Quasi-static Hysteresis Loops Research Articles

A Calculation Method for Static Hysteresis Loop and its Applications

Background: Due to experimental equipment limitations, it is usually difficult to measure the quasi-static hysteresis loop at extremely low frequencies, which inevitably introduces errors in the static hysteresis model. Objective: This study aims to propose a method for calculating the static hysteresis loops of grainoriented silicon steel sheets so as to improve the accuracy of the static and dynamic hysteresis model. Methods: The parameters n0 and V0 in the magnetic field strength expression of the excess loss are determined by the measured losses within the range of 0-100Hz. Subsequently, the dynamic components in the quasi-static hysteresis loops are eliminated. Furthermore, a dynamic hysteresis model is established based on the loss and field separation theory, which incorporates the inverse Preisach model. Results: The dynamic hysteresis loops of the grain-oriented silicon steel sheets are measured in the range of 8-250Hz and compared with the results of both the improved model and the original model. Conclusion: Experimental results demonstrate the effectiveness and accuracy of the improved model. The proposed method for calculating static hysteresis loops has universal applicability and is meaningful for accurate simulation and prediction of magnetic properties in soft magnetic materials.

Preparation and magnetic properties of high DC-bias performance Fe-Si-Nb-B-Cu/carbonyl iron chip inductors

In this study, a gradient temperature rise technique was employed to prepare ultra-fine nanocrystalline alloy magnetic powder with excellent high-frequency and low-loss characteristics. It was found that increasing the holding time effectively refines the grain structure in the perpendicular direction of the Fe-Si-Nb-B-Cu alloy's (220) crystal plane. This refinement contributes to a reduction in eddy current losses within the soft magnetic composite material. The addition of carbonyl iron to the nanocrystalline magnetic powder resulted in further enhancements in the density, strength, and magnetic properties of soft magnetic composites under high-frequency magnetic fields. Consequently, soft magnetic composites exhibiting superior DC bias performance were successfully obtained, with a power loss of 2629.50 kW/m3 at a magnetic induction of 20 mT and a frequency of 3 MHz, and more than 70 % percent permeability in a DC biased magnetic field of 7.96 kA/m. The relationship between relative permeability and quasi-static hysteresis loops was established. Additionally, the dynamic hysteresis loops of the soft magnetic composites revealed a relaxation phenomenon, which elucidated the mechanism behind the variations in power loss with changes in magnetic induction strength and frequency. Finally, through simulations, it was determined that the number of turns and the winding method significantly influenced the internal magnetic field and inductance of the chip inductor. Utilizing this information, a chip inductor with ultra-small inductance, compact size, and excellent DC bias characteristics for 10 A circuits was successfully fabricated.

A dynamic hysteresis prediction model of grain-oriented silicon steel sheet under AC-DC hybrid magnetization

Firstly, a new method for parameter identification of inverted Preisach model is proposed to simulate static DC-biasing hysteresis behavior of the grain-oriented (GO) silicon steel sheet by using the measured quasi-static concentric hysteresis loops under DC-biasing magnetization. Then, the dynamic magnetic field intensity related to excess loss is improved by considering the nonlinear relationship between the statistical parameter V0 and the AC peaked magnetic flux density, DC magnetic field intensity as well as frequency. Finally, a dynamic hysteresis model in form of field separation is presented to predict asymmetric hysteresis curves under multi-harmonic and DC-biasing hybrid magnetization. The simulated hysteresis curves as well as losses under different AC-DC hybrid magnetizations are compared with the measured ones, which verifies the accuracy and effectiveness of the proposed method.

Effective anisotropy in Fe-Ni nanowire arrays with strong dipolar interaction

The effective magnetic anisotropy field Heff of Fex Ni(100-x) (x = 15, 25, 38) nanowires of 65 nm diameter forming ordered arrays within dense alumina templates of ∼35% porosity, was determined. Different values for Heff were obtained depending on the determination method, which were: magnetization evolution along major hysteresis loops; ferromagnetic resonance at 34 GHz; and magnetization switching by curling nucleation (through angular variation of the coercive field). Heff values determined from magnetization measurements differ from those arising from FMR measurements, being these latter quite smaller in every case. No evidence of an easy plane behavior was found, as theoretically predicted for high porosity arrays as ours.These results suggest that new internal degrees of freedom need to be considered for the effective anisotropy description in quasistatic hysteresis loops, during polarization reversal and in ferromagnetic resonance dynamic processes, to understand and model these experimental findings. We discuss possible causes.

The Effect of Magnetization Reversal Frequency on the Dynamic Magnetic Hysteresis of a Plate Made of Electrical Stee

Electrodynamic, quasi-static magnetic hysteresis loops and the form of the domain texture of a single-crystal plate have been experimentally obtained. Using mathematical modeling, the change in the dynamic magnetic hysteresis (the magnetic loss energy per unit volume per magnetization reversal cycle) depending on the frequency of the magnetic field is shown. This dependence is due to the inertia of the magnetization of the sample. With a change in frequency, the dynamic magnetic hysteresis can differ significantly from the hysteresis in the case of quasi-static magnetization reversal.

Magnetostatic interaction in oriented assembly of elongated nanoparticles

The elements of the magneto-dipole (MD) interaction matrix are calculated for a pair of oriented spheroidal magnetic nanoparticles with a semiaxis ratio a/b = 1.25, 1.5, 2.0 and 3.0 as functions of the distance between the particle centers. It is shown that the spherical approximation for the MD interaction matrix is already incorrect at aspect ratios a/b > 1.25, if the distance R between the particle centers is of the order of particle sizes. However, for moderate particle aspect ratios, a/b < 1.5, the first order correction to spherical approximation with respect to a small parameter (a2 – b2)/R2 is shown to be in a good agreement with numerical data. Using exact MD interaction matrix, the quasi-static hysteresis loops of dilute assemblies of oriented clusters of spheroidal nanoparticles with different filling densities are calculated, depending on the direction of the external magnetic field with respect to the particle orientation axis.

Chemical control of polarization in thin strained films of a multiaxial ferroelectric: Phase diagrams and polarization rotation

The emergent behaviors in thin films of a multiaxial ferroelectric (FE) due to electrochemical coupling between the rotating polarization and surface ions are explored within the framework of the 2--4 Landau-Ginzburg-Devonshire (LGD) thermodynamic potential combined with the Stephenson-Highland (SH) approach. The combined LGD-SH approach allows us to describe the electrochemical switching and rotation of a polarization vector in a multiaxial ferroelectric film covered by surface ions with a charge density defined by the oxygen pressure. We calculate phase diagrams, analyze the dependence of polarization components on the applied voltage, and discuss the peculiarities of quasistatic ferroelectric, dielectric, and piezoelectric hysteresis loops in thin strained multiaxial ferroelectric films. The nonlinear surface screening by oxygen ions makes the diagrams very different from the known diagrams of, e.g., strained ${\mathrm{BaTiO}}_{3}$ films. Quite unexpectedly, we predict the appearance of ferroelectric reentrant phases. The obtained results point to the possibility to control the appearance and features of ferroelectric, dielectric, and piezoelectric hysteresis in multiaxial FE films covered with surface ions by varying their concentration via the partial oxygen pressure. The LGD-SH description of a multiaxial FE film can be further implemented within the Bayesian optimization framework, paving the way toward predictive materials optimization.

Magnetostatic Interaction in Oriented Assembly of Elongated Nanoparticles

The elements of the magneto-dipole (MD) interaction matrix are calculated for a pair of oriented spheroidal magnetic nanoparticles with a semiaxes ratio a/b = 1.25, 1.5, 2.0 and 3.0 as a function of the distance between the particle centers. It is shown that the spherical approximation for MD interaction matrix is incorrect already at aspect ratios a/b > 1.25, if the distance R between the particle centers is of the order of particle sizes. However, for moderate particle aspect ratios, a/b < 1.5, the first order correction to spherical approximation with respect to a corresponding small parameter is shown to be in a good agreement with numerical data. Using exact MD interaction matrix, the quasi-static hysteresis loops of dilute assemblies of oriented clusters of spheroidal nanoparticles with different filling densities are calculated, depending on the direction of the external magnetic field with respect to the particle orientation axis.

Hysteresis Modeling in Iron-Dominated Magnets Based on a Multi-Layered NARX Neural Network Approach.

A full-fledged neural network modeling, based on a Multi-layered Nonlinear Autoregressive Exogenous Neural Network (NARX) architecture, is proposed for quasi-static and dynamic hysteresis loops, one of the most challenging topics for computational magnetism. This modeling approach overcomes drawbacks in attaining better than percent-level accuracy of classical and recent approaches for accelerator magnets, that combine hybridization of standard hysteretic models and neural network architectures. By means of an incremental procedure, different Deep Neural Network Architectures are selected, fine-tuned and tested in order to predict magnetic hysteresis in the context of electromagnets. Tests and results show that the proposed NARX architecture best fits the measured magnetic field behavior of a reference quadrupole at CERN. In particular, the proposed modeling framework leads to a percent error below 0.02% for the magnetic field prediction, thus outperforming state of the art approaches and paving a very promising way for future real time applications.

Investigation of the build orientation effect on magnetic properties and Barkhausen Noise of additively manufactured maraging steel 300

Additive manufacturing allows the production of complex geometries with freedom for layers construction. Build orientation causes mechanical anisotropy and may affect the crystallographic structure enabling custom-tailored properties for the product. Despite the production advantages provided by the Powder Bed Fusion (PBF) process, some inherent defects, such as porosity and residual stress need monitoring to guarantee the agreement with the material application’s requirements. Thus, this study examined the magnetic properties and the residual stress of maraging steel 300 specimens built by PBF in three build orientations (XYZ, XYZ-45, and YZX). The Rowland Ring method enabled the assessment of the static magnetization curve and the quasi-static hysteresis loop. The Barkhausen Noise (BN) characterization followed the Design of Experiments (DOE) to investigate anisotropic effects in two perpendicular directions along the surface (φ = 0° and φ = 90°). Magnetic permeability, coercivity, remanence, and power loss changed according to the build orientations used in the PBF process, and possible reasons for these changes associated with the PBF process are discussed. Moreover, residual stresses evaluated by X-ray diffraction for the three build orientations correlated to BNrms with r = 0.99 when φ = 90°. The XYZ specimen revealed a compressive stress, which also decreased the BN intensity, though XYZ-45 and YZX presented tensile residual stresses. Thus, the Barkhausen Noise could be used to inspect the residual stress of parts produced by PBF with different build orientations, improving quality management.

Preparation and characterisation of Fe/Fe3O4 fibres based soft magnetic composites

Soft magnetic composites (FSMCs) have been prepared by using Fe fibres coated with a layer of Fe3O4, this layer playing the role of insulating material. The coating was made via blackening method by simply immersing the fibres in the blackening bath for 5, 10 and 15 min. The formation of the Fe3O4 coating on the surface of the fibres was confirmed by X-ray diffraction. The SEM investigation, used to evaluate the thickness of the coatings, has proved that increasing the coating duration leads to the increase of the coating thickness and complete coverage of the surface of the fibres. Differential scanning calorimetry and thermomagnetic measurements were used to investigate the thermal stability of the composite fibres. The fibres coated with Fe3O4 were compacted at a compaction pressure of 700 MPa to obtain toroidal magnetic cores. The obtained cores were characterised in DC and AC magnetisation regime. The analysis of the quasi-static hysteresis loops evidenced that increasing the thickness of the Fe3O4 leads to a slight deterioration of the compact's magnetic properties. However, as the thickness of the Fe3O4 layer increases, the development of eddy currents at a larger scale is hindered as proved by the AC magnetic investigations. A model for analytic separation of the core losses is proposed. By applying this model to the prepared samples, we are now able to discriminate between the occurring losses and adjust the preparation process of new samples to the targeted characteristics.

Dynamic Hysteresis Loops Modeling of Electrical Steel With Harmonic Components

The broad application of electronic device in the power systems requires a practical model to characterize the hysteresis loops of electrical steel excited with harmonic components. However, the existing dynamic models may not be appropriate for application because of their complexity and neglect of the minor loops caused by harmonics. This article proposes a new algorithm that updates model parameters with magnetization history to modify Tellinen model. The improved model can consider the return-point memory effect to describe the static hysteresis loops containing minor loops. Also, a new dynamic model is built to characterize dynamic loops with harmonic components by combining the improved model with the thin sheet model. The new model only requires the quasi-static major hysteresis loops and dynamic major hysteresis loops under sinusoidal excitation to identify parameters. A comparison between the measured and calculated results under both sinusoidal and harmonic excitations shows good agreement and validates the accuracy of the proposed model.

Advanced approach for static part of loss-surface iron loss model

Hysteresis models allow the prediction of iron losses in materials under complex magnetic excitation, with accuracy depending on their principle and identification procedure. Commonly, to achieve high accuracy, a model may require a broad set of experimental input data, which is in some cases, not easy to obtain. We propose, in this study, a static model focusing on simplicity while still striving for accuracy. Its principle is to represent the variation of the field deviation between reversal curves and a near saturation hysteresis loop. In terms of input data, this model requires the experimental first magnetization curve and a few quasi-static centered hysteresis loops of the material. Following the principle description, the identification procedure, the model validation, as well as a sensitivity study are presented in detail.

Magnetostatic properties of assembly of magnetic vortices

The ultrasonic oscillation of a macroscopic sample in a viscous liquid is used to create magnetic particles of FeCo alloy with an average diameter D ~100 nm. The FeCo particles obtained have a high specific saturation magnetization, Ms = 1960 emu/cm3, close to that of a bulk sample. The hysteresis loop of a magneto-polymer composite prepared from FeCo particles shows low coercive force and a remanent magnetization close to zero. The magnetic saturation of the magnetic composite samples is achieved in a sufficiently strong magnetic field, H = 6.5 kOe. The hysteresis loop features of the magnetic composite have been explained by means of the numerical simulation of the quasistatic hysteresis loops of non-oriented dilute assemblies of spheroidal FeCo particles with various aspect ratios.

Quasistatic hysteresis loops of magnetic nanoparticles in a rotating magnetic field

Quasistatic hysteresis loops of a single-domain magnetic nanoparticle with uniaxial anisotropy in a rotating magnetic field have been calculated. Magnetic hysteresis is shown to exist only in a limited range of reduced magnetic field amplitudes, 0.5 < h0 < 1, where h0 = H0/Ha, H0 is the amplitude of the rotating magnetic field, Ha being the particle anisotropy field. An analytical formula is obtained for the particle coercive force as a function of the reduced field amplitude. In the domain h0 < 0.5 the magnetization reversal of a particle is impossible, since the final energy barrier exists between the potential wells of the particle for all orientations of applied magnetic field. On the other hand, in the domain h0 > 1 the total energy of the nanoparticle has a single energy minimum, so that there is no magnetic hysteresis. Quasistatic hysteresis loops of a randomly oriented assembly of non interacting nanoparticles in a rotating magnetic field are also obtained.

Novel method for construction of high performance nanocrystalline FeCuNbSiB toroidal core

In the current study magnetic, magneto-optical and microstructural properties of the amorphous Fe83Cu1Nb3Si5B8 alloy were properly investigated depending on the external treatments such as annealing and stress annealing. Kinetic nanocrystallization temperatures of certain ribbon were determined at the range of 500–510 °C. The amorphous ribbons produced in the as-spun state were subjected to tensile stress loading with and without rapid heat treatment of 510 °C during 5 s. Behaviors of certain ribbons were extensively investigated in terms of several factors such as magnetic properties, microstructural evaluation, magneto-optical effects and structural deformation by means of quasi-static hysteresis loops, XRD analyses, TEM micrographs, magneto-optical Kerr imaging and nanoindentation test. Present nanocrystalline Fe83Cu1Nb3Si5B8 alloy have allowed yielding not only ultrafine grain structure of around 7.02 nm but also saturation induction of 1.85 T, coercivity of 5.8 A.m−1 and saturation magnetostriction of 6 ppm. Additionally, based upon determined optimum stress annealing circumstances, toroidal nanocrystalline core was produced using a proposed stress induced winding (SIW) system. SIW system based principally on the gradient of the rotational speed of each mandrel in the standard toroidal core winding machine. Structural deformation of the core was determined by an analysis method performed on the ribbon. Accordingly, induced elastic modulus (E), Poisson's ratio (V) and residual strain (ε) in the ribbon under the influence of stress annealing by 200 MPa at 510 °C were found as 7.9 GPa, 0.39 and 0.031, respectively.

A hybrid product-multi-scale model for magneto-elastic behavior of soft magnetic materials

Magnetic properties of electrical steels exhibit a strong sensitivity to mechanical stress; this phenomenon is known as magneto-elastic coupling. Mechanical stress affects microstructural features of soft magnetic materials, which in turn leads to a change in their magnetic characteristics. Therefore, the magneto-elastic coupling in these materials needs to be studied and modeled accurately. This paper is devoted to the development of an analytical magneto-elastic hysteresis model. A recently proposed analytical hysteresis model based on Kádár product approach is modified to model the magnetoelastic effects using a multi-scale approach. The proposed model is validated using the quasi-static hysteresis loops measured for a non-oriented (NO) material (M235-35A) subjected to uni-axial compressive stress and tensile stress. The proposed formalism is applicable to model the reversible effects of stress (in elastic range) and it offers a closed form equation. A stress-dependent coercive parameter is introduced in this equation using a simple numerical procedure. Thus the model can be implemented easily in circuit and field analyses.

Effect of initial susceptibility and relaxation dynamics on radio frequency alternating magnetic field induced heating in superparamagnetic nanoparticle dispersions

Radiofrequency alternating magnetic field (RFAMF) induced heating of superparamagnetic nanoparticle dispersions (magnetic nanofluids) have attracted wide attention due to its superior potential for various industrial and bio-medical applications. Here, we probe the role of initial susceptibility and relaxation dynamics on RFAMF induced heating efficiency of magnetic nanofluids containing oleic acid capped single domain Fe3O4 magnetic nanoparticles (MNP) with nearly similar saturation magnetization values. Our results suggest that the initial susceptibility of MNP plays a major role in RFAMF induced heating efficiency and the variation of MNP size dependant relaxation dynamics alone is not sufficient to account for the field induced heating efficiency. Calculations on quasi-static hysteresis loops revealed a decrease in initial susceptibility with increasing MNP loading due to enhanced dipolar interaction, which resulted in the observed decrease in heating efficiency with increasing MNP concentration. The effect of relaxation dynamics on SAR, probed by varying the base fluid viscosity, showed that the heating efficiency is largely unaffected with increasing medium viscosity for magnetic nanofluids with Neel dominated relaxation modes, whereas heating efficiency decreased by ∼70% for magnetic nanofluids with Brownian dominant relaxation modes. This study attempts to decouple the individual contributions of initial susceptibility and relaxation dynamics and the results obtained are beneficial for designing magnetic nanofluids with enhanced magneto-thermal conversion efficiency.

Time domain analysis of excess loss in electrical steel

The aim of this paper is to present a comprehensive approach to analyse and interpret power loss in ferromagnetic materials with particular attention devoted to excess power loss. Experimental results obtained with an Epstein frame and toroidal core made of electrical steel are presented in the paper, including quasistatic and dynamic hysteresis loops. According to the time waveforms of the measured magnetic field and magnetic flux density, an instantaneous power loss is calculated for the quasistatic and dynamic case. Moreover, the instantaneous power loss due to eddy current is calculated, as well as the instantaneous excess power loss and excess magnetic field. This excess magnetic field is compared to the excess magnetic field calculated by Bertotti?s model. Analysis and discussion of the results obtained is given in the paper.

Magnetic dipolar ordering and hysteresis of geometrically defined nanoparticle clusters

Magnetic nanoparticle clusters have several biomedical and engineering applications, and revealing the basic interplay between particle configuration and magnetic properties is important for tuning the clusters for specific uses. Here, we consider the nanoparticles as macrospins and use computer simulations to determine their magnetic configuration when placed at the vertices of various polyhedra. We find that magnetic dipoles of equal magnitude arrange in flux-closed vortices on a layer basis, giving the structures a null remanent magnetic moment. Assigning a toroidal moment to each layer, we find that the geometrical arrangement, i.e., “triangular packing” vs. “square packing,” of the moments in the adjacent layer determines whether the flux-closed layers are ferrotoroidal (co-rotating vortices) or antiferrotoroidal (counter-rotating vortices). Interestingly, upon adding a single magnetic moment at the center of the polyhedra, the central moment relaxes along one of the principal axes and induces partial alignment of the surrounding moments. The resulting net moment is up to nearly four times that of the single moment added. Furthermore, we model quasi-static hysteresis loops for structures with and without a central moment. We find that a central moment ensures an opening of the hysteresis loop, and the resultant loop areas are typically many-fold larger compared to the same structure without a central moment.