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Hysteresis characteristics of the general spin-S S > 1 ) Heisenberg model have been studied within the effective field approximation. Particular emphasis has been paid on the large negative valued crystal field region. Since spin-S Ising model displays maximum number of 2 S windowed hysteresis loops in this region, this investigation gives the answer of the question: what is the effect of the anisotropy in the exchange interaction on this multiple hysteresis behavior? As an answer, rising number of windows in the hysteresis loops have been observed.

The objective of the present paper is to generalize the vector Preisach hysteresis model to take dynamic effects into account. A comprehensive analysis of the vector behavior has been performed by a single sheet tester with a specimen of round shape. The locus of the magnetic flux density vector has been controlled by a digital measurement set up at different frequency. An inverse vector Preisach hysteresis model has been built up by viscous-type scalar models and an identification procedure has been developed to follow the measured data. Finally, the model has been inserted into a finite element procedure through the fixed point technique to simulate electrical engineering problems.

In this paper the hysteresis energy losses in two non-oriented industrial steels (M400-65A and M800-65A) were determined, by means of an efficient classical Preisach model, which is based on the Pescetti–Biorci method for the identification of the Preisach density. The excess and the total energy losses were also determined, using a statistical framework, based on magnetic object theory. The hysteresis energy losses, in a non-oriented steel alloy, depend on the peak magnetic polarization and they can be computed using a Preisach model, due to the fact that in these materials there is a direct link between the elementary rectangular loops and the discontinuous character of the magnetization process (Barkhausen jumps). To determine the Preisach density it was necessary to measure the normal magnetization curve and the saturation hysteresis cycle. A system of equations was deduced and the Preisach density was calculated for a magnetic polarization of 1.5 T; then the hysteresis cycle was reconstructed. Using the same pattern for the Preisach distribution, it was computed the hysteresis cycle for 1 T. The classical losses were calculated using a well known formula and the excess energy losses were determined by means of the magnetic object theory. The total energy losses were mathematically reconstructed and compared with those, measured experimentally.

Residual stresses in magnetic materials, whether the result of processing or intentional loading, leave their footprint on macroscopic data, such hysteresis loops and differential permeability measurements. A Preisach-type vector model is used to reproduce the phenomenology observed based on assumptions deduced from the data: internal stresses lead to smaller and misaligned grains, hence increased domain wall pinning and angular dispersion of local easy axes, favouring rotation as a magnetization reversal mechanism; misaligned grains contribute to magnetostatic fields opposing the direction of the applied field. The model is using a vector operator which accounts for both reversible and irreversible processes; the Preisach concept for interactions for the role of stress related demagnetizing fields; and a characteristic probability density function which is constructed as a weighed sum of constituent functions: the material is modeled as consisting of various subsystems, e.g. reversal mechanisms or areas subject to strong/weak long range interactions and each subsystem is represented by a constituent probability density function. Our assumptions are validated since the model reproduces the hysteresis loops and differential permeability curves observed experimentally and calculations involving rotating inputs at various residual stress levels are consistent and in agreement with experimental evidence.

In this paper a phenomenological approach, based on a generalization in two dimensions of the classical scalar Preisach model, is exploited and identified to reproduce the magnetization curves obtained by accurate micromagnetic simulations of both isotropic and anisotropic polycrystalline Fe–Si films with different values of the anisotropy constants. The identification problem is realized using a suitable set of analytical equations and performing a best fit procedure to the data obtained from micromagnetic simulations of both scalar and rotational loops. The correct reconstruction of all the magnetization processes, as well as of the associated magnetic losses, is achieved through the choice of a small number of either circular or elliptical hysterons, as well as by the implementation of a simple “moving technique” that is necessary to take into account the non-collinearity between the field and the magnetization that occurs in presence of a global uniaxial anisotropy.

A generalized Jiles–Atherton model is proposed to describe mixed clockwise and counter-clockwise hysteresis loops. While it is physically inconsistent for homogeneous magnetic materials, this mixed type of hysteresis is exhibited by several multi-layer and superlattice materials with antiferromagnetic coupling. The modeling approach is based on a newly developed clockwise hysteretic model using the Jiles–Atherton framework and its linear superposition to the classical counter-clockwise version. The resulting technique is implemented in open-access academic software for hysteresis and simulation samples are presented in the paper.

The magnetic properties of materials are characterized by the variation of flux density with magnetic field. The hysteresis loop is generally dependent on the frequency of excitation. It is well known that the dependence is attributed to the effects of eddy current loss and anomalous (excess) loss. The present work deals with a new approaching method to model the frequency dependence of magnetic hysteresis within the framework of internal state variable theory, the fundamental structure of which is originally based on viscoplasticity theory in continuum mechanics. The hysteresis equations are formulated to be consistent with the general principles of irreversible thermodynamics with internal variables.

In this paper, we present mathematical results regarding a recently introduced vectorization of the Preisach operator. The operator output can be shown to be continuous regardless of the properties of its underlying Preisach distribution. For uniaxial input originating in saturation, the output of the isotropic operator reduces to that of a scalar Preisach operator. We formulate this scalar Preisach operator explicitly and give an example for the reduction. Finally, we apply the results in order to deduce conditions under which the uniaxial scalar curves resulting from the vector Preisach operator are monotone.

The paper deals with the numerical analysis of a rotational single sheet tester with round-shaped specimen (RRSST) which is now under construction. The measurement setup consists of an induction motor the rotor of which has been removed, and its windings have been replaced to a special two phase one which can generate homogeneous magnetic field inside the motor. The two orthogonal components of the magnetic field intensity and of the magnetic flux density vectors can be measured by H -coils and B -coils, respectively. The Finite Element Method (FEM) with the T , Φ–Φ potential formulation has been applied in the simulations. The vector hysteresis property of the specimen has been approximated by the vector Preisach model. Finally, the nonlinear problem has been solved by the fixed-point technique. The aim of the present work is to focus on the design aspects of this kind of measurement system.

Hysteresis modeling describes transition curves corresponding with any change of the magnetic field. Memory properties in the magnetization processes are observed in macroscopic hysteresis curves and described by the return-point-memory and the wiping-out-property according to Madelung. This paper shows that the 3D micromagnetic hysteresis model incorporates these macroscopic memory properties. The model is developed by the authors to describe hysteresis processes starting from the materials microstructure. Simulations on samples with different dislocation densities show that the magnetic states are also similar on a microscopic scale when minor loops are closed.

The convexity inequality for small amplitude loops is used, together with the strict local monotonicity of large amplitude branches in the Preisach model, to derive a global second-order energy bound. Such an estimate is then used for solving a singular Preisach oscillator problem.

Analytical approximation of symmetrical and unsymmetrical hysteresis loops is based on the general description of magnetization consisting of the slow reversible process and more violent irreversible process. The coercivity term in the irreversible component generates symmetrical hysteresis loops, which are used for the approximation of first-order reversal curves and their distribution. Model has been applied to materials with typical S-shaped and rectangular hysteresis loops.

A general model for vector hysteresis is presented. We will show that the model is in agreement with the required thermodynamical properties and with the macroscopic properties observed in the real media. Also the relationship with the Classical Preisach Scalar Model will be discussed.

We prove dissipativity of nonresonant forced non-resonant pendulum with Preisach friction. In a general case we use estimates of the width of hysteresis loop, if the forcing term is quasiperiodic, the equation is always dissipative.

This paper analyzes a non-linear heat diffusion process when the thermal diffusivity behaviour is a hysteretic function of the temperature. Modelling this temperature dependence, the discrete Preisach algorithm as general hysteresis model has been integrated into a non-linear multigrid solver. The hysteretic diffusion shows a heating-cooling asymmetry in character. The presented type of hysteresis speeds up the thermal processes in the modelled systems by a very interesting non-linear way.

In this paper a statistical approach of hysteresis phenomenon is presented. Under the assumption that each magnetic domain can be represented by a random variable a very simple model of hysteresis can be built on. In spite of the simplicity of the model it possesses many important properties of hysteretic behaviour.

First-order reversal curves (FORCs) are used to analyze the kinetic effects described by dynamic Preisach models of hysteresis. It is shown that dynamic processes in magnetic materials strongly affect the symmetry of FORC diagrams. The regions that are most strongly affected when the applied magnetic field varies at high speed are located in the proximity of the diagonal of the FORC diagrams. In these regions, the differential magnetic susceptibility can be negative and result into negative values of the FORC diagrams. An identification technique based on the FORC diagrams is presented for the kinetic parameters of the dynamic Preisach model.

The possibility of considering dynamic effects in three vector hysteresis models is investigated. The friction model of oriented Preisach operators which rotate due to the torque exerted by the external field, the coercive spheres model, the 3D analogue of the classical Preisach model, and a further collective model based on micromagnetic analogy are considered. Furthermore, the “external” dynamic generalization of the static hysteresis models is introduced for the vector case.

Currently applied Preisach models enable approximations of hysteresis loops with the use of a variable density of domains and complicated distribution functions. An alternative method presented in this paper uses constant distribution of domains in a new, hyperbolic diagram of hysteresis. Such approach restores the original direct relation between the magnetization and the area enclosed in the diagram by an external field, and enables simpler and more accurate modeling of hysteresis.

A new neural networks dynamic hysteresis model for piezoceramic actuator is proposed by combining the Preisach model with diagonal recurrent neural networks. The Preisach model is based on elementary rate-independent operators and is not suitable for modeling piezoceramic actuator across a wide frequency band because of the rate-dependent hysteresis characteristic of the piezoceramic actuator. The structure of the developed model is based on the structure of the Preisach model, in which the rate-independent relay hysteresis operators (cells) are replaced by the rate-dependent hysteresis operators of first-order differential equation. The diagonal recurrent neural networks being modified by an adjustable factor can be used to model the hysteresis behavior of the pizeoceramic actuator because its structure is similar to the structure of the modified Preisach model. Therefore, the proposed model not only possesses that of the Preisach model, but also can be used for describing its dynamic hysteresis behavior. Through the experimental results of both the approximation and the prediction, the effectiveness of the neural networks dynamic hysteresis model for the piezoceramic actuator is demonstrated.

In this paper we use a Reduced Vector Preisach Model for a preliminary analysis of rotating hysteresis in laminated Si–Fe steels. After the description of the main facts about the vectorial hysteresis modeling and the formulation of the cross coupling Preisach functionals, we present here a numerical technique for the identification of the model using the hard and easy axis measurements. An applicative example for non oriented grain steels is presented.

The product model of magnetic hysteresis was proposed as a modification of the Preisach model in order to eliminate some shortages of the traditional model. The main novelty of the product model was the emphasis on the differential susceptibility of magnetization curves, namely the introduction of an output-dependent limiting multiplier function. With this the magnetization curve can be described with an indirect mathematical function, whose argument contains the terms of the reversible and the hysteretic irreversible contribution of the magnetization. Experimental data suggest that the Brillouin function is a proper envelope of the indirect function. Fitting procedures and examples of evaluation of experimental data are presented.

The present work proposes a simple magnetic system as a candidate for a Standard Problem for Preisach-based models. The system consists in a regular square array of magnetic particles totally oriented along the direction of application of an external magnetic field. The behavior of such system was numerically simulated for different values of the interaction between particles and of the standard deviation of the critical fields of the particles. The characteristic parameters of the Preisach moving model were worked out during simulations, i.e., the mean value and the standard deviation of the interaction field. For this system, results reveal that the mean interaction field depends linearly on the system magnetization, as the Preisach moving model predicts. Nevertheless, the standard deviation cannot be considered as independent of the magnetization. In fact, the standard deviation shows a maximum at demagnetization and two minima at magnetization saturation. Furthermore, not all the demagnetization states are equivalent. The plot standard deviation vs. magnetization is a multi-valuated curve when the system undergoes an AC demagnetization procedure. In this way, the standard deviation increases as the system goes from coercivity to the AC demagnetized state.

The present paper considers the definition of a class of hysteresis models, based on the superposition of play operators, which can be used to describe magnetic materials and superconductors. As a first step, the paper defines a class of non-local hysteresis models having an inverse operator in a closed form. That class specifies a Preisach model for which the exact inverse is defined. In this frame such a result is a generalization of the well-known result by Krejci. Moreover, a self-contained identification procedure is further addressed by using data measured either on magnetic materials and on superconductors.

Simulation of a simple arrangement and modeling the scalar hysteresis characteristics can be used advantageously when the magnetic field intensity and the magnetization are in the same direction (e.g. toroidal-shaped coil). In many cases, it is not enough to apply the scalar hysteresis model, but a more powerful and more complicated hysteresis model must be developed to describe the vector property of the field quantities. Generally, the magnetic field intensity and the magnetization vectors are not in the same direction, so applying scalar models may give inaccurate numerical results. In this paper a measuring arrangement of 2D vector hysteresis characteristics is performed, measurement results are shown in figures and discussed.

Two isotropic vector hysteresis models are constructed based on the classical Preisach model, to be applied in magnetostatic computations with an integral equation formulation. One model endows complete Preisach operators with orientation governed by a friction-like mechanism. The other approach—a natural generalization of the classical Preisach model—considers a set of vector operators with various coercive fields, mean interaction field (shifted spheres of various radii) and weights. The principles of the inclusion of these models in magnetostatic computations are outlined.

A numerical study of the Dynamic Preisach model of Bertotti (DPM-B) is carried out in time domain and over an unlimited range of magnetise fields and frequencies. It is shown that the well-known approximation of the total loss simulated by the DPM-B by the expression C 0 +C 1 f is a low-frequency limit of a more complex dependence characterised by a faster growth of the excess loss component. The anomalous temporal and frequency behaviour of the DPM-B is revealed by comparing the DPM-B to a recently proposed dynamic hysteresis model, which is compatible with static hysteresis models of any type and provides a desirable excess loss dependence invariable in all frequency range. In such a way, it is shown that the applicability of the phenomenological DPM-B and its modification is constrained to the low frequencies and steady-state periodic regimes.

To represent a ferromagnetic material with the scalar Preisach model the Preisach distribution or the Everett function must be known. In this paper different identification procedures of the scalar Preisach model are summarized. The Everett function is determined in two different ways, from first-order reversal curves and from concentric hysteresis loops. Solving a bilinear system of equations the Preisach distribution is computed pointwise from the major hysteresis loop. In several cases it is convenient to approximate the Preisach distribution analytically. As a novelty of the paper a distribution function for which the Everett function can be expressed in closed form is presented.

A new approach to the dependence of the aftereffect processes in recording materials on the moving parameter of the Preisach model is made in this work. This parameter is usually included as part of the Preisach model in order to take account of the mean interaction field between magnetic moments in magnetic media. The approach has been carried out by means of stochastic inputs applied to the Preisach model. The results presented in the work have been obtained using numerical simulations and reveal magnetization decays comparable to those previously found using the Preisach–Arrhenius model. These results can be summarized in two main ideas. The first one is that the initial decay rate decreases as the moving parameter increases, but a final faster transition follows this initial tendency. A second fact is that there is a certain range of applied magnetic fields so that two equilibrium states can appear.

In this paper, a class of multi-dimensional hysteresis operators of generalized Prandtl–Ishlinskii form is introduced which can be viewed as a possibility to extend the famous one-dimensional Preisach model of hysteresis to higher space dimensions. We study the continuity properties of these hysteresis operators and of the hysteresis potential operators associated with them. It is also indicated, how this class of hysteresis operators can be applied to a class of phase-field systems occurring in the theory of phase transitions with non-conserved order parameters.

This paper addresses an orientation error discovered when the simplified vector Preisach model (SVPM) was applied to an isotropic medium. For a smoothly rotating field, the magnetization of an isotropic medium should rotate smoothly. Instead, the SVPM predicts a ratcheting motion. A correction for this problem is suggested.

In this paper, an integral equation method is presented for the computation of the magnetization and magnetic field intensity in ferromagnetic materials taking into account the hysteresis phenomena. The magnetic behavior of the ferromagnetic body is described by three-dimensional isotropic vector Preisach model. For the solution of the obtained nonlinear equations the fixed-point technique is used.

We represent processes in highly anisotropic, nonhomogeneous, either ferromagnetic or ferrimagnetic materials, by coupling the Maxwell equations with a vector extension of the standard rectangular hysteresis loop. We then derive a two-length-scale vector model via a homogenization procedure. Here, the fine-scale magnetization M depends on the fine-scale magnetic field H , at variance with the corresponding scalar problem. This amends the usual formulation of the vector Preisach model, which is not consistent with the law ∇ · B =0 .

A Preisach model able to adjust to different systems with hysteresis is presented. The related identification scheme involved uses data from a major hysteresis curve and a least-squares error minimization procedure for the parameters of the characteristic density. The output sequence, f ( t ), is obtained by integrating the characteristic probability density function, ρ ( α , β ), of the elementary hysteresis operators, γ ab , operating on the input sequence u ( t ) over the Preisach plane. Once the appropriate operator is chosen and the Preisach plane adjusted accordingly, the parameters of the characteristic density are determined via a least-squares procedure minimizing the error between the experimental major curve and the calculated one. Results using two different scalar operators are discussed. Further, the reliability of the procedure is assessed by considering experimental data regarding two different magnetic samples and a shape-memory alloy sample.

The irreversible response of a ferromagnetic pervoskite SrRuO3 with a Curie temperature TC=160 K has been characterized experimentally by measuring the temperature dependence of the field cooled and zero field cooled moments over the temperature interval 5 K⩽ T ⩽180 K , in a sequence of applied fields up to the coercive field, and also the major hysteresis loop over the field range ∣ha∣⩽40 kOe at a sequence of temperatures which span the ordered phase. The data have been analysed within the framework of a generalized version of the Preisach model of hysteresis which combines thermal fluctuations with the growth of the free energy barriers below TC. The numerical simulations replicate all of the principal structural systematics of the data, and yield details of the spectrum of Barkhausen instabilities in this material.

The critical curves in the Preisach–Neel model are investigated using the numerical solution of master equation with time-dependent magnetic field and temperature. The movement of the thermal boundaries in the Preisach plane is investigated in different magnetization processes. It is shown that the rate variation of the applied field and temperature, which are explicit parameters in this model, can have a strong influence on the configuration of the thermal boundaries. The results are compared with those obtained with critical curve- type Preisach–Neel models using linear and nonlinear energy barrier expression.

The product model is an output-dependent modification of the traditional Preisach model in order to remove its non-real congruency property. The differential susceptibility is proposed to be a product of a magnetization-dependent factor and an expression containing two terms: one for the reversible process and the other an integral of a Preisach type distribution for the irreversible part. Thus the magnetization is an indirect function, in which the saturation is a natural property of the hysteresis model, and the reversible and irreversible parts of the magnetization are added up indirectly. The envelope function is related to the paramagnetic process and in the specific case of uni-axial anisotropy it is a hyperbolic tangent function. The measurement of the anhysteretic curve may provide the direct link to the evaluation methods of experimental data applied for traditional Preisach modeling.

A second-order Preisach model of scalar hysteresis is proposed and investigated. Parameter functions of this model are identified using transition curves of up to the third order. Wiping-out property and the property of invariance in the change of minor loop shape due to elimination of the first input extremum are shown to be the necessary and sufficient conditions for the representation of a given scalar hysteresis relation by the proposed model

This work presents a new methodology for determination of hysteresis curves based on the Jiles–Atherton method. The magnetic induction is adopted as an independent variable which is available in the vector potential magnetic field formulation. The presented method can be directly incorporated in a finite element software.

A method is presented to measure the dependence of the anhysteretic magnetization curve (the anhysteretic magnetization as a function of the internal field after degaussing) on the demagnetization factor N without physically varying N. The relation between the Preisach distribution and the N dependence of the anhysteretic magnetization curve is discussed in a way that is very close to the work of Bertotti. Classes of (moving) Preisach models are identified for which the anhysteretic magnetization curve is independent of the demagnetization factor. It is proven that the anhysteretic magnetization increases with N at fixed internal field, if the Preisach distribution decreases monotonically with increasing Hcent, the internal field value of a Preisach domain. It is shown that the Moving Preisach model may lead to a negative anhysteretic permeability.

Preisach-based aftereffect models are employed to define the ground state of a magnetic system. Four different types of processes due to thermal perturbations, AC demagnetization, Curie point demagnetization and DC demagnetization are reviewed and compared with each other. By modeling the time evolution of the magnetization and magnetic field on the Preisach plane, it is shown that the asymptotic state of the system due to thermal perturbations is the true magnetic ground state.

Subtle and interesting connections between the Preisach model of hysteresis and nonlinear diffusion are discussed. On this basis, Preisach modeling of eddy current hysteresis and superconducting hysteresis is presented. It is stressed that rate-dependent eddy current hysteresis can be fully characterized by its step response. Preisach representation of eddy current hysteresis is then used for the calculation of eddy current losses and the universality of the ‘ f 2 -law’ for these losses is emphasized. Experimental results that provide evidence for remarkable accuracy of the Preisach description of superconducting hysteresis are presented.

A series of measurements has shown that when a material is increasingly magnetized in a given direction, the magnetization perpendicular to this direction decreases to zero. A simplified vector Preisach model, an example of a coupled-hysteron model, has been introduced that incorporates this property into the vector model. In addition, this model satisfies the saturation property and the loss property. It can correctly compute scalar loops, since it is based upon the moving model, which properly corrects the congruency property; and it can incorporate the accommodation model and the aftereffect model to correct the deletion property. In three dimensions, the vector magnetization is computed from the integration of the product of a state vector, Q, and a Preisach function, p, both of which are defined in a six-dimensional Preisach space. The Q's are compared following selection rules determined by the applied field. This paper illustrates the calculation procedures for a complex magnetizing process. A material sample is subjected to a saturating field that is then reduced to zero. The field is then increased in an arbitrary direction while the vector magnetization is measured. Since the model parameters are only determined along the principal axes, the predictive capability of the model is thereby demonstrated. The predicted results of the model compare favorably to the results of experimental measurements.

A generalisation of the dynamic Preisach model is proposed, for which the magnetisation rate d//dt for each Preisach dipole is proportional to the di!erence between the e!ective "eld and a#k / / or b#k / /, where k / is an extra material parameter. With this modi"cation, the area enclosed by the macroscopic hysteresis loops for a sinusoidal #ux, becomes dependent on the magnetisation frequency f according to the law J1#Cf!1. The model has been compared with experimental results on grain oriented Si}Fe alloys and the correlation with the statistical loss theory is shown. ( 2000 Elsevier Science B.V. All rights reserved.

The paper illustrates the evolution of Preisach-type models of hysteresis, involving mean field effect, dynamic effect and vector behaviour and their capability to be included into finite element electromagnetic field computation. The study makes reference to 1D and 2D formulations developed under different simplifying assumptions. Particular attention is devoted to the use of fixed point technique which is found to be very advantageous for the solution of hysteretic problems. Some examples of the analysis of magnetic field problems with hysteresis are finally presented.

We propose stability criteria for differential equations that contain the time derivative of the Preisach operator.

Proposed is a substantially simplified, Preisach-like model for characterization of hysteretic systems, in particular magnetic systems. The main idea is to replace a two-dimensional Preisach density with just two real functions, describing in a {\em unique way} the reversible and irreversible processes. As a byproduct of our model we prove, that the major hysteresis loop alone is insufficient to produce the unique Preisach map. Keywords: magnetic hysteresis; magnetization processes; materials testing; modeling., 7 double spaced pages, 4 figures. Presented at 5th International Symposium on Hysteresis and Micromagnetic Modeling, Budapest, Hungary, May 30th - June 1st, 2005

A phenomenological model of magnetic vector hysteresis is described. Magnetization is expressed as a superposition from the contributions of a large number of pseudoparticles. The free energy of individual particles is assumed to be the sum of a convex component representing anhysteretic behaviour, and a small ripple representing the influence of pinning sites. The ripple component is found to give a dry friction-like hysteresis mechanism. Some comparisons with experiments are given.

The magnetization process of a regular two-dimensional array of small individual, strongly uniaxial magnetic garnet particles, groups of particles and major loop properties of a “macroscopic” sample has been investigated experimentally in an optical magnetometer. These particles correspond to the assumptions of a simple Preisach model. The switching mode is coherent rotation. Each particle has a square hysteresis loop, with no reversible or apparent reversible component. Requirements of wiping-out and congruency properties are satisfied. From measurements of the up- and down switching field on individual particles, the major loop can be reconstructed, and it is shown to be in nearly exact correspondence with the measured one. The transition from individual to collective behavior is smooth and the properties of a system consisting of 100 particles correspond to the major loop behavior. The interaction field for an assembly of 25 particles was calculated numerically. The switching sequence and the magnetization curve for the 25 particles assembly was derived from the calculated interaction fields and found to be in a very good agreement with the measured values.