Magnetization Process in Thin Laminations up to 1 GHz (original) (raw)
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Domain Wall Processes, Rotations, and High-Frequency Losses in Thin Laminations
IEEE Transactions on Magnetics, 2000
We have investigated and modeled the magnetization process in thin amorphous and nanocrystalline ribbons from DC to 1 GHz. These transverse anisotropy laminations, their thickness ranging between 6 and 20 m, display excellent broadband magnetic behavior, ensuing from the dominant role of magnetization rotations. Combination of fluxmetric, aftereffect, and high-speed magneto-optical experiments put in evidence that the domain wall processes, the obvious source of losses at low and medium frequencies in spite of negligible contribution to the magnetization reversal, fully damp on attaining the MHz range. Here the energy dissipation chiefly descends from the rotations and conforms to the so-called classical regime. To describe the high-frequency spin dynamics, the coupled Maxwell and Landau-Lifshitz-Gilbert equations are therefore considered. We have worked out a numerical solution of such equations by a finite element approach, based on a very fine time discretization and a computing scheme preserving the magnetization modulus. From the calculation of hysteresis loop and eddy current density at each mesh point, the separate contributions to the rotational losses by the eddy currents and the spin damping mechanism are obtained. The overall energy loss behavior versus frequency is thus eventually predicted in terms of separate contributions by the domain wall processes and the rotations.
Modeling High-Frequency Magnetic Losses in Transverse Anisotropy Amorphous Ribbons
IEEE Transactions on Magnetics, 2015
The superior high-frequency magnetic behavior of transverse anisotropy amorphous ribbons can be qualitatively interpreted in terms of rotation dominated magnetization process and quantitatively predicted describing the spin dynamics by the Landau-Lifshitz-Gilbert (LLG) equation in association with the electromagnetic diffusion equation. The theory is applied to comprehensive measurements performed on Co-based alloys, tested as field-annealed tapewound rings from dc to 1 GHz with combination of fluxmetric and transmission line methods. The LLG equation is numerically solved considering the role of magnetostatic, exchange, anisotropy, eddy current, and applied fields. It accurately describes the high-frequency energy losses, ensuing from eddy currents, and spin damping. By further considering the low-frequency domain wall contribution, a full scenario for the broadband losses is achieved.
Fluxmetric-magnetooptical approach to broadband energy losses in amorphous ribbons
Journal of Applied …, 2011
The magnetization process in field annealed amorphous ribbons has been investigated from dc to 10 MHz. Loss and permeability measurements, carried out both on single strips and ring samples by means of a broadband fluxmetric setup, have been associated with observations of the domain wall dynamics by high-speed stroboscopic Kerr apparatus. Transverse anisotropy Co-based ribbons exhibit a combination of rotational and domain wall processes, the latter being observed to progressively damp with frequency and coming to a halt on approaching the megahertz range. Given the vanishing direct contribution of the domain walls to the high-frequency magnetization process, the so-called classical loss formulation, associated with the rotational magnetization processes, is expected to correspondingly hold for the energy loss W(f). Under these conditions, W(f) tends to increase linearly with f, which, in view of the expected surge of the skin effect, does not agree with the f 1/2 behavior accordingly predicted by standard formulas. This points to the specific properties of the rotational process and the role played by the exchange torque in connection with incomplete flux penetration.
Broadband magnetic losses in Fe-Si and Fe-Co laminations
We discuss comprehensive broadband (DC -10 kHz) investigations on magnetic losses in Fe-(3 wt%)Si and Fe-Co laminations. In this range of frequencies, the prediction of loss is not easy, because skin effect can be quite important. The theoretical approach generally relies on a dynamic hysteresis model in association with a diffusion equation, but it imposes heavy computational burden. We present here a computationally efficient dynamic hysteresis model based on the Dynamic Preisach Model (DPM), by which one can achieve fast and precise solution of the diffusion equation taking into account the hysteretic constitutive equation of the material. This is achieved at a greatly reduced computational cost with respect to the standard DPM. The loss results provided by this simplified model are at all frequencies in very good agreement with the prediction by the full DPM and with the experiments. Index Terms-Magnetic losses, Fe-Si and Fe-Co laminations, Dynamic Preisach Model, Skin effect.
The power losses in magnetic laminations—the influence of the frequency and DC-bias magnetisation
Physica B: Condensed Matter, 2006
The usual separation of the loss components is based upon the assumption that the hysteresis losses persist as a constant contribution multiplied by the frequency value. The question arises if this assumption is correct. The author of this paper presents the cases in which this way of treating the problem proves to be wrong. Another area of investigations concerns the works under the DC-bias field conditions. The conclusions, coming directly from described cases, permit to formulate the calculation algorithm of the power losses, under deformed magnetic flux conditions.
Rotational Magnetic Losses in Nonoriented Fe–Si and Fe–Co Laminations up to the kilohertz Range
IEEE Transactions on Magnetics, 2014
Literature data on the energy loss behavior of steel sheets under rotating induction are restricted to quite low frequencies, i.e., up to a few hundreds of hertz. This is not sufficient to predict the loss in high-speed electrical machines, where frequencies in the kilohertz range are commonly encountered. We have overcome this difficulty by making loss measurements under alternating and circular induction in 0.2 mm thick Fe-(3 wt%)Si and Fe 49 Co 49 V 2 sheets using a specially designed experimental setup. Peak polarization levels and frequencies up to 1.6 T at 2 kHz have been reached in the Fe-Si laminations, whereas the Fe-Co alloy, endowed with much higher permeability, has been characterized up to 2.1 T at 5 kHz. In the first part of this paper, the measured loss behavior versus peak polarization and magnetizing frequency is presented. In the second part, a loss model for circular induction is proposed, considering the skin effect. To this end, we have derived a simple magnetic constitutive law for the material, assumed to be isotropic, and we have introduced it into the electromagnetic diffusion equation. The solution of this equation by an iterative algorithm provides the induction profile across the sample thickness and eventually the classical loss component, which represents the major contribution to the total loss at high frequencies. Good agreement with the experiments is obtained.
Journal of Applied Physics, 1997
Dynamic hysteresis loop shapes and magnetic power losses are studied in nonoriented Fe-Si laminations exhibiting significant excess losses. Measurements are carried out under controlled sinusoidal induction in the frequency range from 1 Hz to 1.6 kHz, at various peak inductions from 0.25 to 1.5 T. Excess losses are found to obey a f 3/2 law up to frequencies of 200-400 Hz, depending on peak induction. Beyond this limit, definite deviations are observed, due to eddy current shielding. Detailed information on the flux and field distribution in this high frequency regime is obtained by finite element solutions of Maxwell equations employing the dynamic Preisach model to describe quasi-static hysteresis and dynamic wall processes. The agreement between theoretical predictions and measurements is discussed.
Basic principles of magnetization processes and origin of losses in soft magnetic materials
Journal of Magnetism and Magnetic Materials, 1992
Domain wall dynamics can be investigated through properly designed experiments in well oriented single crystals, containing one or a few mobile 180 ° walls. Equations of motion are derived which can be specialized to describe extreme cases, such as quasi-static stochastic wall behavior and eddy-current-induced wall bowing. Concepts and results related to single-wall dynamics can then be exploited, through the use of statistical methods, to assess the phenomenology of eddy-current losses in ordinary materials, where complex domain structures exist. It turns out that the conventional concept of loss separation can be physically justified. A general theoretical framework is consequently worked out, which is solidly verified against power-loss experiments in crystalline and amorphous materials.
Investigation of magnetoimpedance effect in amorphous thin-film microstructures
Journal of Applied Physics, 2005
The magnetoimpedance (MI) effect is based on the magnetic field dependence of the transverse permeability µ of an ac current carrying conductor. Both inductance and skin effect depend on µ, thus causing a change of the impedance Z of amorphous wires, ribbons, and-at very high frequencies-also of thin films. In order to overcome this disadvantage, tri-layer structures of two 20, 50, and 100 nm thin amorphous CoFeB layers with a central 40, 100, and 200 nm thin Cu layer are rf sputtered onto a thermally oxidized Si wafer. 300 µm long strips of 3-20 µm width are structured by plasma etching and connected by ultrasonic bonding to a printed circuitboard. Magnetization curves-both of the plain film and of the structures-parallel and perpendicular with respect to the easy axis of uniaxial anisotropy are measured by the magnetooptical Kerr effect, showing an anisotropy field of 2 kA/m and low coercivity in the hard axis direction. During magnetization reversal, the domain structure in the strips was observed by Kerr microscopy, indicating possible magnetostatic coupling of the two 100 nm magnetic layers. Measurements of the frequency dependence of the complex permeability revealed ferromagnetic resonance at 1.5 GHz. The MI effect was measured by means of a network analyzer (NA), using the complex t/r ratio of the incoming (reference r) and the transmitted t wave through the sample. The NA was calibrated for linear frequency response of t at µ 0 Hs = 12 mT. The unstructured 100/200/100 trilayer (sample size 4 × 8 mm 2) showed a flat MI maximum at 65 MHz, whereas the 6 µm wide strip had a MI maximum of (Z − Z Hs)/Z Hs = 5.7% at 460 MHz with a field of µ 0 H =1.6 mT, applied by a Helmholtz coil pair, parallel to the long axis of the strip, which is oriented perpendicular to the easy axis. The MI maximum of the 50/100/50 structure strips is beyond 500 MHz. The reason of the low measured MI effect is the high contact resistance R c =11Ohm and the inductivity L=3 nH of the 6-7 cm long leads to the strip. Measured by a four wire method, the dc resistance R d = 4 of the 6 µm wide 100/200/100 strip is in good aggreement with the theoretical resistance of the copper layer. If directly integrated in the electronic circuit, the MI effect is increased to about 37%.