First-order Reversal Curve Diagrams Research Articles

VARIFORC: An optimized protocol for calculating non-regular first-order reversal curve (FORC) diagrams

High-resolution first-order reversal curve (FORC) diagrams are increasingly employed to characterize magnetic minerals in sediments, and especially as a magnetofossil detection tool. Conventional processing protocols, however, are not well suited for this purpose because the opposed needs of high resolution and smoothing of noisy data over different regions of the FORC diagram cannot be reconciled. This problem is particularly severe in samples containing non-interacting single-domain particles, whose FORC signature is described by an infinitely narrow, divergent feature called a central ridge. In this paper, a new FORC processing protocol called VARIFORC (VARIable FORC smoothing) is presented for the analysis of non-regular FORC functions, such as those featuring a central ridge. This protocol is based on weighted polynomial regression of rectangular arrays of measurement points whose size is determined by the local properties of the FORC function (i.e. small arrays where high resolution is needed and vice-versa). The resulting FORC diagram is characterized by improved signal-to-noise ratios that pass significance tests over much larger domains. This enables simultaneous quantitative analysis of FORC signatures corresponding to different magnetization processes (e.g. the central ridge produced by single-domain particles and a weak, extended background due to detrital magnetic minerals). VARIFORC has been successfully tested on a magnetofossil-bearing pelagic carbonate sample that has a non-regular FORC function, and on a volcanic ash sample with a typical pseudo-single-domain signature. An unexpected minor central ridge contribution, which is invisible to traditional processing, has been detected in the volcanic ash sample. This finding demonstrates the effectiveness of the new FORC processing protocol and potential new applications of high-resolution FORC measurements.

Micromagnetics and magnetomineralogy of ultrafine magnetite inclusions in the Modipe Gabbro

Iron oxide inclusions in pyroxene crystals from the Modipe Gabbro, Botswana, have been studied to determine their recording fidelity. Hysteresis parameters, first‐order reversal curves, isothermal remanent magnetization acquisition curves, and thermomagnetic data all indicate that the iron oxide occurs as stoichiometric magnetite in the form of single‐domain and/or small pseudo single‐domain particles. Using distributions for the grain shape and nearest‐neighbor spacings determined from optical micrographs as input, a first‐order reversal curve (FORC) diagram was simulated using a numerical micromagnetic model. The simulated FORC diagram was found to closely match the measured FORC distributions. Analysis of the interaction fields in the model found that the standard deviation of the interaction field distribution was 2.7 mT compared to a bulk coercivity of ~20 mT, suggesting that the majority of particles are unlikely to be affected by magnetostatic interactions. Thellier analysis of the samples induced with an initial laboratory thermoremanence yielded near‐perfect behavior. It is suggested that the Modipe Gabbro dated at 2784.0 ± 1.5 (2σ) Ma is potentially an ideal recorder of the geomagnetic field.

Magnetostatic Interaction Investigation of CoFe Alloy Nanowires by First-Order Reversal-Curve Diagrams

Magnetic CoFe alloy nanowires were alternating current (ac)-pulse electrodeposited into the nanopores of hard anodized aluminum oxide templates. The effect of nanowires lengths on the magnetostatic interactions was investigated using first-order reversal-curve (FORC) method. FORC diagrams obtained from nanowire arrays with different lengths show drastic improvement in magnetic properties with decreasing the nanowires length. The coercivity reaches 995 Oe from initially 790 Oe. Also, the squareness enhances from 0.62 to 0.92, showing the decrease in magnetostatic interactions between the nanowires. FORC diagrams prove the decrease in magnetostatic interactions in nanowires with shorter lengths. With decreasing the nanowires length, the spread of distribution in the Hu-direction decreases. It varies from 1600 to 900 Oe when length decreases from 27 to 8 μm. FORC diagrams also reveal formation of nanowire arrays with dominant interacting single domain (SD).

What does a first-order reversal curve diagram really mean? A study case: Array of ferromagnetic nanowires

The magnetic characterization technique of hysteretic materials based on the measurement of the first-order reversal curves (FORC) is one of the most appealing methods recently introduced in hundreds of new laboratories, but due to the complexity of the FORC data analysis, it is not always properly used. This method originated in identification procedures for the classical Preisach model and consequently often the FORC distribution is interpreted as a slightly distorted Preisach distribution. In this paper, we discuss this idea from two points of view derived from the basic assumptions used in the Preisach model. One is that the interaction field is equivalent with a shift of the rectangular hysteron along the applied field axis without changing the intrinsic coercivity. The other is the direct use of switching fields as coordinates, in fact, the ones defining the Preisach plane. We discuss the compatibility between the experimental FORC distribution and the Preisach model developed on the interaction field hypothesis. As a “toy model,” we are using a system of ferromagnetic nanowires, explaining from the physical point of view the complex FORC diagrams as they are obtained in experiments. This explanation gives a fundament for the correct interpretation of the FORC diagram in order to get “Preisach type” information about the system, mainly about the distributions of coercive and interaction fields within the sample. These results are relevant for many ferromagnetic systems and give a valuable guide for understanding the FORC technique and its fundamental link with the Preisach model.

A novel method for identifying the local magnetic viscosity process of heterogeneous magnetic nanostructures

The relaxation mechanism known as magnetic viscosity has been attracting the attention of the scientific community for more than seven decades. However, a complete model to fully describe the phenomenon is difficult to achieve, owing to its possible different sources and microscopic mechanisms. This work proposes a new experimental approach, based on the combination of static and dynamic first-order reversal curve diagrams. With this technique, one can decouple the responsible mechanism presented by different phases of an inhomogeneous magnetic sample. Moreover, it can also be used to distinguish the microscopic origin of magnetic viscosity (i.e. eddy currents or thermal activation). We successfully applied this novel approach to characterize the local viscosity processes occurring in a nanocrystalline Fe-based soft magnetic ribbon. Owing to the generality of its principles, it can be used to investigate the viscosity of a wide range of systems.

Mean field model for ferromagnetic nanowire arrays based on a mechanical analogy

Nanowire arrays have typical distributions of coercive and interaction fields, as revealed in experiments by means of the first-order reversal curve (FORC) method. In an axial applied field, each nanowire is subjected to a state dependent interaction field created by all wires from the array, which strongly influences the switching fields. A mean field model based on Preisach–Krasnosel’skii–Pokrovskii (PKP) hysterons is able to explain the interplay between interactions and critical fields in nanowire arrays and the subtle way in which switching fields are emphasized in FORC diagrams.

Magnetic characterization of FeCo nanowire arrays by first-order reversal curves

FeCo nanowire arrays have been obtained by current pulse electrodeposition into nanoporous alumina templates. First-order reversal curve (FORC) diagrams have been used to investigate magnetostatic interaction and average coercivity of individual FeCo nanowires embedded in porous alumina templates. The FeCo nanowires with a wires length up to 3 μm and wires diameter ranging from 25 to 50 nm showed interacting single-domain behavior. Using FORC diagrams, the spread of coercivity distribution was seen to be almost independent of the wires diameter, but with increase in diameter the inter-wire magnetostatic interaction was increased. It was found that for arrays with higher diameter, the coercivity of the arrays is lower than the average coercivity of the individual wires. It was detected that an increase in wire diameter results in a considerable increase in the spread of the distribution in the Hu direction of FORC distribution. Curve fitting on the experimental data proved a relatively linear relation between interaction field and square diameter of the nanowires.

Physical study of the Cucuteni pottery technology

Most of our knowledge concerning the Cucuteni pottery is based on traditional archaeological methods (typology, style and context analysis) and only a few interdisciplinary studies have been published. As there is a strong interest in revealing the basic pottery technology used by the Cucuteni communities we have investigated a significant number of pottery samples from 22 archaeological sites located in Eastern Romania by several physical analysis techniques: X-ray diffraction (XRD) and by magnetic measurements, including a first-order reversal curve (FORC) diagram study on the samples showing a hysteretic behavior. The main results presented in this study are discussed and compared with actual knowledge on the ancient Cucuteni pottery.

PKP simulation of size effect on interaction field distribution in highly ordered ferromagnetic nanowire arrays

Abstract Perpendicular structured nanowire arrays interaction field distributions (IFDs), as revealed from first-order reversal curves (FORC) diagrams, are related to the presence of the demagnetizing field in the system. Despite the similarity between the geometric properties of bit patterned media and mentioned nanowire arrays, FORC diagrams of these two types of systems are not similar essentially due to the different number of magnetic entities influencing the switch of an individual element. We show that one Preisach–Krasnosel'skii–Pokrovskii (PKP) symmetrical hysteron can be representative of an ideal infinite nanowire array when the field is applied along the wires. Starting from this observation, we present a very simple model based on PKP symmetrical hysterons that can be applied to real finite ferromagnetic nanowire arrays, and is able to describe a wide class of experimentally observed FORC distributions, revealing features due to size effects. We also present IFDs modeled for different geometric characteristics such as array size, interwire distance, and nanowire dimensions, and an identification procedure for the proposed model.

Investigation of the composition-dependent properties of BaTi1−xZrxO3 ceramics prepared by the modified Pechini method

Single phase and dense BaTi1−xZrxO3 (BTZ) ceramics (x = 0.10, 0.15 and 0.20) were obtained from nanopowders synthesised by the modified Pechini method. The evolution of both Raman spectra and low-field dielectric properties against temperature indicated the occurrence of diffuse ferroelectric–paraelectric phase transitions for all the BTZ compositions under investigation. The evolution of first-order reversal curves (FORC) diagrams emphasised the crossover from the ferroelectric towards the relaxor state as the Zr content increased. Lower values of the Curie temperatures than those usually reported earlier in the literature were obtained for all the BTZ samples analysed here. The high-field tunability data completed the low-field and Raman results, showing that by increasing Zr addition, multiple polarisation components with various weights are responsible for the dielectric and ferroelectric properties.

Magnetization processes in micron-scale (CoFe/Pt)n multilayers with perpendicular anisotropy: First-order reversal curves measured by extraordinary Hall effect

First-order reversal curves (FORCs) were recorded using the extraordinary Hall effect in micron-sized crosses of [Co90Fe10 (0.5 nm)/Pt (1.0 nm)]n multilayers with n = 10, 20, and 50, which exhibit perpendicular magnetic anisotropy. Both the major hysteresis loop and the FORCs are compared to previous results, where the magnetization was measured directly on unpatterned stacks using alternating gradient force magnetometry. The FORC diagrams are dominated by two “hysteron” peaks, and their separation increases when n becomes larger. A frustrated domain growth process is suggested in our n = 20 and 50 samples.

First order reversal curve studies of permanent magnets

First order reversal curve (FORC) diagrams are a useful tool to analyze the magnetization processes in magnetic materials. FORC diagrams are computed from measured first order reversal curves on sintered Nd2Fe14B magnets. It is shown that the FORC diagram simplifies if the first order reversal curves a desheared using the macroscopic demagnetizing field given by the geometry of the sample. Furthermore the resulting FORC diagram is almost identical to the FORC diagram measured for a thin platelet of the same material. This opens the possibility to compare experimental FORC diagrams with FORC diagrams computed by micromagnetic simulations.

Paleoposition of the Intertropical Convergence Zone in the eastern Pacific inferred from glacial-interglacial changes in terrigenous and biogenic magnetic mineral fractions

Magnetic properties are increasingly used for paleoclimatic and paleoceanographic studies. Utilizing recently developed proxies, an environmental magnetic study was conducted on the uppermost 12 m sediments of Integrated Ocean Drilling Program Site U1337 in the eastern equatorial Pacific Ocean. This interval is above the Fe-redox boundary, and covers the past ∼800 k.y. The site is located near the present southern boundary of the Intertropical Convergence Zone (ITCZ), and is thus expected to be sensitive to variations of the ITCZ position. The ratio of anhysteretic remanent magnetization susceptibility to saturation isothermal remanent magnetization ( k ARM /SIRM), first-order reversal curve diagrams, and IRM acquisition curves indicate that the magnetic mineral assemblage consists of a dominant biogenic component and a minor terrigenous component. Two groups, the biogenic soft (BS) and hard (BH), are identified for the biogenic component, and probably correspond to different magnetofossil morphology. The BH component, probably carried by elongated magnetofossils, increases in sediments of glacial periods, which are probably in less oxic conditions due to increased ocean productivity. This demonstrates that magnetofossil morphology, which can be discriminated by the rock magnetic technique, is a sensitive indicator of slight oxic-suboxic environmental fluctuations in sediments. Temporal variations of the terrigenous component, most likely transported as eolian dust, were estimated from the k ARM /SIRM ratio and S ratio (ratio of a moderate field IRM to SIRM, representing relative contribution of lower- and higher-coercivity magnetic minerals); significant glacial-interglacial variations occurred at marine isotope stage (MIS) 10 and before, but not after. In addition, coeval upcore increases in sedimentation rates and the BH component were observed, suggesting increased productivity. These observations may indicate that the position of the ITCZ was more southward than today ca. 250 ka and before.

First order reversal curve analysis on NdFeB nanocomposite ribbons subjected to Joule heating treatments

Amorphous precursors with composition Nd4.5Fe72−xCo3+xCr2Al1B17.5 (x=0, 2, 7, 12) were thermally treated by the Joule heating technique with a linearly varying electrical current. The crystallization kinetics was followed by monitoring the resistance of the ribbons during the heating up to the final applied current. Crystallized nanostructured phases coexist with an amorphous matrix, as it was observed by means of Mössbauer Spectroscopy and X-ray diffraction.The irreversible magnetic response of the Joule heated ribbons was analyzed by the First Order Reversal Curves (FORC) diagram technique. For the optimal treatments, associated with the higher maximum energy products for each sample composition, it was found that the main interaction is of a strongly dipolar characteristic. Over annealed samples show a FORC diagram that gives into account of softening, due to grain growth, for those phases precipitated at the first crystallization stage. When it is measured at 20K, the hardest magnetic sample (Fe=72at.%, Co=3at.%, Ifinal=0.5A), exhibits a diagram with characteristics corresponding to dipolar interactions of soft phases. This fact is consistent with an enhancement of the exchange length due to the increase in the soft phase stiffness as it is expected at low temperatures.

Mineral magnetism of dusty olivine: A credible recorder of pre-accretionary remanence

[1] The magnetic properties of olivine-hosted Fe-Ni particles have been studied to assess the potential of “dusty olivine” to retain a pre-accretionary remanence in chondritic meteorites. Both body-centered (bcc) and face-centered cubic (fcc) Fe-Ni phases were formed by reduction of a terrestrial olivine precursor. The presence of Ni complicates the magnetic properties during heating and cooling due to the fcc-bcc martensitic transition. First-order reversal curve (FORC) diagrams contain a central ridge with a broad coercivity distribution extending to 600 mT, attributed to non-interacting single-domain (SD) particles, and a “butterfly” structure extending to 250 mT, attributed to single-vortex (SV) states. SD and SV states were imaged directly using electron holography. The location of the SD/SV boundary is broadly consistent with theoretical predictions. A method to measure the volume of individual SD particles using electron holography is presented. Combining the volume information with constraints on coercivity, we calculate the thermal relaxation characteristics of the particles and demonstrate that the high-coercivity component of remanance would remain stable for 4.6 Ga, even at temperatures approaching the Curie temperature of pure Fe. The high coercivity of the particles, together with the chemical protection offered by the surrounding olivine, is likely to make them resistant to shock remagnetization, isothermal remagnetization and terrestrial weathering, making dusty olivine a credible recorder of pre-accretionary magnetic fields.

Iron Transformations Induced by an Acid-Tolerant Desulfosporosinus Species

The mineralogical transformations of Fe phases induced by an acid-tolerant, Fe(III)- and sulfate-reducing bacterium, Desulfosporosinus sp. strain GBSRB4.2 were evaluated under geochemical conditions associated with acid mine drainage-impacted systems (i.e., low pH and high Fe concentrations). X-ray powder diffractometry coupled with magnetic analysis by first-order reversal curve diagrams were used to evaluate mineral phases produced by GBSRB4.2 in media containing different ratios of Fe(II) and Fe(III). In medium containing Fe predominately in the +II oxidation state, ferrimagnetic, single-domain greigite (Fe₃S₄) was formed, but the addition of Fe(III) inhibited greigite formation. In media that contained abundant Fe(III) [as schwertmannite; Fe₈O₈(OH)₆SO₄ · nH₂O], the activities of strain GBSRB4.2 enhanced the transformation of schwertmannite to goethite (α-FeOOH), due to the increased pH and Fe(II) concentrations that resulted from the activities of GBSRB4.2.

Experimental and Micromagnetic First-Order Reversal Curves Analysis in [Ni-Fe/Zn/Co-Ni-N/Ni-Mn] Spin Valves

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 [Ni-Fe/Zn/Co-Ni-N/Ni-Mn] electrodeposited spin valve. Our purpose was to study the effect of Co-Ni-N layers thicknesses concerning magnetic properties of these spin-valve sandwiches electrodeposited on the Cu substrate. The FORC diagrams for these systems show the existence of two magnetic phases: a soft magnetic phase (corresponding to Ni-Fe layers) and a hard magnetic one (for Co-Ni-N layers). The largest value of GMR we achieved is 33% at room temperature for the sample [Ni-Fe(140 nm)/Zn(13 nm)/Co-Ni-N(190 nm)/Ni-Mn(160 nm)] granular spin-valve stack.

Magnetic properties of magnetite nanoparticles coated with mesoporous silica by sonochemical method

In this paper we present the magnetic properties of mesoporous silica-coated Fe 3O 4 nanoparticles. The coating of magnetite nanoparticles with mesoporous silica shell was performed under ultrasonic irradiation. The obtained mesoporous silica-coated magnetite nanoparticles were characterized by powder X-ray diffraction, focused ion beam-scanning electron microscopy, nitrogen adsorption–desorption isotherms and vibrating sample magnetometer. The hysteretic behavior was studied using first-order reversal curves diagrams. The X-ray diffraction result indicates that the extreme chemical and physical conditions created by acoustic cavitations have an insignificant effect on crystallographic structural characteristic of magnetite nanoparticles. Changes in the coercivity distributions of the magnetite nanoparticles were observed on the first-order reversal curves diagrams for the samples with coated particles compared with the samples containing uncoated particles of magnetite. The coated particles show an increased most probable coercivity of about 20% compared with the uncoated particles which can be associated with an increased anisotropy due to coating even if the interaction field distribution measured on the diagrams are virtually identical for coated/uncoated samples.

Combined use of magnetometry and spectroscopy for identifying magnetofossils in sediments

Identification of the mineral remains of magnetotactic bacteria (MTB), known as magnetofossils, is of particular interest because their occurrence can be used for environmental and climatic reconstructions. Single-domain magnetite particles, which are biomineralized in the cell body of MTB, have characteristic properties that can be used to detect their fossil remains. Acquisition of anhysteretic and isothermal remanent magnetization (ARM and IRM), first-order reversal curve (FORC) diagrams, and ferromagnetic resonance (FMR) spectra were used to detect the magnetic mineral inventory in Holocene lake sediments. A comparative analysis in terms of the discriminatory power of these methods is presented. The FORC diagrams contain two distinct features: a sharp horizontal ridge centered on the horizontal axis Bc and a feature with symmetric spread along the vertical Bb axis. The coercivity spectra derived from the central ridge coincides with that derived from ARM and IRM acquisition curves and is compatible with the presence of noninteracting linear chains of single-domain magnetite. The second feature on FORC diagrams is indicative of interacting particles in clusters. In the FMR spectra from bulk sediment, two populations are separated empirically based on the FORC information. An asymmetric signal is taken to describe the population, which contains single-domain particles in clusters. Empirical spectral separation of this contribution results in FMR spectra that are similar to those of intact MTB, which strongly suggests that a fraction of linear magnetosome chains is present. Combination of FMR and FORC results demonstrates the strong potential of these methods for identifying magnetofossils, based on alignment and interaction patterns of magnetic particles.

Low-temperature domain wall pinning in titanomagnetite: Quantitative modeling of multidomain first-order reversal curve diagrams and AC susceptibility

Domain wall pinning in titanomagnetite has been investigated at low temperatures using first-order reversal curve (FORC) diagrams, AC magnetic susceptibility, and Lorentz transmission electron microscopy. A discontinuous transition from a low-coercivity extrinsic pinning regime to a high-coercivity intrinsic pinning regime is evident in low-temperature FORC diagrams on cooling from 100 to 50 K. Intrinsic pinning is characterized by a “crescent moon” FORC distribution with narrow coercivity distribution centered on 10–20 mT. This crescent-shaped FORC distribution is reproduced using a modification of Neel's (1955) one-dimensional theory of domain wall pinning in a random field. The pinning transition coincides with a thermally activated relaxation process (activation energy 0.13 ± 0.01 eV), attributed to electron hopping. The relaxation and intrinsic pinning are explained as a magnetoelastic aftereffect caused by enhancement of magnetocrystalline anisotropy due to rearrangement and localization of Fe2+−Fe3+ cations within the domain walls. This study provides experimental verification that Neel's theory is an appropriate quantitative framework for the analysis of FORC diagrams in multidomain titanomagnetite and suggests a potential method for the quantitative unmixing of multidomain signals from FORC diagrams in rock and environmental magnetic studies.