Quasi-static Hysteresis Loops Research Articles

Effect of crystallization annealing under loading on the magnetic properties and the structure of a soft magnetic FeSiNbCuB alloy doped with chromium

The changes of quasi-static magnetic hysteresis loops and X-ray diffraction patterns of the Fe73.5Si13.5B9Nb3Cu1 doped to 10 at % chromium instead of iron have been studied to elucidate the influence of the thermomechanical treatment consisting of annealing and cooling of the alloy under the tensile stress (tensile-stress annealing (TSA)) on the magnetic properties and the structure of these alloys. It is shown that the treatment results in the induction of the magnetic anisotropy of the hard axis type at which the magnetization reversal along the direction of applying the external stress during annealing is hampered. The energy of the induced magnetic anisotropy decreases as the chromium content increases. During TSA, the nanocrystal lattices are deformed, and the deformation is retained after cooling. The interplanar spacings increase along the extension direction and decrease in the transverse direction. The deformation anisotropy is observed for crystallographic directions. The anisotropic deformation of the bcc lattice of nanocrystals with high content of the ordered Fe3Si phase characterized by a negative magnetoelastic interaction is the cause of formation of the state with the transverse magnetic anisotropy of the hard axis type.

Comparison of static hysteresis models subject to arbitrary magnetization waveforms

PurposeThis paper aims to compare different static history-independent hysteresis models (mathematical-, behavioural- and physical-based ones) and a history-dependent hysteresis model in terms of parameter identification effort and accuracy.Design/methodology/approachThe discussed models were tested for distorted-excitation waveforms to explore their predictions of complex magnetization curves. Static hysteresis models were evaluated by comparing the calculated and measured major and minor static hysteresis loops.FindingsThe analysis shows that the resulting accuracy of the different hysteresis models is strongly dependent on the excitation waveform, i.e. smooth excitations, distorted flux waveforms, transients or steady-state regimes. Obtained results show significant differences between predictions of discussed static hysteresis models.Research limitations/implicationsThe general aim was to identify the models on a very basic and limited set of measured data, i.e. if possible using only the measured major static loop of the material. The quasi-static major hysteresis loop was measured at Bmax = 1.5 T.Practical/implicationsThe presented analysis allows selection of the most-suited hysteresis model for the sought-for application and appraisal of the individual limitations.Originality/valueThe presented analysis shows differences in intrinsic mechanisms to predict magnetization curves of the majority of the well-known static hysteresis models. The results are essential when selecting the most-suited hysteresis model for a specific application.

Energy losses in mechanically modified bacterial magnetosomes

Magnetosomes are isolated from the Magnetospirillum magneticum strain AMB-1 bacteria. Two samples are compared: magnetosomes normally prepared of a ‘standard’ length and magnetosomes of a short length. Chains of magnetosomes are shortened by mechanical modification (cleavage) by means of sonication treatment. They represent a new geometry of magnetosomes that have not been investigated before. The effect of the sonication is analysed using transmission and electron microscopy, atomic force microscopy, and dynamic light scattering. Scanning imaging reveals three types of shortening effect in a sample of shortened magnetosomes, namely, membrane collapse, membrane destruction, and magnetosome cleavage. Dynamic light scattering shows a reduction of hydrodynamic diameter in a sample of shortened magnetosomes. The magnetic properties of magnetosomes are analysed and compared in DC and AC magnetic fields based on the evaluation of quasi-static hysteresis loops (energy losses) and calorimetric hyperthermia measurements (specific absorption rate), respectively. A sample of shortened magnetosomes behaves magnetically in a different manner, showing that both the energy loss and the specific absorption rate are reduced, and thereby indicates a variation in the heating process. The magnetic properties of magnetosomes, together with the new and stable geometry, are balanced, which opens the way for a better adaptation of the magnetic field parameters for particular applications.

Evaluation of discharge energy density of antiferroelectric ceramics for pulse capacitors

The energy in pulse capacitors need to discharge rapidly to obtain high peak power. However, the discharge energy density of antiferroelectric (AFE) dielectrics for pulse capacitors is traditionally evaluated by hysteresis loop (defined as quasi-static method). To verify whether the quasi-static method is suitable for pulse applications, AFE ceramics Pb0.94La0.04[(Zr0.70Sn0.30)0.86Ti0.14]O3 were prepared, and their discharge energy density was calculated by hysteresis loop and pulse current (defined as dynamic method), respectively. A significant difference was found between these two kinds of results. Under 36 kV/cm, the discharge energy density calculated by 1 Hz hysteresis loop was 0.35 J/cm3 while that by pulse discharge current was only 0.18 J/cm3. It was found that the discharge energy density declined with increasing test frequency (0.1 Hz–100 Hz) and decreased further via dynamic hysteresis loop in microseconds scale. This declination can be explained by the viscous force during the motion of the domain wall. Thus, for pulse capacitors, it is more reasonable and practical to evaluate discharge energy density of AFE by pulse current than by quasi-static hysteresis loop.

Spin-wave thermal population as temperature probe in magnetic tunnel junctions

We study whether a direct measurement of the absolute temperature of a Magnetic Tunnel Junction (MTJ) can be performed using the high frequency electrical noise that it delivers under a finite voltage bias. Our method includes quasi-static hysteresis loop measurements of the MTJ, together with the field-dependence of its spin wave noise spectra. We rely on an analytical modeling of the spectra by assuming independent fluctuations of the different sub-systems of the tunnel junction that are described as macrospin fluctuators. We illustrate our method on perpendicularly magnetized MgO-based MTJs patterned in 50 × 100 nm2 nanopillars. We apply hard axis (in-plane) fields to let the magnetic thermal fluctuations yield finite conductance fluctuations of the MTJ. Instead of the free layer fluctuations that are observed to be affected by both spin-torque and temperature, we use the magnetization fluctuations of the sole reference layers. Their much stronger anisotropy and their much heavier damping render them essentially immune to spin-torque. We illustrate our method by determining current-induced heating of the perpendicularly magnetized tunnel junction at voltages similar to those used in spin-torque memory applications. The absolute temperature can be deduced with a precision of ±60 K, and we can exclude any substantial heating at the spin-torque switching voltage.

Universal behavior of dense clusters of magnetic nanoparticles

A detailed numerical simulation of quasistatic hysteresis loops of dense clusters of interacting magnetic nanoparticles is carried out. Both clusters of magnetically soft and magnetically hard nanoparticles are considered. The clusters are characterized by an average particle diameter D, the cluster radius Rc, the particle saturation magnetization Ms, and the uniaxial anisotropy constant K. The number of particles in the cluster varies between Np = 30 - 120. The particle centers are randomly distributed within the cluster, their easy anisotropy axes being randomly oriented. It is shown that a dilute assembly of identical random clusters of magnetic nanoparticles can be characterized by two dimensionless parameters: 1) the relative strength of magneto-dipole interaction, K/Ms2, and the average particle concentration within the cluster, η = V Np/Vc. Here V is the nanoparticle volume, and Vc is the volume of the cluster, respectively. In the strong interaction limit, Msη/Ha > > 1, where Ha = 2K/Ms is the anisotropy field, the ultimate hysteresis loops of dilute assemblies of clusters have been constructed. In the variables (M/Ms, H/Ms) these hysteresis loops depend only on the particle volume fraction η. In the weak interaction limit, Msη/Ha < < 1, the assembly hysteresis loops in the variables (M/Ms, H/Ha) are close to the standard Stoner-Wohlfarth hysteresis loop.

Modeling of hysteresis loops by Monte Carlo simulation

Recent advances in MC simulations of magnetic properties are rather devoted to non-interacting systems or ultrafast phenomena, while the modeling of quasi-static hysteresis loops of an assembly of spins with strong internal exchange interactions remains limited to specific cases. In the case of any assembly of magnetic moments, we propose MC simulations on the basis of a three dimensional classical Heisenberg model applied to an isolated magnetic slab involving first nearest neighbors exchange interactions and uniaxial anisotropy. Three different algorithms were successively implemented in order to simulate hysteresis loops: the classical free algorithm, the cone algorithm and a mixed one consisting of adding some global rotations. We focus particularly our study on the impact of varying the anisotropic constant parameter on the coercive field for different temperatures and algorithms. A study of the angular acceptation move distribution allows the dynamics of our simulations to be characterized. The results reveal that the coercive field is linearly related to the anisotropy providing that the algorithm and the numeric conditions are carefully chosen. In a general tendency, it is found that the efficiency of the simulation can be greatly enhanced by using the mixed algorithm that mimic the physics of collective behavior. Consequently, this study lead as to better quantified coercive fields measurements resulting from physical phenomena of complex magnetic (nano)architectures with different anisotropy contributions.

3-D Branching of Magnetic Domains on Compressed Si-Fe Steel With Goss Texture

The influence of an applied compressive stress on the hysteresis curve and domain structure in conventional (110) [001] Fe-3%Si steel cut parallel to the rolling direction was studied. Quasi-static hysteresis loops under compressive stress up to 70 MPa were measured. The magnetic domains and magnetization processes were observed by longitudinal Kerr microscopy at different levels of stress. With increasing compressive stress, the domain structure in the demagnetized state evolves from initial simple 180° slab-like domains along the surface-parallel easy axis into stress pattern I, checkerboard pattern, and finally into stress pattern II at high stresses. The checkerboard pattern, observed at the intermediate stress level between 10 and 25 MPa, has not been reported before such thin sheets. The applied magnetic field makes the surface-parallel [001] domains with magnetization in field direction grow into the bulk at the expense of all other domains for all stress levels. The magnetization curves at stress above 10 MPa have a constricted shape with a sudden change of magnetization at a critical fields. The averaged critical field changes linearly with stress with a slope close to theoretical predictions.

An air-cooled Litz wire coil for measuring the high frequency hysteresis loops of magnetic samples--a useful setup for magnetic hyperthermia applications.

A setup for measuring the high-frequency hysteresis loops of magnetic samples is described. An alternating magnetic field in the range 6-100 kHz with amplitude up to 80 mT is produced by a Litz wire coil. The latter is air-cooled using a forced-air approach so no water flow is required to run the setup. High-frequency hysteresis loops are measured using a system of pick-up coils and numerical integration of signals. Reproducible measurements are obtained in the frequency range of 6-56 kHz. Measurement examples on ferrite cylinders and on iron oxide nanoparticle ferrofluids are shown. Comparison with other measurement methods of the hysteresis loop area (complex susceptibility, quasi-static hysteresis loops, and calorific measurements) is provided and shows the coherency of the results obtained with this setup. This setup is well adapted to the magnetic characterization of colloidal solutions of magnetic nanoparticles for magnetic hyperthermia applications.

Influence of applied tensile stress on the hysteresis curve and magnetic domain structure of grain-oriented Fe–3%Si steel

The influence of applied tensile stress on the hysteresis curve and domain structure in conventional (1 1 0)[0 0 1] Fe–3%Si steel, cut parallel to the rolling direction, is studied on samples with different grain sizes. Quasistatic hysteresis loops under tensile stresses up to 70 MPa were measured. The magnetic domains and magnetization processes were observed by longitudinal Kerr microscopy at different levels of stress. It is shown that for stresses exceeding 5–10 MPa the bulk hysteresis loop can be described with good accuracy by the action of an effective field, which is the product of a function of stress and a function of magnetization. The function of stress is approximately linear with a slope of one. Except for the sample with the smallest grains, the function of magnetization is linear in the magnetization range ±1.2–1.5 T, i.e. it has a typical demagnetizing field shape. Domain observation reveals that the effective field is caused by the demagnetizing fields occurring at grain boundaries and at the sheet surface due to the removal of closure domains transverse to the rolling direction by the tensile stress. The closure structure reappears at higher fields. Another indirect indication of demagnetizing fields is the fact that the hysteresis losses drop continuously with stress and changes in the coercive force are small. The effective field of the sample with the smallest grains increases most nonlinearly with stress similar to the behaviour obtained for non-oriented material.

LaBonte's method revisited: An effective steepest descent method for micromagnetic energy minimization

We present a steepest descent energy minimization scheme for micromagnetics. The method searches on a curve that lies on the sphere which keeps the magnitude of the magnetization vector constant. The step size is selected according to a modified Barzilai-Borwein method. Standard linear tetrahedral finite elements are used for space discretization. For the computation of quasistatic hysteresis loops, the steepest descent minimizer is faster than a Landau-Lifshitz micromagnetic solver by more than a factor of two. The speed up on a graphic processor is 4.8 as compared to the fastest single-core central processing unit (CPU) implementation.

High-temperature photo-induced switching and pressure-induced transition in a cooperative molecular spin-crossover material

The thermal and photo-induced switching properties of the recently published molecular spin crossover complex [Fe(H4L)2](ClO4)2·H2O·2(CH3)2CO () have been investigated in detail through Raman spectroscopy. Magnetometric and single crystal X-ray diffraction kinetic studies within the hysteresis loop have proven its metastable character, which allowed establishing the shape of the true, quasi-static hysteresis loop. This is related to the proximity of the temperatures of the thermal high to low spin SCO (T1/2↓) to those of the relaxation of the thermally or photo-generated metastable states (T(TIESST) and T(LIESST), respectively). Green light irradiation within the hysteresis loop results in a complete low to high spin photo-switch. In addition, the SCO of at room temperature can be induced by applying pressure, as followed by Raman spectroscopy.

Static hysteresis loop model with changing parameters

SUMMARY The application of the Jiles–Atherton (J–A) hysteresis model for numerical modeling of measured quasistatic hysteresis loops of non-oriented soft magnetic material is investigated. The J–A model used assumes its parameters are dependent on actual effective magnetic field strength. This is performed by using a new parameter associated with the mathematical description of the J–A model. In this paper, the author demonstrates that these varying parameters and the proposed algorithm of parameter estimation are useful in accurate numerical modeling of the static hysteresis loop. Results of modeling are compared with experimental measurements, demonstrating very good agreement in a wide range of maximum field strength. Copyright © 2013 John Wiley & Sons, Ltd.

Core Loss Prediction in Electrical Machine Laminations Considering Skin Effect and Minor Hysteresis Loops

This paper presents a method for the estimation of core losses in electrical machine laminations exposed to high-frequency and nonsinusoidal excitations by using only low-frequency measurements. The developed model takes into account the nonuniform distribution of the magnetic field inside the lamination. Accurate core loss prediction in the presence of minor loops is achieved using the energetic model to calculate the quasi-static hysteresis loops. The results are verified experimentally by comparing to the measured core losses in laminations exposed to the flux waveforms in different sections of an inset permanent magnet machine. The comparison between measured and calculated core losses shows excellent agreement, confirming the validity of the model.

Numerical modeling of static hysteresis loop using variable parameters

AbstractThe application of the Jiles–Atherton (J–A) hysteresis model for numerical modeling of measured quasistatic hysteresis loops of non‐oriented soft magnetic material is investigated. The J–A model used assumes its parameters are dependent on actual effective magnetic field strength. This is carried out by using a new parameter associated with the mathematical description of the J–A model. In this paper, the author demonstrates that these varying parameters and the proposed algorithm of parameter estimation are useful in accurate numerical modeling of the static hysteresis loop. Results of modeling are compared with experimental measurements, demonstrating very good agreement in a wide range of maximum field strength. Copyright © 2013 John Wiley & Sons, Ltd.

Properties of Dense Assemblies of Magnetic Nanoparticles Promising for Application in Biomedicine

Chemically synthesized iron oxide nanoparticles and magnetosomes produced by magnetotactic bacteria are of great importance for application in biomedicine. In this paper, we discuss the complicated magnetic anisotropy of the nanoparticles, the influence of the magnetostatic interactions, and thermal fluctuations on the behavior of these assemblies. Numerical simulation for dilute assemblies of iron oxide nanoparticles with combined magnetic anisotropy show that the uniaxial shape anisotropy dominates even for small aspect ratios of the particle, L/D≥1.1–1.2. The quasistatic hysteresis loops are calculated for various clusters of bacterial magnetosomes with diameters D=40–60 nm to understand the influence of magnetostatic interactions. The specific absorption rate (SAR) is calculated for assemblies of magnetic nanoparticles dispersed in solid and liquid media. A new electrodynamic method of measurement is used to obtain the SAR of the assembly of bacterial magnetosomes with average diameter D=48 nm.

Subdivision of Hysteresis Loss in Mn-Zn Ferrite Toroidal Cores

The hysteresis loss subdivision method proved to be a strong tool to help in the analysis of different energy dissipation mechanisms along the quasi-static hysteresis loop measured on electrical steels. This paper used the same method to discuss the mechanisms involving the energy loss dissipation in Mn-Zn ferrite toroidal cores. The samples, sintered under controlled atmosphere in industrial conditions, were measured under triangular waveform excitation at very low frequency (5 mHz) and peak flux densities varying from 0.05 T to 0.45 T. The results show a different behavior between the low inductions hysteresis loss (WLI) and the high induction hysteresis loss (WHI) which proves the existence of different energy dissipation mechanisms affecting these loss components.

Photomagnetism of a sym‐cis‐Dithiocyanato Iron(II) Complex with a Tetradentate N,N′‐Bis(2‐pyridylmethyl)1,2‐ethanediamine Ligand

A comprehensive study of the magnetic and photomagnetic behaviors of cis-[Fe(picen)(NCS)(2) ] (picen = N,N'-bis(2-pyridylmethyl)1,2-ethanediamine) was carried out. The spin-equilibration was extremely slow in the vicinity of the thermal spin-transition. When the cooling speed was slower than 0.1 K min(-1), this complex was characterized by an abrupt thermal spin-transition at about 70 K. Measurement of the kinetics in the range 60-70 K was performed to approach the quasi-static hysteresis loop. At low temperatures, the metastable HS state was quenched by a rapid freezing process and the critical T(TIESST) temperature, which was associated with the thermally induced excited spin-state-trapping (TIESST) effect, was measured. At 10 K, this complex also exhibited the well-known light-induced excited spin-state-trapping (LIESST) effect and the T(LIESST) temperature was determined. The kinetics of the metastable HS states, which were generated from the freezing effect and from the light-induced excitation, was studied. Single-crystal X-ray diffraction as a function of speed-cooling and light conditions at 30 K revealed the mechanism of the spin-crossover in this complex as well as some direct relationships between its structural properties and its spin state. This spin-crossover (SCO) material represents a fascinating example in which the metastability of the HS state is in close vicinity to the thermal spin-transition region. Moreover, it is a beautiful example of a complex in which the metastable HS states can be generated, and then compared, either by the freezing effect or by the LIESST effect.

Influence of applied compressive stress on the hysteresis curves and magnetic domain structure of grain-oriented transverse Fe–3%Si steel

The influence of an applied compressive stress on the hysteresis curve and domain structure in conventional (1 1 0) [0 0 1] Fe–3%Si steel cut transverse to the rolling direction is studied. Quasistatic hysteresis loops under compressive stress up to 75 MPa were measured. The magnetic domains and magnetization processes were observed by longitudinal Kerr microscopy at different levels of stress. It is shown that the bulk hysteresis loop can be described with a good accuracy by the action of an effective field, which is the product of the stress and a function of magnetization. Domain observations have shown that the reasons for the effective field are demagnetizing fields due to the disappearance of supplementary domains along [0 1 0] and [1 0 0] at low fields and different domain systems in different grains at moderate fields. The latter are caused by differences in grain sensitivity to stress depending on the degree of misorientation. A decrease in the effective field above 1 T is connected with a transformation of all grains into the same domain system—the column pattern.

Similarity rules of magnetic minor hysteresis loops in Fe and Ni metals

We have studied similarity rules of quasistatic minor hysteresis loops for Fe and Ni single crystals in the wide temperature range from 10 to 600 K. Two similarity rules of M R*/ M a*∼3/4 and W R*/ W F*∼1/6, were found in a medium field range where irreversible movement of Bloch walls plays a crucial role for magnetization; M a *, M R*, W F*, and W R* are magnetization, remanence, hysteresis loss, and remanence work of a minor hysteresis loop. The similarity rules hold true, being almost independent of kinds of ferromagnets, applied stress, and temperature. The origin was discussed from the viewpoint of pinning effects due to dislocations as well as eddy current effects which become predominant at low temperatures for samples with low dislocation density.