Anhysteretic Magnetization Curve Research Articles

The SF and remanence evaluation of magnetic shields based on SST for low-frequency and degaussing situation

As the dominant shielding functional material, the permalloy sheet primarily determines the static and low-frequency shielding performances of magnetically shielded room (MSR). However, the lack of measurement of shielding sheets for practical use would lead to a non-negligible evaluation error in MSR performance. Therefore, an estimation technique of shielding factor (SF) and the remanence of MSR is proposed in this paper while considering the nonlinear magnetic characteristics of the permalloy sheet tested by a single sheet tester for low-frequency field and degaussing situation (L-D-SST). First, a high-accuracy measurement system, comprising L-D-SST (for exciting magnetic field and sensing the corresponding B and H) and the control system (for applying excitation to L-D-SST and amplifying, filtering, and collecting B and H signals), is established. Weak magnetic fields at low frequencies and decaying alternating demagnetizing field excitations are separately applied to the L-D-SST for basic magnetization curves (BM curves) and an anhysteretic magnetization curve (AM curve) tests. Furthermore, the BM and AM curves are respectively integrated with the FEM algorithm for accurate and reliable estimations of the SF and remanence of MSR in an operational state. In addition, the tested magnetic properties are applied for the optimization of MSR shielding quality.

Determining the Anhysteretic Magnetization Curve for a Ferromagnetic Material According to the Limiting Loop Parameters of Its Magnetic Hysteresis

Determining the Anhysteretic Magnetization Curve for a Ferromagnetic Material According to the Limiting Loop Parameters of Its Magnetic Hysteresis

Demagnetization Parameters Evaluation of Magnetic Shields Based on Anhysteretic Magnetization Curve.

To achieve the nearly zero-field environment, demagnetization is an indispensable step for magnetic shields composed of high-permeability material, which adjusts the magnetization of the material to establish magnetic equilibrium with the environmental field and improve the shielding performance. The ideal demagnetization can make the high-permeability material on the anhysteretic magnetization curve to have a higher permeability than on the initial magnetization curve. However, inappropriate parameters of degaussing field cause the magnetization state to deviate from the anhysteretic magnetization curve. Therefore, this article proposes a new assessment criterion to analyze and evaluate the parameters of degaussing field based on the difference between the final magnetization state after demagnetization and theoretical anhysteretic state of the shielding material. By this way, the magnetization states after demagnetizations with different initial amplitude, frequency, period number and envelope attenuation function are calculated based on the dynamic Jiles-Atherton (J-A) model, and their magnetization curves under these demagnetization conditions are also measured and compared, respectively. The lower frequency, appropriate amplitude, sufficient period number and logarithmic envelope attenuation function can make the magnetization state after demagnetization closer to the ideal value, which is also consistent with the static magnetic-shielding performance of a booth-type magnetically shielded room (MSR) under different demagnetization condition.

Experimental studies on the performance of magnetic shields under different magnetization conditions

In recent decades, magnetic shields have provided basic experimental environments for the measurements of extremely weak magnetic fields represented by the biological magnetic signal. Excellent shielding performances, including the low residual field and high shielding factor (SF), are necessary to ensure the quality of these weak magnetic signals and avoid the interference of external magnetic fields. The magnetic shielding performance of the same device can be affected by different degaussing and test conditions, which remains to be systematically studied. In this paper, experiments with variable magnetization conditions, including different degaussing orders, test fields and environmental fields, are established in a nearly zero-field space to simulate the different situations during measurement. The residual field and SF of the cubic shielding device are tested in these cases. Meanwhile, these shielding performances are analyzed from the perspective of the magnetization state and calculated based on the magnetic properties which are tested and fitted by the Jiles–Atherton model. The results show the influence of these different conditions on the shielding performances of the cubic device, consistent with the numerical calculation. Under the same environmental field, the different degaussing order and test field lead to completely different residual field and shielding performance, respectively. The influence of the Earth’s magnetic field on the SF can be ignored due to its tiny equivalent bias field determined by the anhysteretic magnetization curve.

On the anhysteretic magnetization of soft magnetic materials

Electrical steels are still the materials of choice for large-scale transformers and most electric motors. Yet, they may present a nonhomogeneous magnetic nature which prevents describing accurately their anhysteretic magnetization with the Langevin-Weiss model. Although interpolation and extrapolation methods may be used to model any anhysteretic curve, a simple and physically-based model would be of great value for fundamental and applied research. Inspired in the law of partial volumes for gas mixtures, we proposed a law of partial magnetizations for magnetic mixtures. In a two-component system, the model leads to the double Langevin-Weiss function. We also introduced a graphical method and a fitting approach to analyze and model anhysteretic magnetization curves. A semi-log magnetization derivative plot is central to this end. We validated our strategy through well-motivated examples using published data on soft magnets. The single Langevin-Weiss function provided an accurate description of the magnetization of isotropic and anisotropic magnetically homogeneous materials: a soft ferrite and a nanocrystalline alloy, respectively. For modelling a magnetization transverse to the material’s preferred direction, the key is to allow a negative molecular field constant. The double Langevin-Weiss function was suitable for less homogeneous materials, such as a grain-oriented electrical steel magnetized along the rolling direction and a non-oriented electrical steel. Moreover, a highly-grain-oriented electrical steel magnetized transverse to the rolling direction, which exhibits a constricted hysteresis loop, could be modeled in excellent agreement with data. The key for the latter, has been to allow an antiparallel arrangement of the mean magnetization of both components.

Anhysteretic Magnetization Effect on the Centered and Non-Centered Minor Hysteresis Loops in Jiles-Atherton Model

In this paper, an accurate evaluation of minor hysteresis loops using the modified Jiles-Atherton model is presented. This model is based on the anhysteretic magnetization, which is given in most cases by the Langevin equation. The anhysteretic magnetization is characterized by three parameters, the mean field parameter α, the shape parameter of anhysteretic magnetization curve a and the saturation magnetization Ms. The parameters influencing the minor hysteresis loops are a and α. These parameters are expressed usually in the form of simple power laws and they connect the minor loop parameters to the major ones. These expressions are applicable in both centered and non-centered minor loops cases. In the centered minor loops, the parameter k is introduced in order to adjust the width of the minor loops regarding the level of the magnetic excitation. The coefficients of the proposed expressions (γ, β and σ) are obtained by optimization procedure. The proposed approach is validated using measured minor loops in both cases. A close agreement is obtained between modeled and measured ones.

Analysis of vector hysteresis models in comparison to anhysteretic magnetization model

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.

Magnetic properties of selected Fe-based soft magnetic composites interpreted in terms of Jiles-Atherton model parameters

The paper presents the Jiles-Atherton model application to selected Fe-based soft magnetic composites (of different types prepared with the intention of verifying the model), with inner demagnetizing fields consideration implemented. The model fits experimental anhysteretic magnetization curves with very good accuracy, obtaining parameters: the effective domain density, the interdomain coupling and the average magnetic moment of effective domain. The parameters are interpreted in comparison to maximum total and differential permeability, inner demagnetization factor and hysteresis losses. The denser effective domain structure with stronger interdomain coupling is found for the decreasing ferromagnetic filler content and mean particle size, together with higher inner demagnetizing fields, leading to lower number of active magnetic objects, reflected by magnetic properties worsening. The relation of magnetic properties to interdomain coupling strength and effective domain density is specific for each ferromagnetic component of composite. The parameters absolute values are found remarkably different from bulk ferromagnets values in literature, pointing out the specific magnetization reversal of composites.

Experimental Verification of Isotropic and Anisotropic Anhysteretic Magnetization Models.

The anhysteretic magnetization curve is the key element of modeling magnetic hysteresis loops. Despite the fact that it is intensively exploited, known models of anhysteretic curve have not been verified experimentally. This paper presents the validation of four anhysteretic curve models considering four different materials, including isotropic, such as Mn-Zn soft ferrite, as well as anisotropic amorphous and nanocrystalline alloys. The presented results indicate that only the model that considers anisotropic energy is valid for a wide set of modern magnetic materials. The most suitable of the verified models is the anisotropic extension function-based model, which considers uniaxial anisotropy.

Origin of ferromagnetism in Cu-doped ZnO

It is widely reported during last decade on the observation of room temperature ferromagnetism (RTFM) in doped ZnO and other transition metal oxides. However, the origin of RTFM is not understood and highly debated. While investigating the origin of RTFM, magnetic ion doped oxides should be excluded because it is not yet settled whether RTFM is intrinsic or due to the magnetic ion cluster in ZnO. Hence, it is desirable to investigate the origin of RTFM in non-magnetic ion doped ZnO and Cu-doped ZnO will be most suitable for this purpose. The important features of ferromagnetism observed in doped ZnO are (i) observation of RTFM at a doping concentration much below than the percolation threshold of wurtzite ZnO, (ii) temperature independence of magnetization and (iii) almost anhysteretic magnetization curve. We show that all these features of ferromagnetism in ZnO are due to overlapping of bound magnetic polarons (BMPs) which are created by exchange interaction between the spin of Cu2+ ion and spin of the localized hole due to zinc vacancy ({V}_{Zn}). Both the experimental and theoretical investigation show that the exchange interaction between Cu2+-Cu2+ ions mediated by {V}_{Zn} is responsible for RTFM in Cu-doped ZnO.

An Improved Centered Cycle Method for Identifying the Preisach Distribution Function

This paper proposes an improved centered cycle method for identifying the Preisach distribution function based on the non-uniform discretization. The principle and the limits of the centered cycle method are first introduced. Then, the non-uniform discretization method is proposed based on the curvature of the anhysteretic magnetization curve. The numbers of loops for identifying the distribution function are decided by the proportion of the integral of curvature. The method to determine the cell values of the non-uniformly discrete Preisach triangle is also introduced. The proposed method is validated by the laboratory test of a toroidal sample. The results show the higher precision of the proposed method for predicting the hysteresis loop than the centered cycle method by the same number of loops used for identifying.

Anhysteretic Magnetization Measurement Methods for Soft Magnetic Materials.

This article is concerned with the methods for experimentally determining the Anhysteretic Magnetization curve for soft magnetic materials. A new method based on the modern hysteresisgraph system is presented. Known modern and traditional methods based on fluxmeters are presented as well. The experimental results obtained with the described methods for isotropic Mn–Zn ferrite are compared. Lastly, results of validation on NANOPERM® nanocrystalline material are detailed and show negligible hysteresis. The new method allows for accurate Anhysteretic Magnetization curve measurement without software or hardware modifications of standard, commercially available hysteresisgraph systems. The speed and accuracy of the results are improved in comparison with other methods.

Tailoring the structural and magnetic properties of Co-Zn nanosized ferrites for hyperthermia applications

A comparative study of the magnetic properties (magnetic moment, magnetocrystalline anisotropy) and hyperthermia response in Co-Zn spinel nanoparticles is presented. The CoxZn1−xFe2O4 nanoparticles (x = 1, 0.5, 0.4, 0.3, 0.2 and 0.1) were synthesized by co-precipitated method and the morphology and mean crystallite size (around 10 nm) of the nanoparticles were analysed by TEM Microscopy. Regarding the magnetic characterization (SQUID magnetometry), Co-Zn nanoparticles display at room temperature anhysteretic magnetization curves, characteristic of the superparamagnetic behavior. A decrease in the blocking temperature, TB, with Zn content is experimentally detected that can be ascribed to the reduction in the mean nanoparticle size as x decreases. Furthermore, the reduction in the magnetocrystalline anisotropy with Zn inclusion is confirmed through the analysis of TB versus the mean volume of the nanoparticles and the law of approach to saturation. Maximum magnetization is achieved for x = 0.5 as a result of the cation distribution between octahedral and tetrahedral spinel sites, analysed by neutron diffraction studies. The occurrence of a canted spin arrangement (Yafet-Kittel angle) is introduced to properly fit the magnetic spinel structures. Finally, the heating capacity of these spinel ferrites is analyzed under ac magnetic field (magnetic hyperthermia). Maximum SAR (Specific Absorption Rate) values are achieved for x = 0.5 that should be correlated to the maximum magnetic moment of this composition.

Suitability of the double Langevin function for description of anhysteretic magnetization curves in NO and GO electrical steel grades

This paper compares the match obtained using the classical Langevin function, the tanh function as well as a recently by the authors proposed double Langevin function with the measured anhysteretic magnetization curve of three different non-oriented electrical steel grades and one grain-oriented grade. Two standard non-oriented grades and a high-silicon grade (Si content of 6.5%) made by CVD are analyzed. An excellent match is obtained using the double Langevin function, whereas the classical solutions are less appropriate. Thereby, problems such as those due to propagation of approximation errors observed in hysteresis modeling can be bypassed.

Modeling plastic deformation effect on the hysteresis loops of ferromagnetic materials based on modified Jiles-Atherton model

Plastic deformation is one of the most important features that affect the hysteresis magnetic properties of steels, because it changes the dislocation density and affects domain-wall movement and pinning. In order to model the effect of plastic deformation on the magnetic properties, the prevailing Jiles-Atherton (J-A) theory is extensively used. However, the J-A models in a series of papers published by Jiles et al. are not completely consistent. As a result, there exists no uniform formula of magneto-plastic model established by different researchers, based on different J-A models, and various versions given by different mathematic expressions of magneto-plastic model often create difficulty in discriminating the accuracies and effectivenesses of the analyzed results. Therefore, it is necessary to establish an accurate and reasonable magneto-plastic model. In this paper, on the basis of magnetization mechanism of ferrimagnet and plastic deformation model, the effects of plastic deformation on the magnetic characteristic parameters adopted in magneto-plastic model, such as dislocation density, pinning coefficient and scaling constant, are analyzed and the relationship between them is first established. Then, by contrasting the fitting formula of the anhysteretic magnetization curve, the energy conservation equation and the effective magnetic field equation established by different researchers, several queries are proposed, and the irrationality and inaccuracy of the existing magneto-plastic model are elucidated, such as the mixing of anhysteresis magnetization and magnetization, the unreasonably regarding the irreversible magnetization energy as actual total magnetization energy. Thus, the energy conservation equation, the effective magnetic field equation and the anhysteretic magnetization equation are modified, and the differential expression of the magneto-plastic model is re-derived finally. Comparing the results calculated by the existing magneto-plastic models with the experimental results, it is seen indeed that a more sharp change of magnetization appears at small plastic deformation, then, the values of magnetization decrease more slowly with the increase of plastic deformation than those from the models respectively proposed by Li Jian-Wei, Leng Jian-Cheng and Wang Zheng-Dao; the saturation magnetization and residual magnetization decrease with the increase of plastic deformation, the coercive force is increased oppositely and the trend to reach the saturation magnetization becomes gentler, which is more exactly consonant with experiment observation than that calculated by the Sablik's model; additionally, the hysteresis loops of the plastically deformed carbon-steel samples calculated by the modified magneto-plastic model are also in better agreement with the experimental results than those from the existing models. Consequently, the modification is effective, and the modified magneto-plastic model is more accurate to simulate the plastic deformation effect on the magnetic property of ferromagnetic material.

Energy based model for temperature dependent behavior of ferromagnetic materials

An energy based model for temperature dependent anhysteretic magnetization curves of ferromagnetic materials is proposed and benchmarked against experimental data. This is based on the calculation of macroscopic magnetic properties by performing an energy weighted average over all possible orientations of the magnetization vector. Most prior approaches that employ this method are unable to independently account for the effect of both inhomogeneity and temperature in performing the averaging necessary to model experimental data. Here we propose a way to account for both effects simultaneously and benchmark the model against experimental data from ~5K to ~300K for two different materials in both annealed (fewer inhomogeneities) and deformed (more inhomogeneities) samples. This demonstrates that this framework is well suited to simulate temperature dependent experimental magnetic behavior.

Dependence of demagnetizing fields in Fe-based composite materials on magnetic particle size and the resin content

Demagnetizing fields are in general produced by the volume and surface magnetic poles. The structure of soft magnetic composite materials, where the ferromagnetic particles are insulated from each other, causes the formation of demagnetizing fields produced by the particle surfaces. These fields depend on the amount of insulation and on the shapes, clustering and distribution of ferromagnetic particles. In this work the demagnetizing fields in iron–phenolphormaldehyde resin composite samples were investigated experimentally using the method for determining the demagnetization factor from the anhysteretic magnetization curve measurement. The initial magnetization curves were calculated for an ideal composite with 100% filler content using the values of the demagnetization factor. The results on the “ideal” permeability show differences between the samples with different resin content for each granulometric class, which tells about the internal stresses introduced into ferromagnetic material during the compaction process.

Nonequilibrium magnetic response of anisotropic superparamagnetic nanoparticles and possible artifacts in magnetic particle imaging.

Magnetic responses of superparamagnetic nanoparticles to high-frequency AC magnetic fields with sufficiently large amplitudes are numerically simulated to exactly clarify the phenomena occurring in magnetic particle imaging. When the magnetic anisotropy energy inevitable in actual nanoparticles is taken into account in considering the magnetic potential, larger nanoparticles exhibit a delayed response to alternations of the magnetic fields. This kind of delay is rather remarkable in the lower-amplitude range of the field, where the assistance by the Zeeman energy to thermally activated magnetization reversal is insufficient. In some cases, a sign inversion of the third-order harmonic response was found to occur at some specific amplitude, despite the lack in DC bias magnetic field strength. Considering the attenuation of the AC magnetic field generated in the human body, it is possible that the phases of the signals from nanoparticles deep inside the body and those near the body surface are completely different. This may lead to artifacts in the reconstructed image. Furthermore, when the magnetic/thermal torque-driven rotation of the anisotropic nanoparticles as well as the magnetic anisotropy energy are taken into account, the simulated results show that, once the easy axes are aligned toward the direction of the DC bias magnetic field, it takes time to randomize them at the field-free point. During this relaxation, the third-order harmonic response depends highly upon the history of the magnetic field. This is because non-linearity of the anhysteretic magnetization curve for the superparamagnetic nanoparticles varies with the orientations of the easy axes. This history dependence may also lead to another artifact in magnetic particle imaging, when the scanning of the field-free point is faster than the Brownian relaxations.

Non-linear behavior of coercivity to the maximum applied magnetic field in La substituted nanocrystalline cobalt ferrite

The magnetic properties of nanocrystalline cobalt ferrite could be tuned with substituting small amount of non-magnetic rare earth cation at Fe site in cobalt ferrite. The variation in magnetic parameter of samples could also be obtained by measuring its anhysteretic magnetization curve without tailoring its chemical composition. The magnetic parameters such as coercivity, remanent magnetization and saturation magnetization critically depend upon different values of external magnetic fields. In the present study, the anhysteretic magnetization curve of the samples CoFe2−xLaxO4 (x=0.025, 0.05, 0.075 and 0.1) has been recorded and response of coercivity to different maximum values of applied field has been investigated. It has been observed that the response of coercivity to different maximum values of applied field shows non-linear behavior. The analysis of the response of coercivity to different values of applied field in low field regime has been carried out with the help of Rayleigh laws. The analysis of the plot yields significant information about magnetic anisotropy.

Magnetic Hysteresis Loop in a Superparamagnetic State

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.