Hysteresis Loop Measurements Research Articles

The ferromagnetic resonance (FMR) of SrZ hexaferrite (Sr3Co2Fe24O41), and the tuning of FMR with an external magnetic field

The hexagonal Z-type ferrite Sr3Co2Fe24O41 (SrZ) was first synthesised in 2001 and reported as being a room temperature multiferroic material in 2010, with subsequent investigations into its multiferroic properties, but little into high frequency and microwave properties, and ferromagnetic resonance frequency (FMR), which determines its ability as an electromagnetic (EM) absorber and radar absorbing (RAM) stealth material. It was shown that SrZ existed as a majority or single phase after heating in a narrow temperature range between 1170 and 1190 °C using X-ray diffraction (XRD) and measurement of magnetic hysteresis loops, with the sample appearing to be single phase SrZ at 1190 °C. We measured complex permeability and permittivity of a single phase polycrystalline ceramic sample of SrZ between 500 MHz and 8 GHz (X-band). The sample had a relatively high permittivity >17 over this entire frequency range, and it showed a strong ferromagnetic resonance (FMR) at 2.3 GHz. This FMR could also be tuned by the effect of an external magnetic field, by moving a simple bar magnet progressively closer to a toroidal sample. This incurred a very slight shift in the peak up to 2.48 GHz at distances of 2.5–10 cm from the sample – a tuning of ∼5–6% with applied magnetic fields estimated to be 0.11–0.23 T, which is not insignificant. At a close distance of 0.5 mm we got a high degree of tuning of FMR to 3.4 GHz, a large change of 1.07 GHz (= 46% increase) with an applied magnetic field estimated to be 0.40 T. Despite this, the applied field had no significant effect on permittivity over 0.5–8 GHz. Such results have never been reported before, and are significant, as this would enable tuning of the FMR via simple physical/mechanical movement of a bulk alloy magnet, effectively creating a tuneable microwave filter or absorber.

Measurement of Magnetic Hysteresis Loops of the Ni-5at.%W Alloy Substrate as a Function of Temperature in a Stack of 2G HTS-Coated Conductor Annuli

The development of coated conductors with a ferromagnetic substrate and their use in various applications require accurate knowledge of the magnetic properties of the substrate. In this work, we report measurements in the ac regime (30 Hz) of the magnetic hysteresis loops of the Ni-5at.%W alloy ferromagnetic substrate in a stack of second-generation YBa <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> Cu <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">7</sub> (YBCO) tapes cut in the shape of annuli from 46-mm-wide-coated conductors. The stacked annuli form a closed magnetic circuit, which is the ideal configuration due to the absence of demagnetizing effect. The measurements are carried out at four temperatures between 77 K and 293 K. The peak intensity of the relative permeability is not significantly affected in the range of temperature considered. The coercive field dependence on temperature is also investigated. The hysteresis losses <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$Q$</tex-math></inline-formula> as a function of the amplitude of the flux density <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$B_\text{m}$</tex-math></inline-formula> exhibit a power law behavior ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$Q\sim B_\text{m}^{n}$</tex-math></inline-formula> ) at the four temperatures. This power law behavior is also studied at low fields under the presence of a dc bias field. Finally, the hysteresis loops can be reproduced with the Jiles–Atherton model, which is used to estimate the hysteresis parameters and to discuss their temperature dependence.

Effects of Ge addition on the structure, mechanical and magnetic properties of (CoCrFeNi)100-xGex high-entropy alloys

Alloying non-metallic elements can not only change the structure of alloys, but also tailor the mechanical and physical properties. The microstructure, mechanical and magnetic properties of (CoCrFeNi)100-xGex (molar ratio, x = 0 ∼ 33) high-entropy alloys (HEAs) have been systematically studied in this paper. The experimental results show that the (CoCrFeNi)100-xGex HEAs transform from a face-centered cubic (FCC) to a body-centered cubic (BCC) solid solution when 10 ≤ x ≤ 25, and a hexagonal intermetallic compound (IM) formed at x = 33. Tensile measurement revealed that the strength and plasticity of the alloy were enhanced simultaneously with Ge addition in the single FCC region (x ≤ 10), a decrease in ductility but sharp increase of strength was found in the alloys when the BCC phase starts to appear. Theoretical calculations and magnetic hysteresis loop measurements show that the alloys transform gradually from a paramagnetic to a ferromagnetic state at room temperature.

Effect of Cr interlayers on texture and magnetic properties of FeSi films with micrometer thickness

Magnetised soft ferromagnetic films with micrometer thicknesses can be used as π-flippers in spin-echo small-angle neutron scattering instruments. An FeSi film with a total thickness of 2000 nm separated by Cr interlayers (each 10 nm thick) was fabricated using direct-current magnetron sputtering. The thickness of each FeSi layer was 100 nm between adjacent Cr interlayers. Hysteresis loop measurements were performed to characterise the magnetic properties of the FeSi films. X-ray diffraction measurements, high-resolution transmission electron microscopy, and selected-area electron diffraction were used to characterise the texture. Results demonstrated that the saturation magnetisation of the FeSi film separated by Cr interlayers was higher and its coercivity was lower than those of the FeSi film separated by Ta interlayers because of different texture of FeSi layer. The FeSi film separated by Cr interlayers featured FeSi (210) and FeSi (221), and the Cr interlayers presented Cr (110). The FeSi layer between the Cr interlayers demonstrated structural coherency with the upper FeSi layer, and continuity of the lattice fringes from the Cr grains to the FeSi layers was observed. Therefore, degradation in the soft magnetic properties of FeSi films can be prevented by the insertion of Cr interlayers.

A novel estimation model for hysteresis loss based on semi-minor loops

This paper proposes an estimation model of hysteresis loss based on the mapping of the hysteresis loop conducted through tiny material samples with the aid of the Superconducting Quantum Interference Device (SQUID). This approach allows precise measurement of hysteresis loops. The aim of this paper is to develop a precise estimation model for hysteresis loss, one component of core loss, so as to improve the overall estimation accuracy of the entire core loss under complex excitations. First, with the help of the SQUID system and measurements conducted on tiny samples, the proposed model manages to minimize the impact of eddy current throughout the measurement and the modeling of hysteresis loss. This contrasts with the use of the conventional Steinmetz model and its modifications. Moreover, compared with methods including the modified Steinmetz equation (MSE) and the generalized Steinmetz equation (GSE) which merely focuses on the overall iron loss under simple non-sinusoidal excitations, the model presented here enables the estimation of hysteresis loss under complex excitations where multiple peaks and DC-bias take place. This approach will be very useful in situations such as those requiring pulse-width modulation (PWM) excited converters which are quite common on occasions including wind power systems. The estimation error of this model on the actual coil is within 15% under given excitations.

The Effects of Sheet Thickness and Excitation Frequency on Hysteresis Loops of Non-Oriented Electrical Steel.

The paper focuses on modeling the rate dependence of hysteresis loops in conductive magnetic materials. The concept, which was advanced about fifty years ago by Chua, is discussed. It is shown that the viscous-type equation considered by Zirka and co-workers belongs to the class of Chua-type models. The dynamic effects are described with a simple fractional power law. The value of the exponent in the above-mentioned power law may be assessed on the basis of measurements of coercive field strength at different excitation frequencies. To verify the usefulness of the approach, the measurements of hysteresis loops were carried out at several excitation frequencies under standardized conditions for two grades of non-oriented electrical steel. The modeled curves are in a good correspondence with the measured ones. The considered model uses fewer parameters than approaches based on three-term loss separation schemes.

Morphology and magnetic properties of rapidly quenched Fe-B alloys

Crystallization kinetics and the effect of annealing on the microstructure, morphology and magnetic properties of rapidly quenched Fe-B alloys are studied in this paper. Fe-B ribbons with different boron content were prepared ranging from 12 to 25 at%, covering the extended glass formability limit in hypoeutectic compositions to hypereutectic limit. Fe-B alloys were prepared by planar flow casting in the form of ribbons approximately 20 µm thick and 6 mm wide. The chemical compositions are Fe75B25, Fe80B20, Fe83B17, Fe86B14 and Fe88B12. Resistivity measurements were taken place at different heating rates, illustrating the phase transformations, aiding in the calculation of Avrami and Kissinger parameters. Soft magnetic properties of the Fe-B alloys were investigated by hysteresis loop measurements before and after annealing. XRD, DSC, TGA and TEM measurements illustrated the mechanisms of the crystallization process. The crystallization of Fe100-xBx amorphous alloys containing <17 at% Boron occurs by two stages of reaction. In this work, the crystallization process and Curie temperature for Fe100-xBx (12 < x < 25) are studied. Ribbons with boron content above 12 at% were found to be fully amorphous; small amount of quenched-in nano-crystallinity was present in the as-cast alloy with 12 at% B. Each composition has been annealed to achieve 5 %, 50 % and 95 % of crystallinity. In the first stage of crystallization, α-Fe phase with bcc structure crystallizes from amorphous matrix.

High-Performance Broadband Faraday Rotation Spectroscopy of 2D Materials and Thin Magnetic Films.

A Faraday rotation spectroscopy (FRS) technique is presented for measurements on the micrometer scale. Spectral acquisition speeds of about two orders of magnitude faster than state-of-the-art modulation spectroscopy setups are demonstrated. The experimental method is based on charge-coupled-device detection, avoiding speed-limiting components, such as polarization modulators with lock-in amplifiers. At the same time, FRS spectra are obtained with a sensitivity of 20 µrad ( ) over a broad spectral range (525-800 nm), which is on par with state-of-the-art polarization-modulation techniques. The new measurement and analysis technique also automatically cancels unwanted Faraday rotation backgrounds. Using the setup, Faraday rotation spectroscopy of excitons is performed in a hexagonal boron nitride-encapsulated atomically thin semiconductor WS2 under magnetic fields of up to 1.4 T at room temperature and liquid helium temperature. Anexciton g-factor of -4.4 ± 0.3 is determined at room temperature, and -4.2 ± 0.2 at liquid helium temperature. In addition, FRS and hysteresis loop measurements are performed on a 20 nm thick film of an amorphous magnetic Tb20 Fe80 alloy.

Ferroic glass behavior in (Bi,Na)TiO3-based lead-free electroceramics

Ferroic glass materials, that is, relaxors, spin glasses, and strain glasses attract special attention because of their intriguing physical properties and potential for novel technological applications. Here, several characterization techniques are used to demonstrate the occurrence of simultaneous relaxor and strain glass states in the ternary lead-free xBi0.5Na0.5TiO3-yBi0.5K0.5TiO3-zBaTiO3 (BNBK) system. Hysteresis and current density loops measurements at different temperatures for a BNBK ceramic showed typical characteristics observed in BNT based ceramics containing the tetragonal P4bm phase. Above 400 K, slim loops like those of ferroelectric relaxors are observed. A phase transition with simultaneous relaxor and strain glass character is revealed by the dielectric and anelastic characterizations, which opens up a wide spectrum of possible applications. The minimum of elastic modulus shifts to higher temperatures as the frequency increases, obeying the Vogel-Fulcher relation, which clearly shows the occurrence of a strain glass state in this material. Similar characteristics are observed in the imaginary part of the dielectric permittivity, which demonstrates the relaxor character of this phase transition. The origin of this phenomenon was elucidated with the help of structural characterizations, such as Raman spectroscopy and high-resolution synchrotron X-ray diffraction, at different temperatures. This work provides an in-depth understanding of the structural changes that determine the phenomenology behind the observed ferroic glass behavior and the ferroelectric, dielectric, and mechanical properties of this ternary ceramic composition.

Structural and electrical properties of bismuth sodium titanate ceramic

Single-phase lead-free Bi0.5Na0.5TiO3 (BNT) perovskite ferroelectric ceramic was produced using a solid-state reaction method. A detailed investigation of the structural and electrical properties of BNT ceramic is conferred. According to phase analysis employing Rietveld refined X-Ray diffraction, the crystal structure is single phase with rhombohedral (R3C) symmetry. Raman spectra measurement also confirms the rhombohedral structure of BNT by originating numerous peaks from the TiO6 octahedron. The ferroelectric character of the BNT sample was established by a hysteresis loop measurement of polarisation vs electric field (P-E). The remnant polarisation (Pr) and coercive field (Ec) have characteristic values of 1.63 μC/cm2 and 29.91 kV/cm, respectively. The ferroelectric phase change is seen in the temperature-dependent dielectric research, with a transition temperature of 323°C. The compound possessed a low value of tanδ even at a high temperature (500°C) at 1 MHz. The prepared sample exhibited excellent dielectric characteristics from room temperature to high temperatures, making it ideal for various applications.

Multi-frequency hyperthermia characterisation via calorimetry and AC magnetometry measurements

Hyperthermia characterisation of magnetic nanoparticles (MNP) is challenging, with highly variable results reported by different laboratories and large uncertainties associated with the measured values. Here, two experimental methods for probing the heating power of MNP for magnetic field hyperthermia (MFH) therapy are compared. The first technique is calorimetry using a bespoke non-adiabatic system capable of measurements at varying frequencies and intensities of magnetic drive-field. Heat losses during calorimetry were compensated for by incorporating a loss-parameter and fitting process during analysis of the raw measurement data to calculate the sample’s specific loss power (SLP). The second technique was AC magnetometry to measure the sample hysteresis when exposed to drive-fields with variable frequencies and amplitudes. The area of the measured hysteresis loop is used to calculate the SLP. Two distinct commercial magnetic nanoparticle systems (Ferucarbotran and RCL-01) were studied using both measurement techniques at varying drive-field frequencies and intensities. Estimates of the intrinsic loss power (ILP) parameter were made based on detailed analysis of the SLP values for multiple frequencies and intensities for each nanoparticle system and experimental approach. For both nanoparticle systems, the calorimetry technique produced higher estimates of the ILP than the AC magnetometry technique. Despite these variations, the results were encouragingly similar, with all values falling within the calculated uncertainty envelopes and relative differences in the results for the two nanoparticles systems being consistent between the measurement techniques (suggesting systematic errors). Furthermore, the experimentally determined values showed strong agreement with literature. The presented study highlights the potential value of carrying out hyperthermia characterisations with differing drive-field types and measurement methods. This approach can reduce inaccuracies by assisting in identifying outliers and aiding the identification of measurements which fall within the Linear-Response Regime for the given nanoparticle. Thus, the presented approach offers additional security when characterising the ILP of MNP.

Effect of Ta Interlayers on Texture and Magnetic Properties of FeSi Films with Micrometer Thickness.

Magnetized soft ferromagnetic films with micrometer thickness were studied. A FeSi film, with a total thickness of 2000 nm, separated by 10 nm-thick Ta interlayers, was fabricated using the direct-current magnetron sputtering technique. The thickness of each FeSi layer between adjacent Ta layers was 100 nm. Hysteresis loop measurement was used to characterize the magnetic properties of the layer. X-ray diffraction patterns and high-resolution transmission electron microscopy were used to characterize its texture. The experimental results showed that the FeSi film separated by Ta interlayers exhibited a lower saturation magnetization and a higher coercivity than those of the 1140 nm-thick FeSi film. The insertion of Ta interlayers resulted in the disappearance of the crystal plane of FeSi (221), and better texture of the crystal plane of FeSi (210). The FeSi film exhibited a crystal plane of FeSi (210) with a bcc crystalline structure. The Ta interlayers were partially amorphous, exhibiting crystal plane of Ta (002) and TaSi2 (310). The matching of magnetic properties between interlayers and soft magnetic layers played an important role in maintaining its soft magnetic properties.

Magnetized FeSi film with micrometer thickness inserted with Cr layers as [formula omitted]-flippers for neutron spin-echo spectrometry

Magnetized soft ferromagnetic films with micrometer thickness can be used as π-flippers for a spin echo small-angle neutron scattering (SESANS) instrument. Two FeSi monolayers and two FeSi/Cr multilayers were fabricated using a direct-current magnetron sputtering technique. The thicknesses of the two FeSi monolayers were 114 nm and 1140 nm, respectively. The two FeSi/Cr multilayers with 2 and 20 periods, respectively, were composed of FeSi layers having thicknesses of 1000 nm and 100 nm, respectively, and 10 nm-thick Cr layers. Hysteresis loop measurements and X-ray diffraction measurements were used to characterize their magnetic properties and texture, respectively. Polarized neutron flipping efficiency measurements were conducted using the TPNR (Time-of-flight and Polarized Neutron Reflectometer) to determine the flipping efficiency of the FeSi/Cr multilayer with [100 nm FeSi/10 nm Cr]20. The experimental results show that the saturation magnetization of the FeSi-monolayers decreased and the coercivity increased as their thickness increased. The FeSi/Cr multilayer with [100 nm FeSi/10 nm Cr]20 had higher saturation magnetization (1300 emu/cm 3) and lower coercivity than those of [1000 nm FeSi/10 nm Cr]2, although the total thickness of the FeSi layers was almost the same, and its maximum flipping efficiency was up to 98% for polarized neutrons.

Low thermal conductivity in A-site high entropy perovskite relaxor ferroelectric

An A-site disordered high entropy perovskite (Pb1/6Ba1/6Sr1/6Ca1/6Na1/6Bi1/6)TiO3 (PBSCNBi) ceramic was prepared by a solid-state reaction method. XRD and scanning electron microscopy-energy dispersive x ray confirmed a single-phase tetragonal solid solution. Dielectric and hysteresis loop measurements showed relaxor ferroelectricity at room temperature; Curie Weiss fitting gives a Burns temperature (Tb) of 123 °C, and Vogel–Fulcher fitting gives a freezing temperature (Tf) of −67.24 °C, which confirms the room-temperature relaxor ferroelectricity of PBSCNBi. This is attributed to local chemical inhomogeneities in the high entropy ceramics. PBSCNBi also has a low thermal conductivity (1.15 W m−1 K−1 at room temperature) compared to all of its constituent simple perovskites (e.g., BaTiO3, PbTiO3, SrTiO3 CaTiO3, and Na1/2Bi1/2TiO3 in the range of 25–100 °C), which is attributed to the enhanced phonon scattering by both polar nanoregions and the mass contrast effect in the multi-element perovskite. This work demonstrates the great potential of making A-site high entropy ceramics with relaxor ferroelectric properties.

Effects of Crystalline Disorder on Interfacial and Magnetic Properties of Sputtered Topological Insulator/Ferromagnet Heterostructures

Thin films of Topological insulators (TIs) coupled with ferromagnets (FMs) are excellent candidates for energy-efficient spintronics devices. Here, the effect of crystalline structural disorder of TI on interfacial and magnetic properties of sputter-deposited TI/FM, Bi2Te3/Ni80Fe20, heterostructures is reported. Ni and a smaller amount of Fe from Py was found to diffuse across the interface and react with Bi2Te3. For highly crystalline c-axis oriented Bi2Te3 films, a giant enhancement in Gilbert damping is observed, accompanied by an effective out-of-plane magnetic anisotropy and enhanced damping-like spin-orbit torque (DL-SOT), possibly due to the topological surface states (TSS) of Bi2Te3. Furthermore, a spontaneous exchange bias is observed in hysteresis loop measurements at low temperatures. This is because of an antiferromagnetic topological interfacial layer formed by reaction of the diffused Ni with Bi2Te3 which couples with the FM, Ni80Fe20. For increasing disorder of Bi2Te3, a significant weakening of exchange interaction in the AFM interfacial layer is found. These experimental results Abstract length is one paragraph.

Study of the Dynamic Model and Vibration Performance of Pot-Shaped Metal Rubber

Metal rubber has been extensively used in recent years due to its several unique properties, especially in adverse environments. Although many experimental studies have been conducted, theoretical research on metal rubber is still in its infancy. In this work, a dynamic model for the nonlinear characteristics of pot-shaped metal rubber is established on the basis of the asymmetric dynamic model of the wire rope shock absorber and the trace method model. In addition, the corresponding parameters in the model are identified based on the parameter-separation method. The theoretical hysteresis loop obtained using the model and the measured hysteresis loop agree with each other. The results show that the asymmetric dynamic model can better describe the asymmetric dynamic characteristics of pot-shaped metal rubber. Furthermore, a pot-shaped metal rubber vibration reduction system is built to further verify the correctness of the model. This study provides an experimental reference and a theoretical basis for the practical application of pot-shaped metal rubber in the field of three-dimensional vibration reduction.

Unexpected wide tuning of ferroelectric properties by varying the Er concentration in La2-xErx(MoO4)3 (x = 0.75, 1, 1.25) solid solutions

Powder samples of the series La2-xErx(MoO4)3 (x ​= ​0.75, 1, 1.25) were prepared by solid-state reaction from the La and Er trimolybdates. The correlation of the ferroelectric properties with the crystal structure, as a function of the x concentration, was studied by X-ray diffraction (XRD), dielectric and optical spectroscopy, and the ferroelectric hysteresis loop measurements. The β′-Gd2(MoO4)3 structure type was identified by a non-conventional Rietveld method, including a symmetry analysis. Contrary to the expectations, the ferroelectric properties were intensified by the Er3+ concentration increase: the maximum polarization for x ​= ​1.25 reaches one order of magnitude larger than that of x ​= ​0.75, and the Curie temperature increase was around 200 ​K. This unexpected behavior is opposite of that observed for the improper ferroelectrics RE2(MoO4)3, where the ferroelectric properties are enhanced with the RE ionic radius increase. Hence, the series La2-xErx(MoO4)3 show an “wider tuning range” for ferroelectric properties opposite to the rare earth trimolybdate family.

Design and Realization of Ferroelectric Thin Film Physical Parameters Test System Based on Electronic Information Technology

Ferroelectric thin film materials are constantly used in our lives. When testing the physical parameters of the ferroelectric film, the thickness of the film is very small or only nanometers, which will bring great difficulties to the accuracy and sensitivity of the test. To understand the role of electronic information technology in the measurement of the physical parameters of ferroelectric thin films, this paper adopts the sweep field method and the sweep frequency method to test the parameters of the ferroelectric thin film. The system uses PZT film as the test material to complete the electrical hysteresis loop measurement experiment in an extremely clean environment. The system hardware circuit is designed, which can complete the measurement of the electrical hysteresis loop, the output of the sinusoidal signal, the data acquisition, and the power supply of the system. The research results show that the parameters of the traditional PZT film material change greatly during the test. The thickness of the improved PLSZT film is about 10% thinner than that of the PZT film. The result can be better in the parameter test.

FeTiB film materials: Dependence of the magnetic properties and magnetic structure on the phase and structural states

The Fe99.2÷56.6Ti0÷13.2B0÷34 films were prepared by dc magnetron deposition on glass substrates. X-ray diffraction analysis was used to determine the phase composition, volume fractions of formed crystalline phases, their grain sizes and microstrains on the grain scale. The magnetic hysteretic properties, saturation induction Bs (2.1–0.3 T), coercive field Hc (0.6–6 kA/m), relative remanence Br/Bs (0.07–0.37), were determined using measured hysteresis loops. Their shapes indicate the existence of intergranular exchange interaction in all studied films. The magnetic structure parameters of the films were determined by correlation magnetometry. All films are characterized by a stochastic magnetic structure. The magnetic properties and the magnetic structure parameters of the films are substantiated by their phase and structural states. The values of the local parameters of the magnetic structure (rms local anisotropy field D1/2Ha and exchange field HR) follow the parameters of the grain (lattice parameter and grain size), while the macroscopic parameters (Hc and rms stochastic domain anisotropy field D1/2<Ha> ) have a more complex behavior.

On Prandtl–Ishlinskii Hysteresis Modeling of a Loaded Pneumatic Artificial Muscle

Abstract Modeling of the hysteresis nonlinearities of the pneumatic artificial muscle (PAM) is critical when it is proposed to drive various high-precision mechatronics applications. This letter aims to characterize the hysteresis nonlinearities obtained experimentally of the PAM system under the load force effect. The load-dependent Prandtl–Ishlinskii (LDPI) model with a load-dependent weight function is proposed to model the measured hysteresis loop under different load forces. Comparing the measured hysteresis loops to the estimated loops of the LDPI model demonstrates the proposed model’s ability to characterize the asymmetric and load force effects in the hysteresis nonlinearities of the PAMs.