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The purpose of this paper is to describe a finite-element method for the numerical simulation of magnetization and demagnetization processes in ferromagnetic pieces with hysteresis. In particular, the proposed methodology will be applied to compute the remanent flux density after a magnetic particle inspection test on specimens with cylindrical symmetry consisting of three stages: longitudinal magnetization, circular magnetization, and demagnetization.

This paper presents the extension of two 1-D lamination models with magnetic hysteresis to reproduce dynamic hysteresis loops and power loss in grain-oriented (GO) electrical steels. For this purpose, the concept of magnetic viscosity is introduced in the model equations. The applicability and accuracy are demonstrated by means of two GO steels of different thicknesses at magnetizing frequencies up to 1000 Hz. Advantages and limits of the classical approach with and without viscosity and comparisons to measured data are discussed in detail.

A numerical implementation of the classical Stoner–Wohlfarth (SW) model to simulate the magnetization angle of an assembly of SW particles with an effective axis of anisotropy under a rotating applied field is presented. Using an angular distribution for the angle each SW particle is making with the medium’s reference axis, the proposed model successfully simulated lag-angle plots exhibiting the same rotational magnetization behavior measured for different ellipsoidally magnetizable media in the literature. The developed algorithm provides a simple tool for rotational-energy-loss calculations, preserves the physical intuition of the classical SW model, and is computationally faster compared to the Preisach–Stoner–Wohlfarth models. The effect of the angular distribution parameters on the switching transition angle and the algorithm’s potential for modeling additional anisotropies through using different angular distributions are discussed.

This paper presents a detailed theoretical background of the saturation wave model (SWM), which offers a simplified homogenized solution of the nonlinear diffusion phenomena inside soft magnetic steel sheets (SMSSs). The SWM is capable of predicting the complicated dynamic magnetization of SMSS without discretization of the cross section of the SMSSs. Despite its simplicity, the SWM predicts exact solutions of the discussed problems when step-like magnetization curves are assumed and reasonably accurate solutions for real magnetization curves. In this paper, the SWM is analyzed in comparison to the numerical solution of the diffusion phenomena using the parametric magnetodynamic model, where interesting properties of the SWM are discussed and pointed out.

Arrays of nanosized hollow spheres of Ni were studied using micromagnetic simulation by the Object Oriented Micromagnetic Framework. Before all the results, we will present an analysis of the properties for an individual hollow sphere in order to separate the real effects due to the array. The results in this paper are divided into three parts in order to analyze the magnetic behaviors in the static and dynamic regimes. The first part presents calculations for the magnetic field applied parallel to the plane of the array; specifically, we present the magnetization for equilibrium configurations. The obtained magnetization curves show that decreasing the thickness of the shell decreases the coercive field and it is difficult to obtain magnetic saturation. The values of the coercive field obtained in our work are of the same order as reported in experimental studies in the literature. The magnetic response in our study is dominated by the shape effects and we obtained high values for the reduced remanence, $M_{r}/M_{S} = 0.8$ . In the second part of this paper, we have changed the orientation of the magnetic field and calculated hysteresis curves to study the angular dependence of the coercive field and remanence. In thin shells, we have observed how the moments are oriented tangentially to the spherical surface. For the inversion of the magnetic moments we have observed the formation of vortex and onion modes. In the third part of this paper, we present an analysis for the process of magnetization reversal in the dynamic regime. The analysis showed that inversion occurs in the nonhomogeneous configuration. We could see that self-demagnetizing effects are predominant in the magnetic properties of the array. We could also observe that there are two contributions: one due to the shell as an independent object and the other due to the effects of the array.

A model for the vector magnetization of a distribution of uniaxial particles is presented. Recent work by the authors decomposed the magnetization into two components and modeled the total vector magnetization as their vector sum. Anisotropy could be ideally modeled as a constant field, but this leads to a model of unidirectional anisotropy. Considering uniaxial media, such approach will only be valid for small angles. Hence, in this paper, a model is proposed that calculates the total magnetization of a distribution of uniaxial particles as the vector sum of irreversible and reversible components. The magnitude of the irreversible component is modeled using a Preisach differential-equation approach; however, other valid models can be used. The direction of the reversible component is modeled using the minimum energy approach of the classical Stoner–Wohlfarth model. The final result of the model is an unsymmetrical lag-angle plot for intermediate applied field values, which is consistent with the measurements.

The Nd9.5Fe61.5Co10Nb20.5Ti0.5B15.5C0.5 nanocomposite magnets have been prepared by the copper-mold casting technique. The magnetic properties were calculated by the micromagnetic simulation using the magnetic force microscopy image. The influence of different saturation magnetization of amorphous grain boundary phase on the magnetization reversal process was investigated. The simulation results indicate that the coercivity increases with the reducing saturation magnetization of amorphous phase when the grain size varied from 300 to 1000 nm. The magnetization reversal process demonstrates that the magnetic moments of NdFeB phase show the prior inversion at the grain boundaries. Furthermore, the comparison between the anisotropic and isotropic model implies the importance of preparing anisotropic magnets.

This paper presents a vector hysteresis model based on micromagnetic theory. In this model, a magnetization state of a magnetic material is described by a collection of single-domain particles, and magnetic reversal processes due to domain-wall motions are treated approximately as a magnetization flip. The present model is applied to calculation of hysteresis properties of grain-oriented silicon steel. The simulation results show that the anisotropic hysteresis properties and iron loss can be reproduced accurately by the present model.

The magnetic properties of Lycopodium powders from two different sources are investigated. In addition to a characteristic diamagnetism with χ = -8(1) × 10 -6 , there is a Curie-law paramagnetism, which is the dominant contribution to the susceptibility below 20 K, and an additional weak hysteretic signal with a saturation magnetization of magnitude 0.6-1.8 × 10 -3 Am 2 kg -1 at room temperature. After ignition of the powder, the remaining inorganic ash represents just 1.05% of the original mass, but the room temperature magnetization increases only by a factor of 5. The iron content of the Lycopodium, deduced by chemical analysis of the ash is 43-76 ppm. Of this, roughly 3/4 is paramagnetic, and 1/4 is in the form of magnetite.

Die upsetting is an effective method to produce bulk anisotropic Nd-Fe-B magnets with nanostructure and full density [1]. A variety of experimental evidence suggests that the grain boundary a play key role in magnetic hardening [2]. Therefore, the grain boundary diffusion method is an effective way to improve the coercivity of die-upset magnet [3, 4]. However, the special role of the grain boundary after diffusion on both magnetic structure and microstructure of the die upsetting magnets is unclear and controversial. In order to obtain the excellent coercivity in the die-upset nanocrystal-line magnets, it is necessary to get better understanding on the mechanism of the enhanced coercivity. In this work, we have fabricated nanocrystalline Nd-Fe-B magnets by hot pressing and die upsetting methods with low melting point eutectic Nd-Cu alloy addition. The coercivity has been dramatically enhanced by Nd-Cu alloy addition. To investigate mechanism of the enhancement of the coercivity, we observed microstructure and the initial magnetization curve of the die upsetting magnets with different Nd-Cu addition.

In this paper, we discuss the numerical modeling of hysteresis in magnetic steels with oriented and nonoriented grain. The modeling is fully 3-D, but it is applied here to typical 2-D magnetic problems. Starting from a vector generalization of the Preisach model, we introduce here the concept of an operative magnetic field, function of the state of magnetization of the material. This operative field is introduced to reproduce with more accuracy the peculiar behavior of Si-Fe steels approaching the saturation state. The properties of the model are discussed and some examples are reported.

Magnetization curves of superparamagnetic nanoparticles in ac magnetic field are numerically studied by Brownian dynamics simulation with considering a more precisely estimated magnetic torque. Consequently, we confirmed that rotatable nanoparticles with magnetic easy axes show magnetic hysteresis loops without remanence, even when the thermal fluctuations of the magnetizations are much faster than the oscillation of the magnetic fields. The origin is that magnetic alignments of the easy axes by the magnetic torque in the peak period of the oscillations of field alternate with their randomizations by Brownian relaxation in the period when the field becomes almost zero. Because the equilibrium magnetization curve of the aligned nanoparticles is steeper than that of randomly oriented ones, a new kind of hysteresis appears when both the Brownian relaxation time and the characteristic time of the field-driven rotation are comparable to the alternation period of magnetic field. This finding sheds a new light on the widely accepted association between superparamagnetism and the anhysteretic magnetization curves. Furthermore, this knowledge will help reconsideration of the design of biomedical application using magnetic nanoparticles, since it has been optimized assuming magnetic response described by Langevin function.

A new hysteresis model is developed to describe clockwise hysteresis, in which the positive saturation is achieved for positive values of the input. The model is based on the traditional (counter-clockwise) Jiles-Atherton (JA) model and describes the input-output relation in the form of a first-order differential equation. The most important characteristics such as initial susceptibility, coercive fields, remanence, thermal stability, first and higher order reversal curves are discussed. A comparison with other two clockwise hysteresis models of hysteresis (i.e., the Preisach and Bouc-Wen models) is provided. It is proven that the clockwise JA model can describe novel hysteretic behavior that cannot be reproduced by the previous two models. The novel model is also appealing due its relatively simple numerical implementation and its small number of parameters.

Isolated magnetic nanowires have been studied extensively and the magnetization reversal mechanism is well understood in these systems. But when these nanowires are joined together in different architectures, they behave differently and can give novel properties. Using this approach, one can engineer the network architectures to get artificial anisotropy. Here, we report six-fold anisotropy by joining the magnetic nanowires into hexagonal network. For this study, we also benchmark the widely used micromagnetic packages: OOMMF, Nmag, and LLG-simulator. Further, we propose a local hysteresis method by post processing the spatial magnetization information. With this approach we obtained the hysteresis of nanowires to understand the six-fold anisotropy and the reversal mechanism within the hexagonal networks.

We have developed a mathematical tool able to track irreversible processes in magnetic systems described by the Stoner-Wohlfarth model, under any applied field history. A graphic representation is worked out that accounts for interactions, and turns out to be an extension of the one operating in the Preisach model. The response to alternating and rotating magnetizing fields have been investigated in detail. We have found a strategy in dealing with hysteretic memory effects which speeds the computational work needed to get the materials magnetization. This approach can represent a suitable tool aimed at estimate the energy loss and entropy production in magnetic systems.

In this paper, a new method to calculate the critical points (CPs) for a symmetric synthetic antiferromagnet, using the Stoner-Wohlfarth model for each layer is proposed. For given initial conditions, the system has multiple equilibrium states, and consequently, there are multiple energy barriers (EBs), so it is rather difficult to estimate the actual EBs for the real switches. Using the developed method, one can determine all the minimum energy points as well as the saddle points (SPs) based on the solutions of polynomial equations associated to the critical points conditions. These are necessary conditions to estimate the EB. Defining the EB as the difference between the lowest SP and the highest energy minimum for an applied field, one obtains for the lowest values of the EB the well-known critical curves. The plot of the EBs in the field planes is compared with the graphs of the critical curves and the results are discussed.

The existence of the five-fold twinned structures was observed in 3.4 nm FePt nanoparticles, and other n-fold structures were also been found in magnetic nano-grains in recording media. An analytical model, following the spirit of the Stoner-Wohlfarth model, is brought up to study the anisotropy field distribution of FePt or other magnetic nanoparticles with twinned or n-fold structures, based on simple statistical calculations of twin regions' volumes. It is found that the nanoparticle has an effective uniaxial anisotropy, and the average anisotropy field is substantially reduced compared to that of the single crystal. The calculated anisotropy distributions are also compared with the empirical distribution functions used in micromagnetic simulations.

In this paper, we present a new vector hysteresis model, which is derived from the original Jiles-Atherton scalar one. The model presents the magnetic vector induction as the independent variable. A modified Langevin equation is used to represent the anhysteretic vector magnetization, and some model aspects are discussed. A comparison between measured and calculated curves for an anisotropic soft magnetic material is performed to validate the model.

AC magnetization curves of a Stoner-Wohlfarth model system consisting of noninteracting uniaxial single-domain particles are described by Fourier expansion. Two types of hysteresis curves are considered-the first one with a magnetizing field changed in a sine periodical way, and the second one with the magnetization of the system changed in a sine periodical way.

In this paper, we propose the method to analyze the magnetization distribution in magnetoanisotropic materials by using the finite-element method considering the improved variable magnetization and Stoner-Wohlfarth model. By using this method, furthermore, the effect of the eddy currents induced in permanent magnets was analyzed. From the analyzed result, it is clarified how the magnetization distribution affects the performance of the surface permanent magnet-type motors.

The coercivity, time dependent magnetic properties and reversible magnetization behavior for a series of neodymium enriched alloys based on Nd/sub 2/Fe/sub 14/B has been investigated. These studies were carried out in an attempt to elucidate the dramatic increase in the coercivity in these materials with increasing dilution of the magnetic phase (Nd/sub 2/Fe/sub 14/B). Good correlation between the coercivity and the relative average linear sparing between magnetic grains was found for all but the lowest Nd content. As the Nd content is increased the reversible magnetization associated with domain wall pinning decreases. At high dilutions the reversible magnetization behavior is consistent with the predictions of a Stoner-Wohlfarth model of an assembly of noninteracting single domain particles. The magnetic viscosity parameter, /spl Lambda/, does not vary consistently with dilution or coercivity.

A vector hysteresis modeling algorithm is suggested to model the hysteresis phenomena of an isotropic magnetic material. The algorithm combines the Stoner-Wohlfarth and Preisach models. The vector property of each single domain magnetic particle with uniaxial anisotropy, which is supposed to constitute the magnetic material, when the direction and magnitude of applied field are changed is modelled by using the Stoner-Wohlfarth model. The coercive and interaction fields of each particle are modeled by using the Preisach model. In the algorithm the easy axes are assumed randomly distributed over all possible directions. The algorithm reduces to a scalar Preisach model if only one easy axis is defined. The developed algorithm is applied to the analysis of the magnetization of the isotropic rubber ferrite permanent magnet, and the result is compared with experiments.

The planar Hall effect (PHE) and magnetoresistance (MR) measurements have been carried out on a GaMnAs ferromagnetic semiconductor. The PHE and MR spectra exhibit interesting two-step magnetization switching behavior arising from the magnetic anisotropy properties of the system. By fitting the angle-dependent planar Hall resistance (PHR) data taken at 5 kG with the Stoner-Wohlfarth model, the cubic and uniaxial anisotropy constants were independently obtained. The anisotropy constants lead to the precise determination of easy axis direction, which turns out to be in good agreement with the easy axis determined from the angular plot of the switching field. The domain pinning energies were further obtained by fitting the angle dependence of the switching field, including the effect of uniaxial anisotropy

(001) IrMn/CoFe epitaxial bilayers were fabricated on Si substrates at room temperature by using Cu underlayers. A double shifted loop was observed at the axis perpendicular to the exchange bias direction. The dependence of anisotropy on the IrMn thickness was studied. The magnetization reversal was investigated by using vector coil measurements and calculations based on Stoner-Wohlfarth model. A combination of reversible and irreversible rotation was observed for the magnetization reversal along the hard axis. Critical angles and fields at which irreversible rotation occurred were obtained through simulations

Angular dependence of Hex and Hc, and the critical angle behavior are measured in CoFe/MnIr bilayers annealed at 200degC and 340degC. The interfacial exchange coupling anisotropy and the antiferromagnet anisotropy at tAF tc AF as well as for tAF

VMSW (variable magnetization and Stoner Wohlfarth model) method is effective for numerical analysis of anisotropic permanent magnets. This method however, has a serious restriction of the way of dividing elements. Therefore, the conventional VMSW method cannot be applied to the analysis of materials of complicated shape. In this paper, an improved VMSW method is presented. The problem of dividing elements can be solved by using this method.

This paper describes an implementation of the static magnetic hysteresis using the finite element method and a vector hysteresis model. The vector hysteresis model which is extended from the magnetization-dependent Preisach model is adopted. The magnetization of each element is calculated for a given history of the rotating field. The lagging angle of the magnetization for the applied field is evaluated. It is shown that the magnetization characteristics of the magnetic materials under the rotating field can be explained.

Numerically efficient Preisach-based vector hysteresis models for ellipsoidally magnetizable media are presented. Both models are based on orthogonal coupled scalar models and take into consideration the variation in particle switching fields and interaction; however, the coupling mechanism is different in the two models. The rules determining the magnetization state corresponding to the vector applied field are discussed. The basic rotational remanence properties of the models are compatible with observed vector phenomena.

Computations of cylindrically-symmetric magnetization distributions are reported for a perfect and isotropic ferromagnetic sphere. The total energy is minimized numerically for various applied fields, with no constraint other than imposing that symmetry. It is found that the curling configuration at zero field is maintained throughout the whole magnetization process, with only a tilt towards the field direction, which increases with increasing field. There is no hysteresis in such an ideally-soft sphere, and the theoretical initial susceptibility is infinite.

The switching behavior on a nanosecond time scale of a CoCrPt-based perpendicular medium has been studied both experimentally and by simulation. The sample was composed of a granular storage layer with a saturation remanence close to unity and a soft underlayer. The time-dependent remanent coercivity was measured down to 2.3 ns. The results are in good agreement with the extrapolation of the long time data, in accordance with the thermal switching model proposed by Sharrock, with n=2/3. The dependence of the switching field in the nanosecond regime on the initial remanence was studied. The remanent coercivity of the saturated sample was found to be lower than that of a partially demagnetized sample. This counter-intuitive behavior was confirmed by simulation, which elucidated the role of the local demagnetizing field in the switching process. The simulation also showed that the effect is sensitive to the time scale of the initial demagnetization process.

We use the micromagnetic simulation to study the reversible and irreversible magnetization processes of the single-domain elliptical permalloy particles. The magnetization curve of the reversible process, which has no hysteresis, obtained by applying the field along the hard axis of the elliptical particle is almost linear, as is the case in the single-domain ellipsoidal particle. On the other hand, due to the occurrence of the nonuniform reversal, the switching field of the irreversible process, which has hysteresis, is reduced significantly compared to that predicted by the Stoner-Wohlfarth model. The nucleation fields of elliptical particles are calculated as a function of ellipse's aspect ratio, and the function reveals a step-like behavior.

We present a simple analytical model based on the Stoner-Wohlfarth model for the detection of a single magnetic microbead or nanobead by spin valve sensors. Two-dimensional micromagnetic simulations were also performed for the spin valve sensors. It is found that the analytical model fits well with the micromagnetic simulations in the case of the microbead, although it underestimates the effect of a nanobead. Experiments were carried out to detect a single superparamagnetic microbead (Dynabeads/spl reg/ M-280, 2.8 /spl mu/m in diameter) on the fabricated spin valve sensors. The experimental results were found to be consistent with the analytical and micromagnetic models.

The authors describe how the various model parameters needed to describe hysteresis on the basis of the Jiles-Atherton theory can be calculated from experimental measurements of the coercivity, remanence, saturation magnetization, initial anhysteretic susceptibility, initial normal susceptibility, and maximum differential susceptibility. The determination of hysteresis parameters based on this limited set of magnetic properties is of the most practical use since these are the properties of magnetic materials that are most likely to be available. >

Some properties of the moving Preisach model are examined. It is found that this model can introduce hysteresis in materials where it is not intrinsically present. It is shown that the moving model has the wiping-out property, even in the case where a reversible component of magnetization is present in addition to the irreversible component computed by the moving model. The implication of this model to the overwrite problem in magnetic recording is discussed. >

A model of magnetic hysteresis is proposed. It is based on the Stoner-Wohlfarth coherent rotation model, but with a macroscopic mean field interaction (similar to Weiss's molecular field theory), added to represent interaction between domains. Rotation of domain magnetization vectors gives both reversible and irreversible changes in bulk magnetization. A qualitative correlation is obtained between hysteresis curves calculated using this theoretical model and experimentally measured hysteresis curves of a ferrite permanent magnet. >

The basic characterizing parameters of magnetic recording media are critically examined. The applicability and usefulness of the measurement of remanence curves are discussed together with their relationship to time-dependent phenomena. Techniques for the determination of anisotropy fields are also presented. The application of DC and AC magnetic measurement techniques to the characterization of pigment dispersions is briefly discussed. >

Tensor magnetic hysteresis loops for a 25.4 mm (1 inch) ferrite permanent magnet cube have been measured. A hysteresis model based on the Atherton-Beattie model has been developed to explain the measured full tensor hysteresis loops. Both mean field interactions and irreversible Stoner-Wohlfarth type switching are used to account for the observed magnetic hysteresis. The non-zero off-diagonal loops originate from the small deviation of the sample easy axis from the cube edge direction. The magnetic easy axis of the sample can be readily determined from the tensor hysteresis loops.

This paper illustrates the use of the dynamic Preisach model with accommodation in calculating the remanence after the application of two pulses. The DOK model is used to calculate the state-dependent locally reversible magnetization.

A thermally activated Stoner Wohlfarth model is used to calculate coercivity as a function of field rate for systems in which a distribution of particle volumes and easy axis orientations is possible. The analytical treatment of M. El-Hilo, A.M. de Witte, K. O'Grady and R.W. Chantrell [J. Magn. Magn. Mater., vol. 117, pp, L307-L310, 1992], which was based on a critical volume assumption, is found to be in excellent agreement with the model calculations for aligned systems with a distribution of particle volumes. The limitations of analytical theory are shown when a distribution of orientations is included.

A model of hysteresis has been developed earlier in which the susceptibility depends on the displacement of the prevailing magnetization from the anhysteretic. This model does not take into account the effect of magnetocrystalline anisotropy in a material. In the current work, it has been shown that the effect of anisotropy can be incorporated into this model through its effect on the anhysteretic magnetization.

This paper describes a phenomenological model of scalar magnetic hysteresis which is based on the similarity of the processes taking place when a magnetic material is magnetized along the branches of both the main and any minor hysteresis loops. This allows one to form any reversal curve by means of conjugation of the portions which are transplanted from the main loop branches, and to fit the model to a given material.

A new technique for the estimation of interparticle interaction effects in some magnetic systems is developed only on the basis of Fourier description of experimental hysteresis loops and initial magnetization curves, avoiding remanence measurements. This technique is applied for Ba-ferrite powders and for several currently used magnetic recording media. It is found that the results coincide fairly well with these obtained by the commonly accepted /spl Delta/I technique, using remanence curves. >

The paper proposes the interacting Stoner-Wohlfarth particles system (ISWPS) model that could be used to characterize magnetic recording media. The particles of the system are distributed as a function of orientation, anisotropy and interaction fields. Using these distributions and the Stoner-Wohlfarth theory for the isolated particle hysteresis loop one can calculate an equivalent distribution of pseudo-particles each of which characterizes the average behavior of an ensemble of particles from the sample with the same critical and interaction fields. The classical Preisach distribution is replaced with a distribution of Stoner-Wohlfarth pseudo-particles with known hysteresis loops. The agreement between the experimental data obtained for a BASF magnetic computer tape and the results of the simulations is good. >

It is observed after saturation that sequential reverse pulses with fast rise times (

The isothermal remanence curve of a particulate recording medium is shown experimentally to depend upon the method used to achieve the demagnetized state. As-prepared powder samples exhibit larger initial remanence slopes than after AC field demagnetization. This can be interpreted in terms of a higher degree of correlation introduced by the particle-particle interactions during the demagnetization process. Theoretical calculations using a Monte Carlo model give good qualitative agreement with experimental data. >

Magnetization processes are investigated in connection with the heat transfer to the lattice. The temperature was measured of a heat-insulated sample in the course of virgin curves, hysteresis- and minor loops. Thus it is possible to separate reversible and irreversible contributions. The dissipation of magnetization energy is located at the coercivity point. The reversible heat transfer is in agreement with the thermodynamical coefficient in connection with the temperature dependence of saturation magnetization.