First-order Reversal Curve Distribution Research Articles

Determination of demagnetizing factors using first-order reversal curves and ferromagnetic resonance

We present a method to quantitatively analyze magnetizing or demagnetizing interactions in arrayed nano-magnets by combining first-order reversal curve (FORC) and ferromagnetic resonance (FMR) measurement data. We develop a function to predict the resulting FORC distribution given: (1) a Gaussian intrinsic distribution in terms of the internal field and (2) a mean interaction field proportional to the sample’s magnetic moment. We then perform least-squares regression of our model on experimental FORC measurements of a nanowire array and of a thin film. Combining the obtained interaction field with an FMR fit result allows us to algebraically solve for the effective axial and transverse demagnetizing factors. Our experimental demagnetizing factors agree with expected values and provide quantitative evidence of the demagnetizing interaction between nanowires in an array.

Effects of neutron irradiation on magnetic first-order reversal curves in reactor pressure vessel steels

We report results of measurements of first-order reversal curves (FORCs) for neutron irradiated reactor pressure vessel steels to seek their possible application to a nondestructive evaluation of the irradiation hardening. We find a peak position of the FORC distribution, which is the second derivative of measured FORCs, shifts towards zero field after neutron irradiation, associated with the narrowing of the peak width. The observations indicate the progress of the magnetic softening and magnetic homogeneity under neutron irradiation. The present investigations demonstrate that FORCs can offer additional information on microstructural changes due to neutron irradiation, which can not be obtained by a conventional hysteresis method.

Reversible and Irreversible Processes in Drying and Wetting of Soil.

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

Micromagnetic simulations of first-order reversal curves in nanowire arrays using MuMax3

We perform simulations of magnetic reversal in a 3 × 3 array of nanowires using MuMax3 micromagnetic simulation program. We record a series of first-order reversal curves (FORCs) that form distinct branches of ascending minor curves depending on the initial magnetization state. We calculate the FORC distribution, which shows 9 positive primary peaks, representing single reversals of the 9 simulated nanowires. The primary peaks form an interaction field distribution (IFD), a common feature in experimental FORC distributions due to demagnetizing interactions. The FORC distribution also contains positive and negative secondary peaks due to differing magnetization during reversal. We demonstrate the use of MuMax3 simulations to relate FORC distribution features to visualized magnetic configurations.

Thermal aging effects on magnetisation reversals in a pre-deformed Fe-1wt%Cu alloy studied via first-order reversal curves

ABSTRACTWe report the results of measurements of first-order reversal curves (FORCs) for a thermally aged Fe-1wt%Cu alloy with different levels of rolling reduction. We find that the FORC distribution has a peak at high switching and interaction fields for samples with high rolling reductions and that this peak rapidly shifts towards lower fields after aging, which is associated with a narrowing of the peak. Conversely, after aging for more than 10,000 min, the peak exhibits an additional shift towards higher fields, which is associated with a broadening of the peak. These results indicate that both the microstructural homogeneity and the material hardening changes during thermal aging in a competitive way due to recovery and Cu precipitation, which is consistent with small-angle and wide-angle neutron scattering data.

Unraveling the Environment Influence in Bistable Spin-Crossover Particles Using Magnetometric and Calorimetric First-Order Reverse Curves

A first-order reversal curve (FORC) method is used here to analyze the unexpected change of memory characteristic of spin-crossover microparticles embedded in glass-forming or semicrystalline matrices, reflected in the larger hysteresis loop compared to the bulk. The huge reversibility shown by the reversal curves was attributed to the effect of the matrix, implying a variable external pressure and a cutoff–switch on mechanism of particle–matrix interactions. The FORC analysis indicates that heating and cooling processes in the case of matrix-embedded spin-crossover systems are driven by different mechanisms. In complement of standard magnetometry measurements, a calorimetry method, which demands an alternative method to extract FORC distributions, is introduced for tracking the signature of the composite transformation to understand and control the role of embedding matrices.

Investigation of switching behavior of acceptor-doped ferroelectric ceramics

Switching behavior is a general feature in ferroelectrics. The related fatigue effects influenced by defect dipoles in ferroelectrics are still controversial that is focused on the positive and negative effects of oxygen vacancies. Here, we report the polarization switching behavior of acceptor-doped ceramics using the first-order reversal curve (FORC) approach, especially for the abnormal self-rejuvenation effect and the enhanced fatigue endurance in acceptor-doped ceramics. The reversible and irreversible components under electric field in the ceramics were distinguished by the FORC distribution of ideal “hysteron”. The abnormal self-rejuvenation behavior stemmed from dispersive response of hysteron for undoped samples while from the redistribution of defect dipoles for acceptor-doped samples. The self-rejuvenation was induced mainly by the irreversible component. For the fatigue effect, the pinning of domain walls was not the main reason. The re-annealing treatment for a fatigued sample weakened the interactions between the spontaneous polarizations and defect dipoles, but enhanced the dispersion of coercive field. The enhancement of fatigue endurance came from the phase stability of structure in acceptor-doped ceramics, while complex phase evolution existed in undoped ceramic with weak fatigue endurance. Our study shed new light on the interactions between spontaneous polarization and defect dipoles under repetitive AC electric field.

Avoiding the zero-coercivity anomaly in first order reversal curves: FORC+

In conventional FORC (First Order Reversal Curve) analysis of a magnetic system, reversible and low-coercivity irreversible materials are treated as being qualitatively different: the FORC distribution shows low-coercivity materials but completely hides reversible (zero-coercivity) ones. This distinction is artificial – as the coercivity approaches zero, the physical properties of an irreversible material change smoothly into those of a reversible material. We have developed a method (called FORC+, implemented in free software at http://MagVis.org) for displaying the reversible properties of a system (a reversible switching-field distribution, R-SFD) together with the irreversible ones (the usual FORC distribution), so that there is no sudden discontinuity in the display when the coercivity becomes zero. We will define a “FORC+ dataset” to include the usual FORC distribution, the R-SFD, the saturation magnetization, and what we will call the “lost hysteron distribution” (LHD) such that no information is lost – the original FORC curves can be exactly recovered from the FORC+ dataset. We also give an example of the application of FORC+ to real data – it uses a novel complementary-color display that minimizes the need for smoothing. In systems which switch suddenly (thus having sharp structures in the FORC distribution) direct display of un-smoothed raw data allows visualization of sharp structures that would be washed out in a conventional smoothed FORC display.

Temperature dependence of magnetic first-order-reversal-curves for hollow Fe3O4 submicron particles

We report results of temperature dependence of first-order-reversal curves (FORCs) for hollow submicron particles with different outer diameter ranging from 400 to 700 nm. At low temperatures below the Verwey transition temperature, Tv, the FORC distribution exhibits a butterfly-like feature, associated with two pronounced FORC peaks, indicating the formation of a vortex structure for hollow Fe3O4 submicron particles. With increasing temperature from T = 10 K, the intensity of the two peaks steeply decreases and the peaks merge at T ∼ 130 K close to Tv. The results suggest a change of stability of the vortex state with temperature and were explained as due to a change of magnetic anisotropy associated with a structural transition at Tv.

Investigation of Switching Behavior of Acceptor-Doped Ferroelectric Ceramics

Switching behavior is a general feature in ferroelectrics. The related fatigue effects influenced by defect dipoles in ferroelectrics are still controversial that is focused on the positive and negative effect of oxygen vacancies. Here, we report the polarization switching behavior of acceptor-doped ceramics using the first-order reversal curve (FORC) approach, especially for the abnormal self-rejuvenation effect and the enhanced fatigue endurance in acceptor-doped ceramics. The reversible and irreversible components under electric field in the ceramics were distinguished by the FORC distribution of ideal “hysteron”. The abnormal self-rejuvenation behavior stemmed from dispersed response of hysteron for undoped samples while from the redistribution of defect dipoles for acceptor-doped samples. The self-rejuvenation was induced only by the irreversible component. For the fatigue effect, the pinning of domain walls was not the main reason. The re-annealing treatment for a fatigued sample weakened the interactions between the spontaneous polarizations and the defect dipoles, but enhanced the dispersion of coercive field. The structure decomposition was another reason for fatigue effect. The enhancement of fatigue endurance comes from the phase stability of structure in acceptor-doped ceramics, while complex phase evolution exists in undoped ceramic with weak fatigue endurance. Our study shed new light on the interactions between spontaneous polarization and defect dipoles under repetitive AC electric field.

First Order Reversal Curve Study of SmFe₂ Melt-Spun Ribbons.

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

Study on magnetic properties of NiFe/Cu multisegmented nanowire arrays with different Cu thicknesses via FORC analysis: coercivity, interaction, magnetic reversibility

Two sets of the large hexagonally ordered arrays of Ni30Fe70/Cu multisegmented nanowires (NWs) with different non-ferromagnetic (NFM) thicknesses of 4 and 12 nm were grown by ac pulse electrodeposition method into anodic aluminum oxide templates with a pore diameter of 40 nm and 100 nm inter-pore distance. The shape anisotropy of the single domain (SD) FM segments was varied from symmetrical-shaped (aspect ratio ~ 1) to rod-shaped (aspect ratio > 1). X-ray diffraction result showed a change in the crystalline phase from NiFe BCC (110) to Cu FCC (111) with increasing the NFM thickness. First-Order Reversal Curve (FORC) method was used to study magnetizing and demagnetizing interactions among the SD segments of the multisegmented NW arrays. The study mainly has been focused on the clarification of the effect of NFM thickness on magnetostatic interactions in the presence of high reversibility, which was estimated to be more than 50%. Weakening the magnetizing coupling of the FM segments through increasing NFM thickness is recognized by a ridge along the coercivity axis of the FORC diagram. With increasing the NFM thickness, the demagnetizing interactions decrease which can be a direct consequence of decreasing the magnetizing NFM thickness. Increasing the NFM thickness also leads to increasing the magnetic reversibility which is characterized on FORC diagrams by a shift in the FORC distribution to the lower coercivity values.

Magnetic vortex effects on first-order reversal curve (FORC) diagrams for greigite dispersions

First-order reversal curve (FORC) diagrams are used increasingly in geophysics for magnetic domain state identification. The domain state of a magnetic particle is highly sensitive to particle size, about which FORC diagrams provide valuable information. However, the FORC signal of particles with nonuniform magnetisations, which are the main carrier of natural remanent magnetisations in many systems, is still poorly understood. In this study, the properties of non-interacting, randomly oriented dispersions of greigite (Fe3S4) in the uniform single-domain (SD) to non-uniform single-vortex (SV) size range are investigated via micromagnetic calculations. Signals for SD particles (<50nm) are found to be in excellent agreement with previous SD coherent-rotation studies. A transitional range from ∼50nm to ∼80nm is identified for which a mixture of SD and SV behaviour produces complex FORC diagrams. Particles >∼80nm have purely SV behaviour with the remanent state for all particles in the ensemble in the SV state. It is found that for SV ensembles the FORC diagram provides a map of vortex nucleation and annihilation fields and that the FORC distribution peak should not be interpreted as the coercivity of the sample, but as a vortex annihilation field on the path to saturation.

FORC+ analysis of perpendicular magnetic tunnel junctions

We have studied magnetic tunnel junction (MTJ) thin-film stacks using the First Order Reversal Curve (FORC) method. The FORC distribution of these MTJs has very sharp features, unlike most particulate systems or patterned films. These features are hard to study using conventional FORC analysis programs that require smoothing because this washes out the features. We have used a new analysis program (FORC+) that is designed to distinguish fine-scale features from noise without the use of smoothing, to identify these features and gain information about the switching mechanism of the stack.

Forward Modeling of Thermally Activated Single‐Domain Magnetic Particles Applied to First‐Order Reversal Curves

AbstractTheoretical first‐order reversal curves (FORCs) were generated by numerically solving a thermally activated Stoner‐Wohlfarth model for assemblages of randomly oriented magnetic particles. The thermally activated Stoner‐Wohlfarth model extends previous models based on Preisach theory. The new numerical simulations show that the shapes of reversal curves and the FORC distributions are significantly modified by the effect of the thermal energy only if superparamagnetic particles are predominant. However, most assemblages containing moderate amounts of superparamagnetic particles are hardly distinguishable from stable single‐domain assemblages. The most relevant thermal effect is a reduction of coercivity that translates in a shift of the FORC distribution toward the origin. Not all of the distinctive characteristics previously predicted for superparamagnetic grain assemblages were confirmed by our calculations, and most of the observed modifications due to thermal effects can be considered minor. A direct comparison with hysteresis parameters shows that these simpler experiments can be equally effective in characterizing viscous and superparamagnetic particles.

Microscopic reversal magnetization mechanisms in CoCrPt thin films with perpendicular magnetic anisotropy: Fractal structure versus labyrinth stripe domains

The magnetization reversal of CoCrPt thin films has been examined as a function of thickness using magneto-optical Kerr effect (MOKE) microscopy and first-order reversal curves (FORC) techniques. MOKE images show differentiated magnetization reversal regimes for different film thicknesses: while the magnetic domains in 10-nm-thick CoCrPt film resemble a fractal structure, a labyrinth stripe domain configuration is observed for 20-nm-thick films. Although FORC distributions for both cases show two main features related to irreversible processes (propagation and annihilation fields) separated by a mostly flat region, this method can nonetheless distinguish which magnetization reversal process is active according to the horizontal profile of the first FORC peak, or propagation field. A single-peak FORC profile corresponds to the fractal magnetization reversal, whereas a flat-peak FORC profile corresponds to the labyrinth magnetization reversal.

Magnetization Reversal of Three-Dimensional Nickel Anti-Sphere Arrays

Three-dimensional antisphere arrays (3DAAs) of Ni have been fabricated using electrochemical deposition into self-assembled polystyrene sphere templates, which offers the advantage of straightforward scalability. Using the first-order reversal curve (FORC) method, the magnetic reversal mechanism is identified from the characteristic features in the FORC distribution. A left-bending boomerang-like feature is observed in the thinnest sample, which transforms to a ridge oriented along the local coercivity $H_{c}$ axis with increasing sample thickness. This transformation identifies a change in the reversal process from an exchange dominated domain-growth reversal to a localized weakly interacting particle-like reversal. Micromagnetic simulations confirm the decrease in domain growth and increase of pinning behaviors as the thickness of the Ni 3DAAs structure increases, providing strong support to the FORC analysis and interpretation.

Investigation of effects of long-term thermal aging on magnetization process in low-alloy pressure vessel steels using first-order-reversal-curves

We have investigated effects of long-term thermal aging at 550°C up to 10000 h on major-loop coercivity, hysteresis scaling of minor loops, and first-order reversal curves (FORCs) for low-alloy pressure vessel steels with low and high Ni contents. While major-loop coercivity and minor-loop coefficient of the scaling exhibit a gradual decrease with aging for high-Ni steel, those for low-Ni one are very weakly dependent on aging time. On the other hand, we found that FORC distribution becomes steep along both axes of interaction and switching fields and the peak shifts toward a lower switching field for both steels. Considering that there is no significant development of nanoscale precipitates during the aging as revealed with small-angle neutron scattering experiments, a relaxation of lattice strain in a matrix, possibly associated with diffusion of Ni atoms, may dominate magnetic properties at 550°C.

The effects of 10 to &gt;160 GPa shock on the magnetic properties of basalt and diabase

AbstractHypervelocity impacts within the solar system affect both the magnetic remanence and bulk magnetic properties of planetary materials. Spherical shock experiments are a novel way to simulate shock events that enable materials to reach high shock pressures with a variable pressure profile across a single sample (ranging between ∼10 and &gt;160 GPa). Here we present spherical shock experiments on basaltic lava flow and diabase dike samples from the Osler Volcanic Group whose ferromagnetic mineralogy is dominated by pseudo‐single‐domain (titano)magnetite. Our experiments reveal shock‐induced changes in rock magnetic properties including a significant increase in remanent coercivity. Electron and magnetic force microscopy support the interpretation that this coercivity increase is the result of grain fracturing and associated domain wall pinning in multidomain grains. We introduce a method to discriminate between mechanical and thermal effects of shock on magnetic properties. Our approach involves conducting vacuum‐heating experiments on untreated specimens and comparing the hysteresis properties of heated and shocked specimens. First‐order reversal curve (FORC) experiments on untreated, heated, and shocked specimens demonstrate that shock and heating effects are fundamentally different for these samples: shock has a magnetic hardening effect that does not alter the intrinsic shape of FORC distributions, while heating alters the magnetic mineralogy as evident from significant changes in the shape of FORC contours. These experiments contextualize paleomagnetic and rock magnetic data of naturally shocked materials from terrestrial and extraterrestrial impact craters.

Magnetic fingerprint of interfacial coupling between CoFe and nanoscale ferroelectric domain walls

Magnetoelectric coupling in ferromagnetic/multiferroic systems is often manifested in the exchange bias effect, which may have combined contributions from multiple sources, such as domain walls, chemical defects, or strain. In this study we magnetically “fingerprint” the coupling behavior of CoFe grown on epitaxial BiFeO3 (BFO) thin films by magnetometry and the first-order-reversal-curves (FORC). The contribution to exchange bias from 71°, 109° and charged ferroelectric domain walls (DWs) was elucidated by the FORC distribution. CoFe samples grown on BFO with 71° DWs only exhibit an enhancement of the coercivity, but little exchange bias. Samples grown on BFO with 109° DWs and mosaic DWs exhibit a much larger exchange bias, with the main enhancement attributed to 109° and charged DWs. Based on the Malozemoff random field model, a varying-anisotropy model is proposed to account for the exchange bias enhancement. This work sheds light on the relationship between the exchange bias effect of the CoFe/BFO heterointerface and the ferroelectric DWs, and provides a path for multiferroic device analysis and design.