Theory of ferromagnetic hysteresis

bases were introduced in [Smy77] where they are called “R-structures”. Examples of abstract bases are concrete bases of continuous domains, of course, where the relation≺ is the restriction of the order of approximation. Axiom (INT) is satisfied because of Lemma 2.2.15 and because we have required bases in domains to have directed sets of approximants for each element. Other examples are partially ordered sets, where (INT) is satisfied because of reflexivity. We will shortly identify posets as being exactly the bases of compact elements of algebraic domains. In what follows we will use the terminology developed at the beginning of this chapter, even though the relation ≺ on an abstract basis need neither be reflexive nor antisymmetric. This is convenient but in some instances looks more innocent than it is. An idealA in a basis, for example, has the property (following from directedness) that for everyx ∈ A there is another element y ∈ A with x ≺ y. In posets this doesn’t mean anything but here it becomes an important feature. Sometimes this is stressed by using the expression ‘ A is a round ideal’. Note that a set of the form↓x is always an ideal because of (INT) but that it need not contain x itself. We will refrain from calling ↓x ‘principal’ in these circumstances. Definition 2.2.21. For a basis〈B,≺〉 let Idl(B) be the set of all ideals ordered by inclusion. It is called theideal completionof B. Furthermore, leti : B → Idl(B) denote the function which maps x ∈ B to ↓x. If we want to stress the relation with whichB is equipped then we write Idl(B,≺) for the ideal completion. Proposition 2.2.22.Let 〈B,≺〉 be an abstract basis.

Domain theory

https://www.cell.com/cell-host-microbe/pdf/S1931-3128(14)00426-0.pdf

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This study investigated a model theory of the changes in magnetization that a ferromagnetic material undergoes when subjected to an applied uniaxial stress. The description of these effects is shown to be totally different from the description of the changes in the hysteresis curve under a series of constant applied stresses. The main mechanism in the proposed model theory is the unpinning of domain walls by the application of stress, which allows the walls to move and causes a change in the magnetization. This change in magnetization reduces the displacement from the anhysteretic magnetization. In addition, the anhysteretic magnetization itself is changed by the application of stress via the magnetoelastic coupling. It is shown that the effect can be described by an equation in which the rate of change of magnetization with elastic energy is proportional to the displacement of the magnetization from the anhysteretic magnetization. This is termed the 'law of approach'. This law seems to apply when the starting condition of the material is on a major hysteresis loop.

https://iopscience.iop.org/article/10.1088/0022-3727/28/8/001/pdf

Theory of the magnetomechanical effect

This paper reviews and summarizes Maglev train technologies from an electrical engineering point of view and assimilates the results of works over the past three decades carried out all over the world. Many researches and developments concerning the Maglev train have been accomplished; however, they are not always easy to understand. The purpose of this paper is to make the Maglev train technologies clear at a glance. Included are general understandings, technologies, and worldwide practical projects. Further research needs are also addressed.

Review of maglev train technologies

A mathematical theory of hysteresis in ferromagnetic materials is presented based on existing ideas of domain wall motion and domain rotation. Hysteresis is shown to occur as a result of impedances to changes of magnetization such as when domain walls are pinned, while the mutual interactions of the magnetic moments are shown to be of secondary importance in this respect. An equation for the anhysteretic or ideal magnetization curve is derived based on a mean field approximation and this is shown to be dependent on the mutual interactions of the moments but independent of impedances such as pinning. The introduction of a term which measures the impedance to changes in magnetization leads to a simple differential equation of state for a ferromagnet which exhibits all the features of hysteresis. Some modifications of the simple model are necessary in order to bring the solution closer to the real situation. Results are presented which show all the features of hysteresis such as initial magnetization curve, major hysteresis loops, and minor hysteresis loops in excellent agreement with experimental results.

Theory of ferromagnetic hysteresis (invited)

An equation describing the initial magnetisation curve and hysteresis loops of ferromagnetic materials has been derived theoretically based on a mean field approximation. The mutual interaction of the moments is expressed as a coupling coefficient and a restraining force on the motion of the domain walls, caused by the pinning of the walls at defect sites, is expressed as a pinning coefficient. The resulting equation of state for the model is a first order linear differential equation incorporating the two parameters and a scaling parameter λ which represents the ratio of the coupling to the two fields H and M.

Ferromagnetic hysteresis

A theory of the magnetisation process in ferromagnets, based on existing ideas of domain rotation and domain wall motion is presented. This has been developed via a consideration of the various energy terms into a mathematical description of the process leading to an equation of state for a ferromagnet. The differential equation has been solved and a solution containing terms up to the second order presented, showing the essential features of ferromagnetic hysteresis. The theory has then been used to explain the effects of stress on magnetisation. It has been found that the magnetisation approaches the anhysteretic curve when a ferromagnet is subjected to stress and this is the underlying principle behind such changes in magnetisation. The change of magnetisation with stress can not be predicted solely on the basis of the magnetostriction coefficient except in special cases when the initial (zero stress) conditions of magnetisation lie on the anhysteretic. This condition is also approximately satisfied at higher fields.

https://iopscience.iop.org/article/10.1088/0022-3727/17/6/023/pdf

Theory of the magnetisation process in ferromagnets and its application to the magnetomechanical effect

Four magnetization models, now considered as classical, are presented: the Stoner-Wolhfarth model, the Jiles-Atherton model, the Globus model, and the Preisach model. The paper describes the methods each model uses to simulate the magnetization mechanisms, reversible and irreversible processes, major and minor loops, and anhysteretic behavior. Improvements and changes are proposed to the Stoner-Wolhfarth and Globus models. The necessary simplifying assumptions define the limits of applicability of the models. The paper concludes with a table of the main characteristics of each model to help a potential user to make a suitable choice.

David L. Atherton

Papers

Theory of ferromagnetic hysteresis

Theory of ferromagnetic hysteresis (invited)

Ferromagnetic hysteresis

Theory of the magnetisation process in ferromagnets and its application to the magnetomechanical effect

Macroscopic models of magnetization