Comparison of Preisach and Congruency-Based Static Hysteresis Models Applied to Non-Oriented Steels

Study of bistable behaviour in interacting Fe-based microwires by first order reversal curves

In this article, we provide a detailed description of a modeling technique for the capillary hysteresis in a soil-like porous material based on a Generalized Preisach Model. The identification of the reversible and irreversible Preisach distributions was performed with the first-order reversal curve (FORC) diagram technique, which is very popular now in magnetism and in other areas of science to give a fingerprint of the studied system. A special attention was given to the evaluation of the reversible component. In this case, we used a set of data published in 1965 by Morrow and Harris which has been used as a reference by many other researchers since. The advantage of this approach is that the experimental FORC distributions can be described with analytical functions and easily implemented in the mentioned Preisach-type model. Our research is also focused on the development of a characterization tool for the soil using the soil-moisture hysteresis. The systematic use of scanning curves provides a (FORC) diagram linked to the physical properties of the studied soil. The agreement between the experimental data and the Preisach model using the set of parameters found through the FORC technique is really noticeable and gives a good practical option to the researchers to use a method with a strong predictive capability.

Nonlinear diffusion and the Preisach model of hysteresis

<sec> From physical point of view, the “0, 1” read/write operation of ferroelectric memory is based on the polarization switching of ferroelectric memory. Therefore, the reliability of device relies directly on the stability of polarization switching behavior. The polarization behaviors of HfO<sub>2</sub>-based ferroelectric thin films subjected to bipolar cyclic electric field often exhibit wake-up, fatigue and split-up of transient switching current. These unstable switching properties seriously restrict the practical application of this new-type ferroelectric material in memory devices. It therefore becomes the critical task to explore the mechanism behind the complex evolution of polarization switching and find out possible approaches to optimizing the stability. However, it will be extremely difficult to accomplish the task by the traditional characterization methods. First-order reversal curve (FORC) diagram is regarded as “fingerprint identification” in the study of hysteresis systems, and has been used successfully to analyze the characteristic parameters of magnetic materials. The FORC diagram can intuitively determine the type, size and domain status of magnetic particles from distribution of both coercive field and interaction field. Moreover, it is also found that the FORC diagram is sensitive to measuring temperature. </sec><sec> In this work, first, the Preisach model and implementation method of the FORC diagram are introduced. Then using Keithley 4200-SCS equipped with a remote pulse measurement unit, 60 FORCs are recorded for Si-doped HfO<sub>2</sub> ferroelectric thin films experiencing different external field loading histories. By the mathematical treatment, switching density distributions determined by FORC measurements are obtained to explore the evolution of coercive field and bias field. The FORC diagram of pristine film contains three distribution regions with different bias fields, which merge into one distribution with an almost zero bias field after 10<sup>4</sup> wake-up cycles. Two oppositely biased regions can be observed after 2 × 10<sup>9</sup> sub-cycling treatments. Surprisingly, the bias fields nearly vanish again after 10<sup>4</sup> wake-up cycles. The main change of bias field instead of coercive field indicates that the migration of oxygen vacancies is likely to be the dominant mechanism behind the complex polarization switching behavior for HfO<sub>2</sub>-based ferroelectric thin films.</sec>

In this paper, the authors propose a simple and numerically efficient interpolation algorithm capable to approximate the First Order Reversal Curves (FORC) distribution in any point. Using this algorithm as input for a classical Preisach Model one can obtain the magnetization curves of the system used in FORC measurements. In order to improve the precision of the calculus one can adapt different strategies form different variants of Preisach model.

We have studied the use of self-assembled block copolymers to pattern multilayers of Co and Pd on silicon wafers. Stacks ranging from 4 to 12 bilayers of Co(0.3 nm)/Pd(0.8 nm) were sputtered onto Ta/Pd seed layers and capped with 3 nm of Ta, and were found to have perpendicular magnetic anisotropy as-deposited. The block copolymer, PS-PFS, was dissolved in toluene and spun onto the wafers. After heat treatment to phase-separate the polymers, the PS was removed by oxygen plasma ashing. The remaining polymer, PFS, formed self-assembled spheres that were used as masks to ion-mill the Co/Pd multilayers into nanopillars [1]. To study the effect of etch time and etch angle on the coercivity distribution, we synthesized samples in a “design of experiments” grid in these two variables. Scanning electron micrographs showed nanopillars ranging from 10 to 30 nm in diameter, depending primarily on etch time (Fig. 1). M-H loops measured on both patterned and unpatterned wafers showed an increase of up to 113% in coercivity upon patterning. First Order Reversal Curves (FORC) were measured, and the resulting FORC distributions showed different features for the nanopatterned vs. unpatterned films. Fig. 2 shows the FORC curves and the resulting FORC distribution for an unpatterned multilayer [Co/Pd] plotted by (1) FORC+ (MagVis.org), which shows the exact measured FORC density without averaging and (2) the more often used averaged color map, in which information is lost. Both displays show a large positive peak with coercivity (Hc) about 500 Oe, with a “dipole tail” characteristic of switching by domain nucleation and wall motion [2]. In the FORC+ plot, the tail consists of a string of negative (blue, on the left) and positive (orange, on the right) pixels – the variation of density along the tail is smaller in the averaged curve, but this comes at the expense of greatly overestimating the separation between the positive and negative tails.  Fig. 1. SEM image of a patterned [Co(0.3 nm)/Pd(0.8 nm)]12 film: 20 nm diameter pillars. . Fig. 2. Top: FORC curves M(H). Bottom right: FORC+ distribution. Orange is positive, blue negative Left: Smoothed FORC distribution, on the same scale but displaced to left, with color legend.

In Part II of this two-part study, system simulations and experimental correlations of a Shape Memory Alloy (SMA) based vibration isolation device (briefly described in Part I) has been presented. This device consists of layers of preconstrained SMA tubes undergoing pseudoelastic transformations under transverse dynamical loading. In Part II, detailed description of the prototype vibration isolation device, its experimental setup, and actual experimental test results are presented. An extensive parametric study has been conducted on a nonlinear hysteretic dynamical system, representing this vibration isolation device utilizing a physically based simplified SMA model and a Preisach model (an empirical model based on system identification) developed in Part I. Both the physically based simplified SMA model and the modified Preisach model have been utilized to perform experimental correlations with the results obtained from actual testing of the device. Based on the investigations, it has been shown that variable damping and tunable isolation response are major benefits of SMA pseudoelasticity. Correlation of numerical simulations and experimental results has shown that large amplitude displacements causing phase transformations of SMA components present in such a device are necessary for effective reduction in the transmissibility of such dynamical systems. It has also been shown that SMA-based devices can overcome performance trade-offs inherent in typical softening spring-damper vibration isolation systems. In terms of numerically predicting the experimental results, it has been shown that the Preisach model gave relatively accurate results due to better modeling of the actual SMA tube behavior. However, for a generic parametric study, the physically based simplified SMA model has been found to be more useful as it is motivated from the constitutive response of SMAs and hence, could easily incorporate different changes in system conditions.

The first-order reversal curves (FORC) diagram method for the characterization of magnetic materials and of other materials showing hysteretic phenomena is gradually replacing the classical use of the major hysteresis loop or of other selection of magnetization curves. The FORC diagram offers to the experimentalist an image of the sample which can be related to the coercivity and interactions fields acting on the magnetic entities within the sample. Of course, this information should be analyzed carefully since errors in interpretation can be possible in the absence of other related physical or phenomenological models. However, in the wider use of the FORC diagram method there are a number of obstacles. One major problem is that the FORC distribution is not usually easily represented by analytical functions and due to that inconvenient are difficult to handle in Preisach-type simulations. Another solution would be to evaluate the geometric properties of the FORC distribution using statistical formulae applied directly to the experimental FORC. In our previous work [Tanasa et al., 2005], we have presented such a statistical approach of the experimental FORC diagram measured on the thermal hysteresis of spin-transition materials. In the full paper we are presenting in details a set of statistical parameters which can be used directly on experimental FORC distribution.

We report a study of magnetization reversals and skyrmion configurations in two systems, Pt/Co/MgO and Ir/Fe/Co/Pt multilayers, where magnetic skyrmions are stabilized by a combination of dipolar and Dzyaloshinskii–Moriya interactions (DMIs). The First Order Reversal Curve (FORC) diagrams of low-DMI Pt/Co/MgO and high-DMI Ir/Fe/Co/Pt exhibit stark differences, which are identified by micromagnetic simulations to be indicative of hybrid and pure Néel skyrmions, respectively. Tracking the evolution of FORC features in multilayers with dipolar interactions and DMI, we find that the negative FORC valley, typically accompanying the positive FORC peak near saturation, disappears under both reduced dipolar interactions and enhanced DMI. As these conditions favor the formation of pure Néel skyrmions, we propose that the resultant FORC feature—a single positive FORC peak near saturation—can act as a fingerprint for pure Néel skyrmions in multilayers. Our study thus expands on the utility of FORC analysis as a tool for characterizing spin topology in multilayer thin films.

Nanostructured silicon can be used as versatile host material for various magnetic materials, especially a quasi-regular arrangement of the pores / tubes leads to specific magnetic properties occurring from magnetic interactions between the metal-deposits.In the frame of this presentation magnetic interactions between metal deposits embedded within the pores or tubes are investigated. Composite systems consisting of porous silicon (PSi) and silicon nanotubes (SiNTs) with embedded Ni, Co, NiCo and Fe3O4 structures are discussed. Ni, Co and NiCo are electrochemically deposited within the pores by modifying the deposition parameters to achieve deposits with specific geometries. Fe3O4 nanoparticles are previously synthesized and then infiltrated within the nanostructured silicon materials.Magnetic cross-talk between metal deposits can be controlled by the morphology of the PSi (distance between the pores) or SiNTs (wall thickness) and also by the distribution, size and shape of the deposits within the pores. To get a clear knowledge about the magnetic interactions single hysteresis curves are not sufficient and thus first order reversal curves (FORC) are performed at various temperatures. Composites consisting of elongated metal nanostructures and such with embedded nanoparticles are examined and compared. Figure 1 shows the FORC measurement with corresponding FORC diagram of a PSi sample with deposited Co particles which do not magnetically interact.A further realm of this work is the investigation of the temperature-dependency of the magnetization of the nanocomposite systems. The temperature dependent magnetization measurements of the composite systems allow the determination if the samples are ferro- or superparamagnetic, which is an inherent property of isolated particles below a certain critical size. Annealing leads to metal silicide formation which weakens the ferromagnetic behavior. In general magnetite nanoparticles (NPs) are modified in their structural and magnetic phase by the annealing process due to oxidation which leads to different magnetic characteristics. In this work the high-temperature measurements are performed under Ar gas which prevents oxidation of the samples. The magnetic response of the various systems is recorded in dependence on the temperature between 80 and 1273 K to figure out the Curie temperature (TC) of the composites. TC is determined for the different composite systems and compared with the ones of the corresponding bulk materials showing that systems with embedded nanostructures in the range of a few hundred micrometers offer lower TC and such with small nanoparticles much higher TC than the corresponding bulk materials which can be interpreted by some structural change due to the annealing. The lower TC for the samples with elongated metal structures is driven by the fact that the deposits are not essentially single domain.Figure 1: FORC measurements and FORC diagram (inset) of Co-particles of about 60 nm in size deposited in a loose distribution within porous silicon. Magnetic interaction between the particles is not present. Figure 1

A new type of characterization of ferroelectric switching using First Order Reversal Curve (FORC) diagrams based on recording of minor hysteresis loops has been recently proposed. We apply this method to polycrystalline and epitaxial PZT thin films measured under various conditions and compare them to PZT ceramics. In each case we have been able to separate the reversible and irreversible contributions to switching and discuss the most dominant of them in relation to hysteresis loop shapes and ferroelectric switching mechanisms. The FORC diagrams of fatigued PZT exhibit features in agreement with its hysteresis probed at nanoscale and confirm a degradation mechanism based on local imprint. The asymmetrical tail present on measured FORC diagrams has been explained in terms of a nucleation-growth switching process triggered by latent nuclei. All these findings attest the usefulness of the FORC diagrams for both characterizing various types of samples as well as the elucidation of ferroelectrics’ physics.

First-order reversal curves (FORC) and the FORC distribution provide a detailed characterization of the relative proportions of reversible and irreversible components of the magnetization of a material, revealing the dominant interactions in the system. Alloys with the nominal composition SmFe2 were obtained by melt-spinning with a cooper wheel velocity of 30 m/s. X-ray powder diffraction analysis showed a greater part consisting of an amorphous phase and a very small amount of SmFe2 crystalline phase with an average crystallite size of 8 nm. A constant acceleration Mössbauer spectrum, measured at room temperature in transmission mode, was fitted to a continuous distribution of effective fields at the nucleus of the amorphous phase (about 84% of the total area), plus two sextets for the non-equivalent sites of Fe in the SmFe2 crystalline phase. 91 first-order reversal curves were collected in a Quantum Design PPMS-VSM with reversal fields from –800 mT to +800 mT and using a calibration field of 850 mT. The obtained FORC diagrams showed a combined effect of a local interaction field and a mean interaction field, and showed that the reversible magnetization is a function of both, the applied magnetic field and the irreversible magnetization.

Understanding magnetostatic interactions in sediments is important for paleomagnetism and rock magnetism. Magnetostatic interactions are known to affect significantly the efficiency of anhysteretic remanent magnetization (ARM) acquisition, and hence the ratio of ARM susceptibility (χARM) to saturation isothermal remanent magnetization (SIRM), a magnetic grain‐size proxy widely used for environmental applications, can be controlled by magnetostatic interactions. Relative paleointensity estimations may also be influenced by magnetostatic interactions because ARM is often used as a normalizer to correct for the difference in magnetizability of sediments. In this study, characterization of magnetic grains in deep‐sea sediments from the North Pacific Ocean was conducted using first‐order reversal curve (FORC) diagrams and IRM acquisition curves. The FORC diagrams indicate that the magnetic grains consist mainly of a noninteracting single‐domain (SD) component and an interacting SD component, and additionally of a multidomain (MD) component. The relative abundances of these components were semiquantitatively estimated by curve fitting of cross sections along a line parallel to the axis of local interaction fields (Hu) and through a peak in the coercivity (Hc). Three components were fitted assuming a Gaussian distribution of interaction fields (Hu). The IRM acquisition curves can be described by two dominant components assuming a log‐Gaussian distribution. The mean coercivities of the two components are ∼40 and ∼100 mT, respectively. It is estimated that the former component is carried by biogenic magnetite, and roughly corresponds to the noninteracting SD component derived from the FORC diagrams, and that the latter component is carried by eolian maghemite, corresponding to the interacting SD component. The χARM/SIRM ratio decreases with increasing concentration of the interacting SD component. This implies that the χARM/SIRM ratio is significantly affected by magnetostatic interactions and that it does not necessarily reflect magnetic grain size. The effect of magnetostatic interactions on natural remanent magnetization acquisition in sediments is not well understood, but if it is similarly sensitive to the SIRM, normalization by ARM in relative paleointensity estimations would overcompensate for the concentration of magnetic grains and cause the significant coherence between the normalized intensity and the normalizer that has been reported in the literature.

We describe a method for simulating first‐order reversal curve (FORC) diagrams of interacting single‐domain particles. Magnetostatic interactions are calculated in real space, allowing simulations to be performed for particle ensembles with arbitrary geometry. For weakly interacting uniaxial particles, the equilibrium magnetization at each field step is obtained by direct solution of the Stoner‐Wohlfarth model, assuming a quasi‐static distribution of interaction fields. For all other cases, the equilibrium magnetization is calculated using an approximate iterated solution to the Landau‐Lifshitz‐Gilbert equation. Multithreading is employed to allow multiple curves to be computed simultaneously, enabling FORC diagrams to be simulated in reasonable time using a standard desktop computer. Statistical averaging and post processing lead to simulated FORC diagrams that are comparable to their experimental counterparts. The method is applied to several geometries of relevance to rock and environmental magnetism, including densely packed random clusters and partially collapsed chains. The method forms the basis of FORCulator, a freely available software tool with graphical user interface that will enable FORC simulations to become a routine part of rock magnetic studies.

The magnetization process and switching field distribution (SFD) of ion beam patterned MnGa films were discussed based on the first-order reversal curve (FORC) analysis and magnetic force microscope (MFM) observations. The FORC diagrams with so-called “boomerang” shape resulting from the increase of the interaction between “hysterons” that can be associated with ferromagnetic particles and/or domains were confirmed in the patterned MnGa with dot size larger than 520 nm. On the other hand, the shape of the FORC diagram became a simple Gaussian distribution, which is typical in the media comprised of well-isolated magnetic particles, for dot size smaller than 240 nm. The variation of the shape of FORC diagram was closely linked with the domain structure observed by MFM; multidomain in the dot was confirmed for dot size larger than 520 nm while single domain for dot size less than 240 nm. The average switching field of the patterned film increased with decreasing the dot size, indicating that the dot edge damage and exchange interaction through ion-irradiated regions were negligible in the ion-beam patterned MnGa. The SFD also increased with decreasing the dot size. The SFD is considered to result from the existence of the pinning centers in the as-prepared MnGa and also from the dot size fluctuation of the resist masks fabricated by electron beam lithography. The optimization of the fabrication process will be effective to reduce SFD and sufficiently low SFD in high-density MnGa bit patterned media will be achieved by these process optimizations.