First-order Reversal Curve Diagrams Research Articles

FORCinel: An improved algorithm for calculating first‐order reversal curve distributions using locally weighted regression smoothing

We describe a modification to existing algorithms for the calculation of first‐order reversal curve (FORC) diagrams using locally weighted regression smoothing (often referred to as “LOESS” smoothing). The new algorithm offers several advantages over current methods: (1) it allows the FORC distribution to be calculated using a constant smoothing factor all the way to the Hc = 0 axis; (2) noninteger values of the smoothing factor can be specified, enabling finer control over the degree of smoothing and the development of a graphical method for automated selection of the optimum smoothing factor; (3) it performs automated extrapolation across gaps or undefined regions of FORC space. This has two applications: first, bad curves or outlying data points caused by instrumental instabilities can be removed from the data, eliminating artifacts from the final FORC diagram; second, specific regions of interest in the FORC measurement can be masked out in order to investigate their contribution to the final FORC diagram. The new algorithm forms the basis of FORCinel, a new user‐friendly suite of FORC analysis tools with graphical user interface.

Anhysteretic and biased first magnetization curves for Finemet-type toroidal samples

The anhysteretic and a set of biased first magnetization (BFMC) curves together with a set of first-order reversal curves (FORC) were measured and modeled by the hyperbolic T( x) model for a Finemet-type nanocrystalline toroidal sample with a round hysteresis loop. Similar to the FORC diagram, a “fingerprint”-like distribution has been obtained from a set of BFMC curves using the mixed second-derivate method of Pike. It is concluded that while the FORC diagram gives the distribution of coercive fields (or Preisach distribution), the BFMC diagram gives the distribution of the critical field where the domain wall magnetization become unstable and split up.

First order reversal curves identification procedures for vector models of hysteresis

The first order reversal curves (FORCs) technique has been extensively used in the last years for the identification of parameters of Preisach-type models of hysteresis. The technique proved both accurate and robust for the identification of the Preisach distribution function but due to the relatively high computational complexity, it has only been applied to scalar models of hysteresis. The theoretical foundations of the procedure for the identification of parameters of vector Preisach models by using FORCs were established by Mayergoyz. However, to our knowledge, the numerical implementation of the technique has received very little attention in the literature and there is no experimental testing of this technique either. In this paper, we present for the first time results obtained for the identification of the vector Preisach distribution by using FORC diagrams for a magnetic tape with uniaxial anisotropy. We also tested the model with simulated data produced by a vectorial Preisach model in which the pseudoparticles’ equilibrium state was calculated with a Landau–Lifshitz–Gilbert algorithm.

EC-FORC: A New Cyclic-Voltammetry Based Method for Examining Phase Transitions and Predicting Equilibrium

We propose a new, cyclic-voltammetry based experimental technique that can not only differentiate between discontinuous and continuous phase transitions in an adsorbate layer, but also quite accurately recover equilibrium behavior from dynamic analysis of systems with a continuous phase transition. The Electrochemical first-order reversal curve (EC-FORC) diagram for a discontinuous phase transition (nucleation and growth), such as occurs in underpotential deposition, is characterized by a negative region, while such a region does not exist for a continuous phase transition, such as occurs in the electrosorption of Br on Ag(100). Moreover, for systems with a continuous phase transition, the minima of the individual EC-FORCs trace the equilibrium curve, even at very high scan rates. Since obtaining experimental data for the EC-FORC method would require only a simple reprogramming of the potentiostat used in conventional cyclic-voltammetry experiments, we belie ve that this method has significant potential for easy, rapid, in-situ analysis of systems undergoing electrochemical deposition.

Magnetostatic interactions in deep‐sea sediments inferred from first‐order reversal curve diagrams: Implications for relative paleointensity normalization

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.

A first order reversal curve investigation of pressure hysteresis in multiferroics spin transition compound

Spin crossover multiferroic [Fe(PM-BiA)2(NCS)2] is investigated for the first time with the first order reversal curve (FORC) diagram method for its hysteretic pressure behavior. The experimental setup allows the measurements of the high spin fraction as the function of temperature, light intensity, and pressure. The experimental FORC diagrams obtained in compression and releasing modes show significant differences which are in disagreement with the classical Preisach model. Also, stronger kinetic effects are evidenced in the compression mode and possible explanations of this effect considering the viscoelastic behavior are provided.

First-order reversal curve diagrams of magnetic entities with mean interaction field: A physical analysis perspective

A new approach to the quantitative and physical analysis of first-order reversal curve (FORC) diagrams is presented. Each hysteron in the FORC method represents a magnetic cluster. Starting with a model for a ferromagnetic, isotropic, and monodomain sphere, and adding anisotropy and domain structure, three different types of “basic hysterons” are obtained: vertical reversible and irreversible, and linear. The FORC diagrams of basic hysterons with a mean interaction field were obtained by simulation. From them, the relationships between the characteristics of the hysterons and the FORC distribution function were extracted. Different sets of hysterons can lead to the same FORC distribution function. A positive mean interaction field tends to merge the hysterons on the FORC diagram, while a negative mean interaction field introduces repulsion between them.

Early diagenetic greigite as a recorder of the palaeomagnetic signal in Miocene-Pliocene sedimentary rocks of the Carpathian foredeep (Romania)

SUMMARY During the Miocene‐Pliocene, the Carpathian region represented the westernmost part of the so-called Eastern Paratethys, a palaeobioprovince that covered central and eastern Europe as well as parts of southwest Asia. Previous palaeomagnetic investigations provide a highresolution magnetochronology for the sedimentary sequences of the Carpathian foredeep and indicate a marked transition in magnetic carriers from iron oxides to iron sulphides, in Chron C3r. Here, we demonstrate using detailed rock magnetic investigations and scanning electron microscope (SEM) analyses that the major magnetic iron sulphide mineral is greigite (Fe3S4). Thermomagnetic runs indicate an irreversible decrease in magnetization with increasing temperature up to 400 ◦ C and SEM observations indicate octahedral grain morphologies and Fe:S ratios that are indicative of greigite. Hysteresis loops have ‘rectangular’ shapes, which are typical of single domain behaviour, with coercivity and coercivity of remanence at values of Bc = 35‐45 mT and Bcr = 52‐67 mT, respectively. First-order reversal curve diagrams have contours that close around single domain peaks with Bc values of 45‐90 mT. Isothermal remanent magnetization component analysis reveals a small dispersion for the greigite component (dispersion parameter, DP ∼ 0.15 log units) indicating a narrow grain size distribution. A positive fold test, inclination shallowing and two positive reversal tests are additional arguments for the syn-depositional formation of this greigite. We thus argue that (most of) the greigite was formed under early diagenetic conditions, that is, within 1000 yr of deposition of the sediment in this setting, and that it thus can be considered as a reliable recorder of the palaeomagnetic signal in this situation. The appearance of greigite during Chron C3r (between 6.0 and 5.5 Ma) in the Carpathian foredeep is most likely related to regional tectonic and/or climatic events that reshaped the basin configuration and changed the palaeoenvironmental conditions.

First‐order reversal curve (FORC) diagrams of natural and cultured biogenic magnetic particles

First‐order reversal curve (FORC) diagrams are rapidly becoming a standard tool for characterizing magnetic particles because they simultaneously incorporate information regarding magnetostatic interaction and domain states. The simplest interpretation of FORC diagrams of single‐domain (SD) particles is based on the Neel interpretation of Preisach theory, which predicts that the FORC function is the product of a coercivity and an interaction field distribution. Although the underlying assumptions of this interpretation are not correct, a strictly quantitative model of weakly interacting SD grains proves that the distributions of coercivities and interaction fields can be retrieved from a FORC diagram. To test this model, we present the possibility of a quantitative interpretation of FORC diagrams, and we present measurements of samples containing magnetosomes from cultures of magnetotactic bacteria and from a lake sediment. Two samples are investigated under the electron microscope to characterize the geometrical arrangement of the particles. We find that the clustering of otherwise similar particles has a strong influence on FORC diagrams. We also obtained a crude estimate of packing densities form the FORC diagrams, which were consistent with transmission electron microscopy observations and measurements of the anhysteretic remanent magnetization.

Effect of the magnetic field applied during cooling on magnetic hysteresis in the low‐temperature phase of magnetite: First‐order reversal curve (FORC) analysis

The strength of a magnetic field applied during cooling through the Verwey transition can control the low‐temperature (LT) magnetic hysteresis properties of magnetite. This effect is investigated using the first‐order reversal curve (FORC) technique. LT FORC distributions were measured at 20 K from four polycrystalline samples after cooling from 300 K in zero magnetic field or in the presence of a magnetic field (HFC) from a 0.01 to 1.5 T range. The samples represented nearly single‐domain (SD), pseudo‐single‐domain (PSD), and multidomain (MD) magnetic hysteresis behavior. The LT FORC distributions measured from PSD magnetite after zero field cooling are characterized by two distinct maxima located almost symmetrically with respect to the zero interaction field (Hu = 0) axis on a FORC diagram. Application of an intermediate magnetic field (10 mT to 50 mT) during cooling results in a shift of the peaks to near symmetry with respect to the Hu = HFC line. The manifestation of the field‐controlled offset of FORC distribution strongly depends on the direction of the field HFC; the effect is best expressed when a FORC diagram is measured parallel or antiparallel to the cooling field direction. For HFC > 100 mT, the upper peak disappears, and the LT FORC distribution becomes single‐peaked and symmetrical with respect to the Hu = 0 axis. In contrast, no correlation between HFC and features of FORC distributions is observed for SD and MD magnetite. These experimental results provide further support to a phenomenological model which suggests that magnetic hysteresis behavior of monoclinic magnetite is controlled by an intrinsic interplay between the magnetic and crystallographic twin domain structures.

Identification of switching fields in magnetic nanostructures by partial first order reversal curves

A nonparametric approach to the identification of magnetic anisotropies in ferromagnetic nanostructures is described in this article. By an adequate choice of convenient measurement points on the first order reversal curves (FORC), essential information about either switching fields or symmetry of FORC diagrams are obtained from sets of five-point reversal curves only. Numerical simulations performed on assemblies of particles with known switching field distributions indicate that this method presents a high degree of accuracy and can successfully be used in order to characterize individual entities in magnetic nanostructures.

Detection of silica-mediated dissolution of magnetic grains in sediments using FORC diagrams

[1] Recently silica-mediated dissolution has been recognized as a potentially important factor influencing magnetic studies of marine and lacustrine sediments. Although direct evidence for the dissolution of magnetic particles in silica-rich environments is lacking, the process is expected to produce changes in the magnetic grain-size distribution, a hypothesis that is tested in this study on sediments from Lake Tanganyika, East Africa, using First Order Reversal Curves (FORCs). Results from different magnetic intensity zones within the studied samples clearly show changes in the grain-size distribution of magnetic minerals. In particular, zones with high biogenic silica content (BSi) correlated with depletion in fine-grained magnetic material, whereas zones with lower BSi showed no depletion. These results are consistent with the idea that silica-mediated dissolution results in the preferential removal of fine-grained magnetic material, and indicate that FORC diagrams are effective in characterizing silica-mediated dissolution in sediments.

Reversible and quasireversible information in first-order reversal curve diagrams

Two methods for extracting information from first-order reversal curves (FORCs) obtained on low coercivity samples are presented. The proportion of reversibility as a function of applied field can be extracted by calculating the ratio of the initial slope of each FORC to the susceptibility on the major hysteresis loop upper branch at the same field. This gives us the part of the reversal process, a process occurring with zero coercivity, that is, where H=Hr, during the magnetization reversal. In order to be able to see the nonperturbed trace coming from the irreversible processes with a small coercivity compared to the FORC domain, some points have to be added in the H<Hr area in a way that minimizes the discontinuities near H=Hr. This is done by using two functions characterizing the behavior of the magnetization on the H=Hr axis (“extrapolated FORCs”). These methods were used to characterize a CoFeB nanowire array with the applied field perpendicular to the nanowire axis.

Magnetic fingerprints of sub-100nmFe dots

Sub-$100\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ nanomagnets not only are technologically important, but also exhibit complex magnetization reversal behaviors as their dimensions are comparable to typical magnetic domain wall widths. Here we capture magnetic ``fingerprints'' of ${10}^{9}$ Fe nanodots as they undergo a single domain to vortex state transition, using a first-order reversal curve (FORC) method. As the nanodot size increases from $52\phantom{\rule{0.3em}{0ex}}\mathrm{nm}\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}67\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$, the FORC diagrams reveal striking differences, despite only subtle changes in their major hysteresis loops. The $52\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ nanodots exhibit single domain behavior and the coercivity distribution extracted from the FORC distribution agrees well with a calculation based on the measured nanodot size distribution. The 58 and $67\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ nanodots exhibit vortex states, where the nucleation and annihilation of the vortices are manifested as butterflylike features in the FORC distribution and confirmed by micromagnetic simulations. Furthermore, the FORC method gives quantitative measures of the magnetic phase fractions, and vortex nucleation and annihilation fields.

Experimental and micromagnetic first-order reversal curves analysis in NdFeB-based bulk “exchange spring”-type permanent magnets

In this paper we present the results of applying the first-order reversal curves (FORC) diagram experimental method to the analysis of the magnetization processes of NdFeB-based permanents magnets. The FORC diagrams for this kind of exchange spring magnets show the existence of two magnetic phases—a soft magnetic phase and a hard magnetic one. Micromagnetic modeling is used for validating the hypotheses regarding the origin of the different features of the experimental FORC diagrams.

Hysteresis and tunability characteristics of Ba(Zr,Ti)O 3 ceramics described by First Order Reversal Curves diagrams

The First Order Reversal Curves (FORC) diagrams method is proposed for the characterization of the switching process and ac-tunability in BaZr 0.10Ti 0.90O 3 ceramics prepared via solid state reaction. The properties induced by different microstructures, having two extreme grain sizes of 0.75 and 3.3 μm are investigated by monitoring the changes of the FORC diagrams. The maximum of FORC distribution is located at low fields independently on the grain size and no clear separation between the reversible/irreversible contributions to the polarization are found. A higher degree of the local inhomogeneity is characteristic to the fine ceramic. The FORC susceptibility related to the ac-tunability determined on the major hysteresis loop is very sensitive to the grain size: it is much smaller in the fine material, due to the pinning of the domain walls by different types of defective areas.

Characterization of hematite (α‐Fe2O3), goethite (α‐FeOOH), greigite (Fe3S4), and pyrrhotite (Fe7S8) using first‐order reversal curve diagrams

First‐order reversal curve (FORC) diagrams have become a standard tool in rock magnetism, yet magnetite is the only magnetic mineral that is well characterized using FORC diagrams. We present FORC diagrams for predominantly single‐domain (SD) synthetic aluminous hematite (α‐Fe2‐xAlxO3) and goethite (α‐(FeAl)OOH) and natural greigite (Fe3S4) and pyrrhotite (Fe7S8) to constrain interpretation of FORC diagrams from natural samples. Hematite and goethite have low spontaneous magnetizations and negligible magnetic interactions, while greigite and pyrrhotite have higher spontaneous magnetizations and can have strong magnetic interactions. The coercivity of hematite systematically increases with Al content only for samples produced using the same synthesis method, but it is variable for samples produced with different methods even for similar Al content. This precludes use of magnetic coercivity alone to quantify the Al content of natural hematites. Goethite has much higher coercivity than hematite for all measured samples. SD and superparamagnetic (SP) behavior is common in natural greigite samples, with peak coercivities ranging from ∼70 mT (SD) to zero (SP). This range overlaps with that of lower‐coercivity minerals, which can make greigite identification ambiguous at room temperature. Fine‐grained SD pyrrhotite has slightly higher coercivities than greigite, which progressively decreases with increasing grain size within the SD size range and overlaps the range for greigite. While FORC diagrams are useful for magnetic characterization, care is needed in interpretation because of overlaps in the broad range of magnetic properties, which result from variations in domain state, for any magnetic mineral with respect to other minerals.

Increasing the efficiency of paleointensity analyses by selection of samples using first‐order reversal curve diagrams

The global paleointensity database is restricted by the high failure rate of paleointensity analyses. Excluding thermal alteration, failure is usually caused by the presence of multidomain grains and interactions among grains, two properties that can be identified using first‐order reversal curve (FORC) diagrams. We measured FORC diagrams on sister samples of about 200 samples that had been used for Thellier paleointensity determinations and determined criteria to discriminate samples that gave acceptable paleointensity results from those that did not. The three most discriminating criteria are the vertical spread of the FORC distribution (indicative of interactions), expressed as the full width at half maximum (FWHM), the spread of the FORC distribution along the Hc = 0 axis (width), and the bulk coercivity Hc (both indicative of domain state). Setting thresholds at 132 mT for the width of the distribution and 29 mT for the FWHM maximizes the number of unsuccessful rejected samples. Using an additional threshold of Hc = 5.4 mT results in rejection of 32% of unsuccessful samples. Seven samples that barely satisfy the paleointensity selection criteria would also be rejected using these selection criteria. Most of the samples that fail the paleointensity experiment without being detected by our selection criteria have ideal noninteracting single‐domain magnetic properties but fail because of the thermal alteration that results from repeated heating. Being able to eliminate at least one third of unsuccessful samples using our FORC diagram‐based prescreening procedure should provide a significant improvement in efficiency of paleointensity measurements.

Analysis of switching properties of porous ferroelectric ceramics by means of first-order reversal curve diagrams

Particular aspects of the switching properties of the Nb-PZT ceramics with anisotropic porosity (40% relative porosity) were investigated by comparison with the dense ceramics (5% relative porosity) of the same composition by means of the first-order reversal curve (FORC) analysis. The reversible/irreversible components give different contributions to the total polarization: A sharp FORC distribution with an almost negligible reversible component is characteristic to the dense material, while a broad distribution with an important reversible component is characteristic for the porous one. The coercivity corresponding to the maximum of the irreversible component is the same irrespective to the sample density and pore's configuration with respect to the electrodes: ${E}_{c,M}=1.5\phantom{\rule{0.3em}{0ex}}\mathrm{kV}∕\mathrm{mm}$, while the bias fields are zero for the dense ceramic, small and positive; ${E}_{\text{bias},M}=50\phantom{\rule{0.3em}{0ex}}\mathrm{V}∕\mathrm{mm}$, when the major axis of the elongated pores is parallel with the electrodes and negative; ${E}_{\text{bias},M}=\ensuremath{-}100\phantom{\rule{0.3em}{0ex}}\mathrm{V}∕\mathrm{mm}$, when this axis is perpendicular to the electrodes. The influence of the dipolar coupling leading to such bias fields is explained by considering that the particular microstructure is causing a symmetry breaking, decoupling the dipolar interaction (forward or laterally). A dipolar (discrete) model with random orientations of the dipoles' directions was used to simulate this confinement effect. The calculated FORC diagrams lead to the same type of bias as the experimental ones, proving that the lateral confinement gives an intrinsic contribution to the biased $P(E)$ loops observed for the porous ceramics. In addition with other possible extrinsic contributions, this dipolar coupling can be a source of the built-in field in confined ferroelectric structures. The experimental FORC distribution was used as input in a Preisach-type model to recompose the major and symmetric minor hysteresis loops and a remarkable agreement with the experimental data was obtained. The FORC method proves to be an excellent tool in describing the ferroelectric systems, simulating polarization experiments, and predicting outputs of the circuits with ferroelectric capacitors. In the particular case of the porous anisotropic ceramics, the combined experimental and analytical FORC analysis allowed us to probe and to describe qualitatively the presence of the bias field as a result of the geometrical confinement.

Low‐temperature magnetic properties of magnetite using first‐order reversal curve analysis: Implications for the pseudo‐single‐domain state

Low‐temperature magnetic hysteresis properties of nearly stoichiometric magnetite were studied using the first‐order reversal curve (FORC) technique. FORC distributions were measured at 20 K after cooling in zero magnetic field or cooling in the presence of a strong (1.5 T) magnetic field. Five polycrystalline samples ranged in mean grain size and shape, representing mostly single‐domain (SD), pseudo‐single‐domain (PSD), and multidomain (MD) magnetic hysteresis behavior. The FORC distributions measured from PSD magnetite after zero field cooling (ZFC) manifest an unusual behavior, characterized by two distinct maxima located almost symmetrically with respect to the zero interaction field (Hu = 0) axis on a FORC diagram. In contrast, the low‐temperature FORC distributions for SD and MD samples have a single maximum located at the Hu = 0 axis. The appearance of two maxima on low‐temperature FORC distributions is interpreted as a manifestation of a perminvar‐like behavior due to stabilization of the magnetic domain structure by irregularities of crystalline lattice induced by twinning in monoclinic magnetite. The experimental data suggest that the effect of monoclinic twinning on remagnetization is only pronounced within a certain grain size range. The double‐maxima ZFC FORC distribution appears to be a distinctive property of PSD hysteresis behavior, which cannot be reproduced by mixing SD and MD magnetites.