Статті в журналах: "Magnetization vector field"

1

Kushnirenko, A., V. Pryadko, and O. Sinyavsky. "The bioenergetic resonance model at pre-sowing seed crops treatment." Energy and automation, no. 2(54) (June 22, 2021): 97–106. http://dx.doi.org/10.31548/energiya2021.02.097.

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The research is devoted to the study of the behavior of the generalizing magnetization vector in the seeds of agricultural crops under the action of longitudinal constant and transverse alternating magnetic fields by the method of nuclear magnetic resonance. Based on the theoretical studies, the value of the average magnetic susceptibility per unit volume of seed χ and the value of the magnetization vector were determined. For the system of microparticles of cells of plant origin, the average magnetic susceptibility per unit volume of seed is χ = 2.1 · 10-5, and the magnetization vector M=13.125 mA/m at a longitudinal constant magnetic field strength H = 625 A/m. When a weak transverse alternating magnetic field is superimposed on the frequency, the oscillation frequencies of the magnetization vectors M coincide with the field frequency, which is a condition for the occurrence of magnetic resonance. The longitudinal magnetization vector during the transition from the ground state to the excited state (resonant) describes a trajectory in the form of a spiral on the surface of the sphere. A mathematical model for a biological system taking into account the Earth's magnetic field is built. It is established that for the technology of pre-sowing treatment of seeds of agricultural crops, the inductor, which creates a constant magnetic field, must be located so that the vector of the constant magnetic field of the inductor coincides with the vector of the Earth's magnetic field. Keywords: bioenergetic resonance, pre-sowing treatment of crop seeds, direct magnetic field, alternating magnetic field, longitudinal and transverse relaxation

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2

Pedersen, Laust B., and Mehrdad Bastani. "Estimating rock-vector magnetization from coincident measurements of magnetic field and gravity gradient tensor." GEOPHYSICS 81, no. 3 (May 2016): B55—B64. http://dx.doi.org/10.1190/geo2015-0100.1.

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Poisson’s theorem relating components of the magnetic field to components of the gradient of the gravity vector assuming a common source has been cast into a general form. A given magnetization distribution in the terrain or in the underlying crust is propagated into the corresponding magnetic field through the gravity gradient tensor. Conversely, measured magnetic field anomalies and measured gravity gradient tensor anomalies can be used to estimate the unknown magnetization vectors without knowledge of the geometry of the sources. We have tested the method on recently acquired data over a greenstone belt in Northern Sweden. The topographic relief was sufficiently variable to dominate the measured gravity gradient tensor. In practice, we have concentrated on areas where the norm of the gravity gradient tensor reached a maximum so that there was a better chance of identifying isolated sources with well-defined density and magnetization. We have surrounded the selected points by a small window and used all the data lying within that window to estimate the magnetization vectors. We have compared the estimated amplitudes and directions of magnetization with those measured from selected rock samples in the area and found a relatively modest agreement. We have interpreted this as a result of two effects: (1) Measured magnetizations are generally lower than those estimated by this method, and we believe that this is related to the fact that the collection of samples in the field is biased because of a small number of outcrops in most parts of the area. (2) This analysis is biased toward high-amplitude magnetic anomalies; i.e., the estimation procedure works best for high-amplitude magnetic anomalies, in which case, the influence of neighboring anomalies is reduced. The estimated magnetization directions show a strong dominance of remanent magnetization over induced magnetization in agreement with laboratory measurements on rock samples from the area.

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3

Antonov, L. I., A. S. Zhukarev, P. A. Polyakov, and D. G. Skachkov. "Magnetization vector field in a uniaxial ferromagnetic film." Technical Physics 49, no. 3 (March 2004): 363–64. http://dx.doi.org/10.1134/1.1688427.

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4

IVEZIĆ, TOMISLAV. "THE CONSTITUTIVE RELATIONS AND THE MAGNETOELECTRIC EFFECT FOR MOVING MEDIA." International Journal of Modern Physics B 26, no. 08 (March 30, 2012): 1250040. http://dx.doi.org/10.1142/s0217979212500403.

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In this paper the constitutive relations for moving media with homogeneous and isotropic electric and magnetic properties are presented as the connections between the generalized magnetization–polarization bivector [Formula: see text] and the electromagnetic field F. Using the decompositions of F and [Formula: see text], it is shown how the polarization vector P(x) and the magnetization vector M(x) depend on E, B and two different velocity vectors, u — the bulk velocity vector of the medium, and v — the velocity vector of the observers who measure E and B fields. These constitutive relations with four-dimensional geometric quantities, which correctly transform under the Lorentz transformations (LT), are compared with Minkowski's constitutive relations with the 3-vectors and several essential differences are pointed out. They are caused by the fact that, contrary to the general opinion, the usual transformations of the 3-vectors E, B, P, M, etc. are not the LT. The physical explanation is presented for the existence of the magnetoelectric effect in moving media that essentially differs from the traditional one.

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5

Baratchart, Laurent, Cristóbal Villalobos Guillén, and Douglas P. Hardin. "Inverse potential problems in divergence form for measures in the plane." ESAIM: Control, Optimisation and Calculus of Variations 27 (2021): 87. http://dx.doi.org/10.1051/cocv/2021082.

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We study inverse potential problems with source term the divergence of some unknown (ℝ3-valued) measure supported in a plane; e.g., inverse magnetization problems for thin plates. We investigate methods for recovering a magnetization μ by penalizing the measure-theoretic total variation norm ∥μ∥TV , and appealing to the decomposition of divergence-free measures in the plane as superpositions of unit tangent vector fields on rectifiable Jordan curves. In particular, we prove for magnetizations supported in a plane that TV -regularization schemes always have a unique minimizer, even in the presence of noise. It is further shown that TV -norm minimization (among magnetizations generating the same field) uniquely recovers planar magnetizations in the following two cases: (i) when the magnetization is carried by a collection of sufficiently separated line segments and a set that is purely 1-unrectifiable; (ii) when a superset of the support is tree-like. We note that such magnetizations can be recovered via TV -regularization schemes in the zero noise limit by taking the regularization parameter to zero. This suggests definitions of sparsity in the present infinite dimensional context, that generate results akin to compressed sensing.

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6

Khalilov, V. R., Choon-Lin Ho, and Chi Yang. "Condensation and Magnetization of Charged Vector Boson Gas." Modern Physics Letters A 12, no. 27 (September 7, 1997): 1973–81. http://dx.doi.org/10.1142/s0217732397002028.

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The magnetic properties of charged vector boson gas are studied in the very weak, and very strong (near critical value) external magnetic field limits. When the density of the vector boson gas is low, or when the external field is strong, no true Bose–Einstein condensation occurs, though significant amount of bosons will accumulate in the ground state. The gas is ferromagnetic in nature at low temperature. However, Bose–Einstein condensation of vector bosons (scalar bosons as well) is likely to occur in the presence of a uniform weak magnetic field when the gas density is sufficiently high. A transitional density depending on the magnetic field seems to exist below which the vector boson gas changes its property with respect to the Bose–Einstein condensation in a uniform magnetic field.

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7

Donnelly, Claire, Sebastian Gliga, Valerio Scagnoli, Mirko Holler, Jörg Raabe, Laura J. Heyderman, and Manuel Guizar-Sicairos. "Tomographic reconstruction of a three-dimensional magnetization vector field." New Journal of Physics 20, no. 8 (August 7, 2018): 083009. http://dx.doi.org/10.1088/1367-2630/aad35a.

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8

Jin Jiang Zhong, Jian Guo Zhu, YouGuang Guo, and Zhi Wei Lin. "A 3-D vector magnetization model with interaction field." IEEE Transactions on Magnetics 41, no. 5 (May 2005): 1496–99. http://dx.doi.org/10.1109/tmag.2005.845084.

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9

Gouda, Kaiki, and Takashi Nishioka. "Angular-field magnetic phase diagram of b-plane at 4 K of YAlGe-type TbAlGe with zigzag-chain." Journal of Physics: Conference Series 2164, no. 1 (March 1, 2022): 012072. http://dx.doi.org/10.1088/1742-6596/2164/1/012072.

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Abstract Orthorhombic YAlGe-type TbAlGe is expected to have an interesting magnetic anisotropy due to zigzag chains of the Tb ions. We have grown the single crystal for the first time and measured the AC magnetic susceptibility and specific heat from 1.3 K to 60 K, and the vector magnetization for the b-plane up to 7 T at 4 K. The specific heat and AC magnetic susceptibility indicate that there are two antiferromagnetic transitions at T N1 = 38 K and TN2 = 7.6 K, where the transition at T N2 is first-order like. The magnetization curve at 4 K for the a-axis shows a large hysteresis, and metamagnetic transition appears at H 1 = 1.6 T in the field increasing process, and another metamagnetic transition at H2 = 3.5 T in addition to H 1 in the decreasing field process. The magnetization curves of the b- and c-axis are linear up to 7 T. The measurement of vector magnetization at 4 K reflects the hysteresis of the magnetization curve, and there is a large hysteresis. From this vector magnetization measurement, we have made the angular magnetic field phase diagram at 4 K for the b-plane. In this phase diagram, there are phase lines that cannot be obtained by ordinary magnetization measurement.

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10

Angulo, Gretel Quintero, Aurora Pérez Martínez, and Hugo Pérez Rojas. "Condensation of Neutral Vector Bosons with Magnetic Moment." International Journal of Modern Physics: Conference Series 45 (January 2017): 1760047. http://dx.doi.org/10.1142/s2010194517600473.

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We study the equation of motion of neutral vector bosons bearing a magnetic moment (MM). The effective rest mass of vector bosons is a decreasing function of the magnetic field intensity. Consequently a diffuse condensation of the bosons appears below a critical value of the field. For typical values of densities and magnetic fields the magnetization is positive and the neutral boson system can maintain a magnetic field self-consistently. A discussion of the relevance in astrophysics is presented.

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11

ROJAS, H. PÉREZ, and E. RODRÍGUEZ QUERTS. "MAGNETIC FIELDS IN QUANTUM DEGENERATE SYSTEMS AND IN VACUUM." International Journal of Modern Physics D 16, no. 02n03 (February 2007): 165–73. http://dx.doi.org/10.1142/s0218271807009917.

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We consider self-magnetization of charged and neutral vector bosons bearing a magnetic moment in a gas and in vacuum. For charged vector bosons (W bosons) a divergence of the magnetization in both the medium and the electroweak vacuum occurs for the critical field [Formula: see text]. For B > Bwc the system is unstable. This behavior suggests the occurrence of a phase transition at B = Bc, where the field is self-consistently maintained. This mechanism actually prevents B from reaching the critical value Bc. For virtual neutral vector bosons bearing an anomalous magnetic moment, the ground state behavior for [Formula: see text] have a similar behavior. The magnetization in the medium is associated to a Bose–Einstein condensate and we conjecture a similar condensate occurs also in the case of vacuum. The model is applied to virtual electron-positron pairs bosonization in a magnetic field [Formula: see text], where me is the electron mass. This would lead also to vacuum self-magnetization in QED, where in both cases the symmetry breaking is due to a condensate of quasi-massless particles.

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12

Fournier, Dominique, Lindsey J. Heagy, and Douglas W. Oldenburg. "Sparse magnetic vector inversion in spherical coordinates." GEOPHYSICS 85, no. 3 (May 1, 2020): J33—J49. http://dx.doi.org/10.1190/geo2019-0244.1.

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Magnetic vector inversion (MVI) has received considerable attention over recent years for processing magnetic field data that are affected by remanent magnetization. However, the magnetization models obtained with current inversion algorithms are generally too smooth to be easily interpreted geologically. To address this, we have reviewed the MVI formulated in a spherical coordinate system. We tackle convergence issues posed by the nonlinear transformation from Cartesian to spherical coordinates by using an iterative sensitivity weighting approach and a scaling of the spherical parameters. The spherical formulation allows us to impose sparsity assumptions on the magnitude and direction of magnetization independently and, as a result, the inversion recovers simpler and more coherent magnetization orientations. The numerical implementation of our algorithm on large-scale problems is facilitated by discretizing the forward problem using tiled octree meshes. All of our results are generated using the open-source SimPEG software. We determine the enhanced capabilities of our algorithm on a large airborne magnetic survey collected over the Kevitsa Ni-Cu-platinum group elements (PGE) deposit. The recovered magnetization direction inside the ultramafic intrusion and in the host stratigraphy is consistent with laboratory measurements and provides evidence for tectonic deformation.

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13

Kirushev, M. S., Vladimir S. Vlasov, D. A. Pleshev, F. F. Asadullin, Leonid N. Kotov, Vladimir G. Shavrov, and V. I. Shcheglov. "Second Order Precession in the Plate with Cubic Anisotropy and Magnetoelastic Properties." Solid State Phenomena 233-234 (July 2015): 73–78. http://dx.doi.org/10.4028/www.scientific.net/ssp.233-234.73.

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The paper considers the second order precession of the magnetization vector in a perpendicular magnetized anisotropic ferrite plate with magnetoelastic properties. The boundaries of the precession regimes on the frequency and amplitude of the alternating field were defined. The features of the precession of the magnetization vector regimes associated with magnetoelastic properties were revealed.

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14

Xiao, Xiao, Fabian Müller, Martin Marco Nell, and Kay Hameyer. "Modeling anisotropic magnetic hysteresis properties with vector stop model by using finite element method." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 41, no. 2 (December 2, 2021): 752–63. http://dx.doi.org/10.1108/compel-06-2021-0213.

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Purpose This paper aims to use a history-dependent vector stop hysteresis model incorporated into a two dimensional finite elements (FE) simulation environment to solve the magnetic field problems in electrical machines. The vector stop hysteresis model is valid for representing the anisotropic magnetization characteristics of electrical steel sheets. Comparisons of the simulated results with measurements show that the model is well appropriate for the simulation of electrical machines with alternating, rotating and harmonic magnetic flux densities. Design/methodology/approach The anisotropy of the permeability of an electrical steel sheet can be represented by integrating anhysteretic surfaces into the elastic element of a vector hysteresis stop model. The parameters of the vector stop hysteresis model were identified by minimizing the errors between the simulated results and measurements. In this paper, a damped Newton method is applied to solve the nonlinear problem, which ensures a robust convergence of the finite elements simulation with vector stop hysteresis model. Findings Analyzing the measurements of the electrical steel sheets sample obtained from a rotational single sheet tester shows the importance to consider the anisotropic and saturation behavior of the material. Comparing the calculated and measured data corroborates the hypothesis that the presented energy-based vector stop hysteresis model is able to represent these magnetic properties appropriately. To ensure a unique way of hysteresis loops during finite elements simulation, the memory of the vector stop hysteresis model from last time step is kept unchanged during the Newton iterations. Originality/value The results of this work demonstrates that the presented vector hysteresis stop model allows simulation of vector hysteresis effects of electrical steel sheets in electrical machines with a limited amount of measurements. The essential properties of the electrical steel sheets, such as phase shifts, the anisotropy of magnetizations and the magnetization characteristics by alternating, rotating, harmonic magnetization types, can be accurately represented.

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15

Котов, Л. Н., П. А. Северин, В. С. Власов, Д. С. Безносиков, Е. Л. Котова та В. Г. Шавров. "Магнитные и упругие колебания в кристаллах марганец-цинковой шпинели в зависимости от константы анизотропии". Физика твердого тела 60, № 6 (2018): 1142. http://dx.doi.org/10.21883/ftt.2018.06.45989.25m.

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AbstractThe amplitudes of magnetic and elastic vibrations for Mn_0.61Zn_0.35Fe_2.04O_4 spinel crystalline slab are calculated by solving the equations describing the magnetic and elastic dynamics. The anisotropy constants, magnetization, second-order elastic constants and magnetoelastic coupling constants for a studied crystal are expressed as the functions of temperature. The magnetization vector and elastic shear components are found as the functions of the first magnetic anisotropy constant at different values of an external constant magnetic field greater than a saturation field. The procession patterns for normally and tangentially magnetized slabs are displayed for two values of the first anisotropy constant. High absolute values of the first anisotropy constant are shown to refer to reorientation of the magnetization vector.

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Weir, Graham John, George Chisholm, and Jerome Leveneur. "The magnetic field about a three-dimensional block neodymium magnet." ANZIAM Journal 62 (April 25, 2021): 386–405. http://dx.doi.org/10.21914/anziamj.v62.14220.

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Neodymium magnets were independently discovered in 1984 by General Motors and Sumitomo. Today, they are the strongest type of permanent magnets commercially available. They are the most widely used industrial magnets with many applications, including in hard disk drives, cordless tools and magnetic fasteners. We use a vector potential approach, rather than the more usual magnetic potential approach, to derive the three-dimensional (3D) magnetic field for a neodymium magnet, assuming an idealized block geometry and uniform magnetization. For each field or observation point, the 3D solution involves 24 nondimensional quantities, arising from the eight vertex positions of the magnet and the three components of the magnetic field. The only unknown in the model is the value of magnetization, with all other model quantities defined in terms of field position and magnet location. The longitudinal magnetic field component in the direction of magnetization is bounded everywhere, but discontinuous across the magnet faces parallel to the magnetization direction. The transverse magnetic fields are logarithmically unbounded on approaching a vertex of the magnet. doi:10.1017/S1446181120000097

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17

Ribeiro-Filho, Nelson, Rodrigo Bijani, and Cosme Ponte-Neto. "Improving the crosscorrelation method to estimate the total magnetization direction vector of isolated sources: A space-domain approach for unstable inclination values." GEOPHYSICS 85, no. 4 (June 5, 2020): J59—J70. http://dx.doi.org/10.1190/geo2019-0008.1.

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Knowledge of the total magnetization direction of geologic sources is valuable for interpretation of magnetic anomalies. Although the magnetization direction of causative sources is assumed to be induced by the ambient magnetic field, the presence of remanence should not be neglected. An existing method of correlating total and vertical gradients of the reduced-to-the-pole (RTP) anomaly estimates the total magnetization direction well. However, due to the numerical instability of RTP transformation in the Fourier domain, an assumption should be considered for dealing with inclination values at approximately 0°. We have adopted an extension to the standard crosscorrelation method for estimating the total magnetization direction vector, computing the RTP anomaly by means of the classic equivalent layer technique for low inclination values. Additionally, an ideal number of equivalent sources within the layer is considered for reducing the computational demands. To investigate the relevant aspects of the adopted method, two simple synthetic scenarios are presented. First, a magnetic anomaly produced by a homogeneous and isolated vertical dike is considered. This test illustrates the good performance of the adopted approach, finding the true magnetization direction, even for low inclination values. In the second synthetic test, a long-wavelength component is added to the previous magnetic total-field anomaly. In this case, the method adopted here fails to estimate a reliable magnetization direction vector, showing weak performance for strong interfering magnetic anomalies. On the real data example, the application tests an isolated total-field anomaly of the Carajás Mineral Province, in northern Brazil, where the inclination of the ambient magnetic field is close to zero. The obtained results indicate weak remanence in the estimated total magnetization direction vector, which would never be reached in the standard formulation of the crosscorrelation technique.

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18

Lelièvre, Peter G., and Douglas W. Oldenburg. "A 3D total magnetization inversion applicable when significant, complicated remanence is present." GEOPHYSICS 74, no. 3 (May 2009): L21—L30. http://dx.doi.org/10.1190/1.3103249.

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Inversion of magnetic data is complicated by the presence of remanent magnetization. To deal with this problem, we invert magnetic data for a three-component subsurface magnetization vector, as opposed to magnetic susceptibility (a scalar). The magnetization vector can be cast in a Cartesian or spherical framework. In the Cartesian formulation, the total magnetization is split into one component parallel and two components perpendicular to the earth’s field. In the spherical formulation, we invert for magnetization amplitude and the dip and azimuth of the magnetization direction. Our inversion schemes contain flexibility to obtain different types of magnetization models and allow for inclusion of geologic information regarding remanence. Allowing a vector magnetization increases the nonuniqueness of the magnetic inverse problem greatly, but additional information (e.g., knowledge of physical properties or geology) incorporated as constraints can improve the results dramatically. Commonly available information results in complicated nonlinear constraints in the Cartesian formulation. However, moving to a spherical formulation results in simple bound constraints at the expense of a now nonlinear objective function. We test our methods using synthetic and real data from scenarios involving complicated remanence (i.e., many magnetized bodies with many magnetization directions). All tests provide favorable results and our methods compare well against those of other authors.

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19

Sohatsky, Vladimir, Andriy Kostuk, and Myhaylo Savytsky. "Reorientation of Magnetization in Single Crystalline Yttrium Iron Garnet Film under Mechanical Strain." Solid State Phenomena 230 (June 2015): 259–63. http://dx.doi.org/10.4028/www.scientific.net/ssp.230.259.

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The results of the effect of mechanical strain on magnetic anisotropy, the direction of magnetization vector and domain structure of ferrite-garnet film, rigidly connected with the zirconium-titanium lead (PZT) piezoceramic plate are presented. It was established, that applied mechanical strain caused a 90°-reorientation of the magnetization vector from the initial perpendicular-to-plane into in-plane state. This strain acts similarly as applied magnetic field and when it applied simultaneously with the field, the piezovoltage necessary for reorientation is inversely proportional to magnetic field intensity. Such properties makes sandwich structures promising for use in spintronics and optoelectronics as a multicontrolled modulator of light.

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20

Rogovoy, Anatoli A., Oleg V. Stolbov, and Olga S. Stolbova. "The Microstructural Model of the Ferromagnetic Material Behavior in an External Magnetic Field." Magnetochemistry 7, no. 1 (January 1, 2021): 7. http://dx.doi.org/10.3390/magnetochemistry7010007.

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In this paper, the behavior of a ferromagnetic material is considered in the framework of microstructural modeling. The equations describing the behavior of such material in the magnetic field, are constructed based on minimization of total magnetic energy with account of limitations imposed on the spontaneous magnetization vector and scalar magnetic potential. This conditional extremum problem is reduced to the unconditional extremum problem using the Lagrange multiplier. A variational (weak) formulation is written down and linearization of the obtained equations is carried out. Based on the derived relations a solution of a two-dimensional problem of magnetization of a unit cell (a grain of a polycrystal or a single crystal of a ferromagnetic material) is developed using the finite element method. The appearance of domain walls is demonstrated, their thickness is determined, and the history of their movement and collision is described. The graphs of distributions of the magnetization vector in domains and in domain walls in the external magnetic field directed at different angles to the anisotropy axis are constructed and the magnetization curves for a macrospecimen are plotted. The results obtained in the present paper (the thickness of the domain wall, the formation of a 360-degree wall) are in agreement with the ones available in the current literature.

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Antonov, Lev I. "Macroscopic representation of the magnetization vector field in a magnetic substance." Physics-Uspekhi 46, no. 11 (November 30, 2003): 1203–7. http://dx.doi.org/10.1070/pu2003v046n11abeh001315.

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Antonov, Lev I. "Macroscopic representation of the magnetization vector field in a magnetic substance." Uspekhi Fizicheskih Nauk 173, no. 11 (2003): 1241. http://dx.doi.org/10.3367/ufnr.0173.200311f.1241.

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Mohan, K. Aditya, Prabhat KC, Charudatta Phatak, Marc De Graef, and Charles A. Bouman. "Model-Based Iterative Reconstruction of Magnetization Using Vector Field Electron Tomography." IEEE Transactions on Computational Imaging 4, no. 3 (September 2018): 432–46. http://dx.doi.org/10.1109/tci.2018.2838454.

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24

PÉREZ ROJAS, HUGO, and ELIZABETH RODRÍGUEZ QUERTS. "SELF-MAGNETIZATION IN ELECTROWEAK VACUUM AND IN VERY DENSE SYSTEMS." International Journal of Modern Physics E 20, supp02 (December 2011): 168–75. http://dx.doi.org/10.1142/s021830131104075x.

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For charged vector bosons (W bosons) of mass mw, magnetization diverges for B → Bcw, which suggests that if the magnetic field is large enough, it can be self-consistently maintained. For photons bearing an anomalous magnetic moment, having a sufficiently large density, their contribution to magnetization might become of the same order than the applied external field, leading also to self-magnetization. We discuss these models in connection to the case of radiation in equilibrium at high temperature (T ~ mc2) coexisting with hot magnetized electron-positron pairs.

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25

Schliewe, Jörn. "Electrodynamics in Euclidean Space Time Geometries." Open Physics 17, no. 1 (December 30, 2019): 731–42. http://dx.doi.org/10.1515/phys-2019-0077.

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Abstract In this article it is proven that Maxwell’s field equations are invariant for a real orthogonal Cartesian space time coordinate transformation if polarization and magnetization are assumed to be possible in empty space. Furthermore, it is shown that this approach allows wave propagation with finite field energy transport. To consider the presence of polarization and magnetization an alternative Poynting vector has been defined for which the divergence gives the correct change in field energy density.

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Li, Dan Dan, Fu Gui Liu, Yong Jian Li, and Chang Geng Zhang. "Study on the Vector Hysteron in Two-Dimensional Preisach-Stoner-Wohlfarth Model." Applied Mechanics and Materials 341-342 (July 2013): 337–40. http://dx.doi.org/10.4028/www.scientific.net/amm.341-342.337.

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A vector hysteresis model referred to as the Preisach-Stoner-Wohlfarth (PSW) model has been recently presented. The crux of the model is the definition of a vector hysteron. In this paper, the effects of interaction field and applied field angle on the magnetization of the vector hysteron are studied in detail. The center of the hysteresis loops of hysteron is displaced because of the effect of interaction field. The energy loss for each hysteron is verified when the critical surface is crossed.

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27

Tsukerblat, Boris, Alex Tarantul, and Achim Müller. "Nanoscopic Molecular Cluster V15: High-Field Epr and Magnetization at Ultra-Low Temperatures." Chemistry Journal of Moldova 2, no. 1 (December 2007): 17–35. http://dx.doi.org/10.19261/cjm.2007.02(1).17.

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In this paper we give a short overview of our efforts in the understanding of the magnetic properties of the fascinating nanoscopic cluster K6[VIV15As6O42(H2O)]·8H2O (hereafter V15) exhibiting layers of magnetization. We analyze EPR and adiabatic magnetization of the V15 cluster with a triangular VIV3 array causing spin frustration. A model for V15 includes isotropic and antisymmetric (AS) exchange interactions in the general form compatible with the trigonal symmetry. Orientation of the AS vector (but not only its absolute value) is shown to play an important physical role in spin-frustrated systems. We were able to reach perfect fit to the experimental data on the stepwise dependence of magnetization vs. field at ultra-low temperatures. Furthermore, it was possible for the first time to estimate precisely two components of the AS vector coupling constant, namely, in-plane component and the perpendicular part. We show that only intramultiplet transitions in EPR are allowed when the vector of AS exchange is normal to the plane of vanadium triangle, meanwhile the in-plane part of AS exchange gives rise to a series of weak intermultiplet transitions. Experimental data on high-frequency EPR of V15 at low temperatures are discussed. The spin-vibronic effects in trimeric spin frustrated clusters are also studied and an important role of the interplay between the AS exchange and Jahn-Teller interaction is revealed. The results clarify the concept of spin-frustration in view of its magnetic and spectroscopic manifestations in metal clusters.

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Upadhaya, Brijesh, Floran Martin, Paavo Rasilo, Paul Handgruber, Anouar Belahcen, and Antero Arkkio. "Modelling anisotropy in non-oriented electrical steel sheet using vector Jiles–Atherton model." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 36, no. 3 (May 2, 2017): 764–73. http://dx.doi.org/10.1108/compel-09-2016-0399.

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Purpose Non-oriented electrical steel presents anisotropic behaviour. Modelling such anisotropic behaviour has become a necessity for accurate design of electrical machines. The main aim of this study is to model the magnetic anisotropy in the non-oriented electrical steel sheet of grade M400-50A using a phenomenological hysteresis model. Design/methodology/approach The well-known phenomenological vector Jiles–Atherton hysteresis model is modified to correctly model the typical anisotropic behaviour of the non-oriented electrical steel sheet, which is not described correctly by the original vector Jiles–Atherton model. The modification to the vector model is implemented through the anhysteretic magnetization. Instead of the commonly used classical Langevin function, the authors introduced 2D bi-cubic spline to represent the anhysteretic magnetization for modelling the magnetic anisotropy. Findings The proposed model is found to yield good agreement with the measurement data. Comparisons are done between the original vector model and the proposed model. Another comparison is also made between the results obtained considering two different modifications to the anhysteretic magnetization. Originality/value The paper presents an original method to model the anhysteretic magnetization based on projections of the anhysteretic magnetization in the principal axis, and apply such modification to the vector Jiles–Atherton model to account for the magnetic anisotropy. The replacement of the classical Langevin function with the spline resulted in better fitting. The proposed model could be used in the numerical analysis of magnetic field in an electrical application.

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29

Dośpiał, M., M. Nabiałek, M. Szota, and J. Gondro. "The Magnetization Reversal Processes Of Bulk (Nd, Y)-(Fe, Co)-B Alloy In The As-Quenched State." Archives of Metallurgy and Materials 60, no. 3 (September 1, 2015): 1587–90. http://dx.doi.org/10.1515/amm-2015-0277.

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Abstract The magnetization reversal processes of bulk Fe64Co5Nd6Y6B19 alloy in the as-quenched state have been investigated. From the analysis of the initial magnetization curve and differential susceptibility versus an internal magnetic field it was deduced, that the main mechanism of magnetization reversal process is the pinning of domain walls at the grain’s boundaries of the Nd2Fe14B phase. Basing on the dependence of the reversible magnetization component as a function of magnetic field it was found that reversible rotation of a magnetic moment vector and motion of domain walls in multi-domain grains result in high initial values of the reversible component. The presence of at least two maxima on differential susceptibility of irreversible magnetization component in function of magnetic field imply existence of few pinning sites of domain walls in Fe64Co5Nd6Y6B19 alloy. The dominant interactions between particles have been determined on the basis of the Wohlfarth dependence. Such a behavior of Wohlfarth’s plot implies that the dominant interaction between grains becomes short range exchange interactions.

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30

Usov, Nikolai A., Ruslan A. Rytov, and Vasiliy A. Bautin. "Dynamics of superparamagnetic nanoparticles in viscous liquids in rotating magnetic fields." Beilstein Journal of Nanotechnology 10 (November 22, 2019): 2294–303. http://dx.doi.org/10.3762/bjnano.10.221.

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The dynamics of magnetic nanoparticles in a viscous liquid in a rotating magnetic field has been studied by means of numerical simulations and analytical calculations. In the magneto-dynamics approximation three different modes of motion of the unit magnetization vector and particle director are distinguished depending on frequency and amplitude of the rotating magnetic field. The specific absorption rate of a dilute assembly of superparamagnetic nanoparticles in rotating magnetic field is calculated by solving the Landau–Lifshitz stochastic equation for the unit magnetization vector and the stochastic equation for the particle director. At elevated frequencies an optimal range of particle diameters is found where the specific absorption rate of an assembly in a rotating magnetic field has a maximum. It is shown that with an optimal choice of the particle sizes sufficiently large SAR values of the order of 400–500 W/g can be obtained in a rotating magnetic field with a frequency f = 400 kHz and a moderate magnetic field amplitude H 0 = 100 Oe.

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31

Tyatyushkin, Alexander. "Influence of Rotation on the Magnetization of Dilute Suspensions of Magnetic Particles." Solid State Phenomena 233-234 (July 2015): 302–5. http://dx.doi.org/10.4028/www.scientific.net/ssp.233-234.302.

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The influence of rotation on the magnetization of a suspension of spherical magnetic particles in a uniform magnetic field is investigated theoretically with taking into account the inertial effects. A rotation of a single spherical non-Brownian particle with an embedded magnetic moment under action of a rotational flow of the ambient liquid in an applied uniform magnetic field is considered. The system of equations is obtained that determines the rotation of the particle and the instant orientation of its magnetic dipole moment with taking into account both the inertia of the particles and that of the dispersion liquid of the suspension. The magnetization vector of a suspension of non-Brownian spherical magnetic particles is found for the suspension rotating in a uniform constant magnetic field and for that rotating in a sufficiently weak uniform alternating magnetic field. The system of equations is obtained for the function of distribution over the orientations of the magnetic dipole moments for a suspension of Brownian spherical magnetic particles rotating in a uniform magnetic field. The solution to this system of equations is obtained for a suspension rotating in a sufficiently weak alternating magnetic field. With the use of this solution, the magnetization vector of the suspension is found.

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32

MARTÍNEZ, AURORA PÉREZ, HUGO PÉREZ ROJAS, and HERMAN MOSQUERA CUESTA. "BOSE–EINSTEIN CONDENSATION OF CHARGED PARTICLES AND SELF-MAGNETIZATION." International Journal of Modern Physics D 13, no. 07 (August 2004): 1207–11. http://dx.doi.org/10.1142/s0218271804005328.

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We discuss the Bose–Einstein condensation of relativistic vector charged particles in a strong external magnetic field in very dense matter, as may be paired spin-up electrons. We show that for electrons such systems may maintain self-consistently magnetic fields of order in between the interval 1010–1013 Gauss. This could be the origin of large magnetic fields in some white dwarfs, but may also impose bounds due to the arising of strong anisotropy in the pressures, which may produce a transverse collapse of the star.

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33

Zligostev, I. N., M. I. Epov, and A. V. Savluk. "On the measurement of the magnetic induction vector with the use of a three-component magnetometer placed on a mobile carrier." Russian Journal of Geophysical Technologies, no. 4 (March 11, 2022): 47–56. http://dx.doi.org/10.18303/2619-1563-2021-4-47.

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The article describes the use of a vector ferromagnetic magnetometer placed on an unmanned aerial vehicle (UAV). It is shown that solving inverse problems of magnetic prospecting for a vector aeromagnetic survey makes it possible to identify areas with different magnetization. We present a simple, based on standard libraries, software product for processing primary data of three-component fluxgate magnetometers, which allows correctly selecting the magnetic induction vector components when performing magnetic UAV surveys. To build maps, a method for graphical display of a vector field is proposed. On the example of a man-made object, we demonstrate that vector fields measured at different heights provide significantly more information than conventional electromagnetic induction measurements.

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34

Warczewski, Jerzy, Paweł Gusin, and Daniel Wojcieszyk. "Spin glass state structure theory and its application to explain experiments." Acta Crystallographica Section A Foundations and Advances 70, a1 (August 5, 2014): C277. http://dx.doi.org/10.1107/s2053273314097228.

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The authors have found the general description of all the eight fundamental magnetic structures and their symmetry groups (including spin glass state - sgs) with the use of the fibre bundle approach [1]. The structure of sgs turns out to consist in the Gaussian-like randomness of the orientations of all the separate atomic magnetic moments in the sample. It means that the magnetization vector M is also subject to Gaussian distribution. Thus the structure of the sgs is represented by the magnetization vector situated along the generatrix of a certain cone whose axis coincides with the direction of an internal spontaneous magnetic field indispensable for stability of the sgs in a sample [2]. The axis of the 3-dimensional Gaussian distribution mentioned above coincides also with the same direction. Every precession angle of M around this field makes the symmetry operation of sgs once the angle between M and this field remains constant. Thus the symmetry group of sgs turns out to be SO(2). The temperature dependence of magnetic susceptibility of sgs in the alloys CuMn [3] corresponds when heating to the gradual degeneration of the Gaussian distribution of the magnetization vector, and when cooling to its gradual recovery with no hysteresis. In both cases an internal spontaneous magnetic field mentioned above plays an essential role. The interrelation of this field, of the Gaussian distribution mentioned above, of the average kinetic energy of magnetic atoms and of the frustration of orientations of the magnetic moments placed on these atoms will be discussed.

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35

Xiao, Xiao, Fabian Müller, Gregor Bavendiek, and Kay Hameyer. "Analysis of vector hysteresis models in comparison to anhysteretic magnetization model." European Physical Journal Applied Physics 91, no. 2 (August 2020): 20901. http://dx.doi.org/10.1051/epjap/2020200019.

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The design of electrical machines and magnetic actuators requires accurate models to represent hysteresis effects in ferromagnetic materials. The magnetic nonlinearity of the iron core is usually considered by an anhysteretic magnetization curve. With this assumption, hysteresis’ effects in the field computation are completely neglected. This paper presents a comparative study of different hysteresis models, particularly Pragmatic Algebraic Model (PAM) and vector stop model, with regard to a vector anhysteretic anisotropic model. The PAM turns out to be an efficient model implemented with one mathematical equation. The multi cells stop model relies on a consistent thermodynamic formulation, whose dissipation corresponds to a dry friction-like element. Both models implement a constitutive relationship, in which the magnetic flux density vector as independent input and magnetic field strength as output. With a rotational single sheet tester (RSST), various tests for a sample of material FeSi24-50A (FeSi) with a silicon proportion of 2.4 wt% can be proceeded under the application of relevant field distribution. The obtained measured data are applied to parameterize and validate the models. Following numerical experiments the results are compared with those obtained by means of an anhysteretic anisotropic model.

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36

Li, Yaoguo, Jiajia Sun, Shu-Ling Li, and Marcelo Leão-Santos. "A paradigm shift in magnetic data interpretation: Increased value through magnetization inversions." Leading Edge 40, no. 2 (February 2021): 89–98. http://dx.doi.org/10.1190/tle40020089.1.

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Magnetic data are sensitive to both the induced magnetization in rock units caused by the present earth's magnetic field and the remanent magnetization acquired by rock units in past geologic time. Susceptibility is a direct indicator of the magnetic mineral content, whereas remanent magnetization carries information about the formation process and subsequent structural movement of geologic units. The ability to recover and use total magnetization, defined as the vectorial sum of the induced and remanent magnetization, therefore enables us to take full advantage of magnetic data. The exploration geophysics community has achieved significant advances in inverting magnetic data affected by remanent magnetization. It is now feasible to invert any magnetic data set for total magnetization. We provide an overview of the state of the art in magnetization inversion and demonstrate the informational value of inverted magnetization through a set of case studies from mineral exploration problems. We focus on the methods that recover either the magnitude of the total magnetization or the total magnetization vector itself.

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37

Araujo, Jefferson F. D. F., Andre L. A. Reis, Angela A. P. Correa, Elder Yokoyama, Vanderlei C. Oliveira, Leonardo A. F. Mendoza, Marcos A. C. Pacheco, et al. "Scanning Magnetic Microscope Using a Gradiometric Configuration for Characterization of Rock Samples." Materials 12, no. 24 (December 11, 2019): 4154. http://dx.doi.org/10.3390/ma12244154.

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Scanning magnetic microscopy is a tool that has been used to map magnetic fields with good spatial resolution and field sensitivity. This technology has great advantages over other instruments; for example, its operation does not require cryogenic technology, which reduces its operational cost and complexity. Here, we presented a spatial domain technique based on an equivalent layer approach for processing the data set produced by magnetic microscopy. This approach estimated a magnetic moment distribution over a fictitious layer composed by a set of dipoles located below the observation plane. For this purpose, we formulated a linear inverse problem for calculating the magnetic vector and its amplitude. Vector field maps are valuable tools for the magnetic interpretation of samples with a high spatial variability of magnetization. These maps could provide comprehensive information regarding the spatial distribution of magnetic carriers. In addition, this approach might be useful for characterizing isolated areas over samples or investigating the spatial magnetization distribution of bulk samples at the micro and millimeter scales. This technique could be useful for many applications that require samples that need to be mapped without a magnetic field at room temperature, including rock magnetism.

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38

Mendonça, Carlos Alberto. "Automatic determination of the magnetization–density ratio and magnetization inclination from the joint interpretation of 2D gravity and magnetic anomalies." GEOPHYSICS 69, no. 4 (July 2004): 938–48. http://dx.doi.org/10.1190/1.1778237.

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The Poisson theorem establishes a linear relationship between the gravity and magnetic potentials arising from common dense and magnetized bodies with constant magnetization–density ratio and magnetization direction. For geological formations satisfying such constraints (i.e., the Poisson conditions), this theorem provides suitable relationships between the gravity and magnetic anomalies that are useful in interpreting the related data sets. In such applications, both magnetization–density ratio (MDR) and magnetization direction can be estimated, thus helping the subsurface geological mapping from potential field data acquired on the earth's surface. However, no existing method is fully automatic, which has hampered extensive use in routine applications. Such a drawback follows the adoption of equations that, although obeying the Poisson theorem, relate particular components of the gravity and magnetic fields, thus requiring either a known magnetization direction or the implementation of iterative procedures to determine it. To allow one‐pass estimates for both MDR and magnetization direction (more precisely, its inclination projected on the plane normal to the source strike), this paper presents simple analytical solutions for these parameters by relating suitable gravity and magnetic vector fields that are derived from the gravity and magnetic data sets. Because current geophysical surveys usually provide only a single‐field component, a data processing scheme is developed to determine the required components in evaluating the desired vector fields. This is done by applying suitable linear transformations on the measured components according to well‐established filtering techniques in processing gravity and magnetic data. Except for distortions from noise, the proposed method automatically determines the MDR and the projected magnetization inclination for the underlying rocks everywhere the Poisson conditions are satisfied. Two‐dimensional sources are assumed, but no constraint upon their depth and cross‐section shape is required. Distorted estimates only appear close to the sources where at least one of the Poisson conditions is violated. In this case, the proposed technique furnishes apparent values for the rock properties. The abrupt changes of apparent values over contacts detect edges, thus facilitating the mapping of geological boundaries. The proposed technique is used to interpret two profiles across the Appalachian fold belt from the eastern portion of the State of Georgia, and the results are compared with some of the geological information available for the area.

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Augustine, Preethy, Yerol Narayana, and Nandakumar Kalarikkal. "An effective strategy for the development of multiferroic composite nanostructures with enhanced magnetoelectric coupling performance: a perovskite–spinel approach." Nanoscale Advances 3, no. 16 (2021): 4866–77. http://dx.doi.org/10.1039/d1na00376c.

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An energy efficient move toward the regulation of magnetization vector solely with E-field by developing multiferroic (MF) magnetoelectric (ME) nanostructures' have opened up vast avenues for novel low power consumption memories and magnetoelectric devices.

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40

Leuchs, Gerd, Margaret Hawton, and Luis L. Sánchez-Soto. "QED Response of the Vacuum." Physics 2, no. 1 (January 18, 2020): 14–21. http://dx.doi.org/10.3390/physics2010002.

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We present a new perspective on the link between quantum electrodynamics (QED) and Maxwell’s equations. We demonstrate that the interpretation of the electric displacement vector D = ε 0 E , where E is the electric field vector and ε 0 is the permittivity of the vacuum, as vacuum polarization is consistent with QED. A free electromagnetic field polarizes the vacuum, but the polarization and magnetization currents cancel giving zero source current. The speed of light is a universal constant, while the fine structure constant, which couples the electromagnetic field to matter runs, as it should.

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41

Aditya Mohan, K., K. C. Prabhat, Charudatta Phatak, Marc De Graef, and Charles A. Bouman. "Iterative Reconstruction of the Magnetization and Charge Density using Vector Field Electron Tomography." Microscopy and Microanalysis 22, S3 (July 2016): 1686–87. http://dx.doi.org/10.1017/s1431927616009272.

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42

Tsidaeva, Natalia, Viktorija Abaeva, Anatoly Turiev, Elena Enaldieva, Tengiz Butkhuzi, Spartak Khaimanov, and Alena Ramonova. "Anisotropy of the Linear Magnetic Birefridence of Europium Iron Garnet." Key Engineering Materials 605 (April 2014): 548–52. http://dx.doi.org/10.4028/www.scientific.net/kem.605.548.

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The results of investigation of magnetic linear birefringence (MLB) and magnetic linear dichroism (MLD) of Eu3Fe5O12(EuIG) iron garnet on7F07F6optical transitions upon variation of the directions of the magnetization vector I relative to the electric vector E linearly polarized light that propagates through single crystal iron garnets are presented. The measurements were made on Eu3Fe5O12single-crystal samples in the form of plates 100 μm thick cut in the (110) and (100) plane at the temperatures T = 82 and in a magnetic field H= 25 kOe. The absorption spectra of the linearly polarized light were studied. It is shown that MLB and dichroism in the region of the7F07F6absorption band reach values 10-3. First experimentally discovered nonreciprocity of MLB spectra and dichroism with the change of the relative orientation of the magnetization vector I and the light wave vector. This effect may use as a base for the design of the different transducers, for example, magnetooptical optical channels commutator.

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43

Bolotov, A. N., O. O. Novikova, and V. V. Novikov. "The effect of the magnetic field on formation and development of microcracks while friction." Izvestiya MGTU MAMI 9, no. 1-4 (July 10, 2015): 5–9. http://dx.doi.org/10.17816/2074-0530-67093.

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The formation and development of cracks in the sample of ferromagnetic material in magnetized condition were researched. It was shown that magnetic state of material of friction surface most substantially influences the process of its brittle or quasibrittle fracture if cracks open perpendlcularly to magnetization vector. The criterion of unintentional growth of crack in magnetic field was established.

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44

Saerbeck, Thomas, Henning Huckfeldt, Boris P. Toperverg, and Arno Ehresmann. "Magnetic Structure of Ion-Beam Imprinted Stripe Domains Determined by Neutron Scattering." Nanomaterials 10, no. 4 (April 15, 2020): 752. http://dx.doi.org/10.3390/nano10040752.

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We present a detailed analysis of the in-plane magnetic vector configuration in head-to-head/tail-to-tail stripe domain patterns of nominal 5 μm width. The patterns have been created by He-ion bombardment induced magnetic patterning of a CoFe/IrMn3 exchange bias thin-film system. Quantitative information about the chemical and magnetic structure is obtained from polarized neutron reflectometry (PNR) and off-specular scattering (OSS). The technique provides information on the magnetic vector orientation and magnitude along the lateral coordinate of the sample, as well as the chemical and magnetic layer structure as a function of depth. Additional sensitivity to magnetic features is obtained through a neutron wave field resonance, which is fully accounted for in the presented analysis. The scattering reveals a domain width imbalance of 5.3 to 3.7 μm of virgin and bombarded stripes, respectively. Further, we report that the magnetization in the bombarded stripe significantly deviates from the head-to-head arrangement. A domain wall of 0.6 μm with homogeneous magnetization direction is found to separate the two neighboring domains. The results contain detailed information on length scales and magnetization vectors provided by PNR and OSS in absolute units. We illustrate the complementarity of the technique to microscopy techniques for obtaining a quantitative description of imprinted magnetic domain patterns and illustrate its applicability to different sample systems.

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45

Ostrovskaya, Natalia, Vladimir Skidanov, Iulia Iusipova, and Maxims Skvortsov. "BIFURCATION ANALYSIS OF THE DYNAMICAL SYSTEM FOR A THREELAYERED VALVE WITH PERPENDICULAR ANISOTROPY." EPJ Web of Conferences 185 (2018): 01008. http://dx.doi.org/10.1051/epjconf/201818501008.

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The features of switching dynamics in a model of a three-layered valve have been investigated theoretically and numerically. For this purpose, the system of ordinary differential equations in the approximation of the uniform magnetization distribution for the magnetization dynamics in the valve with perpendicular anisotropy was derived. It was shown that in such a system, in contrast with the system for the in-plane anisotropy, there are only two equilibrium positions of the magnetization vector. The stability analysis of the stationary points of the system has been carried out. With its help, the classification of types of dynamics versus field and current values was performed. The regions of limit cycles existence and the regions of optimal magnetization switching were revealed.

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46

Thurston, J. B. "Mapping remanent magnetization using the local phase." GEOPHYSICS 66, no. 4 (July 2001): 1082–89. http://dx.doi.org/10.1190/1.1487055.

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For uniformly magnetized 2‐D contacts, thin sheets, horizontal cylinders, and dykes, the apparent inclination of the magnetization vector (i.e., the inclination projected into a plane perpendicular to the strike of a 2‐D anomaly) can be computed from the difference in the anomaly shapes of the total field and the vertical field. The calculation can be performed using gridded data, resulting in a grid containing estimates of apparent inclination. These estimates take into account varying source‐strike direction. This quantity is important for computing source dip wherever the data are likely to be affected by the presence of remanent magnetization. As well, it is useful for input to forward models computed along profiles perpendicular to strike. Further, without knowledge of source dip, the apparent inclination can be used to map the presence of remanent magnetization. This is an aid to geologic mapping, allowing isolated paleomagnetic measurements to be extrapolated over a broad area. Knowing the extent of remanent magnetization can also help indicate how well the reduction to the pole process will work. The method requires both total‐field and vertical‐field component data. Most modern airborne surveys are conducted with optically pumped magnetometers that record only the total field. To apply the method in these cases requires estimation of the vertical component from the total field using a 2‐D Fourier operator, which in turn requires the assumption that the earth’s field direction is constant over the study region and the induced field is small compared to the ambient field. This restricts application to areas of several hundred square kilometers. Apparent inclination is estimated from synthetic data computed over a generalized cross‐section of the center of the Manicouagan impact structure (Canada) and to measured aeromagnetic data over this structure. The results of the synthetic test indicate that for the northern and southern edges of this source, the method can distinguish the present‐day and paleomagnetic fields with the same spatial resolution as the analytic signal has for identifying magnetization boundaries. Application to the airborne data indicates that where the source strikes at high angles to the declination of the present‐day field, the estimated apparent inclination is influenced by both the remanent and inducing fields. For other strikes the field is almost entirely remanent or no distinction between the present‐day and paleomagnetic fields can be made. As well, the source dip, estimated from the local phase and the estimated apparent inclination, is consistent with previously published results.

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47

Fokina, Nathalie P., and Maia O. Elizbarashvili. "Free Induction Decay and Spin Echo Signals from Spin Triplet States of Axially Asymmetric Objects in Single Crystals in Zero Constant Magnetic Field:." European Journal of Engineering Research and Science 5, no. 7 (July 31, 2020): 813–21. http://dx.doi.org/10.24018/ejers.2020.5.7.2018.

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Anisotropic dynamics of the spin triplet states (STSs) in single crystals with the zero field splitting (ZFS) of their levels by the axially asymmetric Hamiltonian is investigated in zero constant magnetic field (ZF) under the action of the canonically oriented varying magnetic fields. The equations of motion for single transition operators (STOs) corresponding to the definite transition of ZFS are derived. The obtained equations written in terms of one averaged equation for STO vector appeared to be a particular case (for STS) of the universal equation of Feynman et al, which is valid for any kind of perturbation affecting only two levels of any quantum mechanical system. As well as that, our equation is analogous to the Bloch equation without decay for the usual magnetization components of the Zeeman system in a constant magnetic field and a transverse to it varying field. This statement is valid, if the population probabilities of the corresponding levels of STS are not artificially equalized. At that, the motion of the observable macroscopic sample magnetization, which follows from our equations, has quite different character. Here, in terms of this magnetization the signals of the free induction decay and of the two-pulse spin echo are calculated in ZF.

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48

Fokina, Nathalie P., and Maia O. Elizbarashvili. "Free Induction Decay and Spin Echo Signals from Spin Triplet States of Axially Asymmetric Objects in Single Crystals in Zero Constant Magnetic Field:." European Journal of Engineering and Technology Research 5, no. 7 (July 31, 2020): 813–21. http://dx.doi.org/10.24018/ejeng.2020.5.7.2018.

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Анотація:

Anisotropic dynamics of the spin triplet states (STSs) in single crystals with the zero field splitting (ZFS) of their levels by the axially asymmetric Hamiltonian is investigated in zero constant magnetic field (ZF) under the action of the canonically oriented varying magnetic fields. The equations of motion for single transition operators (STOs) corresponding to the definite transition of ZFS are derived. The obtained equations written in terms of one averaged equation for STO vector appeared to be a particular case (for STS) of the universal equation of Feynman et al, which is valid for any kind of perturbation affecting only two levels of any quantum mechanical system. As well as that, our equation is analogous to the Bloch equation without decay for the usual magnetization components of the Zeeman system in a constant magnetic field and a transverse to it varying field. This statement is valid, if the population probabilities of the corresponding levels of STS are not artificially equalized. At that, the motion of the observable macroscopic sample magnetization, which follows from our equations, has quite different character. Here, in terms of this magnetization the signals of the free induction decay and of the two-pulse spin echo are calculated in ZF.

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49

Bronner, Adrien, Marc Munschy, Daniel Sauter, Julie Carlut, Roger Searle, and Alexis Maineult. "Deep-tow 3C magnetic measurement: Solutions for calibration and interpretation." GEOPHYSICS 78, no. 3 (May 1, 2013): J15—J23. http://dx.doi.org/10.1190/geo2012-0214.1.

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Two main problems are encountered in deep-tow 3C magnetic surveys. The first problem is related to instrumental error due to the manufacturing of the sensor, its integration in the towed fish structure, and the magnetization of the vehicle carrying the magnetometer; the second is related to the variation in altitude of the instruments during the dive. We evaluated a new type of calibration approach for deep-tow fluxgate magnetometers. We found that the magnetometer can be calibrated with no recourse to the vehicle attitude (pitch, roll, and heading, as it is usually achieved) but only using the three components recorded by the magnetometer and an approximation of the scalar intensity of the earth’s magnetic field. This method, called scalar calibration, allowed us to eliminate the intrinsic instrumental errors as well as the magnetization effect of the tow vehicle. Thus, despite the low maneuverability of the towed fish during the calibration experiment, we discovered a significant improvement in obtaining accurate magnetic anomaly profiles. Because only the total field anomaly and not the magnetic vector is suitable for this method, we investigated the possibility of calculating the three components via an equivalent-source approach. Therefore, assuming a 2D topographic equivalent layer, we found a stable and a meaningful magnetization of the oceanic crust. We discovered that although magnetic data are acquired along uneven tracks, this model, based on a single linear inversion, is sufficient to provide a first-order depth and magnetization intensity of the crust and also to carry out upward continuation of the total anomalous field as well as its associated vector.

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50

Tuma, Soraya Lozada, and Carlos Alberto Mendonça. "Stepped inversion of magnetic data." GEOPHYSICS 72, no. 3 (May 2007): L21—L30. http://dx.doi.org/10.1190/1.2711661.

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Анотація:

We present a three-step magnetic inversion procedure in which invariant quantities with respect to source parameters are inverted sequentially to give (1) shape cross section, (2) magnetization intensity, and (3) magnetization direction for a 2D (elongated) magnetic source. The quantity first inverted (called here the shape function) is obtained from the ratio of the gradient intensity of the total-field anomaly to the intensity of the anomalous vector field. For homogenous sources, the shape function is invariant with source magnetization and allows reconstruction of the source geometry by attributing an arbitrary magnetization to trial solutions. Once determined, the source shape is fixed and magnetization intensity is estimated by fitting the total gradient of the total-field anomaly (equivalent to the amplitude of the analytic signal of magnetic anomaly). Finally, the source shape and magnetization intensity are fixed and the magnetization direction is determined by fitting the magnetic anomaly. As suggested by numerical modeling and real data application, stepped inversion allows checking whether causative sources are homogeneous. This is possible because the shape function from inhomogeneous sources can be fitted by homogeneous models, but a model obtained in this way fits neither the total gradient of the magnetic anomaly nor the magnetic anomaly itself. Such a criterion seems effective in recognizing strongly inhomogeneous sources. Stepped inversion is tested with numerical experiments, and is used to model a magnetic anomaly from intrusive basic rocks from the Paraná Basin, Brazil.

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