Moving Preisach Model Research Articles

Identification method analyses for the scalar generalized moving Preisach model using major hysteresis loops

A parametric identification strategy for the generalized moving Preisach model is presented. As it requires only the major hysteresis loop (to determine the distribution parameters) and the remanent major hysteresis loop (to determine the moving parameter), it is less sensitive to the presence of the usual experimental errors than other identification methods. The Preisach distribution function is considered to be in general a bivariate function. The method is verified on various commercial magnetic media.

Anhysteretic magnetization and demagnetization factor in Preisach models

The anhysteretic magnetization M/sub an/ depends on the internal field after degaussing H/sub an/ and, possibly, on the demagnetization factor N. Neel's theory of the N dependence is criticized. Classes of Preisach models are identified for which M/sub an/ (H/sub an/) does not depend on N. A numerical method is presented to determine M/sub an/ (H/sub an/, N) from a Preisach model. The zero-field anhysteretic permeability is expressed in terms of the Preisach distribution up to first order in N-k, where k is the parameter of the moving Preisach model.

Application of the Preisach model to nanocrystalline magnets

Experimental results are presented for several exchange-coupled nanocrystalline alloys of composition Sm 18(Fe,Co) 82 with different Fe contents. Minor loops, Henkel plots, and recoil curves are shown to be in excellent agreement with calculations performed using the moving Preisach model (MPM). Experimental reversible and irreversible magnetization components are found to be in excellent agreement with MPM simulations.

On the role of statistics in the applicability of the Preisach transformation

Model systems of magnetic elements are investigated theoretically and experimentally. The elements are single domain, they can be switched "up" and "down", they all have the same magnetic moments but different coercive fields and they interact magnetostatically with each other. The analysis shows that such systems generally cannot be exactly represented either by the classical Preisach model or by the Moving Preisach Model as long as the number of the elements is finite. The representation can be considered unambiguous only if the number of elements approaches infinity.

Reversible processes and magnetic viscosity of nanocrystalline permanent magnets

The accurate determination of the magnetic viscosity parameter Sv requires the calculation of a new parameter η=(∂Mrev/∂Mirr)Hi which describes the dependence of reversible magnetization on irreversible magnetization. Measurements of the magnetic viscosity were performed at 300 K on the major demagnetization curves of two different nanocrystalline permanent magnetic materials: (i) melt-spun and flash-annealed Pr4Fe78B18 and (ii) mechanically alloyed and heat-treated Sm18Fe33Co49. We show that η is proportional to the intrinsic reversible susceptibility χrevi, in good agreement with predictions of the moving Preisach model. Measurements of the reversible susceptibility were made in order to determine η. Experimental values of η are positive on the major demagnetization curve in both materials, resulting in substantial corrections to Sv near Hc.

Implementation of vector moving Preisach model using texture coefficients as easy axis distribution

Vector moving Preisach model was applied to the untextured Co thin film media. The out-of-plane easy axis distribution of the particles was derived directly from the texture coefficient phkl obtained from x-ray diffraction analysis, which corresponds to the fraction of the grains that have {hkl} plane lying parallel to in-plane direction. In order to validate this variable, angular dependence of magnetic properties of CoCrPPt/Cr/glass thin films with two different composition was measured by using a vibrating-sample magnetometer. Simulated results showed little difference from the measured data.

Moving Preisach model analysis of nanocrystalline SmFeCo

Nanocrystalline SmFeCo, prepared by mechanically alloying the elementary powders and subsequent annealing (600 °C/15 min), showed remanence enhancement (η=Ir/Is=0.67) and Hc=18.6 kOe. Starting from the ac-demagnetized state, minor hysteresis loops were determined for magnetic fields up to 70 kOe for numerical calculation of the Preisach function p(hc,hu), where hc and hu are the elementary loop coercive field and interaction field. The numerically determined irreversible part of p(hc,hu) had a form indicating that it could be factored: pirr(hc,hu)=f(hc)g(hu), where f(hc) and g(hu) are log–normal and Gaussian distributions. An analytic expression for p(hc,hu)=f(hc)g(hu)+prev was fitted to experimental hysteresis curves. The analytic expression for p(hc,hu) was used with the moving Preisach model to calculate minor loops and Henkel plots. Agreement between theory and experiment was very good.

Temperature dependence of hysteresis loops in non-oriented SiFe alloys

Measurements of static hysteresis loops in the temperature range from 20 to 500°C are presented. The measured hysteresis curves are described by the moving Preisach model, and the model parameters are discussed in relation to the temperature dependence of magnetization processes.

Magnetic interactions in nanocrystalline SmFeCo

Several samples of enhanced-remanence nanocrystalline Sm15Fe19Co66 were prepared by mechanical alloying of the elementary powders followed by heat treatments. Sample A had a remanence ratio η=σr/σs=0.68 and Hc=7.1 kOe, while, for B, η=0.58 and Hc=10.4 kOe, and, for C, η=0.57 and Hc=12.6 kOe. The isothermal remanent magnetization Mr(H), obtained for different initial demagnetized states (ac, dc+, dc−), and the demagnetization remanence Md(−H), obtained for an initially saturated state, were determined. The ac-demagnetization Henkel plot showed both magnetizing and demagnetizing interactions as observed in other nanocrystalline magnets. A comparison with the moving Preisach model indicates the importance of both mean-field and random interactions.

A vector moving hysteresis model with accommodation

A vector hysteresis model based on the moving Preisach model, that exhibits accommodation, is discussed. It is a vector generalization of the scalar Preisach accommodation model, and is applicable to a wide variety of recording media. Its rotational remanence properties are in agreement with experimentally observed vector accommodation phenomena.

Henkel plots in a thermally demagnetized scalar Preisach model

The implications of thermal demagnetization with respect to the observation of interaction effects in Henkel plots are discussed within the framework of a scalar moving Preisach model. The Preisach distribution is assumed to be a product of a Gaussian coercive field distribution and a Gaussian interaction field distribution. Numerical calculations of the magnetizing and demagnetizing remanences show that, by contrast with other demagnetizing procedures, thermal demagnetization yields Henkel plots whose direction of curvature is uniquely related to the sign of the mean interaction field. In particular, a distribution of interaction fields which is symmetric about the origin yields the same linear Wohlfarth relation as a completely noninteracting system, while demagnetizing (magnetizing)-like mean fields always curve the Henkel plot below (above) the Wohlfarth line. The simple linearity of the Henkel plot in the absence of mean field effects was exploited to evaluate the effectiveness of a recent proposal for experimentally suppressing shape demagnetizing effects in perpendicular recording media. >

Particle orientation distribution and the isothermal remanent magnetization of a fine particle system

The experimental isothermal remanent magnetization (I.R.M.) curves for some particulate recording media are compared with the theoretical results obtained in the Classical Preisach (C.P.) model as well as in a Moving Preisach (M.P.) model with a Gaussian or a log-normal distribution of the critical and interaction fields. The differences between the experimental data and the theory are analyzed. Also discussed is the compatibility between the experimental and the simulated I.R.M. curves for a system of Stoner-Wohlfarth particles with a Gaussian distribution of the angle between the easy axis and the direction of the external magnetic field. >

Experimental Preisach analysis of the Wohlfarth relation (abstract)

The Wohlfarth relation1 states that, for noninteracting particles, the ascending normalized remanent major loop, mD(H), is twice the shifted normalized virgin remanent magnetization. Researchers2 claim to measure the interaction field and characterize it as ‘‘positive’’ and ‘‘negative’’ depending on whether it is ‘‘above’’ or ‘‘below’’ the axis on a Henkel plot or a ΔM plot. It has been shown3 that the moving Preisach model can compute all observed types of ΔM plots by varying only the moving parameter, α, and over only positive values. This type of behavior is characterized by the ratio of α to the standard deviation of the interaction field. In this paper the measured ΔM plot for two commercial recording media, namely longitudinal BaFe and γ-Fe2O3, is presented and the positive moving parameter of each sample is identified. Let us define the operative field of the system by Hop=H+αM, where M is the total magnetization. It is then shown that, when plotted as a function of Hop, all samples deviate from the Wohlfarth relation in the same way, even though they exhibit ‘‘positive’’ and ‘‘negative’’ ΔM when plotted as a function of the applied field, H, as seen in Fig. 1. It will also be shown that deviations from the Wohlfarth relation are due to a combination of parameters, not only the interaction field. The model and the identification algorithm has been used to simulate all the observed ΔM plots.

Interpretation of hysteresis curves and Henkel plots by the Preisach model (invited)

We discuss some properties of the scalar moving Preisach model (MPM) in relation to the description of magnetic interactions. MPM predictions for the behavior of Henkel plots are worked out. The role of the factorization properties of the Preisach distribution and the consequences of the joint presence of mean-field effects and local random interactions are discussed. Literature data are analyzed in the frame of this description, with particular attention to thin-film media with perpendicular magnetization, where mean-field effects are particularly strong. Some of the theoretical predictions are directly tested by hysteresis and Henkel plot measurements performed on SiFe soft alloys. A good agreement, in some cases involving no adjustable parameters, is found.

Experimental study and theoretical interpretation of hysteresis loops and Henkel plots in soft magnetic materials

In this paper we discuss an application of the moving Preisach model (MPM) and the zero-temperature Sherrington-Kirkpatrick spin-glass model (SKM) to the interpretation of hysteresis phenomena in soft materials, with particular attention to the analogies and differences between the models. Both models are compared with hysteresis measurements performed on strips of amorphous Fe-B-Si alloy. We describe experimental data using the same distribution of local coercivities and interactions fields in both of them. The results confirm that the MPM is actually able to reproduce the hysteresis behavior of soft magnetic materials and can be useful to discuss the complicated behavior of the SKM, where we explicitly know the form of interactions.

Investigation of the influence of annealing on the magnetic properties of Metglas using the Preisach model

The moving Preisach model with bi-Gaussian distribution function P( h c, h m) has been identified for the description of the amorphous material Metglas 2605-S2 in the as-cast state, after annealing in air and finally after annealing in a magnetic field parallel to the ribbon axis. A remarkable correlation has been found between changes in the as-cast stress anisotropy, the anisotropy induced by magnetic ordering, and the moving field KM, respectively. The uncertainty in the estimates of the moving constant K was narrowed by the control measurements of non-congruency and of Henkel plots. A comparison of the measured and simulated ac remanence characteristics served as a criterion in the identification process.

Application of the Preisach model to the calculation of magnetization curves and power losses in ferromagnetic materials

The ability of Preisach-type scalar models to describe static and dynamic hysteresis properties is discussed. Three aspects are addressed in particular: the description of reversible magnetization processes, the characterization of magnetic interactions, and the calculation of dynamic hysteresis loops. Applications of the standard Preisach model and of the moving Preisach model to the description of Henkel plots in recording media and to the prediction of power losses in metallic soft magnetic materials are discussed. >

Description of magnetic interactions and Henkel plots by the Preisach hysteresis model

The ability of the scalar Preisach model (PM) to describe magnetic interactions and Henkel plots is discussed. It is shown that the random interactions described by the PM switching field distribution p(/spl alpha/,/spl beta/) always have a net demagnetizing-like effect on remanences. The connection between the properties of p(/spl alpha/,/spl beta/) and those of Henkel plots is investigated. In particular, it is shown that, when p(/spl alpha/,/spl beta/)=f(/spl alpha/)f(/spl minus//spl beta/), the remanence law i/sub d//i/sub /spl infin//=1/spl minus/2/spl radic/i/sub r//i/sub /spl infin//, completely independent of f(/spl alpha/), holds. The joint presence of random interactions and mean-field effects is dealt with through the moving PM (MPM), in which an additional field proportional to magnetization acts on each PM elementary loop. The classification of Henkel plots by MPM is discussed. In particular, it is shown that Henkel plots exhibiting both magnetizing-like and demagnetizing-like deviations are a certain indication of the joint presence of random interactions and magnetizing-like mean-field effects. Theoretical predictions are compared with recent Henkel plot measurements on magnetic recording media, superconductors, thin films, hard magnets, and soft magnetic materials.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Anhysteretic remanent susceptibility and the moving Preisach model

The experimental study of the anhysteretic remanent magnetization of many thin-film particulate media indicates an exponential shape of the anhysteretic remanent susceptibility as a function of the applied magnetic field. The classical Preisach model with a presumed Gaussian distribution cannot satisfactorily explain these experimental data. This difficulty is overcome in the moving Preisach model.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

AC-remanence states as identification criterion of hysteresis modeling

Because various combination of parameters characterizing the moving Preisach model with Gaussian bivariate distribution produce the same values, M s, M r, H c, it has been examined, whether the ac-remanence characteristics could be recommended as an identification criterion. The results of measured and simulated characteristics on two materials with rather different squarenesses are presented.