Real time dynamic domain observation in bulk materials

The paper briefly reviews the development of domain observation techniques used to study basic properties of electrical steels. A new real-time, dynamic, high magnification domain observation technique is presented as an example of a state-of-the-art system, capable of imaging non-repetitive domain wall motion at power frequencies. Advantages of real-time domain observation over stroboscopic magneto-optic studies are presented and the need for real-time observations in developing future loss theories is proposed. Possible relationships between Barkhausen noise, hysteresis and non-repetitive wall motion in electrical steels are suggested and finally examples of non-repetitive wall motion in other magnetic materials are illustrated.     

Dynamics of a domain wall in soft-magnetic materials: barkhausen effect and relation with sandpile models

The CZDE model [P. Cizeau, S Zapperi, G. Durin, and H. E. Stanley, Phys. Rev. Lett. 79, 4669 (1997)] for the dynamics of a domain wall in soft-magnetic materials is investigated. The equation of motion for the domain wall is reduced to a dimensionless form where the control parameters are clearly identified. In this way we show that in soft-magnetic materials with low anisotropies the noise can be approximated by a columnar disorder, and perturbation theory gives a good estimate of the avalanche exponents. Moreover, the resulting exponents are found to be identical to those obtained for directed Abelian sandpile models. The analogies and differences with these models and the question of self-organized criticality in the Barkhausen effect are discussed.     

Visualization of the Barkhausen effect by magnetic force microscopy

By visualization of the Barkhausen effect using magnetic force microscopy we are able to provide detailed information about the physical principles that govern the magnetization reversal of a granular ferromagnetic thin film with perpendicular anisotropy. Individual Barkhausen volumes are localized and distinguished as either newly nucleated or grown by domain wall propagation. The Gaussian size distribution of nucleated Barkhausen volumes indicates an uncorrelated random process, while grown Barkhausen volumes exhibit an inverse power law distribution, which points towards a critical behavior during domain wall motion.     

Tb0.3Dy0.7Fe2合金磁畴偏转的滞回特性研究

研究了不同载荷作用下Tb_0.3Dy_0.7Fe₂合金在压磁和磁弹性效应中磁畴偏转的滞回特性. 基于Stoner-Wolhfarth模型的能量极小原理, 采用绘制自由能-磁畴偏转角度关系曲线的求解方法, 研究了压磁和磁弹性效应中载荷作用下的磁畴角度偏转和磁化过程, 计算分析了不同载荷作用下磁畴偏转的滞回特性. 研究表明, 压磁和磁弹性效应中磁畴偏转均存在明显的滞回、跃迁效应, 其中磁化强度的滞回效应来源于磁畴偏转的角度跃迁; 压磁效应中预加磁场的施加将增大磁化强度的滞回, 同时使滞回曲线向大压应力方向偏移; 磁弹性效应中磁畴偏转的滞回存在两个临界磁场强度, 不同磁场强度下合金具有不同的磁畴偏转路径和磁化滞回曲线, 临界磁场强度的大小取决于预压应力的施加. 理论分析对类磁致伸缩材料磁畴偏转模型的完善和材料器件的设计应用非常有意义.     

Barkhausen noise and domain structure dynamics in Si-Fe at different points of the magnetization curve

In the present relationship between Barkhausen noise and domain structure evolution along the hysteresis loop in 3% Si–Fe has been investigated. The noise power spectrum has been measured vs. induction during cyclic magnetization of the material at a very low constant rate. The obtained results show that the behavior of the noise power along the magnetization curve can be related to the character of the domain structure rearrangements taking place at different levels of induction. Such a connection is reflected in a relationship between the noise power and the shape of the hysteresis loop. The measured noise power spectra are interpreted through the use of a suitable model. This makes possible to connect the shape of the magnetization curve to the microscopic parameters characterizing the dynamic of the domain wall during a large Barkhausen jump.     

Die Temperaturabhängigkeit des magnetischen Barkhausen-Effekts IV

The size distribution of Barkhausen discontinuities (magnetic moment > 6.5 · 10^?7 cgs) of very pure nickel was measured between ?195 and 360 °C on the hysteresis loop. The mean value of internal stresses was changed in a well defined manner by stretching the specimens. For different stress values the variation with temperature of the following properties is given in diagrams: The specific number and the “mean volume”² of discontinuities, the maximal value of Barkhausen susceptibility, the mean deviation of the volume of discontinuities along the hysteresis curve, and some characteristic field strengths defined by reversible and irreversible processes. Conclusions are drawn concerning the coupling of individual wall movements composing a Barkhausen jump.     

DC magnetization of ferromagnetic amorphous wires with local deformation

Experimental DC (VSM) and theoretical hysteresis loops of a ferromagnetic amorphous wire with a deformation in the middle or exposed to local magnetic fields are investigated. Hysteresis loops show two-stage Barkhausen jumps and staircase relaxation. With a local field at the same position, the loop drastically looses its shape and symmetry depending on the magnitude and the direction of the magnetic bias. A model to explain this behavior is proposed. The proposed model is based on the calculation of the magnetic moment distribution of the domain as a result of domain wall motion and nucleation in the inner core of a ferromagnetic wire and is in a good agreement with the experimental results.     

Magnetization reversal in (0 0 1)Fe thin films studied by combining domain images and MOKE hysteresis loops

The magnetization reversal of epitaxial single-crystal Fe films has been studied by combining domain images and hysteresis loops. The reversal is quantitatively described by combining the coherent rotation model and the domain wall displacement model. The pinning energy exerted on the domain walls and the domain wall angle at the switching fields are obtained by fitting this model to experimental hysteresis loops. The field-dependent pinning energy and the domain wall angle in the reversal process, and the contributions of second-order magneto-optic effect to hysteresis loops, are revealed to be two important features of single-crystal Fe films.     

Rotation of the pinning direction in the exchange bias training effect in polycrystalline NiFe/FeMn bilayers

For polycrystalline NiFe/FeMn bilayers, we have observed and quantified the rotation of the pinning direction in the exchange bias training and recovery effects. During consecutive hysteresis loops, the rotation of the pinning direction strongly depends on the magnetization reversal mechanism of the ferromagnet layer. The interfacial uncompensated magnetic moment of antiferromagnetic grains may be irreversibly switched and rotated when the magnetization reversal process of the ferromagnet layer is accompanied by domain wall motion and domain rotation, respectively.     

The effect of hydrogenation on the magnetization reversal process in amorphous ferromagnets

The influence of hydrogenation and dehydrogenation on the power spectra of Barkhausen noise in amorphous alloys has been investigated. It has been shown that after hydrogenation local stress centers occur in amorphous structure. Presence of the centers leads to long-wave fluctuations of domain wall energy which cause the decrease of the number of irreversible domain wall displacements.     

Nondestructive evaluation of isothermally annealed 12% CrMoV steel by magnetic BN measurement

The effects of microstructural evolution during isothermal annealing on structure-sensitive magnetic properties and Barkhausen noise (BN) characteristics have been investigated for 12% CrMoV steel. A rapid decrease in coercive force, remanence, hysteresis loss and hardness took place in accordance with the release of internal stresses from supersaturated martensite after annealing for only 20 minutes at 923 K. BN energy is correspondingly related with three stages of microstructural evolution such as the recovery of strain energy, the increase of precipitates size as a result of Ostwald ripening and the annihilation of dislocation density during isothermal annealing of the specimen. The linear relation between hardness and BN parameters in the magnetization region of irreversible domain wall displacement of 2.4 kA/m suggests that hardness and microstructural evolution could well be evaluated nondestructively by using BN measurements.     

Asymmetric magnetization reversal on exchange biased CoO/Co bilayers

We study magnetic hysteresis loops after field cooling of a CoO/Co bilayer by MOKE and polarized neutron reflectivity. The neutron scattering reveals that the first magnetization reversal after field cooling is dominated by domain wall movement, whereas all subsequent reversals proceed essentially by rotation of the magnetization. In addition, off-specular diffuse scattering indicates that the first magnetization reversal induces an irreversible change of the domain state in the antiferromagnet.     

Determination of the losses induced by irreversible barkhausen jumps of the 180° domain wall moving with a sinusoidal motion in the single domain wall model

The paper presents an analysis of the losses due to irreversible Barkhausen jump of the 180° Bloch wall in the single-domain wall model. The field-intensity and current-density vectors at unit input were determined for a single instantaneous jump. The losses were calculated for the case of the wall moving sinusoidally. The Parseval formula was used at determining the losses, which made it possible to perform calculations. A similar problem was considered by Allia and Vinai who adopted a simplified assumption of the domain of an infinitely long cylindrical shape.     

Hysteresis loss subdivision

Assuming that different energy dissipation mechanisms are at work along hysteresis, a hysteresis loss subdivision procedure has been proposed, using the induction at maximum permeability (around 0.8 T, in electrical steels) as the boundary between the “low-induction” and the “high-induction” regions. This paper reviews the most important results obtained in 10 years of investigation of the effect of microstructure on these components of the hysteresis loss. As maximum induction increases, the “low-induction loss” increases linearly up to 1.2 T, while the “high-induction loss” is zero up to 0.7 T and then increases as a power law with n=5. Low-induction loss behavior is linearly related to H_c between 0.4 and 1.2 T. Grain size has a larger influence on low-induction losses than on high-induction losses. Texture has a much stronger influence on high loss than on low-induction loss, and it is related to the average magnetocrystalline energy. 6.5%Si steel shows smaller hysteresis loss at 1.5 T than 3.5%Si steel only because of its smaler high-induction component. The abrupt increase in hysteresis loss due to very small plastic deformation is strongly related to the high-induction loss component. These results are discussed in terms of energy dissipation mechanisms such as domain wall movement, irreversible rotation and domain wall energy dissipation at domain nucleation and annihilation.     

A general 3-D nonlinear magnetostrictive constitutive model for soft ferromagnetic materials

In this paper, a new general nonlinear magnetostrictive constitutive model is proposed for soft ferromagnetic materials, and it can predict magnetostrictive strain and magnetization curves under various pre-stresses. From the viewpoint of magnetic domain, it is based on the important physical fact that a nonlinear part of the elastic strain produced by magnetic domain wall motion under a pre-stress is responsible for the change of the maximum magnetostrictive strain in accordance with the pre-stress. Then the reduction of magnetostrictive strain from the maximum is caused by the domain rotation. Meanwhile, the magnetization under various pre-stresses in this model is introduced by magnetostrictive effect under the same pre-stress. A simplified 3-D model is put forward by means of linearizing the nonlinear function, i.e. the nonlinear part of the elastic strain produced by domain wall motion, and by using the quartic of magnetization to describe domain rotation. Besides, for the convenience of engineering applications, two-dimensional (plate or film) and one-dimensional (rod) models are also given for isotropic materials and their application ranges are discussed too. In comparison with the experimental data of Kuruzar and Jiles, it is found that this model can predict magnetostrictive strain and magnetization curves under various pre-stresses. The numerical simulation further illustrates that the new model can effectively describe the effects of the pre-stress or residual stress on the magnetization and magnetostrictive strain curves. Additionally, this model can be degenerated to the existing magnetostrictive constitutive model for giant magnetostrictive materials (GMM), i.e. a special soft ferromagnetic material.     

Barkhausen jumps in the motion of a single ferroelectric domain wall

It is shown that the motion of a domain wall in the improper ferroelectric-ferroelastic gadolinium molybdate Gd₂(MoO₄)₃ demonstrates a self-organized critical behavior under polarization reversal. Barkhausen pulses are measured experimentally during the jumpwise motion of a single plane domain wall in monocrystalline plates with artificial pinning centers of the “field inhomogeneity” type.     

Barkhausen effect in magnetic thin films: Experimental noise spectra

In this paper Barkhausen noise spectra are shown that were measured on thin uniaxial 83-17 Ni?Fe films and these spectra were compared with the known magnetic behaviour of these films. On these types of sample the Barkhausen effect had been investigated by Lambeck [1], but their Barkhausen noise spectra have not been investigated so far. The film thicknessd _m in our experiments ranged between 400 and 2400 Å. In this range a change occurs in the dynamics of the magnetization behaviour caused by transitions of the type of domain wall. The results presented here show the very strong dependence of the Barkhausen noise spectra on the type of domain wall. Films with Bloch walls always show a frequency dependence off ^?1.7 in the higher frequency range. Samples in the thickness range where the transition occurs from the Néel wall via the cross-tie wall to the Bloch wall, have exponents between ?1 and ?2. The frequencyf _c above which the measured noise intensity begins to decrease varies very much for the different films. The curve off _c versus film thicknessd _m has the same form as the curve of the domain wall mobilitym versusd _m.