First-order Reversal Curve Method Research Articles

Controlling magnetization reversal in Co/Pt nanostructures with perpendicular anisotropy

We demonstrate a simple method to tailor the magnetization reversal mechanisms of Co/Pt multilayers by depositing them onto large area nanoporous anodized alumina (AAO) with various aspect ratios, A=pore depth/diameter. Magnetization reversal in composite (Co/Pt)/AAO films with large A is governed by strong domain-wall pinning, which gradually transforms into a rotation-dominated reversal for samples with smaller A, as investigated by a first-order reversal curve method in conjunction with analysis of the angular dependent switching fields. The change in the magnetization reversal mode is attributed to topographical changes induced by the aspect ratio of the AAO templates.

Probing magnetic configurations in Co/Cu multilayered nanowires

Magnetic configurations in heterostructures are often difficult to probe when the magnetic entities are buried inside. In this study we have captured magnetic and magnetoresistance “fingerprints” of Co nanodisks embedded in Co/Cu multilayered nanowires using a first-order reversal curve method. In 200 nm diameter nanowires, the magnetic configurations can be tuned by adjusting the Co nanodisk aspect ratio. Nanowires with the thinnest Co nanodisks exhibit single domain behavior, while those with thicker Co reverse via a vortex state. A superposition of giant and anisotropic magnetoresistance is observed, which corresponds to the different magnetic configurations of the Co nanodisks.

First order reversal curves diagrams for describing ferroelectric switching characteristics

First Order Reversal Curves (FORC) are polarization-field dependences described between saturation field Esat and a variable reversal field E,?(-Esat, Esat). The FORC diagrams were proposed to describe some characteristics of the switching process in ferroelectrics. The approach is related to the Preisach model which considers the distribution of the elementary switchable units over their coercive and bias fields. The influence of the anisotropic porosity in Pb(Zr,Ti)O3 bulk ceramics on the FORC distributions demonstrated the existence of a positive/negative bias as a result of the confinement induced by anisotropy. The reducing of grain size in Ba(Zr,Ti)O3 ceramics causes an increase of the ratio of the reversible/irreversible components of the polarization on the FORC distribution indicating the tendency of system towards the superparaelectric state. The FORC method demonstrates to provide a kind of 'fingerprinting' of various types of switching characteristics in ferroic systems. .

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.

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.

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.

Study of impurities effect in spin crossover compounds using first order reversal curves (FORC) method

Using the FORC method, we present in this communication a study on the diluted spin transition materials with the formula [Fe x M 1 − x (btr) 2 (NCS) 2] · H 2O with M = Zn, Co and Ni. We compare the evolution of distributions obtained for different dilutions with the three impurities and we notice that these distributions depend not only on the dilution (1 − x) but also on the impurity used. The statistical analysis shows that the maximum values of the distributions are close to a linear dependence for Zn and Co. The impurity that does not obey this dependence is Ni, which volume is close to the average volumes of high spin and low spin iron atoms. In addition, opposite to others, the complex with Ni impurities presents a rotation of the principal axes.

Extracting the intrinsic switching field distribution in perpendicular media: A comparative analysis

We introduce a method based on the first-order-reversal-curve (FORC) diagram to extract the intrinsic (microscopic) switching-field distribution (SFD) of perpendicular recording media (PRM). To demonstrate the viability of the method, we micromagnetically simulated FORCs for PRM with known SFD. The extracted SFD is compared with the SFD obtained by means of two different methods that are based on recoil loops, too, which, however, rely on mean-field approximations and assumptions on the shape of the SFD. The FORC method turns out to be the most accurate algorithm over the technologically relevant range of magnetic quality factors Q, where the other methods overestimate the width of the SFD.

Magnetization reversal and nanoscopic magnetic-phase separation inLa1−xSrxCoO3

The doped perovskite cobaltite ${\mathrm{La}}_{1\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{CoO}}_{3}$ (LSCO) has been advanced as a model system for studying intrinsic magnetic phase separation. We have employed a first-order reversal curve (FORC) method to probe the amount of irreversible switching in bulk polycrystalline LSCO as a function of Sr doping, field cooling procedure, and temperature. The value of the FORC distribution $\ensuremath{\rho}$ is used as a measure of the extent of irreversible switching. For $x<0.18$, the small values of $\ensuremath{\rho}$ and its ridgelike distribution along local coercivity $({H}_{c})$ and zero bias $({H}_{b})$ are characteristic of noninteracting single domain particles. This is consistent with the formation of an array of isolated nanoscopic ferromagnetic clusters, as observed in previous work. For $x\ensuremath{\geqslant}0.18$, the much larger values of $\ensuremath{\rho}$, the tilting of its distribution towards negative bias field, and the emergence of regions with negative $\ensuremath{\rho}$ are consistent with increased long-range ferromagnetic ordering. The FORC distributions display little dependence on the cooling procedure. With increasing temperature, the fraction of irreversible switching determined from the FORC distribution follows closely the ferromagnetic phase fraction measured by La nuclear magnetic resonance. Our results furthermore demonstrate that the FORC method is a valuable first-pass characterization tool for magnetic-phase separation.

First-order reversal curve analysis of homogeneous nucleation in the two-dimensional kinetic Ising model

The first-order reversal curve (FORC) method is applied to the two-dimensional kinetic Ising model. For the system size and magnetic field chosen, the system reverses by the homogeneous nucleation and growth of many droplets. This makes the dynamics of reversal nearly deterministic, in contrast to the strongly disordered systems previously studied by the FORC method. Consequently, the FORC diagrams appear different from those obtained in previous studies. The Kolmogorov–Johnson–Mehl–Avrami (KJMA) theory of phase transformation by nucleation and growth is applied to the system. Reasonable agreement with the Monte Carlo simulations is found, and the FORC method suggests how the KJMA theory could be extended.

Assessing the ability of first‐order reversal curve (FORC) diagrams to unravel complex magnetic signals

First‐order reversal curve (FORC) diagrams for mixtures of different magnetic phases and bimodal distributions have been measured to examine the efficiency of the FORC method at unraveling complex magnetic signals. The FORC distributions for various magnetic minerals, including magnetite, maghemite, hematite, and goethite, and their linear additivity are assessed. Mixtures containing only hard magnetic minerals like hematite or goethite, which have relatively small spontaneous magnetizations (MS) and large magnetocrystalline anisotropies, can be adequately described by a linear addition of the two end‐members, because there are virtually no magnetostatic interactions between the phases. Mixtures dominated by softer minerals like magnetite and maghemite are more susceptible to interactions and exhibit nonlinear behavior. When a hard phase with low MS like hematite is mixed with a softer phase with high MS like magnetite, it can still be identified using the FORC technique, whereas it is impossible to do so using standard magnetic hysteresis measurements. When the weaker phase can be identified, then weak‐strong mixes add linearly; however, beyond a certain critical concentration the mineral with high MS swamps the magnetic signal and linearity breaks down. It is suggested that the FORC method is highly suitable for identifying small traces of hard magnetic minerals like hematite and goethite in the presence of minerals with high MS such as magnetite.

Influence of magnetostatic interactions on first-order-reversal-curve (FORC) diagrams: a micromagnetic approach

SUMMARY From experiments it is known that magnetostatic interactions between grains strongly affect the magnetic hysteresis behaviour of samples, however, because of the difficulty in predicting the non-linear behaviour, the effect of interactions has not yet been fully incorporated into theoretical models for the recently developed first-order-reversal-curve (FORC) method. For the FORC method to be widely used it is important to have such an understanding, for example, from a geological point of view there are many cases where interactions are known to be important, e.g. bacterial magnetosomes found in sedimentary rocks. Using a 3-D fast-Fourier transforms (FFT) micromagnetic model we have conducted a detailed study of the role of magnetostatic interactions on the FORC diagrams of assemblages of ideal single-domain (SD) magnetite-like grains. We have considered various anisotropies and the importance of the alignment configuration of the particle assemblages. We show that interactions can strongly affect the magnetic behaviour, for example, interacting assemblages of SD grains can display more MD-like FORC diagrams. Associating the FORC diagram with the Preisach diagram, we find that for moderate and weak interacting SD assemblages, the factorization interpretation of the Preisach diagram is correct, and in agreement with recent experimental results.

First‐order reversal curve (FORC) diagrams of elongated single‐domain grains at high and low temperatures

First‐order reversal curve (FORC) diagrams are a new technique for identifying magnetic minerals and characterizing their domain structures and interactions. FORC diagrams have potentially important applications for determining magnetic mineral compositions and grain sizes in paleomagnetism and environmental magnetism. However, the interpretation of the FORC parameters Hc and Hu as being equivalent to microcoercivity and particle interaction field, respectively, needs to be thoroughly tested in order to validate the FORC method. In order to test this interpretation, we measured FORC diagrams on elongated single‐domain particles at temperatures ranging from 20 to 853 K (580°C). The FORC distribution contracts significantly along both axes above 430°C, and the bulk coercive force decreases rapidly. The main causes of these features are decreasing spontaneous magnetization Ms(T) and increasing thermal activation of single‐domain moments pinned by shape anisotropy. A profile through the FORC peak along the Hc axis can be integrated to give a synthetic alternating field demagnetization curve or isothermal remanence curve. The synthesized curves match measured curves quite well at a variety of temperatures, and the FORC median Hc varies approximately in proportion to the bulk coercive force. A profile through the FORC peak parallel to the Hu axis contracts with heating approximately as Ms(T), and the half width of the distribution is similar to independent measures of local interaction fields Hi. These properties support the interpretation of the FORC variables Hc and Hu as being equivalent to microcoercivity Hc and interaction field Hi, respectively.

A model of ferroelectric behavior based on a complete switching density

In this article, a ferroelectric capacitor is characterized by an experimental Preisach density (PD), determined by first order reversal curves (FORC) method. It is experimentally shown that this density, defined under the usual Preisach assumptions, does not allow a complete model of the ferroelectric behavior. Considering the domain walls phenomenon, an extension of the Preisach assumptions is suggested, leading to the complete switching density (CSD) defined on the whole Preisach plane. It is theoretically shown that the experimental PD determined by the FORC method is an exact image of the CSD truncated outside of the so-called Preisach triangle. It is finally verified that the CSD improves the ferroelectric modeling on a wide range of electric field strength, including the Rayleigh zone.