respectively. Observation of 21cm radiation is, in principle, a powerful tool to explore not only the tensor mode but also the cosmological vector mode.

Micromagnetism of MnBi:FeCo thin films

MnBi:FeCo hard-soft bilayers are investigated using micromagnetic simulations with open boundary conditions and two-dimensional (2D) periodic boundary conditions (PBC). Open and PBC yield similar coercivities of about 1.01 T, in agreement with experiment, but the hysteresis-loop shape is very different in the two theoretical approaches. The difference is ascribed to edge effects, which occur in open boundary conditions but not in PBC and experiment. Near the nucleation field, a curling or vortex mode develops in dots with circular cross sections. The curling mode, which is caused by magnetostatic self-interaction, does not negatively affect the high coercivity of 1.01 T. The magnetostatic self-interaction contributes to the favorable second-quadrant behavior of the MnBi:FeCo thin films.

Tuning the magnetic properties of high aligned strontium ferrite nanowires formed in alumina template

Ordered hexagonal array of strontium ferrite nanowires were fabricated by dip coating in alumina templates and the influence of diameter and length on the magnetic properties of high aligned nanowire arrays were studied. The diameter of nanowires, synthesized in high aspect ratios, was changed from 30 to 60 nm while maintaining the same center to center distance between them. The samples were characterized by X-ray diffraction (XRD) and field emission scanning electron microscope (FESEM) equipped with energy dispersive X-ray spectrum (EDS). Magnetic properties of nanowires were measured by a SQUID; the hysteresis loops were obtained with the applied magnetic field parallel and perpendicular to the wire axis. Magnetic properties of nanowire arrays were also investigated as a function of temperature. The Results showed that both coercivity and squareness increased with increasing wire length, while for constant center-to-center distance, coercivity decreased with increasing the diameter. Parallel anisotropy was achieved for 30 ± 4 nm diameter nanowire array having 15 ± 0.01 μm length. A curling mode of magnetization was suggested in strontium nanowires.

Phase-coherent mapping of gravitational-wave backgrounds using ground-based laser interferometers

We extend the formalisms developed in Gair et al. and Cornish and van Haasteren to create maps of gravitational-wave backgrounds using a network of ground-based laser interferometers. We show that in contrast to pulsar timing arrays, which are insensitive to half of the gravitational-wave sky (the curl modes), a network of ground-based interferometers is sensitive to both the gradient and curl components of the background. The spatial separation of a network of interferometers, or of a single interferometer at different times during its rotational and orbital motion around the Sun, allows for recovery of both components. We derive expressions for the response functions of a laser interferometer in the small-antenna limit, and use these expressions to calculate the overlap reduction function for a pair of interferometers. We also construct maximum-likelihood estimates of the + and x-polarization modes of the gravitational-wave sky in terms of the response matrix for a network of ground-based interferometers, evaluated at discrete times during Earth's rotational and orbital motion around the Sun. We demonstrate the feasibility of this approach for some simple simulated backgrounds (a single point source and spatially-extended distributions having only grad or curl components), calculating maximum-likelihood sky maps and uncertainty maps based on the (pseudo)inverse of the response matrix. The distinction between this approach and standard methods for mapping gravitational-wave power is also discussed.