Review of Play and Preisach Models for Hysteresis in Magnetic Materials

Abstract

This paper studies the properties of the Preisach model and the play model, and compare their similarities. Both are history-dependent hysteresis models that are used to model magnetic hysteresis. They are described as discrete sums of simple hysteresis operators but can easily be reformulated as integral equations of continuous distribution functions using either a Preisach weight distribution function or a play distribution function. The models are mostly seen as phenomenological or mathematical tools but can also be related to friction-like pinning of domain-wall motions, where Rayleigh’s law of magnetic hysteresis can be seen as the simplest case on either the play model or the Preisach model. They are poor at modeling other domain behavior, such as nucleation-driven hysteresis. Yet another hysteresis model is the stop model, which can be seen as the inverted version of the play model. This type of model has advantages for expressions linked to energy and can be related to Steinmetz equation of hysteresis losses. The models share several mathematical properties, such as the congruency property and wiping-out property, and both models have a history of dependence that can be described by the series of past reversal points. More generally, it is shown that the many models can be expressed as Preisach models, showing that they can be treated as subcategories of the Preisach type models. These include the play model, the stop model and also the alternative KP-hysteron model.

Acoustic Wave-Induced FeRh Magnetic Phase Transition and Its Application in Antiferromagnetic Pattern Writing and Erasing

“…In our experiment, ΔT ≈ 17 K and ΔT u ≈ 30 K, thus we obtain the evaluated parameters g c0 = 1400 J/kg, σ c = 300 J/kg, and σ u = 850 J/kg. Next, we use the Preisach model 51,52 to analyze the SAWinduced FeRh MPT. Preisach model is a famous historydependent hysteresis model developed in 1935 by Preisach.…”

Iron Loss Calculation Methods for Numerical Analysis of 3D-Printed Rotating Machines: A Review

“…In the case of the inverse model, B(t) is the input and H(t) is the output. There are mainly three physical processes that cause the hysteresis effect in magnetic materials [151]: domain wall motions [151][152][153][154] and the nucleation of domain walls [151]. Many different models have been proposed to explain the hysteresis behaviour in materials with small and large grain sizes.…”

“…These methodologies can be categorised in many ways. Mörée showed that most of them can be mathematically described as Play-and Preisach-type models [151]. The most-general model is the Preisach model because it allows the inclusion of saturation and variations of the hysteresis [151].…”

Harmonic and DC Bias Hysteresis Characteristics Simulation Based on an Improved Preisach Model

“…The concept of the Preisach hysteresis model was proposed by the German physicist F. Preisach in 1935. After improved by several researchers, the classical Preisach model with mathematical expressions was later widely used [ 1 , 2 , 3 ]. The Preisach model can be classified into continuous models and discrete models.…”