Minor Hysteresis Loops Research Articles

Magnetic hysteresis of blocked ferrihydrite nanoparticles

Using minor hysteresis loops in the Stoner–Wohlfarth model allows describing the experimental behavior of the coercive force of minor hysteresis loops in ferrihydrite nanoparticles with a change in the field amplitude. The description allows estimating the parameters of the distribution of the magnetic anisotropy field in nanoparticles. The best agreement of the anisotropy fields estimated by different approaches is achieved for the assumption of uniaxial anisotropy in ferrihydrite nanoparticles.

Exchange bias, and coercivity investigations in hematite nanoparticles

<abstract> <p>Hematite nanoparticles of average size of 20 nm were synthesized using sol-gel method and the structural characterisations were conducted using XRD and TEM. The XRD profile revealed the coexistence of small fraction of maghemite phase along with the main hematite phase. Magnetization versus applied field (M-H) measurements were performed between −5 and 5 T and respectively in the temperatures 2, 10, 30, 50, 70,100,150,200, and 300 K under zero field and 1, 2, 3, 4 T field cooling. At all field-cooling values, the coercivity was found to display a weak temperatures dependence below 150 K and a strong increase above 150 K reaching the largest value of 3352 Oe at 300 K for the field-cooling value of 3 T. Horizontal and vertical hysteresis loop shifts were observed at all temperatures in both the zero-field and field-cooled states. In the field-cooled state, both loop shifts where found to have significant and nonmonotonic field-cooling dependences. However, because saturation magnetization was not attained in all measurements our calculations were based on the minor hysteresis loops. M-H measurements were performed between −9 and 9 T at room temperature under zero field cooling and 1, 2, 3, 4, 5, 6 T field cooling. Saturation magnetization was not attained, and the loops displayed loop shifts similar to those for the ±5 T sweeping field. The highest coercivity value of 4400 Oe is observed for the 6 T field cooled MH loop. The ferromagnetic (FM) contribution towards the total magnetization was separated from the total magnetization and hysteresis loops displayed both horizontal and vertical shifts. The novel results of the temperature and field dependence of exchange bias were attributed mainly to the magnetic exchange coupling between the different magnetic phases (mainly the FM) and the spin-glass-like regions.</p> </abstract>

Effect of high pressure torsion on crystallization and magnetic properties of Fe73.9Cu1Nb3Si15.5B6.6

The effects of severe plastic deformation (SPD) by means of high pressure torsion (HPT) on the soft magnetic properties of the iron-based metallic glass Fe73.9Cu1Nb3Si15.5B6.6 are investigated. With this procedure, it has been possible for the first time to consolidate and deform this high-strength material with a minimum of cracks. X-ray diffraction, differential mechanical and differential scanning analyses, as well as optical and scanning electron microscopy were carried out for characterization of crystallization phenomena and crack formation. For magnetic properties, minor loop hysteresis measurements were done because of their high sensitivity for magnetic structures. Significant influences of HPT-processing on the coercivity as well as on magnetic anisotropy are found and discussed in detail.

A Sensitivity Mapping Technique for Tensile Force and Case Depth Characterization Based on Magnetic Minor Hysteresis Loops

In the nondestructive testing and evaluation area, magnetic major hysteresis loop measurement technology are widely applied for ferromagnetic material evaluation. However the characterization ability of major hysteresis loop measurement technology greatly varies as the evaluated target properties. To solve this limitation, magnetic minor hysteresis loops, which reflect the responses of ferromagnetic material magnetization in a systematic way, is recommend. Inspired by plenty of information carried by the minor loops, the sensitivity mapping technique was developed to achieve the highest sensitivity of minor-loop parameters to the nondestructively evaluated targets. In this study, for the first time, the sensitivity mapping technique is used to measure the tensile force in a steel strand and evaluate the effective case depth in induction-hardened steel rods. The method and procedures for the sensitivity mapping technique are given before experimental detection. The obtained experimental results indicate that the linear correlation between the induced voltage (or the magnetic induction intensity) and the tensile force (or effective case depth) exists at most of the locations in the cluster of minor loops. The obtained sensitivity maps can be used to optimize the applied magnetic field (or excitation current) and the analyzed locations at the minor loops for achieving the highest sensitivity. For the purpose of tensile force measurement, it is suggested that the strand should be firstly magnetized to the near-saturation state and then restored to the remanent state. In this way, the highest sensitivity is obtained as about 15.26 mV/kN. As for the induction-hardened steel rods, the highest sensitivity of magnetic induction intensity to the effective case depth occurs under low magnetic field conditions and the absolute value of the highest sensitivity is about 0.1110 T/mm. This indicates that if the highest sensitivity is required in the case depth evaluation, the induction-hardened steel rods are only required to be weakly magnetized. The proposed sensitivity mapping technique shows the good performance in the high-sensitivity evaluation of tensile force and case depth in ferromagnetic materials and its application scope can be extended to other nondestructive detection fields.

The effect of elastic deformation on the minor hysteresis loops of low carbon steel

The effect of elastic tensile deformations on the magnetic permeability of a structural low-carbon steel 20K (0.23 % C, 0.20 % Si, 0.46 % Mn) at various magnetic states was experimentally studied. To obtain these parameters, the measurements of minor hysteresis loops, which begin in the demagnetized state and in the remanent magnetization state, were carried out. The maximum tensile stress equal to 250 MPa that corresponds to 90 % of the conditional yield strength of studied steel. Stress dependences of the initial and reversible magnetic permeabilities as well as differential magnetic permeability along the descending branch of the minor hysteresis loop, which starts in the remanent magnetization state, are non-monotonic. They have extremums at σ = 50–70 MPa. However, stress dependences of the sums of those parameters are monotonic. The relative changes reach 25 % at tensile stresses of 250 MPa which make the promise of using the sums of magnetic permeabilities as parameters for assessing the magnitude of tensile stresses.

High-frequency power loss mechanisms in ultra-thin amorphous ribbons

Soft magnetic amorphous materials with ultra-low power loss are highly desirable for high-frequency drive applications. The present work demonstrates the high-frequency power loss performance and underlying loss mechanisms in ultra-thin amorphous alloys. This is achieved by rapid-quenching amorphous alloys of Co-, CoFe- and Fe-rich systems, investigating their amorphous atomic structure, quantifying the saturation magnetostriction constants (λs), imaging magnetic domains at remanent magnetization, analyzing magnetization reversal from various magnetization levels, and finally, investigating the material loss performance over a broad frequency range (f = 50 kHz–2 MHz) at various excitation levels (Bm = 25–100 mT). The ultra-high performance of ultra-thin Co-rich amorphous ribbons, as compared to CoFe- and Fe-rich alloys, was attributed to the significantly low eddy current loss, due to the reduced thickness, and a minimal amount of excess loss, owning to minimal magnetoelastic contributions and magnetization reversal by rotation. The underlying loss mechanisms were analyzed by decomposing material loss into primary components and identifying the magnetization reversal mechanisms using minor hysteresis loops. In the Co-rich amorphous alloys, we suggest that magnetization reversal by rotation dominates, at least at low excitations, while in CoFe- and Fe-rich alloys domain wall displacement prevails and contributes significantly to the excess loss up to the MHz frequency range. Magnetization reversal by rotation in Co-rich alloys could be attributed to the zero/near-zero λs, and eventually low residual stress, leading to a homogeneous magnetic domain structure, as compared to the inhomogeneous “fingerprint-like” complex domains in highly magnetostrictive CoFe-rich alloys.

Topological energy barrier for skyrmion lattice formation in MnSi

We report the direct measurement of the topological skyrmion energy barrier through a hysteresis of the skyrmion lattice in the chiral magnet MnSi. Measurements were made using small-angle neutron scattering with a custom-built resistive coil to allow for high-precision minor hysteresis loops. The experimental data was analyzed using an adapted Preisach model to quantify the energy barrier for skyrmion formation and corroborated by the minimum-energy path analysis based on atomistic spin simulations. We reveal that the skyrmion lattice in MnSi forms from the conical phase progressively in small domains, each of which consisting of hundreds of skyrmions, and with an activation barrier of several eV.

A preliminary study on mist CVD-derived ferroelectric Hf1−xZrxO2 films featuring its possibility of suitable operation for non-volatile analog memory

We have newly developed mist CVD-derived Hf1−xZrxO2 films and investigated their physical properties and basic electrical properties for application to ferroelectric analog memory device such as synaptic device for neuromorphic system. It is observed that the films consisted of microcrystal grain including ferroelectric orthorhombic phase by AFM and GIXRD measurements. Both HfO2 and ZrO2 film with 20 nm thickness showed good fatigue endurance against 109 counts of imposed pulse cycling, where some wakeup phenomena were observed. For a range of electric field (up to 1.5 MV cm−1) as memory-writing input with condition of minor ferroelectric hysteresis loop, a linear relationship between the input and resultant polarization at zero electric field, P(E = 0), was obtained. Finally, it is suggested that those films of HfO2, Hf0.55Zr0.45O2 and ZrO2 are basically applicable for the ferroelectric analog memory device. Further investigation is needed in view of degradation against the input electric field and imposed fatigue pulse.

Detection of neutron irradiaton induced degradation of reactor steel by magnetic method

A novel nondestructive method, based on step by step measurement of minor magnetic hysteresis loops was used to determine the neutron irradiation induced degradation of nuclear reactor pressure vessel steel material. This method is called Magnetic Adaptive Testing (MAT), and two types of reactor steel material were investigated: base material type 22NiMoCr37 and weld material type 18MND5. Charpy geometry samples were irradiated by neutrons at the BR2 in SCK•CEN. The neutron irradiation generated structural changes in the material. As a result of our measurement, it was shown that this degradation could be detected by MAT measurements. Charpy impact tests were also done on the investigated samples and the results of these measurement were compared with the nondestructively determined magnetic quantities. It was shown that a closely linear correlation existed between the ductile-to-brittle transition temperature (DBTT) and MAT parameters.

Simulation tool for the Eddy current magnetic signature (EC-MS) non-destructive method

Magnetism has been used for years as a subsidiary method to identify the level of mechanical residual stress through ferromagnetic steels. It is admitted that residual stress strongly modifies the magnetic behavior and consequently the monitored magnetic signatures. However, some of them like the Eddy Current Magnetic Signature (EC-MS) happen to be especially sensitive. EC-MS exhibits drastic changes, strong enough to predict and anticipate the presence of elastic or plastic deformations. The EC-MS signature is obtained by plotting the imaginary part versus the real part of an Eddy current probe impedance, controlling locally a tested sample under the influence of a slowly varying high amplitude magnetic excitation. The superimposition of the weak amplitude, high-frequency magnetic excitation of the Eddy current probe to the quasi-static contribution creates minor hysteresis loop situations where the reversible magnetic contribution is the main provider. EC-MS is, therefore, an exceptional way to observe and characterize this reversible contribution and this over different average magnetic states. This contribution tends to be particularly sensitive to residual stresses and strains, and so is EC-MS. In this article, the Jiles-Atherton-Sablik theory and an improved Dodd and Deeds analytical solution for the simulation of a pancake-type Eddy current coil are combined to simulate EC-MS. From the simulation results, we illustrate and understand why EC-MS is so sensitive to residual stress. Eventually, we justify this method as probably the most indicated magnetic method for the control and evaluation of residual stresses through structural and construction steels.

Calculation of core loss under distorted flux density with minor hysteresis loops for laminated steel structure

Accurate prediction of core losses has been a crucial aspect in the field of electromagnetics for several decades. Extensive experimental results have shown that the core loss under harmonic excitation is more complicated than that under sinusoidal excitations, which means that the traditional core loss calculation methods are no longer applicable under distorted flux. In order to determine an efficient numerical approach when minor hysteresis loops occur, a harmonic magnetic test platform is used to study the effect of the variation of B–H properties on the iron loss and magnetic flux density of grain oriented silicon steel lamination under different supply voltages. A simple method, which could be used to predict the iron losses in thin laminations due to a number of non-sinusoidal waveforms with or without minor loops, for estimating the iron loss based on the loss separation method is proposed. The errors are substantially lower than those of conventional models while saving time.

Nondestructive Investigation of Neutron Irradiation Generated Structural Changes of Reactor Steel Material by Magnetic Hysteresis Method

The neutron irradiation embrittlement of four different types of nuclear pressure vessel materials (three base metals and one weld material) were investigated by a magnetic nondestructive testing method, magnetic adaptive testing (MAT). The method is based on the measurement of minor magnetic hysteresis loops on Charpy specimens irradiated by neutrons in the BR2 reactor. Due to the neutron irradiation, the structure of the material was modified. The Charpy impact method is suitable for destructive characterization of material embrittlement. The results of Charpy impact test measurements at SCK CEN Belgian Nuclear Research Centre were compared with the nondestructively measured magnetic parameters. A definite correlation was found between magnetic descriptors and the ductile-to-brittle transition temperature (DBTT), regardless of the type of material or irradiation condition. The results suggest that this “calibration curve“ can be used to estimate the DBTT from non-destructive measurements.

Comparison in magnetic properties of ferritic stainless steels measured using bar and ring samples

Stainless steels are an important class of alloys, and are already used in a broad range of applications, especially used as electronic information materials. To take advantage of their magnetic characteristics, many fundamental magnetic problems involving stainless steels must be further studied. In this paper, magnetic measuring of ferrite stainless steels are conducted using the ring samples and bar samples in different magnetic fields, which are both frequently used in industry for quality control. From the magnetic parameters obtained from the major loops of both samples, such as Br, Hc, μ r, Js and H μmax, large differences were found, revealing that, in ferrite stainless steel two kinds of samples can get quite a different result. The reasons are discussed. Furthermore, the benefits of both kinds of samples are discussed in terms of sample dimensions, anisotropy, demagnetization field, and inclusions. Moreover, the typical magnetic data obtained from the major and minor hysteresis loops are also discussed.

Iron Loss Modelling of Electrical Traction Motors for Improved Prediction of Higher Harmonic Losses

A Finite Element (FE) modelling approach is presented to account for the core losses in electrical machines that are generated by higher harmonic frequencies, for example those caused by Pulse Width Modulation (PWM) switching or by space harmonics due to the machine geometry. The model builds further on a post-processing calculation tool that was recently developed to take into account the magnetic skin effect in electrical steel laminations at high frequencies, and extends this by a more detailed loss analysis of the minor hysteresis loops that are caused by the higher harmonics. Further, these tools for high-frequency loss analysis are integrated into a complete electrical machine model with separate consideration of the major and minor loops. The modelling approach relies strongly on extensive magnetic measurement data of the electrical steel, in order to accurately predict the different loss components for minor hysteresis loops as a function of the DC bias field, frequency and amplitude of the minor loop. Results from the model are shown for an automotive traction motor, illustrating the losses caused by PWM harmonics and demonstrating the relevance of including the skin effect in these calculations.

A measurement method of minor hysteresis loss of electrical steel sheet by means of a single sheet tester

This paper investigates measurement methods of iron losses of asymmetric minor hysteresis loops of electrical steel sheets by means of a single sheet tester. As inverter-driven electric machines have been increased, consideration of harmonic iron losses is indispensable to design highly-efficient electric machines. In general, measurement of iron losses of asymmetric minor hysteresis loops has been carried out by using a fluxmeter to detect a dc component in addition to ac components measured by means of a B-coil because the asymmetric minor loops are dc-biased. However, the fluxmeter has a drift problem which results in inaccurate evaluation of harmonic iron losses. Therefore, the distorted waveform method which adopts only ac measurement is conceived. Furthermore, the dc-biased method is improved by estimating the dc components from a normal magnetization curve, which is obtained by connecting tips of symmetric hysteresis loops. In order to demonstrate their effectiveness, the iron losses of asymmetric minor hysteresis loops of non- and high permeability grain-oriented electrical steel sheets are measured up to the high flux density region.

Probing magnetism of individual nano-structures using Nb [formula omitted]-SQUIDs in hysteresis free mode

The magnetization reversal of an individual magnetic nano-structure has been best studied using a μ-SQUID. An optimum inductive shunt helps in eliminating the hysteresis in μ-SQUID’s current voltage characteristics, giving thus a direct voltage readout of magnetic flux with high bandwidth and sensitivity. Here we report on a new μ-SQUID magnetometry setup for studying the magnetism of individual magnetic nano-structures. The switching field anisotropy of Permalloy nano-needles was studied using both hysteretic and non–hysteretic μ-SQUID modes. The observed anisotropy fits well the magnetization reversal through curling mode under the Néel-Brown model as well as micromagnetic simulations. The latter show a reversal through vortex nucleation and annihilation whose signatures we observe through minor hysteresis loops in experiments. Some preliminary magnetization reversal studies on Fe3O4 nano-particles using a non–hysteretic μ-SQUID mode are also briefly discussed.

An Investigation of Magnetic Hysteresis Error in Kibble Balances

Yoke-based permanent magnetic circuits are widely used in Kibble balance experiments. In these magnetic systems, the coil current, with positive and negative signs in two steps of the weighing measurement, can cause an additional magnetic flux in the circuit, and hence, a magnetic field change at the coil position. The magnetic field change due to the coil current and related systematic effects have been studied with the assumption that the yoke material does not contain any magnetic hysteresis. In this article, we present an explanation of the magnetic hysteresis error in Kibble balance measurements. An evaluation technique based on measuring yoke minor hysteresis loops is proposed to estimate the effect. The dependence of the magnetic hysteresis effect and some possible optimizations for suppressing this effect are discussed.

Magnetic and cryogenic magnetocaloric properties of NaGdF4 nanocrystals

We studied the magnetic and magnetocaloric properties of NaGdF4 nanocrystals (NCs), which are crystallized in the P63/m hexagonal structure. Analyzing M(T, H) data, we found an existence of ferromagnetic and antiferromagnetic interactions in NCs. This gives rise to a minor hysteresis loop at temperatures T ≤ 3 K and magnetic fields H = 1–40 kOe. Particularly, at temperatures T = 2–25 K, NaGdF4 NCs show a large magnetocaloric effect (MCE). For a field change ΔH = 60 kOe, the maximum magnetic entropy change (|ΔSmax|) at ∼3.2 K and the relative cooling power (RCP) are about 50.5 J/kg K and 410 J/kg, respectively. These values are larger than those obtained from conventional cryogenic materials reported previously. Having considered the MCE vs the internal field (Hi), we have found that |ΔSmax(Hi)| values increase about 8%–34% compared with the |ΔSmax(H)| values. Magnetic-field dependences of both |ΔSmax| and RCP obey the power law y=axn. The assessments of a magnetic-order exponent n and the analyses of M2(H/M) and N(T,H) data proved NaGdF4 NCs exhibit a short-range magnetic order and undergo a second-order phase transition.

A Non-Linear Permanent Magnet Working Point Migration Model and its Application to Simulation of a Polarized Magnetic System

The paper addresses the issue of the working point migration in non-linear permanent magnets (PM). Starting from the considerations of energy, a novel working-point migration (WPM) model is proposed which can be incorporated into a magnetic equivalent circuit (MEC). The basic theory of working-point migration is discussed which focus on the second quadrant of the magnetic hysteresis loop. The calculation method of the WPM model is proposed based on the relationship between the recoil line model and the affine transformation hysteresis loop. The establishment method for the resultant working point is described by combining the demagnetization curve and the recoil line models in the minor hysteresis loop. The static characteristic of a bistable polarized magnetic system (BPMS), as used in actuators, is calculated using the magnetic circuit method based on the WPM, while a finite element model (FEM) is also derived. The calculation method for the WPM used in MEC is also discussed. The WPM based MEC model yields reasonable results, compared with FEM, of the latching force but with much faster calculation speeds. Furthermore, the working-point state of the PM is clearly illustrated. The test system of the BPMS prototype is established. The test data and WPM model calculation results are compared. It is shown that the WPM model provides accurate prediction of static characteristics of an electromagnetic system.

Depolarization Field in Ferroelectric Nonvolatile Memory Considering Minor Loop Operation

This letter investigates the depolarization field in a metal-ferroelectric-metal-insulator-metal (MFMIM) nonvolatile memory (NVM) considering the minor hysteresis loop operation. Our study indicates that, different from previous studies merely considering the major loop operation, the depolarization field for the ferroelectric undergoing the minor loop increases with decreasing oxide thickness. In other words, in addition to suppressing the gate leakage, thicker oxide thickness is favorable to lower the depolarization field and improves the retention for a given memory window (MW). This letter may provide insights for device design of ferroelectric nonvolatile memories.