Magnetic Vector Research Articles

Neutron-powder-diffraction studies of the nuclear and magnetic structure of the double-perovskite CaxSr2−xWMnO6 (x = 0.5, 1.0, and 1.5)

The nuclear and magnetic structures of CaxSr2−xWMnO6 (x = 0.5, 1.0, 1.5) have been investigated by neutron diffraction at 295, 30 or 40 K, and 4 or 5 K. The compounds crystallized in the monoclinic symmetry with a space group P21/n. The nuclear structure consists of ordered WO6 and Mn2+O6 octahedral frameworks, with lattice constant a decreasing more rapidly than b with increasing Ca content. No structural change was found around the magnetic transition temperature, although the Mn octahedron below the magnetic order temperature exhibited a slightly compressed Jahn–Teller distortion (0.1–0.3 Å) along the c axis. A standard magnetic model was used to solve the magnetic structure, with the Mn magnetic moments ferromagnetically coupled along the a axis and anti-ferromagnetically coupled along the b and c axes, resulting in a magnetic propagation vector of k = (0,1/2, 1/2) and a magnetic superlattice of 1a × 2b × 2c. In each crystallographic cell, the Mn1–Mn2 atoms are antiferromagnetically configurated, compensating the total moment to zero by symmetry. A layer-type magnetism along the (111) crystallographic plane was confirmed to couple antiferromagnetically between these planes and ferromagnetically within them. The magnetic structure refinement confirmed an average Mn moment of 4.5 μB. Also, it reveals that the collinear magnetic Mn configuration has three possible spin orientations, namely, (with their standard deviation) [μx = (3.3 ± 0.4) μB, μy = (2.5 ± 0.3) μB, μz = (−0.7 ± 0.7) μB], [μx = (3.0 ± 0.4) μB, μy = (0.5 ± 0.2) μB, μz = (−2.8 ± 0.2) μB, and [μx = (−1.8 ± 0.4) μB, μy = (2.9 ± 0.2) μB, μz = (−2.4 ± 0.3) μB. The first configuration is estimated to be the ground state, while the other magnetic configurations are an optimum local value derived from the refinements. Combined with the density functional theory calculations, these experimental results confirm a high-spin state Mn2+ (d5) electron configuration.

Features of the formation of the nutation line in nuclear magnetic magnetometers and flow meters with flowing liquid.

The mechanism of formation of a nutation line in a flowing liquid is considered. New ones have been developed equations of motion of the longitudinal and transverse components of the magnetization vector in the nutation coil, which take into account the inhomogeneity of the magnetic field ΔH_0 in the zone of influence of the radio frequency field H_1 on the flowing liquid. The equations also take into account the nature of the change in the value of the magnetic field inhomogeneity ΔH_0 when the fluid moves along the nutation coil. The results of experimental studies of the shape of the nutation line are presented. Theoretical calculations are compared with experimental data.

DKIST Unveils the Serpentine Topology of Quiet Sun Magnetism in the Photosphere

We present the first quiet Sun spectropolarimetric observations obtained with the Visible SpectroPolarimeter at the 4 m Daniel K. Inouye Solar Telescope. We recorded observations in a wavelength range that includes the magnetically sensitive Fe i 6301.5/6302.5 Å doublet. With an estimated spatial resolution of 0.″08, this represents the highest spatial resolution full-vector spectropolarimetric observations ever obtained of the quiet Sun. We identified 53 small-scale magnetic elements, including 47 magnetic loops and four unipolar magnetic patches, with linear and circular polarization detected in all of them. Of particular interest is a magnetic element in which the polarity of the magnetic vector appears to change three times in only 400 km and which has linear polarization signals throughout. We find complex Stokes V profiles at the polarity inversion lines of magnetic loops and discover degenerate solutions, as we are unable to conclusively determine whether these arise due to gradients in the atmospheric parameters or smearing of opposite-polarity signals. We analyze a granule that notably has linear and circular polarization signals throughout, providing an opportunity to explore its magnetic properties. On this small scale, we see the magnetic field strength range from 25 G at the granular boundary to 2 kG in the intergranular lane (IGL) and sanity-check the values with the weak and strong field approximations. A value of 2 kG in the IGL is among the highest measurements ever recorded for the internetwork.

Relaxation of relativistic pair plasma in a massive photon field

The relaxation of relativistic hot electron–positron plasma is investigated by incorporating the effect of non-zero photon mass, and a quadruple Beltrami (QB) relaxed state for the magnetic vector potential is derived. The QB state is a linear superposition of four single force-free fields and is characterized by four self-organized structures of different length scales. The analysis of QB states shows that for certain values of generalized helicities at lower relativistic temperatures, plasma shows diamagnetic behaviour. It is also noteworthy that the inclusion of non-zero photon mass naturally provides the possibility of multiscale structure formation in the relaxed state. In this scenario, one of the field structures is significantly larger than the Compton wavelength of photons, while the other three structures are on the scale of the electron skin depth. The potential implications of this QB state for astrophysical environments are also discussed.

Effect of Magnetic Shunts on Shell-Type Transformers Characteristics

A three-dimensional analysis of the leakage magnetic field in a transformer with beveled edges in a magnetic shunt is described. This paper contains a mathematical description of the finite element method used in performing numerical calculations. Formulas allowing to determine the differential and integral parameters of the magnetic field were presented. Magnetic flux density distributions and the points with high values were determined in the shell-type core and movable shunt sub-areas. For different positions of the magnetic shunt, the short-circuit transformer reactance was calculated as the integral parameter of the above-mentioned magnetic field analysis. Their amounts for the extreme positions of the shunt were given, as well. The movable magnetic shunt geometry impact on the short-circuit current value is given. In order to validate the calculation results, the research included some point measurements of magnetic flux density vectors and the winding reactances as well, and good compliance with the simulation data has been obtained. Thus, this analysis can also be applied to other objects with movable shunts in their magnetic systems.

Energy loss and hysteresis of reversible magnetization processes in iron-based soft magnetic composites

The paper focuses on investigation of the hysteresis originating from the reversible magnetization processes and the quantification of the corresponding energy dissipation, on soft magnetic composite materials differing in various parameters so exhibiting different proportions of magnetization processes types during quasi-static magnetizing reversal under different maximum inductions. It was confirmed that reversible magnetization processes show hysteresis too and generate energy losses. These losses come from frictional effects accompanying local rotations of spins at the microscopical view of all magnetization processes including the reversible ones. It was found that the area of a hysteresis loop obtained by the integration of reversible permeability reveals approximately the proportion of reversible magnetization vector rotations, which produce energy loss much more than reversible domain wall displacements.

Geodynamic Aspects of Magnetic Data Analysis and Tectonic–Paleomagnetic Mapping in the Easternmost Mediterranean: A Review

The Easternmost Mediterranean is a transition region from the ocean to the continent where the spreading and collision zones of the lithospheric plates join. The methodology of paleomagnetic mapping of the transition zones is based on combining geological and geophysical techniques for continental and oceanic platforms: magnetic data interpretation, paleomagnetic reconstructions, results of magnetized rock radiometric dating, satellite data analysis, tectonic–structural reconstructions, biogeographical studies, and utilization of different geophysical survey results. The satellite-derived gravity map reflects practically all significant tectonic units in the region, which assists us in the supposed paleomagnetic mapping. The satellite-derived and aeromagnetic maps with the tectonic features and the map of Curie discontinuity of Israel indicate the complexity of this region. Advanced magnetic data analysis supported by paleomagnetic data attraction and other geological–geophysical methods allowed the revealing of the block of oceanic crust with the Kiama paleomagnetic zone relating to the Early Permian age. A narrow reversely magnetized Earth crust block was revealed in the Lower Galilee. Some examples of advanced magnetic anomaly analysis are presented for several areas where the magnetization vector inclination is other than the modern direction: the Sea of Galilee, Carmel, Rosh-Ha-Ayin, Malqishon, and Hebron. In Israeli land, for the combined paleomagnetic mapping, the well-studied using paleomagnetic and radiometric methods (as well as tectonic–structural) areas were selected: (1) Makhtesh Ramon, (2) the Sea of Galilee with the adjoining zones, (3) Carmel, (4) Hula, and (5) Hermon. It is shown that the regional analysis of paleomagnetic data distribution played an essential role in detecting the influence of the recently recognized counterclockwise rotating mantle structure on the near-surface layers.

Effect of the passive damping plate on the vertical stability of permanent magnet electrodynamic suspension system

AbstractThe vertical stability of permanent magnet (PM) electrodynamic suspension (EDS) system with a passive damping plate is studied because of the well‐known under‐damped nature of the EDS suspension system. The passive damping plate is installed under the Halbach permanent magnet array. When the vehicle‐mounted Halbach array and passive damping plate move to cut the track conductive plate, the 2D eddy current force is derived by establishing equations of magnetic vector potentials and using the Maxwell stress tensor method. And a 2D finite‐element model (FEM) is built to validate the accuracy of the derived levitation force equation. Based on the derived levitation force equation, the vertical stability of the PM EDS system with a passive damping plate and the effects of the main parameters on the damping ratio are analysed.

Magnetoelastic Losses in the Linear Response Region for Three- and Four-Axis Idealized Magnets

In the presented studies, a description of the losses related to relaxation processes in idealized three- and four-axis ferromagnets, as well as ferrites, is considered for the case of a linear response (small perturbations) on the basis of a macroscopic approach. The description takes into account reversible 90° displacements of domain walls (DW) of concentrations (с), ways of DW pinning by linear defects, and processes of DW displacements and rotations of the spontaneous magnetization vector I⃗s, caused by a longitudinal elastic stress wave σ. As a result, the anisotropy of amplitude-independent losses emerges due to displacement processes. Frequency dependence of losses is obtained with consideration of the magnetic symmetry of the crystal, its magnetostructural parameters, and the concentration of magnetic phases ci. The paper also describes the internal frictionn Q-1, the absorption coefficient a, the velocity of propagation of elastic vibrations v and the Δ (1/E)-effect, thus allowing to reveal the texture in the distribution of DWs by their types.
 It is shown that if the relaxation times of rotation processes τ = β / 2K1 and displacement processes τc = βс / mω20 are the same, then the maxima of the dependence of internal friction on frequency Qc-1(ω) and QB-1(ω) superimpose on each other.
 The revealed features of magneto-elastic energy dissipation are of interest for laboratory studies and have promising applications in practice for determining the orientation of crystals, describing the texture, and calculating the differential ΔЕ-effect in magnets. The features of the ΔЕ-effect for the considered cases are also revealed.

Accelerated 3D FEA of an Axial Flux Machine by Exclusively Using the Magnetic Scalar Potential

This article focuses on increasing the computational efficiency of 3D multi-static magnetic finite element analysis (FEA) for electrical machines (EMs), which have a magnetic field evolving in 3D space. Although 3D FEA is crucial for analyzing these machines and their operational behavior, it is computationally expensive. A novel approach is proposed in order to solve the magnetic field equations by exclusively using the magnetic scalar potential. For this purpose, virtual variable permanent magnets (vPMs) are introduced to model the impact of the machine’s coils. The effect on which this approach is based is derived from and explained by Maxwell’s equations. To validate the new approach, an axial flux machine (AFM) is simulated using both 2D and 3D FEA with the magnetic vector potential and current-carrying coils as a reference. The results demonstrate a high level of agreement between the new approach and the reference simulations as well as an acceleration of the computation by a factor of 15 or even more. Additionally, the research provides valuable insights into meshing techniques and torque calculation for EMs in FEA.

Electromagnetic field detectors based on spintronics devices

The paper proposes a model of an electromagnetic radiation sensor that uses the precession of the magnetization vector in a ferromagnet (ferromagnetic resonance) as a result of absorbing the energy of an incident electromagnetic wave, the generation of a spin current as a result of this precession, the generation of a spin-polarized current as a result of the passage of a spin current in a non-magnetic metal, and a change in the direction of magnetization of a ferromagnetic layer with a low coercive force (free layer) due to the passage of a spin-polarized current. Then the radiation will be detected by its effect on the electrical resistance of the entire structure, which depends on the mutual directions (parallel or antiparallel) of magnetization of the free and fixed (with a large coercive force) ferromagnetic layers (phenomenon of giant magnetic resistance). The dependence of the spin-polarized current in the device on the frequency and amplitude of the incident electromagnetic wave with linear polarization was calculated. A method of calculating the range of amplitude and frequency values of radiation that can be detected by the sensor has been developed. The parameters of this model are the detection time and the number of spin gates in one sensor. Calculations are given for a ferromagnetic layer made of permalloy and for spin valves with four different critical current values that determine the process of remagnetization of the free layer: 20, 50, 100, and 200 microamps.

Spatial magnetization profile in spherical nanomagnets with surface anisotropy: Green's function approach

We consider a single spherical nanomagnet and investigate the spatial magnetization profile in the continuum approach, using the Green's function formalism. The energy of the (many-spin) nanomagnet comprises an isotropic exchange interaction, a uniaxial anisotropy in the core and Néel's surface anisotropy, and an external magnetic field. We derive a semi-analytical expression for the magnetization vector field for an arbitrary position r within and on the boundary of the nanomagnet, as a solution of a homogeneous Helmholtz equation with inhomogeneous Neumann boundary conditions. In the absence of core anisotropy, we use the solution of this boundary problem and infer approximate analytical expressions for the components m α , α = x, y, z, as a function of the radial distance r and the direction solid angle. Then, we study the effects of the nanomagnet's size and surface anisotropy on the spatial behavior of the net magnetic moment. In the presence of a core anisotropy, an approximate analytical solution is only available for a position r located on the surface,i.e. r = R n, where R is the radius of the nanomagnet and n the verse of the normal to the surface. This solution yields the maximum spin deviation as a result of the competition between the uniaxial core anisotropy and Néel's surface anisotropy. Along with these (semi-)analytical calculations, we have solved a system of coupled Landau–Lifshitz equations written for the atomic spins, and compared the results with the Green's function approach. For a plausible comparison with experiments, e.g. using the technique of small-angle magnetic neutron scattering, we have averaged over the direction solid angle and derived the spatial profile in terms of the distance r. We believe that the predictions of the present study could help to characterize and understand the effects of size and surface anisotropy on the magnetization configurations in nanomagnet assemblies such as arrays of well-spaced platelets.

Precession of magnetic moments with change of their orientations

In the work the precession of the magnetization vector in nano-sized magnets is induced by a femtosecond laser pulse, the frequency of which lies in the transparency region of the magnet material. It is shown that an alternating magnetic field applied to the XOY plane generates the magnetic equilibrium position vectors and elliptical precession occurs if a constant magnetic field acts along the Z axis. In this case the precession angle changes periodically in time and the precession frequency is determined by the amplitude of the total magnetic field.

3D Hybrid Segmented Layer Modeling of On-Load Magnetic Fields and Torques for Coreless Axial-Flux Permanent Magnet Synchronous Motor

This paper presents a novel 3-dimensional hybrid segmented layer model (3D HSLM) for coreless axial-flux permanent magnet synchronous motors (AFPMSMs). In the proposed 3D HSLM, the magnetic field sources are divided into the PM array and current-driven electro-magnets, which are captured by the combination of the magnetic scalar potential and vector potential models. This paper proposes a geometry function and cylindrical harmonic index modulation functions in order to correctly capture the curvature effect by the PMs and coils with arbitrary shapes and also the radial edge effect from the finite lengths of the rotor and the stator. The proposed modeling method also enables accurate estimation of the motor characteristics on the on-load conditions using the magnetic vector potential model. The fidelity of the proposed 3D HSLM is validated against the equivalent FEM models for various cases with different PM and coil shapes, in terms of the airgap magnetic fields, motor torque, and flux linkage. The comparison results show that the proposed 3D HSLM yields a modeling accuracy of more than 98% while significantly reducing the calculation time by two orders of magnitude as compared to the FEM models.

Hybrid Simulation and Quasi-linear Theory of Bi-Kappa Proton Instabilities

The quasi-steady states of collisionless plasmas in space (e.g., in the solar wind and planetary environments) are governed by the interactions of charged particles with wave fluctuations. These interactions are responsible not only for the dissipation of plasma waves but also for their excitation. The present analysis focuses on two instabilities, mirror and electromagnetic ion cyclotron instabilities, associated with the same proton temperature anisotropy T ⊥ > T ∥ (where ⊥, ∥ are directions defined with respect to the local magnetic field vector). Theories relying on standard Maxwellian models fail to link these two instabilities (i.e., predicted thresholds) to the proton quasi-stable anisotropies measured in situ in a completely satisfactory manner. Here we revisit these instabilities by modeling protons with the generalized bi-Kappa (bi-κ power-law) distribution, and by a comparative analysis of a 2D hybrid simulation with the velocity-moment-based quasi-linear (QL) theory. It is shown that the two methods feature qualitative and, even to some extent, quantitative agreement. The reduced QL analysis based upon the assumption of a time-dependent bi-Kappa model thus becomes a valuable theoretical approach that can be incorporated into the present studies of solar wind dynamics.

Study of the Effect of Inverse Magnetostriction in Ferromagnet/Ferroelectric Heterostructures Using Ab Initio Calculations

Fe/BaTiO3, Fe/SrTiO3, Co/BaTiO3, and Co/SrTiO3 heterostructures, which exhibit magnetoelectric effect, have been investigated. It is shown that the magnetic properties of thin ferromagnetic films can be controlled using an external electric field. The structural, electronic, and magnetic properties of the heterostructures have been investigated applying ab initio calculation methods. It is shown that, using the inverse piezoelectric effect, one can reduce the absolute value of the ferromagnet magnetization vector. This approach may be a basis for controlling the properties of one of the ferromagnetic layers of a superconducting spin valve and, as a consequence, the superconducting properties of the valve.

PEAT DEPOSITS AS A NEW SOURCE OF PALEOMAGNETIC RECORDS IN THE HOLOCENE AS EXEMPLIFIED BY THE ETRUSSIA EXCURSION

The paper presents the results of microprobe, paleomagnetic and rock magnetic studies on peats from the Tyapka peat section (Khabarovsk region) formed 4 thousand years. Alternating field demagnetization of peats yielded a horizon of 57–109 cm (1833–3083 cal. BP) with negative inclination values of the magnetization vector, which corresponds to the geomagnetic Etrussia excursion. Obtaining relative paleointensity estimates for peats was pioneered, which are consistent with the literature archeomagnetic data for the western part of Eurasia. It was found that the Etrussia excursion took place against the background of increased values of the Earth’s magnetic field, and its duration was ~ 1200 years.

A fully discrete finite element method for a constrained transport model of the incompressible MHD equations

In this paper, we propose and analyze a fully discrete finite element method for a constrained transport (CT) model of the incompressible magnetohydrodynamic (MHD) equations. The spatial discretization is based on mixed finite elements, where the hydrodynamic unknowns are approximated by stable finite element pairs, the magnetic field and magnetic vector potential are discretized by H(curl)-conforming edge element. The time marching is combining a backward Euler scheme and some subtle implicit-explicit treatments for nonlinear and coupling terms. With these treatments, the fully discrete scheme is linear in the implementation and the computation of the magnetic vector potential is decoupled from the whole coupled system. The most attractive feature of this scheme that it can yield the exactly divergence-free magnetic field and current density on the discrete level. The unique solvability and unconditional stability of the scheme are also proved rigorously. By utilizing the energy argument, error estimates for the velocity, magnetic field and magnetic vector potential are further demonstrated under the low regularity hypothesis for the exact solutions. Numerical results are provided to verify the theoretical analysis and to show the effectiveness of the proposed scheme.

The influence of the δ-doping on the electron transport with the finite periodic magnetic barriers nanostructure

Periodic nanostructure is a novel method to manipulate the electronic properties in electronics. An efficient method in this paper is proposed to judge whether m identical periods’ magnetic nanostructure is a periodic structure by judging whether its physical structure and its magnetic vector potential structure both keep periodic. By investigating the influence of the [Formula: see text]-doping potential on the electron transport properties with m identical periods’ magnetic barrier nanostructure of InAs system, it shows that, firstly, the resonant peak of transmission probability, conductance, and spin polarization has been induced by splitting into (2[Formula: see text]) folds with m units nanostructure, respectively, especially when the resonant peak of transmission probability is almost close to 1 as the incident energy is lower; secondly, the height of [Formula: see text]-doping potential has an extensive influence on the resonant peak of transmission probability, which the resonant peak will be more dependent of the height of [Formula: see text]-doping potential increasing. Meanwhile, the conductance will be decreased with the height of [Formula: see text]-doping potential increasing.

Classification of Killing magnetic curves in ℍ3

In this paper, we study classification of magnetic curves corresponding to Killing vector fields of [Formula: see text]. First, we solve the geodesic equation analytically. Then we calculate the trajectories generated by all the six Killing vector fields, which are considered as magnetic field vectors, by using perturbation method up to first-order with respect to the strength of the magnetic field. We present a comparison of our solution with the numerical solution for one case. We also prove that 3-dimensional [Formula: see text]-Kenmotsu manifolds cannot have any magnetic vector field in the direction of their Reeb vector fields.