Energetic Model Of Ferromagnetic Hysteresis Research Articles

Energetic model of ferromagnetic hysteresis

PurposeThe purpose of this paper is to present a model to describe the nonlinear and hysteretic properties of ferromagnetic materials.Design/methodology/approachThe energetic model of ferromagnetic hysteresis evolved from some well‐known concepts in ferromagnetism in the last years. The magnetisation process is calculated from energy balance and statistical domain behaviour. Based on vectorial, anisotropic, multi‐domain considerations an isotropic, scalar model is derived, which gives quite simple equations to describe the nonlinear, hysteretic magnetisation process.FindingsThe presented simulations for steel samples and ferrite samples show very nice correspondence with measurements.Originality/valueThe scalar model seems to be especially suited for integration into finite element modelling or into simulations of electro‐magnetic circuits.

Relation between physical and phenomenological aspects in the framework of an energetic hysteresis model

In this work, an interpretation of the underlying physical and phenomenological aspects is presented in a way that the magnetization process is considered as a process of order. For this purpose the energetic model of ferromagnetic hysteresis is modified so that the local magnetic energy terms, such as anisotropy or applied field energy, are condensed to the corresponding statistical domain classes via expectation values. Furthermore, the anhysteretic magnetization curve is interpreted as a consequence of internal entropy changes, relative to an a priori defined domain configuration at the demagnetized state. Finally, irreversible energy terms take dissipative losses into account.

Calculation and measurement of the magnetization process in orthoferrites

The prediction of non-linear behaviour of ferromagnetic material—represented by the hysteresis loop—is the aim of this work. By means of the energetic model of ferromagnetic hysteresis it is possible to generate hysteresis loops containing the characteristics of yttrium orthoferrite. In this way, produced loops will be compared with the measured hysteresis loops of a single plate of yttrium orthoferrite.

Magnetic loss measurement and calculation of a DC/DC converter

The use of a tapped inductor in the classical sepic converter leads to a high step-down ratio thus avoiding the extreme duty cycles of the active switch and the high peak currents in the active and passive switches. The function and some stress data of such a converter are summarized and the flux density and the current through the inductor during start-up are measured and simulated by the energetic model of ferromagnetic hysteresis and the magnetic losses of the inductors are calculated.

Hysteresis modeling and measurement for two-dimensional particle assemblies

The increasing accuracy of circuit data storage simulations demands reliable models for the magnetic behaviour of the magnetic storage material. This paper introduces and compares the results of measurements and the results of model calculations by applying the Jiles–Atherton model, and the energetic model of ferromagnetic hysteresis by Hauser. The results show good agreement for uniaxial particle assemblies.

Hysteresis of nanocrystalline R–Fe–B

The energetic model of ferromagnetic hysteresis calculates the magnetic state of materials by minimizing the total energy function for statistical domain behavior. The approach shows good agreement with the magnetization curves of mechanically alloyed Pr 9Fe 85B 6 powder, heat treated at different temperatures.

Isotropic hysteresis modeling of Fe–Co–B alloys

The energetic model of ferromagnetic hysteresis calculates the magnetic state of materials by minimizing the total energy function for statistical domain behavior. The physical constants of this model are derived from anisotropy energy constants, initial susceptibility, coercivity, and saturation magnetization. The approach shows a good agreement to the magnetization curves of FeCoB strips, also in dependence of applied stress.

Statistical hysteresis model for anisotropic and isotropic magnetic materials

The energetic model of ferromagnetic hysteresis is generalized for isotropic materials. All reversible contributions of the domain wall movements are described by a reversible field strength. The probability for an elastic movement to proceed is decreasing with increasing'distance from pinning centers. The physical constants of this model are derived from initial susceptibility, coercivity, and saturation magnetization. The approach shows a good agreement to the magnetization curves of both soft and hard magnetic, anisotropic and isotropic materials.

Magnetization reversal and statistical domain behaviour

The energetic model of ferromagnetic hysteresis calculates the magnetic state of anisotropic materials by minimizing the total energy of the magnetic structure. Magnetocrystalline anisotropy, shape anisotropy and strain energy give the easy directions for the domains. All reversible contributions of the domain wall movements are described by a reversible field strength. The domain walls move reversibly until an individual Barkhausen jump occurs. From this point the irreversible losses start to accumulate. At a point of field reversal the magnetic state of the material is classified by changing the parameters of the irreversible energy in dependence of the so far covered irreversible jumps. The physical constants of this model are derived from anisotropic energy contributions, initial susceptibility, coercivity, and saturation magnetization.

Magnetization reversal and small lancettes calculated by statistic domain behavior (abstract)

The energetic model of ferromagnetic hysteresis calculates the magnetic state of anisotropic ferromagnetic materials by minimizing the total energy function ET=EH+EM. The energy of the material EM is divided into reversible (statistic domain behavior) and irreversible terms. The applied field H (energy EH) causes reversible domain wall displacements si until an individual Barkhausen jump starting position sA is reached. The probability density pa(sA) is assumed to be decreasing with increasing sA: pa=(Ka/Kc)exp [−(Ka/Kc)sA] (adaptive constant Ka). Kc describes the influence of the total magnetic state on pa at points of magnetization reversal; Kc=1 for the initial magnetization curve. The losses Er during an irreversible Barkhausen jump (wall friction Kr) are increasing with si: Er=Kr[si−sA−(Kc/Ka)(Kc−1)] and Kc depends on the covered displacements si at a point of field reversal: Kcnew=2−Kcboldexp[−(Ka/Kcold) si]. This follows from the condition of steadiness at these points. The physical constants of this model are derived from anisotropic energy contributions, initial susceptibility, coercivity, and saturation magnetization. The approach shows a good agreement to measurements to the stability of small lancettes of (110)[001] 3.5% FeSi steel sheets, magnetized in the rolling direction.

Energetic model of ferromagnetic hysteresis 2: Magnetization calculations of (110)[001] FeSi sheets by statistic domain behavior

An energetic model of statistic domain behavior is applied on the magnetization process of grain oriented FeSi-steel sheets. The physical constants of the model are derived from anisotropic energy contributions, initial susceptibility, coercivity, and saturation magnetization. Calculated in the [100], [011], and [111] – directions, the hysteretic magnetization curves indicate good agreement with measurements from the demagnetized state up to saturation. The better correspondence between theory and experiments at weak fields is achieved by using realistic initial occupation probabilities for the domain structure. This assumption leads to complex mutual dependencies of the statistic domain’s volume fractions, which have not been considered in previous works.

Energetic model of ferromagnetic hysteresis

Calculations of a total energy function are used to describe a theory of hysteresis effects in crystalline, ferromagnetic materials. This model is applied on the cubic structure of FeSi crystals, which are oriented in a (110)[001] texture. The magnetic energy of the crystal is separated in reversible and irreversible parts: The reversible energy is expressed by magnetocrystalline anisotropy and shape anisotropy. They are responsible for the rotation of the domain magnetization at strong fields. At weak fields the reversible interaction of the domain wall motion with the stray fields of pinning centers (nonmagnetic inclusions, grain boundaries or inner strains) is described by a probability function of statistic domain behavior. The irreversible energy is caused by these pinning centers, too, and can be explained by the interaction losses of the magnetic moments in the Bloch wall with the crystal lattice during an irreversible Barkhausen jump. The energy of the applied field is added to these two parts and the magnetic state of the material is represented by the minima of the total energy function. The results show all features of hysteresis such as initial magnetization curve and major and minor hysteresis loops in good agreement with measurements on grain oriented 3,5% silicon-steel with Goss texture.