First-order Reversal Curve Measurements Research Articles

Design and development of a first order reversal curve measurement enabled variable temperature vibrating sample magnetometer

In this paper we present the design, construction and calibration of a sensitive vibrating sample magnetometer (VSM) and temperature variable setup with a capability to measure magnetization of magnetic materials from 100 K to 400 K with First Order Reversal Curve (FORC) measurement facility. It uses a bipolar power supply to energize an electromagnet capable of attaining ±1 Tesla field, subwoofer speaker for vibrating the sample and the induced voltage in four coil setup is measured by a lock-in amplifier. All hardware is controlled by a customized LabView program. The cryostat is designed such that the temperature can be varied continuously from 100 K to 400 K using liquid nitrogen up to room temperature and forced nitrogen gas/air for high temperatures study. We report here the VSM sensitivity of up to 10−2 emu/gm and can measure much weaker signals. The FORC protocol in this system is implemented via a dedicated virtual instrument in LabView capable of magnetic field reversal and termination at appropriate point to study domain nucleation field. The detailed analysis of the data is done using the open-source resources. We present the FORC measurement for Co0.5Zn0.5Fe2O4, a ferrimagnet. To establish the sensitivity of the instrument we present the results of magnetization measurement with temperature and phase transition study of La0.4Ca0.6MnO3 and La0.75Sr0.25MnO3.

The physical origin of inhomogeneous field within HfO2-based ferroelectric capacitor

In this work, the origins of the inhomogeneous field within the HfO2-based ferroelectric (FE) capacitor are investigated. We propose a model to simulate the relationship between the reversed polarization and the applied pulses with different amplitudes and durations. The electric field distribution is considered to be influenced by the ferroelectric layer thickness (tFE) and the built-in field (Eb). Then, the distribution parameters of both two physical factors and the Merz law, which define the switching dynamics, could be obtained by fitting the experimental results. Comparing with the results of high-resolution transmission electron microscope and first-order reversal curve measurements, it can be reasonably concluded that the physical origin of the inhomogeneous field in HfO2-based ferroelectrics is the random distribution of tFE and Eb. This work improves the understanding of the switching dynamics by providing the origins of the inhomogeneous field in an FE film.

Angular first-order reversal curve analysis of FeNi/Cu multilayered nanowire arrays with different diameters

The main goal of the emerging field of spintronics is the shrinkage of materials and devices while improving their magnetic performance for a variety of applications, especially three-dimensional information storage. This stipulates the understanding of fundamental magnetic mechanisms such as magnetization reversal and switching events in multilayer systems with tunable size. Here, a porous anodic alumina membrane-assisted electrochemical deposition method is employed to fabricate FeNi/Cu multilayered nanowire arrays (MNWAs) with diameters in the range of D = 35–80 nm. Angular magnetic properties of these MNWAs are investigated via hysteresis loop and first-order reversal curve (FORC) measurements for angle fields of 0° ≤ θ ≤ 90°. While the former indicates the existence of different contributions of vortex domain wall propagation for smaller (D ≤50 nm) and larger (D >50 nm) diameters, the latter reveals the occurrence of single vortex states, depending on θ and D. Moreover, at θ = 0°, a transition from single domain to multidomain-like behavior appears to occur with increasing D from 35 to 80 nm based on FORC diagrams, significantly influencing magnetization reversibility of magnetic FeNi segments with relatively high aspect ratios (>5). The variation of magnetostatic interactions with respect to θ is discussed and compared at each diameter as an effective factor in determining angular magnetic properties. Also, the axial variation behavior of coercivity as a function of D is correlated with changes in the reversible percentage, shedding light on the expectations from the vortex domain wall propagation.

Magnetization processes in two-dimensional arrays of iron nanowires

Arrays of iron nanowires (NWs) obtained by template-assisted electrodeposition constitute a promising composite material characterized by a combination of high magnetization in the filler and perpendicular magnetic anisotropy. The properties of these composites arise from the interplay between the behavior of individual NWs and their magnetostatic interactions. In this study, we investigated NW arrays with identical wire diameters but varying spatial arrangements. Major hysteresis loops were studied under various field directions relative to the NW axis. Key parameters such as the slope of the magnetization curve, saturation magnetization, and coercive force were quantified. Additionally, FORC (First Order Reversal Curve) measurements were conducted with the field oriented longitudinally with respect to the NW, offering insights into the inhomogeneity of the demagnetizing field influenced by the NW array's configuration. In the sample with the highest NW density, we observed isotropic behavior of the effective demagnetizing field, and we proposed an explanation for this phenomenon using the effective media approach. Micromagnetic simulations revealed that the magnetic behavior of individual NWs with a 100 nm diameter can be described as an interchange between volumes characterized by vortex and uniform magnetization patterns. Calculations of the demagnetizing field using the effective medium model demonstrated excellent agreement with experimental data across arrays featuring different NW densities. Remarkably, the quantitative consistency of coercive field values obtained from micromagnetic simulations and experimental measurements in the range of angles from 0° to 45° for the studied samples underscores the structural homogeneity of the obtained NWs.

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.

Study of the long time relaxation of the weak ferroelectricity in PbZrO3 antiferroelectric thin film using Positive Up Negative Down and First Order Reversal Curves measurements

The weak ferroelectric contribution to the polarization of antiferroelectric lead zirconate (PZO) thin films has been investigated using PUND (Positive Up Negative Down) pulse measurements and hysterons decomposition by First Order Reversal Curves (FORC) technique. The PUND allows decomposing the measured current, obtained from the polarization-electric field loop measurements, into a switching and a non-switching contribution. We show that the weak ferroelectric phase is enhanced when a large electric field has been previously applied to the material, in order to switch from the antiferroelectric to the ferroelectric phase. Using the PUND measurement at fields below the antiferroelectric to ferroelectric phase transition, the polarization loop corresponding only to the ferroelectric switching contribution has been determined revealing that this contribution to the overall polarization is small. FORC measurements, however, indicate that the ferroelectric phase is present at different fields. At low fields, a quite homogeneous distribution of hysterons exists and at large field, a high concentration of hysterons at a field near to the antiferroelectric to ferroelectric phase transition can be seen. Moreover, when changing the delay between pulses of the PUND and the FORC measurements, we show that this weak ferroelectricity contribution is metastable and decreases with time.

Understanding magnetic interactions and reversal mechanisms in a spinodally decomposed cobalt ferrite using first order reversal curves

Cobalt ferrites exhibit widely varied magnetic behaviour due to the presence of a miscibility gap leading to the formation of periodic self-assembled nanostructures via spinodal decomposition. Periodicity and amplitude of the compositional fluctuations can be controlled by thermodynamic and kinetic processing parameters which allows for careful tuning of the magnetic properties. Although reports have shown evidence of spinodal decomposition, there is a lack of detailed characterization of the magnetic interactions and reversal mechanisms in these materials. In this work we use high-resolution first order reversal curves (FORC) measurements to understand the underlying magnetic processes occurring in a cobalt ferrite with a nominal composition of Co1.8Fe1.2O4 before (calcined) and after spinodal decomposition (annealed). Additionally, FORC measurements with preconditioning fields were conducted to separate the interaction signatures at low coercive fields by biasing the sample in positive and negative mean fields. Microstructural characterization using TEM combined with EDS showed uniform chemistry in the calcined sample and the presence of Fe rich and Co rich regions in the annealed sample, due to spinodal decomposition. Signs of positive exchange interactions were observed in both calcined and annealed samples. This work presents the first detailed magnetic characterization of magnetic interactions in a nanostructured cobalt ferrite, and provides an example of magnetic characterization of nanostructured ferrites using FORC.

In-plane magnetic anisotropy and magnetization reversal in phase-separated (La0.5Pr0.5)0.625Ca0.375MnO3 thin films

The dynamics and interaction of different electronic phases near the metal-to-insulator transition of the phase-separated ${({\mathrm{La}}_{0.5}{\mathrm{Pr}}_{0.5})}_{0.625}{\mathrm{Ca}}_{0.375}\mathrm{Mn}{\mathrm{O}}_{3}$ (LPCMO) thin film grown on NGO substrate was studied using the first-order reversal curves (FORC) diagram method for electric transport measurements. The in-plane angle-dependent remanence and coercivity field in the region of the ferromagnet metallic phase was measured using the macroscopic magnetization technique. These measurements suggest an in-plane uniaxial magnetic anisotropy for the film with a uniaxial anisotropic constant (Ku) of $\ensuremath{\sim}1.2\ifmmode\times\else\texttimes\fi{}{10}^{6}\phantom{\rule{0.16em}{0ex}}\mathrm{erg}/\mathrm{c}{\mathrm{m}}^{3}$ at 20 K. The angle dependence of the coercivity is best described by 1/cos\ensuremath{\theta} dependence indicating that the magnetization reversal occurs mainly through the depinning of the domain wall, a signature of nucleation and propagation mechanism. The correlation of FORC measurements, resistance relaxation, and macroscopic magnetic measurements indicate a fast reversal of electronic and magnetic phases towards the denser phase region and strong interaction of different phases for the LPCMO system.

Element-specific first order reversal curves measured by magnetic transmission x-ray microscopy

The first-order reversal curve (FORC) method is a macroscopic measurement technique that can be used to extract quantitative and microscopic properties of hysteretic systems. Using magnetic transmission x-ray microscopy (MTXM), local element-specific FORC measurements are performed on a 20 nm thick film of CoTb. The FORCs measured with microscopy reveal a step-by-step domain evolution under the magnetic field cycling protocol and provide a direct visualization of the mechanistic interpretation of FORC diagrams. They are compared with magnetometry FORCs and show good quantitative agreement. Furthermore, the high spatial resolution and element-specific sensitivity of MTXM provide new capabilities to measure FORCs in small regions or specific phases within multicomponent systems, including buried layers in heterostructures. The ability to perform FORCs on very small features is demonstrated with the MTXM-FORC measurement of a rectangular microstructure with vortex-like Landau structures. This work demonstrates the confluence of two uniquely powerful techniques to achieve quantitative insight into nanoscale magnetic behavior.

Antiferromagnet thickness dependence and rotatable spins in exchange biased CoO/Fe films

The emergence of exchange bias and coercivity enhancement has been investigated in epitaxial CoO/Fe films with varied antiferromagnet (AF) thicknesses, even smaller than the critical value where the frozen CoO spins are detectable. Vector magnetometry and first-order reversal curve (FORC) measurements reveal different CoO thickness dependence of the exchange bias and coercivity enhancement, including the evolution of magnetization reversal from a high coercivity, low bias phase due to rotatable CoO moments to a high bias, low coercivity phase due to frozen CoO moments. The AF domain state is found to be metastable, which can be reoriented by external and exchange fields prior to the appearance of frozen spins, pointing to a generic origin of the training effect. Monte Carlo simulations show that the AF anisotropy energy barrier and the rotatable spins induced by magnetic field and exchange interaction at the interface are responsible for the observed effects.

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.

Observation and Characterization of Recoverable Fatigue Process Under Low-Electric Field (<1.8MV/cm) in HfZrO Ferroelectric Film

It is widely believed that the fatigue process of ferroelectric HfZrO (HZO) film is a permanent damage and unrecoverable, which can be regarded as a Time Dependent Dielectric Breakdown (TDDB) process. In this work, the fatigue process of HZO film under low-electric field is found to be irrelevant to defect generation. Furthermore, this fatigued device can be recovered by higher voltage stimulus and then switch normally with lower voltage pulses. This observed recoverable fatigue process is systematically investigated by the conductance method and the first-order reversal curve (FORC) measurement and the mechanism is attributed to electron de-trapping. This observed recoverable fatigue process gives the new insights on the endurance failure mechanism of HZO film under low-electric field.

Fast and universal approach for quantitative measurements of bistable hysteretic systems

Accurate and fast characterization of hysteretic systems can accelerate progress in fields as diverse as biomedicine, sensors, data storage, and logic devices. Here, we introduce a fast approach to determine magnetic parameters (intrinsic coercivities of elementary domains, interaction fields between the domains, and the variances of both) of bistable hysteretic systems. The approach uses the first few points in first-order reversal curves (FORC) to mathematically and empirically determine the projections of traditional FORC diagrams onto the reversal field and applied field axes. Since this projection approach only requires a few points per each reversal curve (rather than 100+ points for 100+ curves compared to the traditional FORC method), the time of measurement is reduced by 50-100x over traditional FORC measurements. In addition, the projection results do not contain the typical FORC artifacts that have been disputed for decades. As a proof of concept, the projection analysis was used to determine the magnetic parameters of several arrays of bistable magnetic nanowires (MNWs), and the results were compared with the hysteresis loop and FORC results. For non-interacting arrays of MNWs, all three methods give the intrinsic coercivity with minor difference. While, the differences become significant for the interacting arrays of the MNWs that will be discussed in details.

Unexpected Light-Induced Thermal Hysteresis in Matrix Embedded Low Cooperative Spin Crossover Microparticles

The embedding of spin-crossover micro- or nanocrystals in various surroundings dramatically changes their functionalities based on first-order spin transitions. The dampening of their internal cooperativity, together with introducing a new kind of interactions occurring at interfaces between spin-crossover particles and their environment, results in spectacular effects, as an enhanced hysteresis with non-cooperative transitions. In this work, we deal with the influence of the embedding matrix on the light-induced thermal hysteresis (LITH) in the case of spin-crossover microparticles of Fe(phen)2(NCS)2. Despite the low cooperativity of this compound, the competition between the continuous photoexcitation towards the metastable high spin state and the relaxation down to low spin ground state leads to a light-induced thermal hysteresis, with a quasi-static width of around 10 K. This unexpected hysteresis is explained by considering a switch-on/cutoff mechanism of the particle–matrix interactions in the framework of a mean-field approach based on negative external pressures, with Gaussian distributed variations and of an Ising-like model with various interactions with the environment. Additional first-order reversal curves measurements and corresponding calculated distributions are in line with relaxations under light and confirm the existence of a non-kinetic LITH.

Structural and magnetic properties of La-doped strontium-hexaferrites ceramics obtained by spark-plasma sintering

Polycrystalline samples of Sr1−xLaxFe12O19 (x = 0.1, 0.3, and 0.6) hexaferrite were prepared by spark-plasma sintering (SPS) and its structural and magnetic properties have been investigated. The SPS process were performed under vacuum, at 900 °C, and in only 5 min. X-ray powder diffraction patterns showed that before SPS sintering samples are composed by several phases where the SrFe12O19 (SrM) is not higher than 12%. From Rietveld refinement method, we have found that after SPS process the content of SrM phase increased, in mean, up to 68%. However, it was found the presence of secondary phase such as α-Fe2O3 and LaFeO3 (%) whose phase content also vary with increasing the La-content. A finite element simulation model were used to study the temperature evolution within the sample during the SPS treatment. Magnetization measurements at room temperature yielded values of saturation magnetization between ~43 to ~27 emu/g and coercivities, HcB, in the range 3.11 to 2.88 kOe with increasing x. The influence and possible interaction between detected magnetic phases was studied by means of first-order reversal curves (FORCs) measurements. Results indicated that magnetic behavior of the La-doped strontium hexaferrites obtained by SPS technique are analogous a system composed of a broad distribution particles that are exchange-coupled with a certain number of other of neighboring particles. From FORC maps the coercivity profiles of the studied samples were extracted. The asymmetric behavior of these profiles were related to a broad distribution of the particle size and/or the influence of the secondary magnetic phases.

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.

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.

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.

Magnetic and Dielectric Response of CoFe2O4-SrFe12O19 Nanocomposites

Soft magnetic phase cobalt ferrite (CoFe2O4) and hard magnetic phase strontium ferrite (SrFe12O19) were synthesized by co-precipitation route. Nanocomposite S:H-1:2 was prepared comprising soft (S) and hard (H) phases in the weight ratio of 1:2, higher ratio corresponding to SrFe12O19. The average crystallite size of CoFe2O4 and SrFe12O19 as obtained from refinement data was 19 nm and 50 nm respectively. Lattice strain evaluated using the Williamson-Hall plot was observed as 0.53%, 0.17%, and 0.61% for CoFe2O4, SrFe12O19, and S:H-1:2. Room temperature magnetic measurements were performed revealing the presence of exchange interaction present in the prepared composite. First-order reversal curve (FORC) measurements were performed for further confirming the exchange behavior of S:H-1:2. The maximum energy product obtained for S:H-1:2 was 0.067 MGOe which is greater than CoFe2O4 and SrFe12O19. Low dielectric loss was observed from impedance measurements. Presence of exchange coupling and low dielectric loss makes S:H-1:2 a potential candidate for microwave absorption.

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>