Preisach Diagram Research Articles

Comparison of Limiting Loop Model and Elemental Operator Model for Magnetic Hysteresis of Ferromagnetic Materials

This paper introduces a comparative study of two different hysteresis models, limiting loop model and elemental operator model. The former is regarded as a mathematical approach based on the traditional Preisach model. To circumvent the difficulty of determining the distribution function in the Preisach model, the data of the limiting hysteresis loop and a function transform on the Preisach diagram are employed. The latter is a physical method which adopts a vectorial elemental operator with biaxial anisotropy based on the magnetization mechanisms of the ferromagnetic material. These two models are analyzed and compared in terms of the underlying principle, numerical implementation, and calculation accuracy in this paper. To verify the introduced models, the magnetic properties of non-oriented silicon steel Lycore-140 and soft magnetic composite material Somaloy 500 under alternating excitations are measured and compared with simulated results, which show the validity and practicability of the models but with different calculation accuracy and speed.

Stress-associated changes in the magnetic properties of high strength steels

The stress-associated and the stress-induced changes in the magnetic properties of ferromagnetic materials have been identified and studied for more than a century. The results typically show multiple patterns which vary depending on the specimen under study and the mechanism by which the stress is applied. The measurements presented in the literature for iron, nickel, and steels show two unique magnetic features; the stress crossover and the bulging of the magnetization loop. The existence of these features in the magnetization measurements of different sets of high strength steel is studied. A statistical interpretation of the Preisach diagram is utilized to explain and model their existence. The modified DOK Preisach model effectively simulated the two features.

An Experimental Decision of Field Parameter for Hard Magnetic Materials Using Minor Loops

For use of the Moving model as the improved Preisach model, there is a problem to decide the field parameter of sample material. In this paper, a method using minor loop permeability is proposed as an experimental decision one for the field parameter. It is shown that this method for hard magnetic materials is effective like the method used the Preisach diagram divided to two areas, another experimental decision one. Corresponding with values of the field parameter from the experimental two methods, the validity of the method using minor loop permeability could be confirmed.

Direct measurement of preisach diagram from microhystersis loops at various delay times

We report a direct and practical method of characterizing interaction field utilizing microhysteresis loops within an element area at submicrometer scale (0.34 /spl mu/m/spl times/0.34 /spl mu/m), on perpendicular anisotropic magnetic thin film material. The magnetization reversal behaviors at submicrometer scale were observed with various applied delay times under a series of applied magnetic fields. Our studies provide evidence of the asymmetrical behavior of microhysterons due to the interaction field of nearby magnetic elements.

Influence of magnetostatic interactions on first-order-reversal-curve (FORC) diagrams: a micromagnetic approach

SUMMARY From experiments it is known that magnetostatic interactions between grains strongly affect the magnetic hysteresis behaviour of samples, however, because of the difficulty in predicting the non-linear behaviour, the effect of interactions has not yet been fully incorporated into theoretical models for the recently developed first-order-reversal-curve (FORC) method. For the FORC method to be widely used it is important to have such an understanding, for example, from a geological point of view there are many cases where interactions are known to be important, e.g. bacterial magnetosomes found in sedimentary rocks. Using a 3-D fast-Fourier transforms (FFT) micromagnetic model we have conducted a detailed study of the role of magnetostatic interactions on the FORC diagrams of assemblages of ideal single-domain (SD) magnetite-like grains. We have considered various anisotropies and the importance of the alignment configuration of the particle assemblages. We show that interactions can strongly affect the magnetic behaviour, for example, interacting assemblages of SD grains can display more MD-like FORC diagrams. Associating the FORC diagram with the Preisach diagram, we find that for moderate and weak interacting SD assemblages, the factorization interpretation of the Preisach diagram is correct, and in agreement with recent experimental results.

有限要素解析に用いる補間Ｐｒｅｉｓａｃｈモデルの提案

This paper introduces a interpolation Preisach model. The first step in analysis of the model is calculating a maximum of eight conditions of the Preisach diagram at the points of divided fields, which are located on both sides of the actual field changed in direction. The condition of the Preisach diagram is separated into plus or minus values by a step-shaped interface due to past magnetic history. Next, the magnetization corresponding to the actual fields is linearly interpolated using previously calculated values. Magnetic field analysis with the model becomes possible in the case of occurrence of an optional reversal field. The model is used for simple magnetic field analysis of a magnetic sample ring. The model's validity is confirmed by agreement between the analytical results and actual measurements.

First-order reversal curve (FORC) diagrams for pseudo-single-domain magnetites at high temperature

The recently developed first-order reversal curve (FORC) technique for rapidly examining magnetic domain state has great potential for paleomagnetic and environmental magnetic investigations. However, there are still some gaps in the basic understanding of FORC diagrams, in particular the behavior of pseudo-single-domain (PSD) grains and the contribution of magnetostatic interactions. In this paper we address some of these problems. We report the first FORC diagrams measurements on narrowly sized and well-characterized synthetic PSD through multidomain (MD) magnetite samples. The FORC diagrams evolve with grain size from single-domain (SD)-like to MD-like through the PSD grain size range. Since each sample contains grains of essentially a single size, individual PSD grains evidently contain contributions from both SD-like and MD-like magnetic moments, in proportions that vary with grain size; the evolving FORC diagrams cannot be due to physical mixtures of SD and MD grains of widely different sizes. The FORC diagrams were all asymmetric. Small PSD samples have FORC diagrams with a distinctive closed-contour structure. The distributions of the larger MD grains display no peak, and lie closer to the interaction-field axis. To assess the effect of magnetostatic interactions, we measured FORC diagrams between room temperature and the Curie temperature. On heating the FORC distributions contract without changing shape until ∼500°C. Above this temperature the diagrams become more MD-like, and in addition become more symmetric. The temperature dependence of the interaction-field parameter is proportional to that of the saturation magnetization, in accordance with Néel’s interpretation of the Preisach diagram. The decrease in asymmetry with heating suggests that the origin of the asymmetry lies in magnetostatic interactions. The magnetic hysteresis parameters as a function of temperature were determined from the FORC curves. As the grain size decreased the normalized coercive force was found to decrease more rapidly with temperature.

Characteristic correlations between the Δm* interaction curves and the Preisach diagram in particulate media

Magnetic interparticle interactions are analyzed by Δm* curves calculated from the initial magnetization curve and the hysteresis loop, instead of the usual deviation Δm based on remanence curves. This study is made on tapes of acicular CrO2 particles and on tapes of CoTi-doped Ba ferrite platelet-shaped particles. The standard Preisach map of the samples is experimentally constructed and the Δm* values, computed from this map, and the values agree fairly well with the Δm* curves measured for the ac demagnetized state and various dc demagnetized states. We describe a procedure for remagnetizing the dc demagnetized samples. For the acicular particles, the peak of the remagnetized curves is lower than that computed from the Preisach map. The opposite occurs for the platelet-shaped particles. This different behavior is ascribed to the different influence of the statistical interaction field and the mean interaction field.

Analysis of magnetic forces and rotational losses of high-Tc superconducting magnetic bearings by Preisach's diagram

A flywheel system using a high-Tc superconducting bearing is researched to apply for a power storage system. The authors analyzed the magnetization of the high-Tc superconducting bulk using Preisach's diagrams. They calculated the magnetic forces and rotational losses of radial type high-Tc superconducting bearings by the electromagnetic simulation using the magnetization. In this paper, the authors calculate the magnetic force and loss of the bearing regarding the parameters of the bearing size and the characteristics of the permanent magnet. It was found that the magnetic force is affected due to the size and the characteristics of the permanent magnet. This calculation method is considered to be satisfactory for application to large scale bearings.

Isothermal magnetization of samples with stable Preisach function: A survey of hysteresis, remanence, and rock magnetic parameters

Isothermal magnetization curves, like hysteresis loops, initial curves, back field curves, acquisition curves and demagnetizing curves of isothermal remanent magnetization, are commonly used for rock magnetic purposes. In this study we investigate the relations among these curves and other useful magnetization curves (saturation initial curve and induced and remanent hysteretic magnetization curves) in order to compare coercivity and domain state parameters which can be derived from them. Most natural samples, especially sediments, are weakly magnetic and possess relatively stable Preisach functions. Their magnetization states can therefore be described by classical Preisach theory. This approach verifies well‐known rules and establishes some formerly unreported relations between isothermal magnetization curves and parameters. It is possible to point out sets of mathematically independent isothermal magnetization curves and to state theoretical interrelations between dependent curves by simply inspecting Preisach diagrams. Furthermore, we define six elemental isothermal magnetization curves from a general partition scheme of the Preisach diagram. They can be easily obtained from common measurements and generate all above mentioned curves. The experimental applicability of our results is demonstrated for three (single‐domain, pseudo‐single‐domain, multidomain) marine sediment samples. A physical rationale of the elemental curves reveals favorable properties for the investigation of interaction and domain state. As a spin‐off from the general results, a new hysteresis‐based procedure for the measurement of Hcr is presented. We also propose an apparently more robust hysteresis‐derived domain state parameter and a generalized version of the well‐known R parameter. All presented methods can be applied without actually measuring Preisach functions.

The Preisach diagram, Wohlfarth's remanence formula and magnetic interactions

Generalised Preisach diagram (moving model) was applied to study magnetic interactions in weak magnetic samples (natural pyrrhotite-bearing rocks). The approach was applied to experimental data and verified using differential remanence derived from a Wohlfarth's remanence formula. It is shown that introducing the mean interaction field improves the Preisach diagram and negative, positive and even oscillating type of interactions, as observed using the Wohlfarth's remanence formula, can be elucidated and interpreted. >

The microstructure and domain structure of multiphase oxidized titanomagnetites

An estimation of the domain state of 15 natural and synthetic samples containing both homogeneous and multiphase oxidized titanomagnetites was made by means of J rs J s and H cr H c ratios, the Lowrie-Fuller criterion, the thermomagnetic criterion, F criterion and the Preisach diagram. The J rs J s and H cr H c ratios and the Lowrie-Fuller criterion are shown to be not sufficiently informative for a determination of the domain state. In the case where the lamellae thickness became thinner than 0.1 μm, titanomagnetite grains demonstrate multidomain behaviour independent of the size of the interlamellar regions (cells). If the lamellae become thicker than 0.1 μm the domain state depends on the size of the cells. Single-domain behaviour is obtained for a cell size less than 1 × 1 μm; in agreement with the results of others, larger cells have multidomain properties.

Modelling of hysteresis processes in magnetic rock samples using the Preisach diagram

A method of modelling the properties of magnetic hysteresis for application in rock magnetism is presented. Special attention is focused on the analytical expression of the model function and on the modelling of reversible changes, which are topical in this field of application. A haematite sample is used as an example to demonstrate the model, and the problems of the stability of the Preisach diagram are discussed.

Ac-bias recording and Preisach diagrams

Preisach diagrams can be useful for modeling the magnetic properties of particulate media. On such diagrams, magnetic applied fields are supposed to have a well-determined direction. However, in magnetic recording processes, the applied magnetic fields change both in magnitude and direction. We report an extension of the well-known coherent switching mode for fine particles that makes possible the definition of an effective longitudinal applied field which depends on both longitudinal and transverse components of the externally applied field. The possibilities of Preisach diagrams are explored in the case of reasonably well-aligned particulate media, and a model of ac-biased magnetic recording for such media is presented. It is shown that, knowing the longitudinal and transversal profiles of magnetic head fields and the magnitude of the writing current, it is possible to determine the zones of Preisach diagrams, which correspond to dipoles switched + or −, and the zone corresponding to the unaffected dipoles, which remain in the initial state. The effect of angular dependence of particle switching fields is naturally included, and magnetic remanence in the direction perpendicular to alignment may be obtained whenever the Preisach diagram is also available for that direction.

Preisach diagrams and anhysteresis: do they measure interactions?

Traditionally, it is assumed that the off-diagonal distribution on the Preisach diagram and the inverse anhysteretic susceptibility as a function of DC field strength measure the spectrum of magnetostatic particle interactions in single-domain (SD) samples. To test this assumption, we have measured Preisach diagrams and anhysteretic remanence acquisition curves at a series of temperatures up to the Curie point for samples containing SD and small pseudo-single-domain (PSD) magnetites and maghemites. Preisach diagrams were also determined at room temperature only for a suite of PSD to multi-domain (MD) magnetites with mean sizes ranging from 2 to 100 μm. In the latter Preisach diagrams, the diagonal distributions, which are thought to represent microcoercivity spectra, changed from peaked, SD-like distributions for the smallest grains to typical quasi-exponential MD distributions for the largest grains. The transverse or off-diagonal distributions broadened enormously over the same grain-size range, probably indicating that self-demagnetizing fields become more influential in the larger grains. In the SD and small PSD samples, the diagonal and transverse Preisach distributions contracted about equal amounts at each high-temperature step. Both distributions changed approximately in proportion to bulk coercive force, HC(T), and not in proportion to saturation magnetization, Ms(T). Such a temperature dependence was expected for the diagonal distribution, which depends on crystalline and shape anisotropies. It was not anticipated for the transverse distribution, as magnetostatic interactions should vary with temperature as MS(T). Inverse anhysteretic susceptibilities at first changed like MS(T), but at the higher temperatures they also decreased in proportion to HC(T). Therefore the off-diagonal Preisach distribution seems to be affected more by microcoercivity than by magnetostatic phenomena such as particle interaction or self-demagnetization, at least in this suite of samples, and inverse anhysteretic susceptibility is also a dubious measure of interaction strength. A preliminary theoretical model is presented in which an interaction field acting perpendicular to the easy axis of anisotropy considerably reduces the particle coercivity. Thus the diagonal Preisach distribution is not independent of interactions. However, it remains unclear why the off-diagonal distribution is not independent of coercivity.

Generalized Preisach model of hysteresis — theory and experiment

A new approach to the Preisach hysteresis model is presented. Special attention is focused on the analytical expression of the model function. α-Fe2O3 natural sample is used to demonstrate the model, and the latest findings in the problem of the stability of the Preisach diagram are discussed.

Effect of the shape demagnetizing field on the stability of the Preisach diagram

In this paper it is proven that, in general, the shape-demagnetizing-field transformation breaks, or modifies, the stability of the Preisach diagram PD. The proof is based on the Mayergoyz's theorem. A new theorem which gives the necessary and sufficient conditions for the invariance of such a stability is also proven. Moreover, a rigorous mathematical base for feedback generalizations of the Preisach model PM is given. These results are relevant not only for a proper interpretation of magnetic hysteresis measurements, but also, more generally, for the mathematical modelling of any kind of hysteretic system regardless of the physical origin of hysteresis nonlinearities.

An extended Preisach model for hysteresis processes

A new model for describing hysteresis is proposed. The magnetization is separated into reversible and irreversible parts. The irreversible part is described by a new extended Preisach diagram and the reversible part by a Langevin function. Satisfactory agreement with experiment has been obtained.

A new approach to Preisach diagrams

Magnetization processes are complex. A simple Preisach diagram can describe only the irreversible component of magnetization. An extended Preisach model is introduced, including a reversible magnetization component given by a Langevin function which describes low-field experimental hysteresis loops very well. A family of anhysteretic curves are shown that are dependent on the amplitude and form of the ac used to generate them and the turning points on the M-H plane.

Analysis of the irreversible processes of magnetization in steel

Magnetization changes are due to both reversible and irreversible processes. Preisach diagrams can be used to represent irreversible changes but a reversible component must be added to give the total magnetization change. We show that the reversible magnetization component can be separated experimentally by incremental field reversals. It is a function of M, H and the magnetic history. The remaining irreversible magnetization changes can be represented on a Preisach diagram. Experimental and calculated hysteresis loops, using reversible and irreversible components, are shown for a 1 percent Mn steel.