First-order Reversal Curve Diagrams Research Articles

Understanding the interaction of soft and hard magnetic components in NdFeB with first-order reversal curves

First-order reversal curve (FORC) measurements are a powerful tool to study magnetization reversal processes and interactions in heterogeneous systems with broad coercivity distributions. In NdFeB hard magnets an additional soft magnetic component is often observed possibly originating from damaged surface grains. Here we use FORC to study the reversal processes and interactions in these permanent magnets at different temperatures between 50 and 350 K. The measured reversal curves reveal a strongly coupled switching of the soft and hard magnetic components above 250 K. Below this temperature the two components are decoupled and switch almost independently. This decrease in effective interaction at lower temperatures is also observed in the FORC diagrams by a relative reduction in intensity of the so called interaction peak. This result proves that FORC is a powerful method, contributing to a better understanding of magnetization reversal processes and interactions in permanent magnets.

First-order reversal curve diagram and its application in investigation of polarization switching behavior of HfO<sub>2</sub>-based ferroelectric thin films

<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>

Intergranular interaction in nanocrystalline Ce-Fe-B melt-spinning ribbons via first-order reversal curve analysis

First-order reversal curve (FORC) diagram, which visualizes the variation of magnetic interaction on a field plane, has been applied to nanocrystalline Ce-Fe-B melt-spinning ribbons. The FORC diagram exhibits different vertical spread along the Hu axis when the applied field is parallel or perpendicular to the ribbon surface. The discrepancy of vertical spread corresponds to different intergranular interactions, which can also be verified by Henkel plot, another method to identify the interactions. The larger vertical spread on the Hu axis along the perpendicular direction is ascribed to the dominance of magnetostatic interaction, while the smaller one along the parallel direction indicates the existence of stronger exchange coupling interaction. The remanence enhancement effect along the parallel direction further confirms the existence of exchange coupling. These indicate that a FORC diagram is a powerful evaluation method for distinguishing different magnetic interactions in permanent magnets. Moreover, Lorentz transmission electron microscopy was used to analyze the magnetic domain structure of nanocrystalline Ce-Fe-B melt-spinning ribbons.

Influence of annealing temperature on degradation efficiency and iron oxide transformations in CeO2/Fe-oxide sorbents

The microstructural and physical properties of magnetically separable CeO2 (5 wt.%)/Fe-oxide sorbents, applicable for the decomposition of organophosphorus pesticides, are analyzed in dependence on calcination temperature. The sorbents are prepared using a two-step procedure: (1) synthesis of magnetite core from cheap and commercially available raw materials; and (2) the formation of cerium (III) carbonate by precipitation with the ammonium hydrogen carbonate, containing re-dispersed magnetite. The cerous carbonate/magnetite precursor is annealed in a muffle furnace at temperatures ranging from 473 to 1073 K for 2 h to obtain the CeO2/Fe-oxide reactive sorbents. Structural characterization of the samples is performed using X-ray diffraction, scanning electron microscopy, Raman and Fourier transform infrared spectroscopy. Magnetic properties are obtained from hysteresis loops, field-cooled and zero-field-cooled curves, first-order reversal curve (FORC) diagrams, and Henkel plots. Sorbents exhibit an increase in coercivity from 0.2 kA/m to about 20 kA/m and a decrease in saturation magnetization from roughly 50 Am2/kg to 1 Am2/kg after annealing at 973 K. This deterioration of magnetic properties is caused by the transformation of magnetite and maghemite into weakly ferromagnetic hematite, with a typical peak in FORC diagram and a Morin transition at about 200 K. The degradation efficiency towards parathion and paraoxon methyl is about 30% for samples annealed from 473 K to 773 K.

Monitoring the evolution of Fe3O4 mesocrystal morphology using first-order reversal curves

We report the results of systematic measurements of first-order reversal curves (FORCs) for magnetite (Fe3O4) mesocrystals during the reaction process, where small nanoparticles, all with the same crystallographic orientation, form a cluster, and as the reaction time increases, grow in size. The FORC distribution exhibits a single peak in the FORC diagram, whose position gradually shifts toward a higher coercivity as the reaction time increases, which is associated with the broadening of the peak along both the coercivity and local interaction field axes. In addition, the FORC distribution peak is slightly displaced toward a negative local interaction field. These observations suggest the magnetic hardening and the presence of a positive (magnetizing) mean field acting on an individual nanoparticle from the surrounding nanoparticles within a mesocrystal. As the reaction time is further increased, nanoparticles constituting a mesocrystal split into porous nanoparticles, which is associated with a further shift of the FORC peak toward a higher coercivity. The present study demonstrates that FORCs can be a powerful tool for monitoring the morphology evolution of magnetic mesocrystals composed of small nanoparticles.

Relation of the average interaction field with the coercive and interaction field distributions in First order reversal curve diagrams of nanowire arrays

First-order reversal curve diagrams, or FORC diagrams, have been studied to determine if the widths of their distributions along the interaction and coercivity axes can be related to the mean-field magnetization dependent interaction field (MDIF). Arrays of nanowires with diameters ranging from 18 up to 100 nm and packing fractions varying from 0.4 to 12% have been analyzed. The mean-field MDIF has been measured using the remanence curves and used as a measuring scale on the FORC diagrams. Based on these measurements, the full width of the interaction field distribution and the full width at half maximum (FWHM) of the FORC distribution profile along the interaction field direction are shown to be proportional to the MDIF, and the relation between them is found. Moreover, by interpreting the full width of the coercive field distribution in terms of the dipolar induced shearing, a simple relation is found between the width of this distribution and the MDIF. Furthermore, we show that the width of the FORC distribution along the coercive field axis is equal to the width of the switching field distribution obtained by the derivation of the DC remanence curve. This was further verified with the switching field distribution determined using in-field magnetic force microscopy (MFM) for very low density nanowires. The results are further supported by the good agreement found between the experiments and the values calculated using the mean-field model, which provides analytical expressions for both FORC distributions.

FORC signatures and switching-field distributions of dipolar coupled nanowire-based hysterons

Analysis of first-order reversal curves (FORCs) is a powerful tool to probe irreversible switching events in nanomagnet assemblies. As in essence switching events are related to the intrinsic properties of the constituents and their interactions, the resulting FORC diagrams contain much information that can be cross-linked and complex to deconvolute. In order to quantify the relevant parameters that drive the FORC diagrams of arrays of perpendicularly magnetized nanomagnets, we present step-by-step simulations of assemblies of hysterons to determine the specific signatures related to different known inputs. While we explored the consequences of dipolar interactions using either mean field or magnetostatic approaches, we completed by taking the hysteron switching field distribution (SFD) as either normal or lognormal. We demonstrated that the transition between FORC diagrams composed of an isolated interaction field distribution (IFD) and a wishbone shape operates via the SFD deviation, σHsw, in the presence of a weakly dispersed interaction field. In the presence of a magnetostatic interaction field, the IFD profile is peaked and a coercive field distribution (CFD) sums to the IFD as σHsw increases. A transition between IFD + CFD and wishbone shapes is clearly demonstrated as a function of the interaction field deviation σHint. In addition, we demonstrate that whatever the considered cases, σHswcan be quantitatively extracted from the FORC diagrams within an error inferior to 10%. These findings are of interest for dipolar coupled perpendicularly magnetized nanomagnets, as in assemblies of magnetic nanowires and nanopillars, as well as bit patterned media.

Unmixing biogenic and terrigenous magnetic mineral components in red clay of the Pacific Ocean using principal component analyses of first-order reversal curve diagrams and paleoenvironmental implications

Red clay widely occupies the seafloor of pelagic environments in middle latitudes, and potentially preserves long paleoceanographic records. We conducted a rock-magnetic study of Pacific Ocean red clay to elucidate paleoenvironmental changes. Three piston cores from the western North Pacific Ocean and IODP Hole U1365A cores in the South Pacific Ocean were studied here. Principal component analyses applied to first-order reversal curve diagrams (FORC-PCA) reveals three magnetic components (endmembers EM1 through EM3) in a core of the western North Pacific. EM1, which represents the features of interacting single-domain (SD) and vortex states, is interpreted to be of terrigenous origin. EM2 and EM3 are carried by non-interacting SD grains with different coercivity distributions, which are interpreted to be of biogenic origin. The EM1 contribution suddenly increases upcore at a depth of ~ 2.7 m, which indicates increased eolian dust input. The age of this event is estimated to be around the Eocene–Oligocene (E/O) boundary. Transmission electron microscopy reveals that EM2 is dominated by magnetofossils with equant octahedral morphology, while EM3 has a higher proportion of bullet-shaped magnetofossils. An increased EM3 contribution from ~ 6.7 to 8.2 m suggests that the sediments were in the oxic–anoxic transition zone (OATZ), although the core is oxidized in its entire depth now. The chemical conditions of OATZ may have been caused by higher biogenic productivity near the equator. FORC-PCA of Hole U1365A cores identified two EMs, terrigenous (EM1) and biogenic (EM2). The coercivity distribution of the biogenic component at Hole U1365A is similar to that of the lower coercivity biogenic component in the western North Pacific. A sudden upcore terrigenous-component increase is also evident at Hole U1365A with an estimated age around the E/O boundary. The increased terrigenous component may have been caused by the gradual tectonic drift of the sites on the lee of arid continental regions in Asia and Australia, respectively. Alternatively, the eolian increase may have been coeval in the both hemispheres and associated with the global cooling at the E/O boundary.

Assessment and Integration of Bulk and Component‐Specific Methods for Identifying Mineral Magnetic Assemblages in Environmental Magnetism

AbstractMagnetic parameters are used extensively to interpret magnetic mineral assemblage variations in environmental studies. Conventional room temperature measurements of bulk magnetic parameters, like the anhysteretic remanent magnetization (ARM) and the ratio of the susceptibility of ARM to magnetic susceptibility (χ), can reflect, respectively, magnetic mineral concentration and/or particle size variations in sediments, although they are not necessarily well suited for identifying magnetic components within individual magnetic mineral assemblages. More advanced techniques, such as first‐order reversal curve (FORC) diagrams and low‐temperature (LT) magnetic measurements, can enable detailed discrimination of magnetic assemblages. Here, we integrate conventional bulk magnetic measurements alongside FORC diagrams, LT measurements, and X‐ray fluorescence core‐scan data, transmission electron microscope observations, and principal component analysis of FORC diagrams to identify and quantify magnetic mineral assemblages in eastern Mediterranean sediments. The studied sediments were selected because they contain complexly varying mixtures of detrital, biogenic, and diagenetically altered magnetic mineral assemblages that were deposited under varying oxic (organic‐poor marls) to anoxic (organic‐rich sapropels) conditions. Conventional bulk magnetic parameters provide continuous records of environmental magnetic variations, while more time‐consuming LT and FORC measurements on selected samples provide direct ground‐truthing of mineral magnetic assemblages that enables calculation of magnetization contributions of different end members. Thus, a combination of conventional bulk parameters and advanced magnetic techniques can provide detailed records from which the meaning of environmental magnetic signals can be unlocked.

Effect of mesoscopic magnetomechanical hysteresis on magnetization curves and first-order reversal curve diagrams of magnetoactive elastomers

Magnetoactive elastomers may display magnetic hysteresis, even if they are filled only with magnetically soft particles. In this work we discuss application of the first-order reversal curve (FORC) analysis to identify and study hysteresis of that kind. To obtain theoretical magnetization curves and FORC diagrams for the composites in question, a simple model comprising two magnetically soft particles embedded in an elastic environment is proposed. Elucidation of the features present in FORC diagrams is conducted using computer simulation. Despite the simplicity of the model, it allows one to explain the origin of diagonal ridge patterns, which turn up in the FORC diagrams of elastomer composites with magnetically soft filler, and to quantify the experimental results. As the ridge pattern of the diagrams is inherently exclusive to such types of materials, it could be useful for their diagnostics.

Estimation of Magnetic Anisotropy of Individual Magnetite Nanoparticles for Magnetic Hyperthermia.

Ideal interaction-free magnetite nanoparticles were prepared, and their magnetic properties were measured to clarify the true nature of magnetic anisotropy of individual magnetite nanoparticles at the nanoscale and to analyze the shape, surface, and crystalline anisotropy contributions. Spherical (17.7 nm), cubic (10.6 nm), and octahedral-shaped magnetite nanoparticles with average sizes ranging from 7.6 to 23.4 nm were synthesized using solution techniques. Then, these nanoparticles were coated with silica at appropriate shell thicknesses to prepare magnetic interaction-free samples, and their noninteractive nature was confirmed through first-order reversal curve diagrams. For these well-isolated nanoparticles, remanent magnetizations of the hysteresis loops are just equal to a half of the saturation magnetization. This result clearly indicates that uniaxial magnetic anisotropy is predominant in each nanoparticle. In order to clarify the details of the uniaxial magnetic anisotropy, the analysis of blocking temperature-switching field distribution diagrams is constructed based on thermal decay curves of isothermal remanent magnetization at various applied fields. The obtained effective magnetic anisotropy constant Keff is distributed around 10-20 kJ/m3 and has insignificant size dependence. This result seems inconsistent with the inverse proportion relation of Keff with size predicted for surface magnetic anisotropy. The theoretical calculation suggested that the crystalline magnetic anisotropy plays a major role in magnetic properties of the magnetite nanoparticles at lower temperatures. However, it should be noted that Keff seems slightly different for the different shapes. The above study indicates that control size, shape, and interparticle interactions is required to strictly discuss such delicate differences of magnetic anisotropy of individual magnetite nanoparticles for the design of thermal seeds for magnetic hyperthermia.

Composition-driven crystal structure transformation and magnetic properties of electrodeposited Co–W alloy nanowires

Abstract The cobalt (Co)–tungsten (W) alloys exhibit unique combinations of mechanical and magnetic properties, biocompatibility, resistance against corrosion, wear, and high-temperature, which makes them desirable materials for various practical applications. A nanoporous template with incorporated Co–W alloy nanowires is a soft magnetic composite, whose dielectric and magnetic properties can be tuned through the host material, pore distribution and size, Co–W composition and crystal structure, and geometry of the nanowires. Here, we report the composition-dependent structural and magnetic properties of Co–W alloy nanowires embedded in alumina templates by electrodeposition. The addition of W transforms cobalt from the crystalline hexagonal-close-packed (hcp) Co to a mixed nanocrystalline/amorphous-like Co(W) solid solution with ferromagnetic behavior and composition similar to that of the weakly magnetic Co3W compound. The combination of the approach to magnetic saturation, anisotropy field distribution method, micromagnetic simulations, and first-order reversal curve diagram identification method elucidates the structure-driven magnetization reversal processes in both individual nanowires and magnetostatically coupled array as a whole.

Enhancement of zero-field skyrmion density in [Pt/Co/Fe/Ir]2 multilayers at room temperature by the first-order reversal curve

Magnetic skyrmions are novel topological spin textures on the nanoscale, and significant efforts have been taken to improve their zero-field density at room temperature (RT). In this work, we reported an approach of improving zero-field skyrmion density in [Pt/Co/Fe/Ir]2 multilayers at RT by using the first-order reversal curve (FORC) technique to obtain information on the irreversible or reversible behaviors in the magnetization switching process. It was found from the FORC diagram that the magnetization reversal mechanism can be characterized into three stages: (1) reversible labyrinth stripe domains expanding or shrinking stage; (2) irreversible stripe domains fracturing stage; and (3) irreversible skyrmion annihilation stage. Furthermore, the zero-field skyrmion density can be highly improved by choosing reversal fields from the irreversible stripe domains fracturing stage. The highest skyrmion density was approached according to the maximum FORC distribution ρ. Our results have established the FORC measurement as a valuable tool for investigating magnetic multilayers of high skyrmion densities.

Magnetic vortex formation in hollow Fe3O4 submicron particles studied using first-order reversal curves

We report results of first-order reversal curves (FORCs) measurements for hollow Fe3O4 submicron spherical particles, varying particle size from 400 to 700 nm. For all the samples, the FORC diagrams exhibit a butterfly-like feature of distribution peaks, being characteristic to the vortex formation. With increasing temperature from 10 K nucleation and annihilation fields of a vortex sharply increase and become almost constant above the Verwey transition temperature (Tv∼115 K). This reflects temperature-dependent magnetocrystalline anisotropy, associated with a structural transition at Tv. Above Tv the field range at which a vortex state is stable increases with increasing particle size, indicating that an increasing contribution of demagnetizing fields dominates a vortex stability for larger hollow particles.

Micromagnetic simulations of first-order reversal curve (FORC) diagrams of framboidal greigite

SUMMARY Greigite is a sensitive environmental indicator and occurs commonly in nature as magnetostatically interacting framboids. Until now only the magnetic response of isolated non-interacting greigite particles have been modelled micromagnetically. We present here hysteresis and first-order reversal curve (FORC) simulations for framboidal greigite (Fe3S4), and compare results to those for isolated particles of a similar size. We demonstrate that these magnetostatic interactions alter significantly the framboid FORC response compared to isolated particles, which makes the magnetic response similar to that of much larger (multidomain) grains. We also demonstrate that framboidal signals plot in different regions of a FORC diagram, which facilitates differentiation between framboidal and isolated grain signals. Given that large greigite crystals are rarely observed in microscopy studies of natural samples, we suggest that identification of multidomain-like FORC signals in samples known to contain abundant greigite could be interpreted as evidence for framboidal greigite.

Magnetization reversal behavior and first-order reversal curve diagrams in high-coercivity Zr-doped α-Fe/Nd2Fe14B nanocomposite alloys

In the present work, the magnetization reversal behavior for the melt spinning (Nd0.8Ce0.2)2Fe12Co2−xZrxB (x = 0, 0.5) permanent alloys with high coercivity was investigated by analyzing the hysteresis curves and the recoil loops. Compared to the Zr-free alloy, the Zr-doped sample obtains higher magnetic properties: coercivity of Hcj = 650.5 kA·m−1, squareness of Hk/Hcj = 0.76 and maximum energy product of (BH)max = 131.0 kJ·m−3. The first-order reversal curves (FORCs) analysis was taken to identify optimal conditions of exchange coupling for the Zr-free and Zr-doped alloys. The coercivity mechanism of the α-Fe/Nd2Fe14B nanocomposite alloys was analyzed by the angular dependence of the coercive field as measured for the Zr-doped sample. The results show that the magnetic reverse process of the Zr-doped sample can be explained by the pinning model.

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

Amorphous ferromagnetic Fe-based microwires (MWs) have a magnetic structure consisting mainly of a single longitudinal domain and small closure domains at both ends. A rectangular hysteresis loop is then observed according to the fast domain wall propagation along the microwire. This type of material is a good physical example of the idea of a magnetic relay hysteron as described in Preisach model of hysteresis. The hysteron was defined as a mathematical operator acting on the field and producing rectangular loops whose superposition gives out the hysteresis loop. The hysteron idealization is frequently used to describe and interpret FORC (First Order Reversal Curve) diagrams by comparison with Preisach plane. The central idea of this work is to study the FORCs of a real physical sample that behaves closely to the ideal hysteron, both isolated and interacting with a twofold aim. On one hand, providing a better understanding of FORC measurements, and, on the other, analyzing the magnetization reversal processes in microwires with rectangular hysteresis loops. While for a single microwire the behaviour is that expected for a hysteron, both in the hysteresis loop and in the FORC diagram, the magnetostatic interaction between two microwires breaks with the ideal behaviour due to the change in the domain wall mobility at the end of the wires.

Mesoscale magnetic rings: Complex magnetization reversal uncovered by FORC

In this work, we investigate mesoscopic amorphous magnetic rings prepared by ion-implantation. The analysis is carried out combining conventional magnetization vs field measurements alongside MOKE microscopy imaging and, for the first time, first-order reversal curves (FORCs). With the information extracted from the FORC diagram, we can identify the presence of typical onion and vortex magnetic configurations, and also determine with high resolution the fields connected to their formation, stability, and annihilation. Furthermore, depending on the field and history, two different onion configurations exist, characterized by the presence of transverse or vortex domain walls. The FORC data reveal the different reversible/irreversible nature of the annihilation of the two onion configurations, and a signal peculiar of the presence of vortex domain walls. All these crucial information are not accessible with conventional M(H) loops, demonstrating that FORCs offer a unique perspective for the investigation of the physical phenomena of magnetic elements with complex geometries.

Measuring FORCs diagrams in computer simulations as a mean to gain microscopic insight

FORCs (first-order reversal curves) diagrams prove to be an efficient experimental technique to investigate magnetic interactions in complex systems. In experiments, as a rule, it is difficult to relate actual microstructural changes to the evolution of FORCs diagrams. Here, using Molecular Dynamics simulations, we calculate FORCs for two simple models of a magnetic elastomer. The simplicity of these models allows to relate directly both, the rigidity of the matrix and the magnetoelastic coupling to the shape and intensity of FORCs diagrams.

3D interacting magnetic multilayered nanowire arrays: the emergence and evolution of new first-order reversal curve features

The crucial role of magnetostatic interactions in tuning properties of storage devices based on magnetic nanowires (NWs) has recently been highlighted by advanced characterization techniques including the first-order reversal curve (FORC) analysis, evaluating physical entities constituting conventional 2D NW systems. Herein, FORC diagrams of ferromagnetic (FM)/non-magnetic (NM) multilayered NW arrays are simulated using Monte Carlo calculations, involving magnetostatic interactions between segments in 3D space. The FM length is constant to 6 µm whereas the NM length (LNM) varies from 10 to 300 nm, significantly influencing interwire and intrasegment interactions of neighboring NWs and coupled segments along the NW length. Intriguingly, this is accompanied with the emergence of two new FORC diagram features in addition to the typical demagnetizing-type feature, indicating complex behavior of the 3D interacting NWs with the same anisotropy field for each FM segment. The FORC coercivity of the emerging features is tracked individually, presenting evolution as a function of LNM. Our results also evidence an increase in interwire and intrasegment interactions when increasing NW diameter, being in accordance with total magnetostatic energy calculations.