First-order Reversal Curve Distribution Research Articles

Investigation of transverse exchange-springs in electrodeposited nano-heterostructured films through first-order reversal curve analysis

The prerequisite of efficient exchange-spring nano-heterostructures, i.e., tuning both hard and soft phases at a nanometer level, has posed significant preparation challenges to ensure effective exchange-coupling. Here, we present a novel approach to fabricate transverse exchange-spring nano-heterostructures using single starting material through an “in situ” electrodeposition technique at room temperature. Utilizing modified acidic bath chemistry and controlled hydrogen evolution, we successfully prepared stress-free, shiny, fine-grained amorphous, and nanocrystalline Co-rich cobalt phosphorus films. These nano-heterostructured films exhibit a unique non-collinear anisotropy-driven transverse exchange-spring behavior, investigated systematically under ambient conditions. The comprehensive functional analyses reveal that intricate interplay between in-plane (IP) anisotropy of amorphous phase and out-of-plane (OOP) anisotropy generating from a nanocrystalline structure compete with each other, while producing characteristic stripe domain structures to novel corrugated stripe domain shapes. The angle-dependent first-order reversal curve distributions demonstrate new insights into the magnetic reversal mechanisms, further confirming the non-exchange-spring and exchange-spring nature of the films depending on the prevalent interfacial exchange coupling. Formation of anisotropy-driven metastable-state due to competition between IP and OOP anisotropy at a particular OOP orientation has led the normal exchange-spring structures to a transverse exchange-spring structure. Micromagnetic simulations, in excellent agreement with experimental data, further elucidate the formation of characteristic stripe domain patterns and the influence of anisotropy on the magnetic properties. The innovative methodology and detailed functional analysis presented here offer significant understanding to the field of exchange-spring magnetic materials, including anisotropy-driven metastable states, demonstrating the potential for scalable and cost-effective fabrication of advanced nano-heterostructures with tailored magnetic properties.

Micromagnetic Determination of the FORC Response of Paleomagnetically Significant Magnetite Assemblages

AbstractMicromagnetic modeling allows the systematic study of the effects of particle size and shape on the first‐order reversal curve (FORC) magnetic hysteresis response for magnetite particles in the single‐domain (SD) and pseudo‐single domain (PSD) particle size range. The interpretation of FORCs, though widely used, has been highly subjective. Here, we use micromagnetics to model randomly oriented distributions of particles to allow more physically meaningful interpretations. We show that one commonly found type of PSD particle—namely the single vortex (SV) particle—has far more complex signals than SD particles, with multiple peaks and troughs in the FORC distribution, where the peaks have higher switching fields for larger SV particles. Particles in the SD to SV transition zone have the lowest switching fields. Symmetrical and prolate particles display similar behavior, with distinctive peaks forming near the vertical axis of the FORC diagram. In contrast, highly oblate particles produce “butterfly” structures, suggesting that these are potentially diagnostic of particle morphology. We also consider FORC diagrams for distributions of particle sizes and shapes and produce an online application that users can use to build their own FORC distributions. There is good agreement between the model predictions for distributions of particle sizes and shapes, and the published experimental literature.

Effects of Mn doping on the conduction mechanism and dielectric nonlinearity of Na0.5Bi0.5TiO3 thin film

In this work, the conduction mechanism and dielectric nonlinearity of undoped and Mn-doped Na0.5Bi0.5TiO3 (NBT) films were investigated. The potential conduction mechanism in relatively low electric fields should be dominated by hopping conduction rather than typical Ohmic conduction. In the high electric field region, the conduction mechanism is dominated by Poole–Frenkel emission and Schottky emission. The enhancement of electrical insulation of NBT films after Mn doping was shown to result from a decrease in oxygen vacancies and elevation of the conduction energy barrier. Furthermore, significant improvements in the nonlinearity of both the dielectric constant and polarization of Mn-doped NBT films were observed, as indicated by the results of Rayleigh fitting and first-order reversal curve distributions. Such enhancements were attributed to the reduction in domain wall pinning, decreased interference from electrostatic potential and improved leakage characteristics.

Magnetization process of cubic Fe3O4 submicron particles: First-order reversal curves and neutron diffraction studies

We have studied magnetization process of 260 nm sized cubic Fe3O4 particles below and above the Verwey transition temperature Tv∼ 110 K, by measurements of magnetic first-order reversal curves (FORCs) and high-resolution power neutron diffraction. The FORC diagram exhibits two distinct FORC distribution peaks below Tv, which shift towards the origin, merge into a single peak on heating, whereas only a single FORC peak appears above Tv. Neutron diffraction measurements under magnetic fields revealed a minimum of the magnetic intensity at a magnetic field of ∼−300 Oe, being close to the reversal field where the FORC peak is located. These results were interpreted as due to a reorientation and reversal of a spin vortex core, which accompany a large magnetic irreversibility.

Disentangling between static and kinetic effects in the hysteresis of spin crossover molecular magnets

"We investigate the kinetic hysteresis of spin crossover molecular magnets, with the aim of unravelling the link between static and dynamical effects observed in the first order reversal curves (FORC) diagrams. Using a mean-field model, we establish how the FORCs distributions are influenced by both the kinetic effects and the physical parameters of the system."

Investigation of magnetization reversal and domain structures in perpendicular synthetic antiferromagnets by first-order reversal curves and magneto-optical Kerr effect

Perpendicular synthetic-antiferromagnet (p-SAF) has broad applications in spin-transfer-torque magnetic random access memory and magnetic sensors. In this study, the p-SAF films consisting of (Co/Ni)3]/Ir(t Ir)/[(Ni/Co)3 are fabricated by magnetron sputtering technology. We study the domain structure and switching field distribution in p-SAF by changing the thickness of the infrared space layer. The strongest exchange coupling field (H ex) is observed when the thickness of Ir layer (t Ir) is 0.7 nm and becoming weak according to the Ruderman–Kittel–Kasuya–Yosida-type coupling at 1.05 nm, 2.1 nm, 4.55 nm, and 4.9 nm in sequence. Furthermore, the domain switching process between the upper Co/Ni stack and the bottom Co/Ni stack is different because of the antiferromagnet coupling. Compared with ferromagnet coupling films, the antiferromagnet samples possess three irreversible reversal regions in the first-order reversal curve distribution. With t Ir increasing, these irreversible reversal regions become denser and smaller. The results from this study will help us understand the details of the magnetization reversal process in the p-SAF.

Enhancement of recoverable energy density and efficiency of K0.5Na0.5NbO3 ceramic modified by Bi(Mg0.5Zr0.5)O3

As one of the most popular lead-free energy storage materials, K0.5Na0.5NbO3 (KNN)-based ceramics are expected to replace lead-based ceramics due to their high dielectric constant, high Curie temperature, and environmental friendliness. However, the high remnant polarization (Pr) and low breakdown strength (BDS) of KNN ceramic lead to its low energy storage properties, which limits its applications in energy storage field. In this work, the energy storage properties of KNN ceramic were improved by reducing average grain size and enhancing relaxor behavior. The 0.85K0.5Na0.5NbO3-0.15Bi(Mg0.5Zr0.5)O3 (0.85KNN-0.15BMZ) ceramic prepared by the solid state method not only has high recoverable energy storage density value (Wrec) of 3.47 J cm-3 but also has high energy storage efficiency value (η) of 89.14% at a high applied electric field of 320 kV/cm. In addition, the Wrec and η of 0.85KNN-0.15BMZ ceramic fluctuate slightly over the whole temperature range of 20–120 °C at 200 kV/cm, showing excellent temperature stability. At the same time, it can be concluded by first-order reversal curve distribution that 0.85KNN-0.15BMZ ceramic has excellent energy storage properties due to their enhanced relaxor behavior. In summary, the 0.85KNN-0.15BMZ ceramic can be used as the novel dielectric capacitor materials.

Magnetic Interactions in Wiegand Wires Evaluated by First-Order Reversal Curves.

Wiegand wires exhibit a unique fast magnetization reversal feature in the soft layer that is accompanied by a large Barkhausen jump, which is also known as the Wiegand effect. However, the magnetic structure and interaction in Wiegand wires cannot be evaluated by conventional magnetization hysteresis curves. We analyzed the magnetic properties of Wiegand wires at various lengths by measuring the first-order reversal curves (FORCs) and by evaluating the FORC diagram from a series of FORCs. In particular, we used a FeCoV Wiegand wire with a magnetic soft outer layer, an intermediate layer, and a hard core. The magnetization of the various layers in the wire could be identified from the FORC diagrams. Furthermore, based on the interaction between multiple layers, the positive and negative polarity of the FORC distribution was clarified.

Resolving magnetic contributions in BiFeO3 nanoparticles using First order reversal curves

BiFeO3 (BFO) nanoparticles (NPs) were studied using First-Order Reversal Curve (FORC) and temperature-dependent magnetometry measurements. The BFO NPs were fabricated by a sol–gel method, while the crystal structure and the average particle radius were obtained by powder X-ray diffraction analysis and Small-Angle X-Ray Scattering (SAXS) measurements, respectively. The NP size varies below and above the typical bulk BFO spin cycloid length (λ= 62 nm). Below λ, the NPs show ferromagnetic-like hysteresis loops where the saturation magnetization decreases while nanoparticle size rises. This magnetic behavior changes for NP size over λ, which only exhibits a paramagnetic contribution. The FORC distributions indicate the presence of two competing size-dependent contributions to the observed magnetic signal Also, the FORC distributions show that in the ferromagnetic regime there are two competing size-dependent contributions to the observed magnetic signal. Our results suggest the existence of a magnetic core–shell structure in NPs below λ, possibly driven by the strong spin–lattice coupling.

FORC analysis of nanopatterned vs unpatterned films: Coercivity and switching mechanisms

We have studied the use of self-assembled block copolymers to pattern multilayers of Co and Pd on silicon wafers. Stacks ranging from four to twelve bilayers of Co (0.3 nm)/Pd (0.8 nm) were sputtered onto Ta/Pd seed layers and capped with 3 nm of Ta and were found to have perpendicular magnetic anisotropy as-deposited. The block copolymer polystyrene-block-poly(ferrocenyl dimethylsilane) (PS-b-PFS) was dissolved in toluene and spun onto the wafers. The polymers were phase-separated by heat treatment, leaving self-assembled PFS spheres embedded in PS, which was removed by oxygen-plasma ashing. The PFS spheres were then used as masks to ion-mill the Co/Pd multilayers into nanopillars. To study the effect of etch time and etch angle on the coercivity distribution, we synthesized samples in a Design of Experiments-(DoE)- in these two factors. Scanning electron micrographs showed nanopillars ranging from 15 to 30 nm in diameter, depending primarily on etch time. M-H loops measured on both patterned and unpatterned wafers showed an increase of up to 130% in overall coercivity upon patterning. First Order Reversal Curves (FORC) were measured, and the resulting FORC distributions displayed using a smoothing program (FORCinel) and one that can display the raw data without smoothing (FORC+). We find that FORC+ reveals information about fine-scale structure and switching mechanism that cannot be seen in the smoothed display.

Domain Dynamics and Local Level Switching Behaviors of Sol–Gel Nanopowder-Derived Lead-Free Piezoelectric Bi0.5(Na0.78K0.22)0.5TiO3 Ceramics

The material properties of sol–gel nanopowder-derived lead-free Bi0.5(Na0.78K0.22)0.5TiO3 (BNKT) ceramics are systematically investigated for high-response piezoelectric device applications. To elucidate the principle of the domain dynamics and local level ferroelectric switching behaviors of environmentally friendly BNKT ceramics, we systematically analyze the Rayleigh parameters and the first-order reversal curve (FORC) of the BNKT ceramics and compare the results with those of the standard measurement method. Based on the characterization of Rayleigh parameters, it is clarified that the contribution of the domain-wall motion of the sol–gel-derived BNKT ceramics is higher than that of solid-state reaction-derived ceramics. We also analyze the FORC distribution diagram-associated hysteron density functions for visualizing reversible and irreversible contributions of domain walls and switching behaviors above the Rayleigh regime. The switching behaviors are explained by considering the defects and microstructural differences of the BNKT ceramics, which are affected by both reversible and irreversible contributions. The sol–gel-derived BNKT ceramics show highly localized and well-defined FORC distribution diagrams with the sharp maximum of the irreversible component and the low reversible contribution, which clearly indicate more homogeneous switching properties and less defects than solid-state reaction-derived ceramics because each switching unit gives almost identical contributions to the total polarization. In this study, the developed technique and gained information are used to explore a fundamental understanding of the domain dynamics and local level switching behaviors of lead-free piezoelectric ceramics. We believe that our investigation certainly positions itself in various multifunctional electronic applications without using toxic lead-based piezoelectrics.

Magnetic Domain State and Anisotropy in Hematite (α‐Fe2O3) From First‐Order Reversal Curve Diagrams

AbstractHematite carries magnetic signals of interest in tectonic, paleoclimatic, paleomagnetic, and planetary studies. First‐order reversal curve (FORC) diagrams have become an important tool for assessing the domain state of, and magnetostatic interactions among, magnetic particles in such studies. We present here FORC diagrams for diverse hematite samples, which provide a catalog for comparison with other studies and explain key features observed for hematite. Ridge‐type signatures typical of uniaxial single‐domain particle assemblages and “kidney‐shaped” FORC signatures, and combinations of these responses, occur commonly in natural and synthetic hematite. Asymmetric features that arise from the triaxial basal plane anisotropy of hematite contribute to vertical spreading in kidney‐shaped FORC distributions and are intrinsic responses even for magnetostatically noninteracting particles. The dominant FORC distribution type in a sample (ridge, kidney‐shaped, or mixture) depends on the balance between uniaxial/triaxial switching. The identified signals explain magnetization switching and anisotropy features that are intrinsic to the magnetic properties of hematite and other materials with multiaxial magnetic anisotropy.

High-frequency GMI hysteresis effect analysis by first-order reversal curve (FORC) method

In this work, we investigate the giant magnetoimpedance (GMI) hysteresis at high-frequency (10 MHz – 1 GHz) of Co-based amorphous magnetic ribbons. The first-order reversal curve (FORC) method was used to analyze their hysteretic behavior present at a low magnetic field (below 7 Oe). Results show that the GMI hysteresis is related to both the system magnetic anisotropy and the current frequency (through the skin depth). The GMI hysteresis gradually decreases upon frequency increase before disappearing, while a clockwise rotation of the FORC distributions is observed. These results are attributed to a heterogeneous magnetic structure in the magnetic ribbon volume. On the other side, while the cut-off frequency depends on the magnetic anisotropy strength, an inverted GMI hysteresis revives for the higher anisotropy ribbon. Above this frequency inversion, FORC results indicate a hardening of the effective switching field as a thicker region is probed. We propose that in this case, the stronger perpendicular anisotropy creates important differences between the superficial and volumetric anisotropy, enough to induce interaction between the two regions of different magnetization directions. This sensitive FORC protocol can be applied for investigating the GMI hysteresis, and thus the complex magnetic structure of several soft magnetic systems.

Temperature-modulated magnetic skyrmion phases and transformations analysis from first-order reversal curve study

We performed a temperature-modulated first-order reversal curve (FORC) study on a Pt/Co/Fe/Ir magnetic stack that exhibited a magnetic phase transition from isolated skyrmions to skyrmion lattice with increasing temperature. Using in situ magneto-optical Kerr imaging, a generalized description of domain transformations associated with the FORC distribution peaks at both their reversal and sweeping field are derived to allow for direct analysis from the FORC diagram. The sweeping field of the peak, which is commonly ignored in analysis, is identified as the process of domain propagation or nucleation towards terminal domain separation. This process is found to be essential in inducing magnetization irreversibility to reveal domain transformations. In addition, a model characterized by the FORC distribution peaks was developed to describe the transition from the isolated skyrmion to skyrmion lattice phase as well as to identify important field ranges for the transformations. This study establishes an intuitive form of analysis for the otherwise abstract data of FORC distribution for the characterization of magnetic skyrmions in the active field of skyrmionics.

Magnetic investigations on irradiation-induced nanoscale precipitation in reactor pressure vessel steels: A first-order reversal curve study

We have investigated magnetic properties for reactor pressure vessel model alloys with variable Cu contents, subjected to neutron irradiation up to a fluence of 9 × 10 19 n cm − 2 . Unlike a monotonic increase of microhardness with neutron fluence, the major-loop coercivity decreases at a higher fluence and the decrease becomes larger for the alloy containing a higher amount of Cu. The measurements of first-order reversal curves (FORCs) for the high-Cu alloy show that the position of the FORC distribution peak shifts toward a lower coercivity just after neutron irradiation, followed by a slight increase, associated with the broadening along both the coercivity and interaction field axes. The results can be explained by the enhancement of magnetic inhomogeneity in a matrix due to Cu precipitation and an increasing magnetostatic interaction between local magnetic regions with different coercivity. The magnetic method using FORCs can be a possible technique which provides in-depth information on microstructural changes due to neutron irradiation, which is not obtained by measurements of a conventional major hysteresis loop.

Reconstructing phase-resolved hysteresis loops from first-order reversal curves

The first order reversal curve (FORC) method is a magnetometry based technique used to capture nanoscale magnetic phase separation and interactions with macroscopic measurements using minor hysteresis loop analysis. This makes the FORC technique a powerful tool in the analysis of complex systems which cannot be effectively probed using localized techniques. However, recovering quantitative details about the identified phases which can be compared to traditionally measured metrics remains an enigmatic challenge. We demonstrate a technique to reconstruct phase-resolved magnetic hysteresis loops by selectively integrating the measured FORC distribution. From these minor loops, the traditional metrics—including the coercivity and saturation field, and the remanent and saturation magnetization—can be determined. In order to perform this analysis, special consideration must be paid to the accurate quantitative management of the so-called reversible features. This technique is demonstrated on three representative materials systems, high anisotropy FeCuPt thin-films, Fe nanodots, and SmCo/Fe exchange spring magnet films, and shows excellent agreement with the direct measured major loop, as well as the phase separated loops.

Evidence of residual ferroelectric contribution in antiferroelectric lead-zirconate thin films by first-order reversal curves

In this study, two different methods have been used in order to characterize lead-zirconate antiferroelectric thin film elaborated by a modified sol-gel process: First-Order Reversal Curves (FORC) measurements and impedance spectroscopy coupled to hyperbolic law analysis. Approaches at low and high applied electric fields allow concluding on the presence of a weak residual ferroelectric behavior even if this contribution is not visible on the polarization-electric field loops. Moreover, the weak ferroelectric phase seems to switch only when the phase of the antiferroelectric cells is modified and no coalescence of ferroelectric domains at the low field occurs due to a well distribution of small residual ferroelectric clusters in the material. The main goal of this paper is to show that FORC distribution measurements and impedance spectroscopy coupled to the hyperbolic law analysis are very sensitive and complementary methods.

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.

Mechanism of the enhanced coercivity for the dual-main-phase Ce\u2013Fe\u2013B magnet

The high coercivity of Nd–Fe–B magnets can also be obtained in the Ce–Fe–B magnets fabricated via the dual-main-phase (DMP) method in which the high abundance Ce was used to substitute Nd(Pr). The inhomogeneous distributions of the matrix grains in the DMP magnet play a key role in the enhanced magnetic performance. Compared with the single-phase magnet, more grain boundary phases encapsulating the matrix 2:14:1 grain are formed in the DMP magnet, which reduce the exchange coupling between adjacent magnetic grains. The switching field distribution and the interaction field distribution of the Ce–Fe–B magnets were determined by the first-order-reversal curves (FORC). The switching field peaks around 6 kOe, 11 kOe and 12 kOe in the FORC distribution indicate that three major reversal components coexist for the DMP magnet. The overlapp of the second and third switching field peaks reveals the presence of a pinning interaction within individual magnetic grains with a core–shell structure, which further improve the coercivity of the magnet.

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.