Magnetic Charge Distribution Research Articles

Finding an analytical solution for the cylinder’s fluxmetric demagnetizing factor using spherical harmonics

The work examines an analytical solution for calculating the fluxmetric demagnetizing factor of cylindrical magnets at large values of magnetic susceptibility and an arbitrary value of elongation. The application of the analytical solution for calculating the demagnetizing factor significantly simplifies the modeling and calculation of magnetic characteristics of cylindrical technical objects. A simplified analytical model of the scalar potential of the magnetic field of a cylinder with infinite magnetic favorability, inductively magnetized in a uniform magnetic field, was constructed using an approximate representation of the distribution of fictitious magnetic charges on its surface. The method of spherical harmonic analysis for the magnetic field was used, which made it possible to obtain an analytical representation of the demagnetization field in the central cross section of the cylinder. Limitation of the harmonic series of this representation by seven first harmonics is proposed, and an additional amplitude factor is applied to correct the contribution of the first harmonic to the demagnetization field. This made it possible to compensate for the distortion of the magnetic field near the ends of the cylinder and bring the simplified analytical model closer to the target mathematical model with a uniform demagnetization magnetic field. The reliability of the results of calculating the fluxmetric demagnetizing factor according to the derived formula was evaluated by comparing them with the known results obtained using the numerical method of calculation and according to empirical formulas. It is shown that the proposed approach makes it possible to obtain reliable results of calculating the fluxmetric demagnetizing factor with a deviation of up to 5 % at infinite favorability in the range of cylinder elongation values from 0.01 to 500

Revealing emergent magnetic charge in an antiferromagnet with diamond quantum magnetometry.

Whirling topological textures play a key role in exotic phases of magnetic materials and are promising for logic and memory applications. In antiferromagnets, these textures exhibit enhanced stability and faster dynamics with respect to their ferromagnetic counterparts, but they are also difficult to study due to their vanishing net magnetic moment. One technique that meets the demand of highly sensitive vectorial magnetic field sensing with negligible backaction is diamond quantum magnetometry. Here we show that an archetypal antiferromagnet-haematite-hosts a rich tapestry of monopolar, dipolar and quadrupolar emergent magnetic charge distributions. The direct read-out of the previously inaccessible vorticity of an antiferromagnetic spin texture provides the crucial connection to its magnetic charge through a duality relation. Our work defines a paradigmatic class of magnetic systems to explore two-dimensional monopolar physics, and highlights the transformative role that diamond quantum magnetometry could play in exploring emergent phenomena in quantum materials.

An improved magnetic dipole model for MFL testing based on non-uniform magnetic charge distribution

ABSTRACT Magnetic flux leakage (MFL) signal prediction is important in ferromagnetic defect evaluation and reconstruction. At present, the magnetic dipole model (MDM) is the most widely applied method because of its high efficiency. However, it has low accuracy when applied to analysing complex defects (complex in profile and magnetic permeability) due to the original setting of uniform magnetic charge distribution. To solve the issue, this paper proposes an improved MDM method for MFL inspection of ferromagnetic materials by calculating the non-uniform magnetic charge distribution. It partly applies the finite volume method (FVM) to derive the magnetic charge distribution on the defect surface, which makes it able to take into account the defect’s profile and magnetic permeability distribution. The new magnetic charge distribution can increase the MDM’s accuracy for complex defect MFL field prediction with little extra cost. Experimental results show that, when compared with traditional MDM, the proposed one can achieve a maximum 69% decrease in root mean squared error when analysing complex defects. Compared with the numerical method, the computation time could reach a great reduction.

Observation and formation mechanism of 360° domain wall rings in synthetic anti-ferromagnets with interlayer chiral interactions

The interlayer Dzyaloshinskii–Moriya interaction (IL-DMI) chirally couples spins in different ferromagnetic layers of multilayer heterostructures. So far, samples with IL-DMI have been investigated utilizing magnetometry and magnetotransport techniques, where the interaction manifests as a tunable chiral exchange bias field. Here, we investigate the nanoscale configuration of the magnetization vector in a synthetic anti-ferromagnet (SAF) with IL-DMI, after applying demagnetizing field sequences. We add different global magnetic field offsets to the demagnetizing sequence in order to investigate the states that form when the IL-DMI exchange bias field is fully or partially compensated. For magnetic imaging and vector reconstruction of the remanent magnetic states, we utilize x-ray magnetic circular dichroism photoemission electron microscopy, evidencing the formation of 360° domain wall rings of typically 0.5–3.0 μm in diameter. These spin textures are only observed when the exchange bias field due to the IL-DMI is not perfectly compensated by the magnetic field offset. From a combination of micromagnetic simulations, magnetic charge distribution, and topology arguments, we conclude that a non-zero remanent effective field with components both parallel and perpendicular to the anisotropy axis of the SAF is necessary to observe the rings. This work shows how the exchange bias field due to IL-DMI can lead to complex metastable spin states during reversal, important for the development of future spintronic devices.

Exact multicentered static point charge source distributions in the Born–Infeld theory of nonlinear electromagnetism and presence of electric and magnetic currents

Exact multicentered solutions to the governing equations of the Born–Infeld nonlinear theory of electrodynamics describing distributions of electric, magnetic, and dyonic point charge sources are constructed explicitly for the first time. The method of construction may effectively be adapted to obtain such solutions in generalized theories as well. As a consequence, the solutions unveil that, in order to achieve a balance between such multicentered electric or magnetic point charge distribution in equilibrium, a static magnetic or electric current must be present, resulting in non-conservativeness of the induced electric or magnetic intensity field, respectively and universally. Moreover, it is also shown that the methods of construction and conclusions drawn in the multicentered situation may be extended to obtain exact solutions and similar conclusions, explicitly, in the situation of continuously distributed charge source problems.

Exploring the phase diagram of 3D artificial spin-ice

Artificial spin-ices consist of lithographic arrays of single-domain magnetic nanowires organised into frustrated lattices. These geometries are usually two-dimensional, allowing a direct exploration of physics associated with frustration, topology and emergence. Recently, three-dimensional geometries have been realised, in which transport of emergent monopoles can be directly visualised upon the surface. Here we carry out an exploration of the three-dimensional artificial spin-ice phase diagram, whereby dipoles are placed within a diamond-bond lattice geometry. We find a rich phase diagram, consisting of a double-charged monopole crystal, a single-charged monopole crystal and conventional spin-ice with pinch points associated with a Coulomb phase. In experimental demagnetised systems, broken symmetry forces formation of ferromagnetic stripes upon the surface, forbidding the lower energy double-charged monopole crystal. Instead, we observe crystallites of single magnetic charge, superimposed upon an ice background. The crystallites are found to form due to the distribution of magnetic charge around the 3D vertex, which locally favours monopole formation.

Research on the Forward Solving Method of Defect Leakage Signal Based on the Non-Uniform Magnetic Charge Model.

Pipeline magnetic flux leakage inspection is widely used in the evaluation of material defect detection due to its advantages of having no coupling agent and easy implementation. The quantification of defect size is an important part of magnetic flux leakage testing. Defects of different geometrical dimensions produce signal waveforms with different characteristics after excitation. The key to achieving defect quantification is an accurate description of the relationship between the magnetic leakage signal and the size. In this paper, a calculation model for solving the defect leakage field based on the non-uniform magnetic charge distribution of magnetic dipoles is developed. Based on the traditional uniformly distributed magnetic charge model, the magnetic charge density distribution model is improved. Considering the variation of magnetic charge density with different depth positions, the triaxial signal characteristics of the defect are obtained by vector synthesis calculation. Simultaneous design of excitation pulling experiment. The leakage field distribution of rectangular defects with different geometries is analyzed. The experimental results show that the change in defect size will have an impact on the area of the defect leakage field distribution, and the larger the length and wider the width of the defect, the more sensitive the impact on the leakage field distribution. The solution model is consistent with the experimentally obtained leakage signal distribution law, and the model is a practical guide by which to improve the quality of defect evaluation.

Engineering the electronic structure on MXenes via multidimensional component interlayer insertion for enhanced electromagnetic shielding

• CNTs/Ni hybrids were used as an isolation agent to disperse Ti 3 C 2 T x sheets in the interlayers, which form a multiple-dimensional laminated structure. • Introduction of 2D hexagonal magnetic Ni flakes boosts interfacial polarization and magnetic-responding ability, visualized by electron holography. • The 3D freestanding films can achieve precise regulation of components and excellent EMI shielding performance (67.4 dB). MXene-based functional electromagnetic interference (EMI) shielding films are highly desirable for modern integrated electronic and telecommunication systems in aerospace, military, artificial intelligence, and smart and wearable electronics field. In this work, 3D freestanding Ti 3 C 2 T x /CNTs/Ni film assembled by 1D multi-walled carbon nanotubes (MWCNTs)/Ni and 2D Ti 3 C 2 T x MXene sheets was synthesized by a facile vacuum filtration process. By electrostatic incorporation, hexagonal nickel plates embed on the CNTs and then the CNTs/Ni insert into the Ti 3 C 2 T x layers to form magnetized Ti 3 C 2 T x -based functional film with a compact and laminated structure. Due to the outstanding electron migration capacity in the highly conductive Ti 3 C 2 T x sheet and multiple internal reflections from porous and segregated structures, the optimized Ti 3 C 2 T x /CNTs/Ni composite films show excellent EMI shielding effectiveness of 67.4 dB with electrical conductivity of 744 S cm –1 . Surprisingly, a magnetization compensation strategy is built to boost the EMI shielding effectiveness with decreased conductivity. Meanwhile, the visual magnetic coupling phenomenon and charge distribution in the heterogeneous interfaces could be observed in the reconstructed electron holography images. Those encouraging results shed light on novel magnetized MXene-based functional films for high-performance EMI shielding.

Study of MFL signal identification in pipelines based on non-uniform magnetic charge distribution patterns

Magnetic flux leakage (MFL), a pipeline internal detection, is the mainstream technology for international oil and gas pipeline safety maintenance. To address the problem of large errors in the assessment of defects in pipeline inspection by existing theoretical analysis models, this paper introduces the charge density parameter to establish a mathematical model of non-uniform magnetic charge for pipeline leakage detection and calculates the non-uniform distribution pattern of magnetic charge on the defect side wall. The contour plot method is proposed to visually analyze the size of defects. To compare the error between uniform and non-uniform models, and verify the correctness of the theoretical model, experiments were systematically conducted on the X70 pipeline with internal MFL technology. The results show that: the magnetic charge distribution curve is symmetrically shaped at the center of the defect, with a valley at the center and two peaks at the defect edge. As the defect depth and width increase, the magnetic charge density increases sharply near the surface and edge. The peak-to-valley spacing and peak-to-valley values in the contour map of the MFL signal can directly reflect the location and size of defects. The signal characteristic values follow the trend of a first-order decreasing exponential function as the value of the lift-off increases. The first-order derivative of the signal characteristic value tends to decrease and then increase as the mesh size decreases, and the extreme point of the derivative curve is the best mesh size.

Calculation of field and force of Halbach arrays: Improved magnetic charge method for irregular magnetized magnets

Permanent magnets (PMs) are widely used in magnetic machinery. To better predict the performance of PMs, the magnetic field and force need to be calculated. In general applications, PMs are usually magnetized in a direction parallel to their symmetry axes, and the equivalent magnetic charge method (EMCM) can be used to calculate the corresponding magnetic field and force. However, in some particular cases, such as Halbach arrays, the magnetizing directions or shapes of PMs are irregular and cannot be modeled by the normal EMCM that is limited to the magnets with regular shapes and magnetizing directions. In this paper, an improved EMCM is proposed to calculate PMs with irregular magnetizing directions and shapes. The general rules of magnetic charge distribution are given. The standard forms for calculating magnets with irregular magnetizing directions are obtained through the orthogonal decomposition of the magnetizing direction to simplify the calculation. As an illustration, semi-analytical expressions for magnetic field and force of arc-shaped PMs with irregular magnetizing direction are obtained. Furthermore, the application of this method to calculate the 3-D magnetic field and axial magnetic force of Halbach arrays is discussed and compared with the finite element method (FEM) and experimental measurement. It shows that the improved EMCM has good accuracy and greatly reduces the time cost, which can provide reference for the structure design.

The Relationship between Tribo-Magnetization and Wear State during Reciprocating Sliding

In order to investigate the relationship between tribo-magnetization and wear phenomena, a series of sliding-friction tests were carried out using a pin-on-block reciprocator type device, which was specially designed to generate sliding friction and to detect magnetic fields. The tribological behavior was observed by a charge-coupled device (CCD) camera in real time, and the magnetic signal was detected by using a two-axis magnetic sensor. It was found that as the friction continues, both the tangential and the normal components of magnetic field on the material surface increase gradually, and that both the average value of the tangential magnetic field ΔH(x)mean and the peak-to-peak value of the normal magnetic field Vpp at the wear scar clearly reflect changes of the wear state. Furthermore, in order to better understand the tribo-magnetization phenomenon, the changes of surface morphology and wear debris in different wear stages were analyzed. Moreover, an improved magnetic dipole model that considered the distribution of magnetic charges on the worn surface was established. This model can successfully describe the tribo-magnetization phenomenon during the stable wear stage, and should be useful for characterizing frictional wear phenomena in the future.

Estimation method for inverse problems with linear forward operator and its application to magnetization estimation from magnetic force microscopy images using deep learning

ABSTRACT This study considers an inverse problem, where the corresponding forward problem is given by a finite-dimensional linear operator T. The inverse problem has the following form: It is assumed that the number of patterns that the unknown quantity can take is finite. Then, even if the unknown quantity may be uniquely determined from the data. This case is the subject of this study. We propose a method for solving this inverse problem using numerical calculations. A famous inverse problem requires the estimation of the unknown magnetization distribution or magnetic charge distribution in an anisotropic permanent magnet sample from the magnetic force microscopy images. It is known that the solution of this problem is not unique in general. In this work, we consider the case where a magnetic sample comprises cubic cells, and the unknown magnetic moment is oriented either upward or downward in each cell. This discretized problem is an example of the above-mentioned inverse problem: Numerical calculations were carried out to solve this model problem employing our method and deep learning. The experimental results show that the magnetization can be estimated roughly up to a certain depth.

Analytical solution of magneto-mechanical magnetic dipole model for metal magnetic memory method

Magnetic dipole theory has been widely and successfully used to explain the leakage magnetic field signals. Because the model parameter such as magnetic dipole density is not easy to quantify, magnetic dipole theory often needs normalizing in application, which is considered to be unsuitable for quantitatively analyzing the magnetic memory signals with the stress effect. In this paper, the theoretical model of magneto-mechanical coupling magnetic dipole is established, which is suitable for analyzing the stress effect on magnetic signals in magnetic memory testing method. Based on the ferromagnetic theory, the equivalent field under the combined action of the applied load and the magnetic field is determined. And then, the magneto-mechanical analytical model is obtained for the isotropic ferromagnetic material under the weak magnetic field based on the first-order magnetization approximation in the weak magnetization state. Under the assumptions of rectangular and V-shaped magnetic charge distribution for the two-dimensional magnetic signal problem, the theoretical analytical models of the magnetic memory signals from the smooth and cracked specimens, and the analytical models of the magnetic memory signal induced by the rectangular and V-shaped surface defect are established. Based on the analytical solution of the proposed magneto-mechanical magnetic dipole theory, the difference in signal between before and after the failure of the specimen, the signal from the rectangular and V-shaped defect, and other influencing factors and laws of the magnetic signal are analyzed in detail. In particular, the influence of stress, environmental magnetic field, defect morphology and size, lift-off effect, specimen size and other factors on magnetic memory signals can be described based on the analytical solution of magneto-mechanical magnetic dipole models proposed in this paper. The proposed analytical model of magneto-mechanical magnetic dipole in this paper is simple and easy to use, and the present research shows that the proposed analytical solution in this paper can explain some basic experimental phenomena and laws in magnetic memory testing experiments. In addition, the precise magneto-mechanical coupling quantitative model combined with the finite element analysis method is still needed for accurately analyzing the magnetic memory signals in experiment.

Growth mechanism and electronic and magnetic properties of AgnTi alloy clusters

The growth behavior and electronic and magnetic properties of AgnTi (n = 1–16) clusters have been studied by using density functional theory and unbiased structure prediction method. Geometry optimizations indicate that a Ti atom in low-energy AgnTi cluster occupies the highest coordination position. The growth of the ground state structure shows an obvious regularity. The infrared, Raman and photoelectron spectra of AgnTi isomers have been simulated and can be used for their structural identification in the future. The AgnTi clusters with 19 and 17 valence electrons are respectively the easiest to lose and obtain one electron. The stability and chemical activity of the most stable structures have been analyzed by means of the averaged binding energy, dissociation energy and the gap of energy level. It is found that the Ag14Ti cluster has greater stability and large energy gap and can be regarded as a superatom. Silver-titanium cluster as a CO adsorption material must have very small size or the concentration of Ti atoms must reach a certain value. The calculation of magnetic moment and charge distribution shows that the magnetic moment of Ti atom in AgnTi cluster increases almost completely for n = 1–8, and significantly decreases or quenches for n = 9–16. The charge transfer between Ti and Ag atoms is the main reason for the change of magnetic moment of Ti atom.

Effects of magnetic monopoles charge on the cracking reversal processes in artificial square ices

In this paper we perform nanofabrication of square artificial spin ices with different lattice parameters, in order to investigate the roles of vertex excitation on the features of the system. In particular, the character of magnetic charge distribution asymmetry on the vertices are observed under magnetic hysteresis loop experiments. We then compare our results with simulation using an emergent Hamiltonian containing objects such as magnetic monopoles and dipoles in the vertices of the array (instead of the usual Hamiltonian based on the dipolar interactions among the magnetic nanoislands). All possible interactions between these objects are considered (monopole-monopole, monopole-dipole and dipole-dipole). Using realistic parameters we observe very good match between experiments and theory, which allow us to better understand the system dynamics in function of monopole charge intensity.

Atomic-like charge qubit in a carbon nanotube enabling electric and magnetic field nano-sensing

Quantum sensing techniques have been successful in pushing the sensitivity limits in numerous fields, and hold promise for scanning probes that study nano-scale devices and materials. However, forming a nano-scale qubit that is simple and robust enough to be placed on a scanning tip, and sensitive enough to detect various physical observables, is still a great challenge. Here, we demonstrate, in a carbon nanotube, an implementation of a charge qubit that achieves these requirements. Our qubit’s basis states are formed from the natural electronic wavefunctions in a single quantum dot. Different magnetic moments and charge distributions of these wavefunctions make it sensitive to magnetic and electric fields, while difference in their electrical transport allows a simple transport-based readout mechanism. We demonstrate electric field sensitivity better than that of a single electron transistor, and DC magnetic field sensitivity comparable to that of NV centers. Due to its simplicity, this qubit can be fabricated using conventional techniques. These features make this atomic-like qubit a powerful tool, enabling a variety of imaging experiments.

Research on Features of Pipeline Crack Signal Based on Weak Magnetic Method.

Quantitative online detection of microcracks in long-distance oil and gas pipelines is an international problem, and the effective detection method is still lacking. In this paper, a mathematical model of non-uniform distribution of crack magnetic charges is established based on the stress distribution laws of pipeline cracks under internal pressure. The weak magnetic signal characteristics of pipeline cracks with different sizes are analyzed. The internal pressure increasing factor of weak magnetic signals are extracted to analyze the corresponding relationship between crack size and weak magnetic signals. The experimental study of the X70 pipeline is carried out. The results show that the axial component of the weak magnetic signal at the crack has a maximum value near the tip, and a minimum value appears in the middle of the crack. The internal pressure increasing factor is introduced to quantify the weak magnetic signal, the crack is in a safe state (not expanding) when the internal pressure increasing factor is positive, the weak magnetic signal has a linear relationship with the crack size. However, the crack is in a dangerous state when the internal pressure increasing factor is negative, and the pipeline crack will expand as the internal pressure increases.

Enhancing the saturation magnetisation in Ni doped ZnO thin films by TOPO functionalization

Abstract The saturation magnetization in Ni doped ZnO thin films have been triggered by altering the electronic configuration of ZnO by surface functionalization with Trioctail Phosphine Oxide (TOPO). Initially, Ni doped (3, 5 and 7 mol %) ZnO thin films have been grown by RF magnetron sputtering and the same were functionalized with Trioctylphosphine oxide (TOPO) later by spin coating. The XRD analysis confirms the hexagonal wurtzite structure of grown films. It has been found that lower grain size for both unfunctionalized and functionalized 5 mol% Ni doped ZnO films. PL emission at around 530 nm reveals the presence of oxygen vacancies which is actually cause for origin of ferromagnetism. The saturation magnetization values of 5.70 emu/cm3, 10.14 emu/cm3 and 8.51 emu/cm3 obtained for Ni doped ZnO films from VSM have been enhanced to 7.81 emu/cm3, 11.51 emu/cm3 and 9.61 emu/cm3 upon TOPO functionalization. The high saturation magnetization in 5 mol% Ni doped ZnO film is attributed to lower crystallite size (high grain boundaries) and higher oxygen vacancies. The Zn-P bond observed in the XPS spectrum reveals the formation of the surface layer between Zn and P atom which is responsible for the enhancement of saturation magnetization. The presence of peak at 1146 cm−1 in Raman spectra also confirms the presence of functionalized element, P from TOPO. The simple mechanism based on the bound magnetic poloran and charge distribution has been proposed to explain the origin of room temperature ferromagnetism.

Topologically protected superconducting ratchet effect generated by spin-ice nanomagnets

We have designed, fabricated and tested a robust superconducting ratchet device based on topologically frustrated spin ice nanomagnets. The device is made of a magnetic Co honeycomb array embedded in a superconducting Nb film. This device is based on three simple mechanisms: (i) the topology of the Co honeycomb array frustrates in-plane magnetic configurations in the array yielding a distribution of magnetic charges which can be ordered or disordered with in-plane magnetic fields, following spin ice rules; (ii) the local vertex magnetization, which consists of a magnetic half vortex with two charged magnetic Néel walls; (iii) the interaction between superconducting vortices and the asymmetric potentials provided by the Néel walls. The combination of these elements leads to a superconducting ratchet effect. Thus, superconducting vortices driven by alternating forces and moving on magnetic half vortices generate a unidirectional net vortex flow. This ratchet effect is independent of the distribution of magnetic charges in the array.

Geometry and 2-Hilbert space for nonassociative magnetic translations

We suggest a geometric approach to quantisation of the twisted Poisson structure underlying the dynamics of charged particles in fields of generic smooth distributions of magnetic charge, and dually of closed strings in locally non-geometric flux backgrounds, which naturally allows for representations of nonassociative magnetic translation operators. We show how one can use the 2-Hilbert space of sections of a bundle gerbe in a putative framework for canonical quantisation. We define a parallel transport on bundle gerbes on $\mathbb{R}^d$ and show that it naturally furnishes weak projective 2-representations of the translation group on this 2-Hilbert space. We obtain a notion of covariant derivative on a bundle gerbe and a novel perspective on the fake curvature condition.