Magnetic Vector Research Articles

Er-driven incommensurate to commensurate magnetic phase transition of Fe in the spin-chain compound BaErFeO4

Magnetic phase transitions and structures of the spin-chain compound BaErFeO4 were investigated by measurements of magnetic properties (specific heat, magnetic susceptibility) and neutron diffraction. The lattice geometry of the orthorhombic crystal structure (space group ) of the BaRFeO4 compounds (R=Dy–Yb, Y) supports frustrations which lead to multiple magnetic phase transitions with complex magnetic structures. BaErFeO4 undergoes three successive magnetic phase transitions at TN1=49K, TN2=33.4K, and TN3=3.4K. In contrast with the previously investigated BaRFeO4 (R=Y, Tm, Yb) compounds, all with incommensurate magnetic propagation vectors k1=(0,0,kz), BaErFeO4 is the first member in this series that shows a phase transition from an incommensurate (k1 below TN1) to a commensurate magnetic structure with k2=(12,0,12) below TN2. In the crystal structure, all magnetic ions (Fe1, Fe2, Er1, and Er2) are part of chains propagating along the b axis. Below TN1, strong antiferromagnetic (AFM) Fe-Fe spin-exchange coupling between square pyramidal (Fe1) and octahedral (Fe2) centers generates a collinear AFM structure with a constant size of the ordered Fe moments and a constant magnetic phase inside each chain of Fe3+ cations. Exchange coupling between the Fe chains is much weaker. At TN2, 3d−4f exchange interactions induce an ordered moment at the Er3+ ions, which results in a change of the direction of the ordered Fe moments from the b direction (above TN2) to inside the ac plane (below TN2) and a change from an incommensurate (k1 above TN2) to a commensurate (k2 below TN2) AFM structure. Toward lower temperature, 4f−4f exchange interactions become stronger and create at TN3 a constant magnetic phase inside each chain of Er3+ cations. At TN2 and TN3, the magnetic susceptibility shows sharp decreases that coincide with large increases of the correlation length of the magnetic structure. The unique magnetic structures of BaErFeO4 are compared with those of other BaRFeO4 compounds by considering experimental and theoretical aspects. ©2024 American Physical Society 2024 American Physical Society

Surface charge and surface current densities at material boundaries

In electromagnetism, materials with a polarization density P→ or a magnetization density M→ are known to exhibit a bound surface charge density σb=P→·n̂ or a surface current density κ→b=M→×n̂, respectively, where n̂ is the unit vector perpendicular to the material boundary surface, directed outward. These expressions can be obtained from volume integrations for the electric potential V, or the magnetic vector potential A→, in which the integrals are restricted to the material volumes delimited by their respective boundaries. In that case, applying the divergence theorem leads to surface integrals on material boundaries and to the above-mentioned surface quantities. In this paper, a simple derivation is presented, which shows that both σb and κ→b are included in the expressions for the volume charge or current densities, provided that the divergence and curl operators are evaluated at the boundary so as to account for discontinuities at interfaces.

Machine learning based classification of vector field configurations

Magnetic materials at the nanoscale are important for science and technology. A key aspect for their research and advancement is the understanding of the emerging magnetization vector field configurations within samples and devices. A systematic parameter space exploration—varying for example material parameters, temperature, or sample geometry—leads to the creation of many thousands of field configurations that need to be sighted and classified. This task is usually carried out manually, for example by looking at a visual representation of the field configurations. We report that it is possible to automate this process using an unsupervised machine learning algorithm, greatly reducing the human effort. We use a combination of convolutional auto-encoder and density-based spatial clustering of applications with noise (DBSCAN) algorithm. To evaluate the method, we create the magnetic phase diagram of a FeGe disc as a function of changing external magnetic field using computer simulation to generate the configurations. We find that the classification algorithm is accurate, fast, requires little human intervention, and compares well against the published results in the literature on the same material geometry and range of external fields. Our study shows that machine learning can be a powerful tool in the research of magnetic materials by automating the classification of magnetization field configurations.

Analytical Solution of Eddy Current in Parallel Conducting Strips for Low-frequency Shielding Purposes

In instrumentation systems, shielding is the main issue that judges the performance of the system. The electromagnetic (EM) noise may affect the performance of the instrumentation system if inadequate protection is reached. It is considered the main source of unprotectable interference that may affect these systems in many cases. In this paper, shielding is attained by wrapping the source carrying signal with periodic thin conductive strips separated by slots or openings. This arrangement will protect the sources from the outside EM fields. Shielding factor and shielding efficiency are studied by extracting magnetic fields. For this purpose, an analytical solution based on solving Laplace’s equation for the magnetic vector potential in the region of interest is presented. A closed form of the induced eddy current in the conductive strips is calculated based on Fourier series expansion. Furthermore, numerical simulation using the commercial software MWS CST is employed to validate the analytical solution. The performance of the proposed shielding structure is studied and analyzed in terms of shielding factor and shielding efficiency. The outcomes of both methods are showing very good agreement.

Application of bioinspired geomagnetic sensor measurements and geomagnetic map modeling based on neural networks in simulated navigation

A geomagnetic field is a vector field in which the strength and direction are related to geographical location. Geomagnetic navigation technology, which uses collected geomagnetic field information to achieve positioning and navigation, has the advantages of reliability, stability, accuracy, and concealment. With the deepening research on geomagnetic navigation, bioinspired geomagnetic navigation technology has also been developed, which mainly studies and imitates the magnetic sensing mechanism and navigation behavior of animals, providing new research ideas for geomagnetic navigation technology. The magnetic particle hypothesis and free radical pair hypothesis are two mainstream mechanisms of biological sensing using the geomagnetic field, and studies have shown that these two mechanisms may be coupled within organisms. In this study, we propose a bioinspired weak magnetic vector (BWMV) sensor based on the joint sensing mechanism of magnetic particles and free radicals. It consists of a magnetic rod made of soft magnetic material and a tunnel magnetoresistance (TMR) sensor array. A magnetic rod was used to simulate magnetic particles to convert magnetic field angle information into magnetic field intensity distribution information, and the TMR sensor array was used to simulate the perception of the magnetic field distribution by free radicals. In addition, artificial neural networks (ANNs) were used for BWMV sensors to obtain the mapping relationship between the magnetic field distribution and parameters, which can be used for geomagnetic navigation. To verify the navigation effect of the BWMV sensor in the laboratory, a simulated geomagnetic navigation device was built, and the high-precision mapping relationship from geomagnetic parameters to latitude and longitude information of the selected navigation area was obtained through another ANN. Finally, the effectiveness of the BWMV sensor based on ANNs for geomagnetic navigation is verified using simulated navigation experiments.

Construction and interpretation of high-order image information based on NV optical magnetic vector detection.

Tensor imaging can provide more comprehensive information about spatial physical properties, but it is a high-dimensional physical quantity that is difficult to observe directly. This paper proposes a fast-transform magnetic tensor imaging method based on the NV magnetic detection technique. The Euler deconvolution interprets the magnetic tensor data to obtain the target three-dimensional (3D) boundary information. Fast magnetic vector imaging was performed using optical detection of magnetic resonance (ODMR) to verify the method's feasibility. The complete tensor data was obtained based on the transformation of the vector magnetic imaging data, which was subsequently solved, and the contour information of the objective was restored. In addition, a fast magnetic moment judgment model and an angular transformation model of the observation space are developed in this paper to reduce the influence of the magnetic moment direction on the results and to help interpret the magnetic tensor data. Finally, the experiment realizes the localization, judgment of magnetic moment direction, and 3D boundary identification of a micron-sized tiny magnet with a spatial resolution of 10 µm, a model accuracy of 90.1%, and a magnetic moment direction error of 4.2°.

Optical quantum conformable normalized and recursional model in Minkowski space

In this paper, we construct electromagnetic conformable timelike particles with Bishop model in Minkowski space. Also, we obtain conformable derivatives of Γt\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Gamma \\left( {\ extbf{t}}\\right) $$\\end{document}, Γm1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Gamma \\left( {\ extbf{m}}_{1}\\right) $$\\end{document}, Γm2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Gamma \\left( {\ extbf{m}}_{2}\\right) $$\\end{document} Lorentz forces. Then, we compute normalizing and recursion operators of magnetic vector fields according to Bishop model. Finally, we determine F–W conformable derivatives for normalizing and recursional operators.

Spin-Valve-Controlled Triggering of Superconductivity

We have studied the proximity effect in an SF1S1F2s superconducting spin valve consisting of a massive superconducting electrode (S) and a multilayer structure formed by thin ferromagnetic (F1,2) and superconducting (S1, s) layers. Within the framework of the Usadel equations, we have shown that changing the mutual orientation of the magnetization vectors of the F1,2 layers from parallel to antiparallel serves to trigger superconductivity in the outer thin s-film. We studied the changes in the pair potential in the outer s-film and found the regions of parameters with a significant spin-valve effect. The strongest effect occurs in the region of parameters where the pair-potential sign is changed in the parallel state. This feature reveals new ways to design devices with highly tunable inductance and critical current.

Fast Magnetization Vector Inversion Method with Undulating Observation Surface in Spherical Coordinate for Revealing Lunar Weak Magnetic Anomaly Feature

The three-dimensional magnetic vector structure (magnetization intensity and direction) of the planet can be effectively used to analyze the characteristics of its formation and operation. However, the quick acquisition of a large region of the magnetic vector structure of the planet with bigger observation surfaces undulation is hard and indispensable. We firstly proposed a fast magnetization vector inversion method for the inversion of a magnetic anomaly with the undulating observation surfaces in the spherical coordinate system, which first transforms the data to a plane when the data are distributed on a surface. Then, it uses a block-Toeplitz-Toeplitz-block (BTTB)-FFT to achieve fast inversion with the constraint that the magnetization intensities of the grids between the transformed observation surfaces and the terrain are zero. In addition, Gramian constraint term is used to reduce the ambiguity of the magnetic vector inversion. The theoretical model tests show that the proposed method can effectively improve the computational efficiency by 23 times in the 60 × 60 × 10 grid division compared to the conventional inversion method, and the accuracy of the two computation methods is comparable. The root-mean-square error of the magnetization intensity is only 0.017, and the angle error is within 1°. The magnetization vector structure shows that the largest crater diameter does not exceed 340 km in the Mare Australe region, the amplitude of the magnetic anomaly is much higher than the current meteorite impact simulation results, and the depth of the magnetic source is less than 10 km, which cannot be explained by the impact simulation experiments. In addition, the magnetization directions of adjacent sources differ by 122° (or 238°), and the high-frequency dynamics of the Moon as well as the short-lived dynamics may be responsible for this phenomenon. The magnetization directions of the three adjacent sources in the Mare Crisium region are close to each other and differ in depth with different cooling times, making it difficult to record the transient fields produced by meteorite impacts. In addition to the above characteristics, the magnetization direction of the magnetic sources in both regions is uniformly distributed without reflecting the dispersion of the magnetization direction of the meteorite impact magnetic field. Therefore, it can be inferred that the magnetic anomalies in these two regions are related to the generator hypothesis.

Magnetoelastic effect of kimberlite host rocks (Yakutsk diamondiferous province)

The purpose of the research is to conduct petro- and paleomagnetic studies of Early Paleozoic rocks of the carbonate basement of a number of diamond deposits in the Yakutsk diamondiferous province in order to study the changes in petrophysical parameter values in the dynamic influence zone of a kimberlite pipe. It is shown that the formation of kimberlite diatremes accompanied by pulsating explosions shifting upwards brings about thermoelastic stress fields in the kimberlite-bearing medium, which are characterized by epigenetic changes and associated petrophysical heterogeneities (petrophysical anomalies). Petromagnetic heterogeneities of burning and stress are, therefore, some of these petrophysical anomalies, within which kimberlite-bearing rocks have contrastingly changed their original magnetic characteristics under the action of thermodynamic processes. Primarily, petromagnetic anomalies are reflected in the changed nature of the anisotropy of magnetic susceptibility: from sedimentary to dyke geotype. In addition, petromagnetic anomalies of magnetic susceptibility can be accompanied by the formation of metachronous natural residual magnetization vectors in kimberlite host rocks. The dimensions of petromagnetic anomalies (petromagnetic heterogeneities) may significantly exceed the size of the kimberlite pipe itself, which facilitates identification and delineation of the most promising areas. Besides, the magnetoelastic effect can create zones close to the kimberlite bodies that are hardly permeable for relatively viscous, protocrystal-rich mafic magmas. This is the reason for their wedging out along petrophysical barriers that is presented by splitting into thin tongues, formation of trap-free windows and corridors, toroidal shafts with sharply increasing thickness in intrusions, etc. Having relatively elevated values of magnetic and density parameters, such forms of igneous formations will be reflected in the observed geophysical fields. Thus, it is reasonable to consider petromagnetic anomalies as an important petrophysical search criterion for the detection of bedrock kimberlite bodies.

Analysis of Varying Temperature Regimes in a Conductive Strip during Induction Heating under a Quasi-Steady Electromagnetic Field

Transition processes in a steel conductive strip are analyzed during its induction heating under a quasi-steady electromagnetic field. In particular, the temperature field in the strip is studied. A method of solving corresponding initial boundary problems in a two-dimensional mathematical model for differential equations of electrodynamics and heat conduction is developed. The Joule heat and the temperature are determined with a high level of accuracy. The defining functions are the temperature and component of the magnetic field intensity vector tangent to the bases and end planes of the strip. To find them, we use cubic approximation of the defining functions’ distribution along the thickness coordinate. The original two-dimensional initial boundary value problems for the defining functions are reduced to one-dimensional initial boundary value problems on their integral characteristics. General solutions for these problems are obtained using the finite integral transformation by the transverse variable and the Laplace transform of the integral by time. Integral characteristics’ expressions are represented as convolutions for functions that describe homogeneous solutions of one-dimensional initial boundary value problems and limiting values of defining functions on the bases and end planes of the strip. The change of temperature under a varying regime in the dimensionless Fourier time and temperature distribution over the strip cross-section in a steady state depending on the parameters of induction heating and the Biot number are numerically analyzed. Varying and constant temperature regimes of the strip under conditions of the near-surface and continuous induction heating are studied.

Error analysis of the linearized Crank-Nicolson FEM for the incompressible vector potential magnetohydrodynamic system

A linearized fully discrete Crank-Nicolson finite element scheme is proposed for solving the three-dimensional incompressible magnetohydrodynamic equations based on a magnetic vector potential formulation, where the magnetic induction is written to a rotation of magnetic vector potential. By using the MINI element and lowest order Nédélec edge element to approximate the velocity field and pressure of fluid and magnetic vector potential, respectively, the numerical solution of magnetic induction can preserve the exactly divergence-free condition in fully discrete level. Error estimates for the velocity field and magnetic vector potential are rigorously analyzed under some reasonable regularity assumptions of exact solution. Finally, numerical results are given to support the theoretical analysis.

An improved attitude estimation algorithm for suppressing magnetic vector disturbance based on extended Kalman filter

This paper proposes an improved attitude estimation algorithm based on the extended Kalman filter (EKF), and it is applied to suppress the accuracy reduction in attitude estimation caused by fusing magnetometer data under large angular motion. In the proposed attitude estimation structure, the approximate variance of the estimated horizontal northbound magnetic vector is used to dynamically adjust the participation of magnetometer data in attitude estimation, as the approximate variance increases significantly under large angular motion and fusing magnetometer data will reduce estimation accuracy. A three-axis position-velocity controlled turntable is used to conduct rocking experiments for validating the proposed attitude estimation algorithm. The results show a significant improvement in yaw angle estimation accuracy with the proposed attitude estimation algorithm and correspondingly enhance the distribution of pitch and roll angle errors.

A Fokker–Planck Framework for Studying the Variability of the Magnetic Field Direction in the Alfvénic Streams of the Solar Wind

Turbulent rotations of the magnetic field vector are observed in the Alfvénic streams of the solar wind where the magnetic field strength remains close to a constant. They can lead to reversals of the radial magnetic field component or switchbacks. It is not ruled out from the data that the rotations are divisible into the sum of small random angular deflections. In this work, we develop tools aimed at the analysis of the one-point statistical properties of the directional fluctuations of the magnetic field vector in the solar wind. The angular fluctuations are modeled by a drift-diffusion process which admits the exponential distribution as steady-state solution. Realizations of the stochastic process are obtained by solving the corresponding Langevin equation. It is shown that the cumulative effects of consecutive small-angle deflections can yield frequent reversals of the magnetic field vector even when the concentration parameter of the directional data is large. The majority of the rotations are associated with nearly transverse magnetic field fluctuations in this case.

Nonlinear Pauli equation

<abstract> <p>In the framework of the self-consistent Maxwell-Pauli theory, the non-linear Pauli equation is obtained. Stationary and nonstationary solutions of the nonlinear Pauli equation for the hydrogen atom are studied. We show that spontaneous emission and the related rearrangement of the internal structure of an atom, which is traditionally called a spontaneous transition, have a simple and natural description in the framework of classical field theory without any quantization and additional hypotheses. The behavior of the intrinsic magnetic moment (spin) of an EW in an external magnetic field is considered. We show that, according to the self-consistent Maxwell-Pauli theory, in a weak magnetic field, the intrinsic magnetic moment of an EW is always oriented parallel to the magnetic field strength vector, while in a strong magnetic field, depending on the initial orientation of the intrinsic magnetic moment, two orientations are realized: either parallel or antiparallel to the magnetic field strength vector.</p> </abstract>

Coherent THz spin dynamics in antiferromagnets beyond the approximation of the Néel vector

Controlled generation of coherent spin waves with highest possible frequencies and shortest possible wavelengths is a cornerstone of spintronics and magnonics. Here, using Heisenberg antiferromagnet RbMnF3, we demonstrate that laser-induced THz spin dynamics corresponding to pairs of mutually coherent counter-propagating spin waves with the wavevectors up to the edge of the Brillouin zone cannot be understood in terms of magnetization and antiferromagnetic (Néel) vectors, conventionally used to describe spin waves. Instead, we propose to model such spin dynamics using the spin correlation function. We derive a quantum-mechanical equation of motion for the latter and emphasize that unlike the magnetization and antiferromagnetic vectors the spin correlations in antiferromagnets do not exhibit inertia.

3D Polarisation of a Structured Laser Beam and Prospects for its Application to Charged Particle Acceleration

A Structured Laser Beam (SLB) is a type of optical beam with spatially inhomogeneous 3D polarisation structures. Generating SLBs from vector beams allows the creation of Hollow Structured Laser Beams (HSLB) with a dark central core. In this way, atypical electric and magnetic field vectors, which are purely longitudinally polarized in the dark zones of the beam, are obtained. The SLB spatial distribution can also include regions with both the electric and magnetic fields longitudinally polarized and oriented in the same or opposite directions. The SLB has a transverse distribution similar to that of a Bessel beam but can theoretically propagate to infinity, therefore giving the potential to generate strong, longitudinally oriented electric fields over long distances, which could possibly allow the acceleration of charged particles. The results of the study of this phenomenon, including simulations of the spatial distribution of the electromagnetic field components, are presented in this paper.

Research on the design of a novel composite solenoid model ship simulation magnetic source based on DTW

In order to study the simulation ability of a solenoid on a ship magnetic field, a new composite model based on a double row magnetic dipole array model with an ellipsoid was designed. The time-domain characteristics, such as magnetic field characteristics, magnetic inclination cosine, magnetic field scalar gradient, and magnetic field spatial distribution characteristics, were extracted. It was verified that the model can accurately simulate the magnetic field characteristics of ships through ship model experiments and simulation analysis. To further quantitatively and accurately analyze the simulation ability of the composite model for ship magnetic fields, a dynamic time wrapping measurement method based on one-dimensional time series was adopted to calculate the similarity of four characteristic quantities: magnetic field vector, magnetic field modulus, magnetic inclination cosine, and magnetic field scalar gradient. The results showed that the composite model has high simulation ability for ship magnetic fields.

THRESHOLD EFFECT IN DUSTY CLUSTERS IN A MAGNETIC FIELD

The process of occurrence of rotational motion of dusty plasma in a longitudinal magnetic field was investigated. It was experimentally found that the occurrence of rotation depends on the number of dust particles in the direction perpendicular to the magnetic induction vector, as well as on their vertical position in the dust trap (i.e., the magnitude of the electric field). The value of the threshold for the appearance of rotation in the magnetic field at a constant number of particles depends on the particle size and discharge conditions. The parameters of the experiment are selected, at which the effect manifests itself in detail. It has been established that for stationary rotation, a stable position of dust particles in the cross section is required, which corresponds to the filling of the shells of a rotating dust structure.

Enhanced chiroptical activity for narrow deep-blue emission in axial chiral frameworks via three-dimensional interlocking.

The advancement of desirable circularly polarized luminescence (CPL) emitters is predominantly constrained by the effective regulation of magnetic and electric transition vectors, particularly within the deep-blue spectral domain. Herein, we present four pairs of novel chiral emitters with systematically varied molecular rigidity, symmetry, and chiral centers to elucidate the intrinsic coupling of key molecular parameters influencing their chiroptical properties. Notably, the incorporation of appropriate intramolecular 3D-interlocking within a natural binaphthyl chirality skeleton offers an effective approach to achieving both significantly narrowed full width at half maximum (FWHM, as low as 18 nm) and substantially enhanced chiroptical activity (luminous dissymmetry factor, g PL, up to 3.0 × 10-3). Additionally, introducing a secondary chiral center closely parallel to the primary chiral plane facilitates strong chiral-chiral interactions, further affording a 50% improvement in their g PL values. As a demonstration, vacuum-deposited circularly polarized organic light-emitting diodes incorporating these pure fluorescent emitters exhibit outstanding electroluminescent performance, with maximum external quantum efficiency exceeding 5.35%, favorable FWHM of approximately 25 nm, and extreme CIE y values below 0.03.