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DFG Schwerpunktprogramm 1681

In this letter, we present a numerical model of magnetization dynamics that is based on the classical Stoner–Wohlfarth model and the Landau–Lifshitz–Gilbert equation. This approach uses a series of coefficients for the interpolation of the time needed by the magnetic moment to reach equilibrium and a linear system of equations for the variation in time of the angular components of the magnetization. The dynamic Stoner–Wohlfarth model will be used to accurately replicate the dynamic behavior of macrospins with significantly improved numerical efficiency when a constant or variable external magnetic field is applied.

Orientador: Prof. Dr. Fabio Furlan Ferreira Coorientador: Prof. Dr. Ronei Miotto Dissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Física, Santo André, 2022. O foco deste trabalho foi estudar como alguns fatores físicos influenciam na eficiência da magneto-hipertermia, para isso desenvolveu-se uma série de rotinas que executam um algoritmo baseado em Monte-Carlo cinético e que utiliza o modelo de Stoner-Wohlfarth como base. Esse algoritmo foi validado através de comparações entre resultados teóricos e experimentais e com comparações com outros algoritmos já validados na literatura. As rotinas criadas se mostraram uma poderosa ferramenta computacional útil para realização de estudos sistemáticos de fluídos magnéticos sobre diferentes condições. Com ele foi possível estudar as influências das características do campo magnético externo, da concentração dos fluídos magnéticos, das diferentes formas de aglomerados entre outros fatores. Do ponto de vista de custo computacional o algoritmo baseado no modelo de Stoner-Wohlfarth aliado ao método de Monte-Carlo cinético se mostrou mais barato do que algoritmos que integram a equação de Landau-Lifshitz-Gilbert diretamente, porém ambos observam mesmas tendências e o software desenvolvido neste trabalho permite simular sistemas mais próximos dos estudados experimentalmente, o que a torna uma ferramenta indicada para os estudos desejados neste trabalho. Além do legado de um algoritmo robusto e de baixo custo computacional, a partir do uso destas rotinas foi possível entender alguns aspectos fundamentais do processo de liberação de calor, como por exemplo o fato da formação de aglomerados poder contribuir para o aumento da energia liberada devido a criação de vínculos entre os eixos fáceis de magnetização das nanopartículas. As simulações mostraram que as cadeias lineares paralelas ao campo externo são o formato de aglomerado que mais contribui para o processo de liberação de calor. Por fim foi possível obter-se a demonstração de que deve haver um tamanho ótimo de cadeias lineares, fato já observado experimentalmente por colaboradores e que foi comprovado pelas simulações. The focus in this work was to study how some physical factors influence the efficiency of magneto-hyperthermia, thereunto a series of routines were developed, this routines run an algorithm based on kinetic Monte-Carlo and that uses the Stoner-Wohlfarth model as a basis. This algorithm was validated through comparisons between theoretical and experimental results besides comparisons with other algorithms already validated in the literature. The created routines proved to be a powerful computational tool useful for carrying out systematic studies of magnetic fluids under different conditions. Through the use of this algorithm was possible to study the influences of the characteristics of the external magnetic field, the concentration of magnetic fluids, the different forms of aggregates, among other factors. From the point of view of computational cost, the algorithm based on the Stoner-Wohlfarth model combined with the kinetic Monte-Carlo method proved to be more efficiency than algorithms that integrate the Landau-Lifshitz-Gilbert equation directly, but both observe the same trends and the software developed in this work allows simulating systems closer to those studied experimentally, which makes it a better tool for the desired studies in this work. Besides to the legacy of a robust and low computational cost algorithm, using these routines it was possible to understand some fundamental aspects of the heat release process, such as the fact that the formation of aggregates can contribute to the increase in the energy released due to creation of constraints between the easy magnetization axes of nanoparticles. The simulations showed that the linear chains parallel to the external field are the aggregates shape that most contributes to the heat release process. Finally, it was possible to demonstrate that there must be an optimal size of linear chains, a fact already observed experimentally by collaborators and which was proven by simulations as well.

Magnetic field sensors based on the giant magnetoresistance (GMR) effect have a number of practical current and future applications. We report on a modeling of the magnetoresistive response of moving spin-valve (SV) GMR sensors combined in certain cluster networks to an inhomogeneous magnetic field of a label. We predicted a large variety of sensor responses dependent on the number of sensors in the cluster, their types of interconnections, the orientation of the cluster, and the trajectory of sensor motion relative to the label. The model included a specific shape of the label, producing an inhomogeneous magnetic field. The results can be used for the optimal design of positioning devices.

Periodic systems of magnetic nanoparticles are now of interest as they support GHz spin waves. Their equilibrium configurations, switchable with the external magnetic field, are crucial for such applications. We study infinite and finite chains of particles of two shapes (i) ellipsoidal and (ii) rectangular stripes with long axes perpendicular to the chain axis. A variable magnetic field is applied parallel to the long axes. Micromagnetic simulations are compared with the corresponding discrete spin models (Stoner-Wohlfarth model, S-W). An antiferromagnetic configuration is the ground state for all the systems at vanishing field but a ferromagnetic configuration occurs when the field is strong enough. The switching of the infinite chains to the reversed ferromagnetic configuration proceeds directly for the ellipsoids and by an intermediate configuration, in which the magnetization within the particle is non-uniform, in the case of the stripes. The non-uniform configurations are well represented by tilted states in S-W model. Important differences are found in the finite analogs: the switching of ellipsoids becomes multistage and starts from the innermost particles relatively well reproduced with S-W model, whereas the reversal of the stripes, starts from the outermost particles and has no analog in S-W model. Practical consequences of the findings are discussed.

The Stoner–Wohlfarth model predicts the crossing of the ascending and descending branches of the hysteretic magnetization curve. This crossing behavior has widely been dismissed, with the claim that it violates the laws of thermodynamics. Experimental verification of hysteresis branch crossing has not been acknowledged in the literature. Here we show, both theoretically and experimentally, that the crossing of the ascending and descending branches of the magnetization curve is a robust, reproducible phenomenon which does not violate any fundamental law.

The modeling of hysteresis curves of bonded ferrite magnets is discussed. Hysteresis of anisotropic magnets were calculated according to the Stoner-Wohlfarth Model, for the cosn (theta) distribution. The crystallographic texture has significant effect on the hysteresis curve. Two different samples were examined, one isotropic and another anisotropic. The anisotropy field of strontium ferrite magnets was determined to be 19.5 kOe. The Mr/Ms ratio of the anisotropic bonded magnet was estimated as 0.8.

The purpose of this paper is to describe a finite-element method for the numerical simulation of magnetization and demagnetization processes in ferromagnetic pieces with hysteresis. In particular, the proposed methodology will be applied to compute the remanent flux density after a magnetic particle inspection test on specimens with cylindrical symmetry consisting of three stages: longitudinal magnetization, circular magnetization, and demagnetization.

This paper presents the extension of two 1-D lamination models with magnetic hysteresis to reproduce dynamic hysteresis loops and power loss in grain-oriented (GO) electrical steels. For this purpose, the concept of magnetic viscosity is introduced in the model equations. The applicability and accuracy are demonstrated by means of two GO steels of different thicknesses at magnetizing frequencies up to 1000 Hz. Advantages and limits of the classical approach with and without viscosity and comparisons to measured data are discussed in detail.

A numerical implementation of the classical Stoner–Wohlfarth (SW) model to simulate the magnetization angle of an assembly of SW particles with an effective axis of anisotropy under a rotating applied field is presented. Using an angular distribution for the angle each SW particle is making with the medium’s reference axis, the proposed model successfully simulated lag-angle plots exhibiting the same rotational magnetization behavior measured for different ellipsoidally magnetizable media in the literature. The developed algorithm provides a simple tool for rotational-energy-loss calculations, preserves the physical intuition of the classical SW model, and is computationally faster compared to the Preisach–Stoner–Wohlfarth models. The effect of the angular distribution parameters on the switching transition angle and the algorithm’s potential for modeling additional anisotropies through using different angular distributions are discussed.

Anisotropy constants of magnetic materials are typically determined through angle-resolved Ferromagnetic Resonance (ar-FMR) and torque magnetometry, which can be time consuming measurements, thus limiting their utility. The Stoner–Wohlfarth model can be used to numerically fit measured magnetic hysteresis curves to more easily determine these anisotropy constants. To demonstrate this, 10 nm bct FexCoyMnz single-crystal films grown by molecular beam epitaxy on MgO(001) substrates were investigated. The hysteresis behavior measured by vibrating sample magnetometry was least-squares fit against numerically calculated hysteresis curves generated from the Stoner–Wohlfarth model to extract the anisotropy constants. The cubic anisotropy of different compositions of FeCoMn films was at ∼104 J/m3, which is on the same order of magnitude of bct Fe and Co thin films measured by ar-FMR and torque magnetometry techniques.

International audience; A series of strontium hexaferrites (Sr-HF) compounds, doped with a low amount of manganese SrFe12-xMnxO19 (where x = 0.00, 0.03 and 0.05), were prepared by a sol-gel method. Structural and microstructural characterizations were performed by X-ray diffraction (XRD) and scanning electronic microscopy (SEM) in order to determine some basic properties such as lattice parameters and particles size. Moreover, magnetic properties of the samples were measured in a temperature range from 2 to 900 K. The results show that the transition temperature (TC) decreases from 764 to 721 K with Mn doping at x = 0.05 content. Also, temperature and doping effects on the coercivity (Hc), the remanent magnetization (Mr) and the magnetization of saturation (MS) were discussed considering the Stoner - Wohlfarth model. A slight improvement of the magnetic properties (Hc =5.56 kOe, Mr =49.99 emu/g, MS =101.9 emu/g (i.e. 19.37 µB/u.f)) for low content (x = 0.03) is evidenced, yielding to promising material for permanent magnet devices. This improvement was explained by the relationship between the microstructure and to the effective magnetic anisotropy.

In this work we present a faster modified protocol for first order reversal curve (FORC) measurements. The main idea of this procedure is to use the information of the ascending and descending branches constructed through successive sweeps of magnetic field. The new method reduces the number of field sweeps to almost one half as compared to the traditional method. The length of each branch is reduced faster than in the usual FORC protocol. The new method implies not only a new measurement protocol but also a new recipe for the previous treatment of the data. After of these pre-processing, the FORC diagram can be obtained by the conventional methods. In the present work we show that the new FORC procedure leads to results identical to the conventional method if the system under study follows the Stoner-Wohlfarth model with interactions that do not depend of the magnetic state (up or down) of the entities, as in the Preisach model. More specifically, if the coercive and interactions fields are not correlated, and the hysteresis loops have a square shape. Some numerical examples show the comparison between the usual FORC procedure and the propose one. We also discuss that it is possible to find some differences in the case of real systems, due to the magnetic interactions. There is no reason to prefer one FORC method over the other from the point of view of the information to be obtained. On the contrary, the use of both methods could open doors for a more accurate and deep analysis. Fil: de Biasi, Emilio. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina

Purpose Magnetization is one of the most important parameters of magnetic fluids. The shape of the magnetization curve often determines the application of a fluid in a device. On the basis of the magnetization curve, it is also possible to estimate, for example, the distribution and size of the particles in a magnetic fluid carrier fluid. The aim of this paper is to present a new approach for estimating the magnetization curve. Design/methodology/approach The proposed method is an iterative method based on the measurement of magnetic induction on a test stand. To determine the magnetization curve, a numerical simulation of the magnetic field distributions for the preliminary magnetization curve should also be performed. Numerical simulations for modified forms of the magnetization curve are performed until the difference between the results obtained by the measurement and numerical simulation are the smallest. Findings This paper presents the results of magnetization curve research for ferrofluids and magnetorheological fluids. Originality/value The discussed method shows the possibilities of using numerical simulations of magnetic field distribution to determine the magnetic properties of magnetic fluids. This method may be an alternative for estimating the magnetization curve of the magnetic fluid compared to other methods.

A formula has been derived for calculating the main magnetization curve of steels from the strength of the magnetizing field and the measurement results of the magnetization of technical saturation, coercive force, and residual magnetization. We analyzed the influence of material magnetic properties on the approximation of its magnetization to technical saturation.

This paper presents a detailed theoretical background of the saturation wave model (SWM), which offers a simplified homogenized solution of the nonlinear diffusion phenomena inside soft magnetic steel sheets (SMSSs). The SWM is capable of predicting the complicated dynamic magnetization of SMSS without discretization of the cross section of the SMSSs. Despite its simplicity, the SWM predicts exact solutions of the discussed problems when step-like magnetization curves are assumed and reasonably accurate solutions for real magnetization curves. In this paper, the SWM is analyzed in comparison to the numerical solution of the diffusion phenomena using the parametric magnetodynamic model, where interesting properties of the SWM are discussed and pointed out.

Magnetization curves of an YFe3 single crystal were measured along the basal plane and the c-axis within the temperature range of 2–600 K. Their analysis provided temperature dependencies of the parameter p = ( M ep − M ha ) / M ep characterizing saturation magnetization anisotropy and magnetocrystalline anisotropy constants K1 and K2. The latter was obtained using the modified Sucksmith-Thompson method and the numeric technique of approximation which takes into account slight misorientation between applied magnetic field and the hard magnetization axis allowing to describe magnetization curves accurately.

Nickel substituted manganese ferrite [NixMn1−xFe2O4 (x = 0.2)] nanoplates with cubic shape and controlled sizes were fabricated by chemical coprecipitation technique. Structural analyses confirmed the formation of single phase crystalline nanoplates in the size range 8–24 nm. Magnetic studies showed that coercivity as a function of plate length goes through a maximum, peaking at 162 Oe and then decreases for larger nanoplates, indicating that the single domain limit for NixMn1−xFe2O4 (x = 0.2) is ∼21 nm. While negligible coercivity at below 10 nm confirms the superparamagnetic limit in the range 8–10 nm for these nanoplates. Saturation magnetization of the samples was found to increase linearly with plate length in the single domain regime, however this increase was observed slower for the larger nanoplates. Typical blocking effects were studied in the temperature range 20–300 K and it was found the superparamagnetic blocking temperature increases monotonically with increasing size of the nanoplates. The results are discussed in terms of the enhanced surface roles and variation of surface and effective anisotropies with size of the nanoplates that strongly influence their magnetic properties within the domain of Stoner Wohlfarth model for ferromagnetic systems.

The isotropic Stoner-Wohlfarth model can be applied for the determination of the anisotropy field in powders. Samples of strontium ferrite - SrFe12O19 – were measured in Vibrating Sample Magnetometer (VSM). By means of the fitting of the first quadrant of the hysteresis curve the anisotropy field was estimated as 19-20 kOe for the SrFe12O19 phase. The main advantage of the method is its simplicity, because compacting or sintering of the powder samples is not necessary

Arrays of nanosized hollow spheres of Ni were studied using micromagnetic simulation by the Object Oriented Micromagnetic Framework. Before all the results, we will present an analysis of the properties for an individual hollow sphere in order to separate the real effects due to the array. The results in this paper are divided into three parts in order to analyze the magnetic behaviors in the static and dynamic regimes. The first part presents calculations for the magnetic field applied parallel to the plane of the array; specifically, we present the magnetization for equilibrium configurations. The obtained magnetization curves show that decreasing the thickness of the shell decreases the coercive field and it is difficult to obtain magnetic saturation. The values of the coercive field obtained in our work are of the same order as reported in experimental studies in the literature. The magnetic response in our study is dominated by the shape effects and we obtained high values for the reduced remanence, $M_{r}/M_{S} = 0.8$ . In the second part of this paper, we have changed the orientation of the magnetic field and calculated hysteresis curves to study the angular dependence of the coercive field and remanence. In thin shells, we have observed how the moments are oriented tangentially to the spherical surface. For the inversion of the magnetic moments we have observed the formation of vortex and onion modes. In the third part of this paper, we present an analysis for the process of magnetization reversal in the dynamic regime. The analysis showed that inversion occurs in the nonhomogeneous configuration. We could see that self-demagnetizing effects are predominant in the magnetic properties of the array. We could also observe that there are two contributions: one due to the shell as an independent object and the other due to the effects of the array.

The Stoner-Wohlfarth is the most used model of magnetic hysteresis, but its computation is time-consuming. We use machine learning to approximate piecewise this model by easy-to-compute analytic functions. Our parametrization is suitable for fast quantitative evaluations and fitting experimental data, which we exemplify., Comment: 5 pages, 4 figures

We have produced hot-deformed Nd-Fe-B magnets from commercial (MQU-F) Nd-Fe-B ribbons. The spark-plasma-sintering technique was used to deform the samples under low pressures of 40 MPa. The initial stages of the hot-deformation process were investigated in terms of microstructures and magnetic properties. Hot-deformed magnets with different deformation ratios were produced and the dependence of the remanence on the deformation ratio was determined. In the initial stages of the hot-deformation process, a cone-like shape of the magnet was observed for the first time. The experimental data can be qualitatively interpreted by applying the basic Stoner–Wohlfarth model.

In the fabrication of soft magnetic composite materials, the iron powder particles are submitted to a high-pressure compaction process that should be considered in the modeling of magnetic hysteresis. This paper introduces a novel approach for modeling the stress-dependent magnetic hysteresis, based on the Stoner–Wohlfarth (S–W) model. Moreover, for determining the S–W particle equilibrium orientation directly, an extended S–W astroid method, which considering the stress effect, is presented. To verify this presented model, the magnetic hysteresis phenomenon of SOMALOY 500 are measured and simulated. The comparison between the two results shows that this model is feasible and effective, which can be applied to practical engineering.

The Alnico magnets (also called Ticonal) have coercivity attributed to shape anisotropy. The conditions for appearing this type of anisotropy are discussed, and the principal is the existence of elongated grains parallel to the easy magnetization axis. A very important detail is that the conditions assumed in the Stoner Wohlfarth model have to be obeyed. The assumptions are i) ferromagnetic phase with single domain particle size and ii) grains without magnetic interaction between them, magnetically insulated by a grain boundary paramagnetic phase. In Alnico magnets, the coercivity mechanism is coherent rotation of single domain size particles.

A model for the vector magnetization of a distribution of uniaxial particles is presented. Recent work by the authors decomposed the magnetization into two components and modeled the total vector magnetization as their vector sum. Anisotropy could be ideally modeled as a constant field, but this leads to a model of unidirectional anisotropy. Considering uniaxial media, such approach will only be valid for small angles. Hence, in this paper, a model is proposed that calculates the total magnetization of a distribution of uniaxial particles as the vector sum of irreversible and reversible components. The magnitude of the irreversible component is modeled using a Preisach differential-equation approach; however, other valid models can be used. The direction of the reversible component is modeled using the minimum energy approach of the classical Stoner–Wohlfarth model. The final result of the model is an unsymmetrical lag-angle plot for intermediate applied field values, which is consistent with the measurements.

The ratios of Fe/Co and Fe/B in a ferromagnetic alloy system, Fe(87-x-y) Co(x) Ti7 Zr6 By (x = 20, 30, and 40 at% and y = 2 and 4 at%), which was produced by the melt-spinning technique in the form of thin ribbons, were investigated to improve the saturation magnetization. The thermal properties T(x) were in the range of 792.0 K to 838.0 K, and it decreased by decreasing Fe/Co ratio. In the as-spun amorphous ribbons, the saturation magnetization and coercivity ranged from 137.5 emu/g to 164.2 emu/g and from 0.027 Oe to 1.245 Oe, respectively. The optimum Fe/Co ratio for the Fe(83-x) Co(x) Ti7 Zr6 B4 system was determined to be 64:36. In other words, the optimum system was Fe60 Co25 Ti7 Zr6 B2, which exhibited robust soft magnetic properties, such as a low coercivity of 0.252 Oe, and high saturation magnetization of 164.2 emu/g (1.55 T). Also, in this system, magnetic properties such as the saturation magnetization and coercivity increased with decreasing Fe/Co ratio.

Apparent magnetization mapping is a technique to estimate magnetization distribution in the subsurface magnetic layer from the observed magnetic data, of benefit in identifying lithologic units and delineating magnetic geologic boundaries. The conventional approaches for apparent magnetization mapping usually neglect effects of remanence, resulting in large geologic deviation and the occurrence of negative magnetization when the magnetic layer contains strong remanent magnetization. We have developed a space-domain inversion approach for apparent magnetization mapping based on the amplitude of magnetic anomaly (AMA), the analytic signal (AS), and the normalized source strength (NSS) to reduce effects of remanent magnetization. The AMA, AS, and NSS are three common quantities insensitive or weakly sensitive to the remanence transformed from the magnetic total field anomaly or components. The magnetic layer underground is first divided into a regular grid of vertical rectangular prisms, each having a cross-sectional area of one grid square and a uniform magnetization. Then, an iterative algorithm is adopted to invert each quantity of the AMA, AS, and NSS to obtain an optimum value of magnetization of each prism in the magnetic layer. The inversion approach permits the top and bottom surfaces of the magnetic layer to be constant or variable in depth, and requires no prior information of magnetization directions. Our tests on the synthetic and real data from the metallic ores area in the southern margin of North China have proved the feasibility and robustness of the presented inversion approach. All of the AMA, AS, and NSS inversions produced nonnegative magnetization distribution in the magnetic layer. Also, the AS and NSS inversions produced a better resolution of magnetization distribution than that of the AMA.

A numerical extension of the simple Stoner–Wohlfarth model to the case of bi-dimensional angular distributions of easy axis is provided. The results are particularized in case of step-like, Gaussian-like and user defined distributions. In spite of its simplicity, the model can be applied to magnetically textured thin films and multilayers with in-plane magnetic anisotropy, independently on the texture source. Exemplifications are provided for a simple ferromagnetic textured FeCo film as well as for a FeMn/FeCo/Cu/FeCo spin valve structure.

The Nd9.5Fe61.5Co10Nb20.5Ti0.5B15.5C0.5 nanocomposite magnets have been prepared by the copper-mold casting technique. The magnetic properties were calculated by the micromagnetic simulation using the magnetic force microscopy image. The influence of different saturation magnetization of amorphous grain boundary phase on the magnetization reversal process was investigated. The simulation results indicate that the coercivity increases with the reducing saturation magnetization of amorphous phase when the grain size varied from 300 to 1000 nm. The magnetization reversal process demonstrates that the magnetic moments of NdFeB phase show the prior inversion at the grain boundaries. Furthermore, the comparison between the anisotropic and isotropic model implies the importance of preparing anisotropic magnets.