Analytical solution of Everett integral using Lorentzian Preisach function approximation

In this paper, we take in to account the Lorentzian function, already proposed as analytical function approximation in scalar Preisach-type modeling of hysteresis of soft magnetic materials. Preliminarily, we point out the properties of the Lorentzian function and the physical and mathematical meaning of its parameters. Successively, we show how the use of the Lorentzian function approximation allows to solve in complete analytical way the Everett's integral. In particular, we present in the paper the analytical expression in closed form of the first magnetization curve, of the symmetric and non-symmetric minor loops, and of the first- and second-order reversal curves. In addition, we show the use of the complete analytical formulas of the symmetric magnetic loops above-mentioned, applied to a simple identification procedure of the Lorentzian function parameters, by the knowledge of the measured major loop. Finally, in order to show the practical use of the analytical expression found, some computation examples and comparisons with experimental data are shown.     

Modelling of magnetic cores for power electronics applications

A Preisach product model, called here modified scalar preisach model (MSPM) is applied to predict the hysteretic behaviour of soft ferrite cores for power electronics applications. The paper discuss the main points of the model and explains a possible way to identify the modelling parameters by the experimental curves of the major loops and of the virgin material magnetization. In the final part of the paper a series of experimental tests are presented, and the capability of the model to predict the power losses and the waveforms of current and voltages in a power electronic system in which is placed a soft ferrite core is shown.     

A Preisach-based hysteresis model for magnetic and ferroelectric hysteresis

In this paper we present a model for hysteretic nonlinearities with non-local memories. This model can be applied to describe hysteretic material behavior. Common applications are ferromagnetic or ferroelectric materials. Our model consists of an analytic function and a Preisach operator. We define a continuous Preisach weight function and introduce a method for the identification of the model parameters. The model parameters are customized to a set of symmetric hysteresis curves. We verify our model for a soft magnetic material, a hard magnetic material and the ferroelectric behavior of some piezoelectric material. After that, non-symmetric curves like the virgin curve are predicted very well by the model. It is especially useful, if forced magnetization or polarization, that appears beyond technical saturation, come into account.     

Experimental determination of Preisach distribution functions in magnetic cores

This paper deals with the experimental analysis of the hysteresis behaviour of magnetic cores. Either laminated iron cores, or soft ferrite cores are taken into account in the paper. The series of major loops and the related virgin curves have been measured at appropriate very low frequencies for each type of magnetic material, in order to have data with negligible dynamic effects. These data have been used to determine the Preisach distribution functions for each material, as described either in the classical preisach scalar model (CSPM) or in a modified product model, and some notes and comments about the shapes found are given.     

Relation between the microstructural properties of electrical steels and the Preisach modelling

In this paper, the relation of the microstructural properties of electrical steels and the material parameters in the dynamic Preisach model is established. Particular experimental work was performed in order to separate the influence of grain size from the crystallographic texture. First, the parameters defined in the dynamic Preisach model has been fitted using the hysteresis loss characteristics. Next, we identified and separated the effect of average grain size from the crystallographic texture on each material parameter defined in the Lorentzian–Preisach distribution function. Here, the same texture dependence was identified for all kinds of magnetisation processes, i.e. for the irreversible and reversible parts of the quasi-static magnetisation and for the AC excess loss behaviour. Finally, the Preisach distribution function is rewritten explicitly including the grain size and crystallographic texture dependence.     

Color dielectric model with two scalar fields

SU(2) Yang-Mills theory coupled in a non-minimal way to two scalar fields is discussed. For the massless scalar fields a family of finite energy solutions generated by an external, static electric charge is found. Additionally, there is a single solution which can be interpreted as a confining one. Similar solutions have been obtained in the magnetic sector. In the case of massive scalar fields the Coulomb problem is investigated. We find that asymptotic behavior of the fields can also, for some values of the parameters of the model, give confinement of the electric charge. Quite interestingly one glueball-meson coupling gives the linear confining potential. Finally, it is shown how, for one non-dynamical scalar field, we can derive the color dielectric generalization of the Pagels-Tomboulis model.Received: 22 April 2003, Published online: 12 September 2003     

Dependence of the anhysteretic magnetization on the demagnetization factor

A method is presented to measure the dependence of the anhysteretic magnetization curve (the anhysteretic magnetization as a function of the internal field after degaussing) on the demagnetization factor N without physically varying N. The relation between the Preisach distribution and the N dependence of the anhysteretic magnetization curve is discussed in a way that is very close to the work of Bertotti. Classes of (moving) Preisach models are identified for which the anhysteretic magnetization curve is independent of the demagnetization factor. It is proven that the anhysteretic magnetization increases with N at fixed internal field, if the Preisach distribution decreases monotonically with increasing H_cent, the internal field value of a Preisach domain. It is shown that the Moving Preisach model may lead to a negative anhysteretic permeability.     

On the product Preisach model of hysteresis

The product model is an output-dependent modification of the traditional Preisach model in order to remove its non-real congruency property. The differential susceptibility is proposed to be a product of a magnetization-dependent factor and an expression containing two terms: one for the reversible process and the other an integral of a Preisach type distribution for the irreversible part. Thus the magnetization is an indirect function, in which the saturation is a natural property of the hysteresis model, and the reversible and irreversible parts of the magnetization are added up indirectly. The envelope function is related to the paramagnetic process and in the specific case of uni-axial anisotropy it is a hyperbolic tangent function. The measurement of the anhysteretic curve may provide the direct link to the evaluation methods of experimental data applied for traditional Preisach modeling.     

Magnetic properties of <Superscript>3</Superscript>He on the recursive lattices

We considered the Heisenberg model on the recursive lattices with multi-spin interaction in a strong magnetic field as an approximation of the two-dimensional kagome lattice, as well as hexagonal recursive lattices as an approximation of triangular lattice, for solid ³He. In a strong magnetic field it is possible to approximate the Heisenberg model with the Izing one. Using dynamic approach, we obtain exact recursion relations for partition functions. Diagrams of the magnetization versus external magnetic field with different spin-exchange parameters and temperatures are presented. Magnetization plateaux, bifurcation points, and doublings are obtained.     

Preisach modeling of aftereffect in a magneto-optical medium with perpendicular magnetization

The aftereffect of Co/Pt multilayer films with perpendicular magnetization has been measured with a magneto-optical Kerr effect (MOKE) magnetometer and calculated with a newly developed Preisach model. Compared to materials such as traditional magnetic recording media, Co/Pt multilayer films show a more complete picture of the progression of aftereffect because the magnetization of this material decays from saturation almost all the way to a ground state in a reasonable length of time. The magnetization measurements for times equal to negative and positive infinity are asymptotically horizontal, with a transition region that is linear on a logarithmic time scale. In contrast, typical published aftereffect analyses exhibit only a very small percentage of the total aftereffect that could be observed if time were not a factor in making measurements. A Preisach–Arrhenius model is used to calculate the magnetic aftereffect in the Co/Pt multilayer. Comparisons of the model to experimental results show not only the validity of the model, but also its value in predicting very short-time and long-time aftereffect behavior, and low levels of aftereffect occurring in noisy data, all of which are difficult to observe experimentally.     

Modeling of magnetic material displaying magnetic aftereffect with slow decay rates

For magnetic materials that display slow decay rates, the entire relaxation process cannot be observed experimentally within a reasonable time interval. While magnetic aftereffect behavior has been understood and analyzed quantitatively in general, the important parameters of magnetic materials with slow decay cannot be easily extracted. We present comprehensive experimental characterization of time, field, and temperature dependence of magnetic properties of a magnetic nanocomposite, which exhibits slow decay. Based on the measurement results and previously developed Preisach–Arrhenius model, we propose an analytical model that can predict the shape of the entire aftereffect curves at different temperatures with only the major hysteresis loop and one aftereffect curve at a specific holding field within the region of interest. The model is validated with both simulated data and measured data. This model allows the derivation of an analytical formula for the time variation of the magnetization based on a Gaussian distribution.     

“Aharonov-Bohm antiferromagnetism” and compensation points in the lattice of quantum rings

We investigate the magnetic properties of the lattice of non-interacting quantum rings using the 2D rotator model. The exact analytic expressions for the free energy as well as for the magnetization and magnetic susceptibility are found and analyzed. It is shown that such a system can be considered as a system with antiferromagnetic-like properties. We have shown also that all observable quantities in this case (free energy, entropy, magnetization) are periodic functions of the magnetic flux through the ring's area (as well known, such a behavior is typical for the Aharonov-Bohm effect). For the lattice of quantum rings with two different geometric parameters we investigate the ordinary compensation points (“temperature compensation points”, i.e. points at which the magnetization vanishes at fixed values of the magnetic field strength). It is shown that the positions of compensation points in the temperature scale are very sensitive to small changes in the magnetic field strength.     

Waves in magnetic fluids with equilibrium and frozen-in magnetizations

It is shown that, in an ideal magnetic fluid with equilibrium magnetization, a single hydrodynamic mode is present. This case qualitatively differs from the other limiting case of an ideal magnetic fluid with frozen magnetization, in which three hydrodynamic modes propagate. The theoretical calculations are found to agree well with experimental data for the anisotropy of ultrasound in a water-based magnetic fluid in the frozen magnetization approximation.     

Zero—field—cooled and field—cooled magnetizations and magnetic susceptibility of itinerant ferromagnet SrRuO3

Zero-field-cooled(ZFC) magnetization,field-cooled(FC) magnetization,ac magnetic susceptibility and major hysteresis loops of itinerant ferromagnet SrRuO3 have been measured at magnetic ordering temperatures ranging from 5 to 160K.An empirical model is proposed to calculate the measured ZFC magnetization.The result indicates that the calculated ZFC magnetization compares well with the measured one.Based on the generalized Preisach model.both the ZFC and FC curves are reproduced by numerical simulations.The critical temperature and critical exponents are determined by measuring the ac magnetic susceptibility in different bias magnetic fields at temperatures in the vicinity of the point of phase transition.     

Isotropic vector Preisach particle

A Preisach-type pseudoparticle is proposed, to describe macroscopic vector magnetic behaviour of isotropic materials. The magnitude of magnetization is computed by means of the classical Preisach model with the projection of field strength on its direction as input. The orientation of the magnetization vector is governed by the equilibrium between its vector product with the field strength and a friction-like opposing torque proportional to the square of its magnitude. The behaviour of the model is studied in various conditions and the results compared to experiments reported in literature.     

Vector Preisach hysteresis modeling: Measurement, identification and application

The paper presents a Preisach model to simulate the vector hysteresis properties of ferromagnetic materials. The vector behavior has been studied using a single sheet tester with a disk-shaped specimen at low frequency. The locus of the magnetic flux density vector has been controlled by a digital measurement system. An inverse vector Preisach hysteresis model has been developed and identified by applying the measured data. Finally, the inverse model has been inserted into a finite element procedure through the fixed point technique and the reduced magnetic scalar potential formulation to simulate the measurement system. The applicability of the measurement system as well as the developed model has been proven by comparing measured and simulated results.     

Nonlinear domain-wall dynamics in a system of two magnetic layers

The nonlinear dynamics of the magnetization in a spin-valve structure is investigated. Equations describing the dynamics of the magnetization in such a structure are obtained. The stability of the solution corresponding to a motionless flat domain wall is investigated. The nonlinear domain-wall dynamics are investigated in the approximation of a strong exchange interaction between the magnetic layers and in the approximation of a large magnetostatic energy. In the former case the nonlinear dynamical equations are shown to be similar to the equations describing the dynamics of the magnetization in a weak ferromagnet, and in the latter case they are similar to the equations of motion of a magnetic vortex (i.e., a vertical Bloch line) in a domain wall. Zh. éksp. Teor. Fiz. 116, 1365–1374 (October 1999)     

Conformal groups and conformally equivalent isometry groups

It is shown that if ann dimensional Riemannian or pseudo-Riemannian manifold admits a proper conformal scalar, every (local) conformal group is conformally isometric, and that if it admits a proper conformal gradient every (local) conformal group is conformally homothetic. In the Riemannian case there is always a conformal scalar unless the metric is conformally Euclidean. In the case of a Lorentzian 4-manifold it is proved that the only metrics with no conformal scalars (and hence the only ones admitting a (local) conformal group not conformally isometric) are either conformal to the plane wave metric with parallel rays or conformally Minkowskian.     

Second-order Preisach model of scalar hysteresis

A second-order Preisach model of scalar hysteresis is proposed and investigated. Parameter functions of this model are identified using transition curves of up to the third order. Wiping-out property and the property of invariance in the change of minor loop shape due to elimination of the first input extremum are shown to be the necessary and sufficient conditions for the representation of a given scalar hysteresis relation by the proposed model     

Low-frequency magnetic noise in micron-scale magnetic tunnel junctions

We have observed low-frequency noise due to quasiequilibrium thermal magnetization fluctuations in micron-scale magnetic tunnel junctions (MTJs). This strongly field-dependent magnetic noise occurs within the magnetic hysteresis loops, either as 1/f or Lorentzian (random telegraph) noise. We attribute it to the thermally excited hopping of magnetic domain walls between pinning sites. Our results show that magnetic stability is a crucial factor in reducing the low-frequency noise in small MTJs.