Magnetoelastic Energy Research Articles

Electronic structure modification and negative magnetostriction in Fe-Ga alloy of D03 structure with Ga content variation

The influence of a change in the Ga content on the magnetostrictive properties of the Fe3Ga alloy with the D03 structure has been studied by density functional theory methods. The change in the stoichiometry of the alloy under study was carried out by replacing the Fe atoms with Ga. The replacement leads to a significant change in the electronic structure of the systems under study, which leads to a significant increase in the density of electronic states near the Fermi level. This effect leads to an increase in the magnetoelastic energy, which leads to an increase in the value of the magnetostrictive coefficient λ001. A further increase in λ001 occurs due to a decrease in the shear modulus, which occurs due to an increase in the number of loosening bonds in the system with an increase in the Ga content. The resulting dependence of λ001 on the Ga content, although they show an increase in the absolute value of the coefficient λ001, but give its negative values, in contrast to the positive value of magnetostriction observed in the experiment. Solving the problem of matching the sign of the theoretical and experimental values of the magnetostrictive coefficients requires further research.

An Extension of the Vector-Play Model to the Case of Magneto-Elastic Loadings

The influence of mechanical stress on the magnetic hysteretic behavior is modeled through the association of a reversible simplified multiscale approach, and a macroscopic energy-based magnetic hysteresis model in a vector-play form. A phenomenological description of the dissipation parameters under mechanical stress is proposed. The non-monotonic effect of tensile stress on the magnetic permeability is modeled using a second-order development in the magneto-elastic energy. Material parameters for both reversible and irreversible behavior are identified from experimental characterization under mechanical stress performed on a DC04 electrical steel. The experimental tests include anhysteretic and hysteretic measurements. Modeling results of the anhysteretic magnetic permeability, the coercive field, and the remanent induction under several levels of peak magnetic field and uniaxial mechanical stress are satisfactorily compared with those obtained experimentally. The model is shown to reasonably predict the hysteresis losses under tensile and compressive stress, as well as the response of the material under a complex magnetic field waveform with harmonic content.

Nonlinear modeling and efficacy of VIV-based energy harvesters: Monostable and bistable designs

In this effort, performance of a magnetoelastic multi-stability energy harvester is investigated in monostable and bistable configurations while working under combination of vortex-induced vibration (VIV) and base excitation. For this purpose, a mathematical model is developed that accounts for coupled lift force, magnetic force, cylinder’s motion, and generated voltage. First, a linear analysis is carried out to investigate the effects of electrical load resistance on the coupled natural frequency of the system and its impact on the synchronization region. Static and frequency analyses are performed to identify the point of buckling based on the distance between the magnets. Then, a reduced-order model based on the Galerkin discretization is derived to investigate the effects of various nonlinearities on the harvester’s response. A convergence analysis is examined up till seven modes and it is found that three modes are sufficient. To compare the efficacy of the energy harvester at same coupled frequency in monostable and bistable regimes, three pairs of datasets are selected. Various parametric studies are presented to investigate the impacts of distance between the magnets, electrical load resistance, frequency, and wind speed. This study not only presents one of its kind quantitative comparisons of performance of the energy harvester working in monostable and bistable regimes at same coupled frequency but also provides an insight to performance of the harvester under combined effect of VIV and base excitation. In this regard, quenching phenomenon is visible. In addition, performance trends in pre-synchronization region, synchronization region, hysteresis region, and post synchronization regions are explained by presenting four wind speed graphs together. Some phase portraits and time histories are included for further exploration. In nutshell, the study is very useful for understanding of monostable and bistable designs and their working under VIV as well as hybrid excitations.

A Kirchhoff-like theory for hard magnetic rods under geometrically nonlinear deformation in three dimensions

Magneto-rheological elastomers (MREs) are functional materials that can be actuated by applying an external magnetic field. MREs comprise a composite of hard magnetic particles dispersed into a nonmagnetic elastomeric (soft) matrix. Hard MREs have been receiving particular attention because the programmed magnetization remains unchanged upon actuation. Motivated by a new realm of applications, there have been significant theoretical developments in the continuum (three-dimensional) description of hard MREs. In this paper, we derive an effective theory for MRE rods (slender, mono-dimensional structures) under geometrically nonlinear deformation in three dimensions. Our theory is based on reducing the three-dimensional magneto-elastic energy functional for the hard MREs into an one-dimensional Kirchhoff-like description (centerline-based). Restricting the theory to two dimensions, we reproduce previous works on planar deformations. For further validation in the general case of three-dimensional deformation, we perform precision experiments with both naturally straight and curved rods under either constant or constant-gradient magnetic fields. Our theoretical predictions are in excellent agreement with both discrete simulations and precision-model experiments. Finally, we discuss some limitations of our framework, as highlighted by the experiments, where long-range dipole–dipole interactions, which are neglected in the theory, can play a role.

Large stress-induced anisotropy in soft magnetic films for synthetic spin valves

We obtain a large in-plane magnetic uniaxial anisotropy in the soft magnetic Fe60Co20B20 (FeCoB) thin films prepared by rotational sputtering. The anisotropy field (Ha) of 75 to 175 Oe was found in the films with wide ranged thickness from 2.5 to 100 nm, which was attributed to the magnetoelastic energy in association with anisotropic tensile stress. This stress-induced anisotropy has outstanding thermal stability that survives up to 350 °C in the annealing process. The similar large uniaxial anisotropy can be realized in other soft magnetic thin films, such as Fe, Co, Ni, FeCo, and NiFe, with the same synthesis technique. The anisotropic FeCoB film was used as a free layer in a synthetic spin valve. A linear resistance change against external field with a range wider than ±100 Oe together with a significantly reduced coercivity of ∼1.1 Oe (∼8.5 Oe in the case with isotropic free layer) was observed in the transfer curve. The results of this work not only confirm the feasibility of films with large stress-induced magnetic anisotropy as a functional layer in spin-valve devices but also demonstrate a simple synthesis route to induce the magnetic anisotropy, which provides an additional control parameter for the spintronic device design.

Strain Modulation of Magnonic Frequency Comb by Magnon–Skyrmion Interaction in Ferromagnetic Materials

The magnonic frequency comb (MFC) induced by magnon–skyrmion interaction not only exhibits interesting nonlinear physics but also can be used to detect magnetic solitons and defects in ferromagnetic materials. Modulating the tooth spacing of MFC is crucial for its application in magnon‐based devices. Herein, it is demonstrated from micromagnetic simulations that the MFC tooth spacing of ferromagnetic thin film can be effectively modulated by a biaxial in‐plane strain via magnetoelastic coupling. It is found that the MFC tooth spacing increases with the increase of compressive strain and decreases with the increase of tensile strain. The strain modulation of MFC tooth spacing stems from the strain‐dependent magnetocrystalline anisotropy. The detailed energy analysis shows that the larger the tooth spacing is, the higher the exchange energy is, and the lower the magnetoelastic and anisotropy energies are. In addition, when the biaxial in‐plane strain becomes nonequally axial (or anisotropic), the tooth spacing becomes smaller, accompanied by a decrease in the magnetoelastic energy. The results of this study suggest an effective way to modulate the tooth spacing of MFC by strain, which may hold a promise for application in tunable magnon‐based devices.

MAELAS 2.0: A new version of a computer program for the calculation of magneto-elastic properties

MAELAS is a computer program for the calculation of magnetocrystalline anisotropy energy, anisotropic magnetostrictive coefficients and magnetoelastic constants in an automated way. The method originally implemented in version 1.0 of MAELAS was based on the length optimization of the unit cell, proposed by Wu and Freeman, to calculate the anisotropic magnetostrictive coefficients. We present here a revised and updated version (v2.0) of MAELAS, where we added a new methodology to compute anisotropic magnetoelastic constants from a linear fitting of the energy versus applied strain. We analyze and compare the accuracy of both methods showing that the new approach is more reliable and robust than the one implemented in version 1.0, especially for non-cubic crystal symmetries. This analysis also helps us find that the accuracy of the method implemented in version 1.0 could be improved by using deformation gradients derived from the equilibrium magnetoelastic strain tensor, as well as potential future alternative methods like the strain optimization method. Additionally, we clarify the role of the demagnetized state in the fractional change in length, and derive the expression for saturation magnetostriction for polycrystals with trigonal, tetragonal and orthorhombic crystal symmetry. In this new version, we also fix some issues related to trigonal crystal symmetry found in version 1.0. Program summaryProgram title: MAELASCPC Library link to program files:https://doi.org/10.17632/gxcdg3z7t6.2Developer's repository link:https://github.com/pnieves2019/MAELASCode Ocean capsule:https://codeocean.com/capsule/2689126Licensing provisions: BSD 3-clauseProgramming language: Python3Journal reference of previous version: P. Nieves, S. Arapan, S.H. Zhang, A.P. Kądzielawa, R.F. Zhang and D. Legut, Comput. Phys. Commun. 264, 107964 (2021)Does the new version supersede the previous version?: YesReasons for the new version: To implement a more accurate methodology to compute magnetoelastic constants and magnetostrictive coefficients, and fix some issues related to trigonal crystal symmetry.Summary of revisions:•New method to calculate magnetoelastic constants and magnetostrictive coefficients derived from the magnetoelastic energy.•Correction of the trigonal crystal symmetry.•Implementation of the saturation magnetostriction for polycrystals with trigonal, tetragonal and orthorhombic crystal symmetry.•In the visualization tool MAELASviewer, we included the possibility to choose the type of reference demagnetized state in the calculation of the fractional change in length.Nature of problem: To calculate anisotropic magnetostrictive coefficients and magnetoelastic constants in an automated way based on Density Functional Theory methods.Solution method: In the first stage, the unit cell is relaxed through a spin-polarized calculation without spin-orbit coupling (SOC). Next, after a crystal symmetry analysis, a set of deformed lattice and spin configurations are generated using the pymatgen library [1]. The energy of these states is calculated by the Vienna Ab-initio Simulation Package (VASP) [2], including SOC. The anisotropic magnetoelastic constants are derived from the fitting of these energies to a linear polynomial. Finally, if the elastic tensor is provided [3], then the magnetostrictive coefficients are also calculated from the theoretical relations between elastic and magnetoelastic constants.Additional comments including restrictions and unusual features: This version supports the following crystal systems: Cubic (point groups 432, 4¯3m, m3¯m), Hexagonal (6mm, 622, 6¯2m, 6/mmm), Trigonal (32, 3m, 3¯m), Tetragonal (4mm, 422, 4¯2m, 4/mmm) and Orthorhombic (222, 2mm, mmm).

Stress-Induced Self-Magnetic Flux Leakage at Stress Concentration Zone

The residual magnetization technique is a new method for detecting stress concentration zones (SCZs) in ferromagnetic materials. Local rising of stress at SCZs, such as cracks, results in the development of local elastic and plastic deformation. The two deformation regimes produce different magnetic characteristics, which have competing effects on self-magnetic-flux-leakage signals. In the present research, samples with three different groove depths were subjected to different tensile stress levels. A surface scanning system was used to record the variation of magnetic signals at grooves of varying depth under steadily increasing stress conditions. The results show that elastic deformation increases peak-to-peak values of normal magnetic components and a maximum gradient of the normal magnetic component in the direction of applied stress, while the development of local plastic deformation reduces signal intensity at groove locations. The magnetic object (MO) model is used to explain the mechanism for excess flux leakage field at SCZs as being due to the conversion of magnetoelastic energy—introduced by the application of tensile stress up to the local yield point—into magnetostatic surface poles that are sensed as an increase in the normal component of leakage.

A tool to predict coercivity in magnetic materials

Magnetic coercivity is often viewed to be lower in alloys with negligible (or zero) values of the anisotropy constant. However, this explains little about the dramatic drop in coercivity in FeNi alloys at a non-zero anisotropy value. Here, we develop a theoretical and computational tool to investigate the fundamental interplay between material constants that govern coercivity in bulk magnetic alloys. The two distinguishing features of our coercivity tool are that: (a) we introduce a large localized disturbance, such as a spike-like magnetic domain, that provides a nucleation barrier for magnetization reversal; and (b) we account for magneto-elastic energy—however small—in addition to the anisotropy and magnetostatic energy terms. We apply this coercivity tool to show that the interactions between local instabilities and material constants, such as anisotropy and magnetostriction constants, are key factors that govern magnetic coercivity in bulk alloys. Using our model, we show that coercivity is minimum at the permalloy composition (Fe21.5Ni78.5) at which the alloy’s anisotropy constant is not zero. We systematically vary the values of the anisotropy and magnetostriction constants, around the permalloy composition, and identify new combinations of material constants at which coercivity is small. More broadly, our coercivity tool provides a theoretical framework to potentially discover novel magnetic materials with low coercivity.

A Tool to Predict Coercivity in Magnetic Materials

Magnetic coercivity is often viewed to be lower in alloys with negligible (or zero) values of the anisotropy constant. However, this explains little about the dramatic drop in coercivity in FeNi alloys at a nonzero anisotropy value. Here, we develop a theoretical and computational tool to investigate the fundamental interplay between material constants that govern coercivity in bulk magnetic alloys. The two distinguishing features of our coercivity tool are that: (a) we introduce a large localized disturbance, such as a spike-like magnetic domain, that provides a nucleation barrier for magnetization reversal; and (b) we account for magneto-elastic energy---however small---in addition to the anisotropy and magnetostatic energy terms. We apply this coercivity tool to show that the interactions between local instabilities and material constants, such as anisotropy and magnetostriction constants, are key factors that govern magnetic coercivity in bulk alloys. Using our model, we show that coercivity is minimum at the permalloy composition at which the alloy's anisotropy constant is not zero. We systematically vary the values of the anisotropy and magnetostriction constants, around the permalloy composition, and identify new combinations of material constants at which coercivity is small. More broadly, our coercivity tool provides a theoretical framework to potentially discover novel magnetic materials with low coercivity.

Finite element modeling and characterization of a magnetoelastic broadband energy harvester

Piezoelectric-based vibration energy harvesters have been extensively developed to the end of replacing low-power batteries. However, matching the frequency of the ambient vibration is not always possible and to broaden the frequency response of the harvesters, different proof-of-concept devices have been developed. This work presents a miniaturized device intended for magnetoelastic broadband vibration energy harvesting. The device consists of a silicon beam where ferromagnetic foils act as proof mass and interacts with an external pair of permanent magnets. The interaction is first simulated using a Finite Element Method (FEM) model for different distances between the magnets and beam (a) and between the magnets (b). This is done for both an attractive and a repulsive magnet configuration and the calculation is performed for a set of a and b values. Both spring softening and hardening effects are observed for the two magnet configurations. The attractive configuration has a monostable potential energy landscape with an associated spring softening for a large range of a and b values which makes this configuration very useful for energy harvesting applications. The attractive configuration is experimentally investigated by impedance measurements. These measurements are performed for a ∈ [400 μm, 2500 μm] and b ∈ [320 μm, 3140 μm] and a region that allows for broadband harvesting is found experimentally. Compared to the linear case the largest spring softening effect yielded a decrease in the effective spring constant of 74%, a decrease in the resonant frequency of 49%, and the coupling coefficient was increased with a factor of 2.6.

Deterministic reversal of single magnetic vortex circulation by an electric field

The ability to control magnetic vortex is critical for their potential applications in spintronic devices. Traditional methods including magnetic field, spin-polarized current etc. have been used to flip the core and/or reverse circulation of vortex. However, it is challenging for deterministic electric-field control of the single magnetic vortex textures with time-reversal broken symmetry and no planar magnetic anisotropy. Here it is reported that a deterministic reversal of single magnetic vortex circulation can be driven back and forth by a space-varying strain in multiferroic heterostructures, which is controlled by using a bi-axial pulsed electric field. Phase-field simulation reveals the mechanism of the emerging magnetoelastic energy with the space variation and visualizes the reversal pathway of the vortex. This deterministic electric-field control of the single magnetic vortex textures demonstrates a new approach to integrate the low-dimensional spin texture into the magnetoelectric thin film devices with low energy consumption.

FE2 simulations of magnetorheological elastomers: influence of microscopic boundary conditions, microstructures and free space on the macroscopic responses of MREs

In the current work, the response of heterogeneous magnetorheological elastomers (MREs) which are loaded by external magnetic fields in the absence and also in the presence of free space is studied. A fully-coupled two-scale finite element computational homogenization procedure is used to derive the material response at the macro-scale from the averaged response of the underlying micro-scale problem. Different combinations of boundary conditions, that satisfy the Hill-Mandel condition and are based on the primary variables of the magneto-elastic enthalpy and energy functionals are applied to solve the micro-scale boundary value problem. Furthermore, the influences of various microstructures on the macroscopic response of the MREs are investigated. The results indicate that the choice of microscopic boundary conditions and microstructure types can significantly affect the macroscopic responses of MREs.

Role of magnetostrictive effect in magnetization dynamics of SmFe thin films

Laser induced magnetization dynamic behaviors of SmxFe1–x thin films with tunable x (0.25 ≤ x ≤ 0.5) are investigated by the time-resolved magneto-optical Kerr effect. It is found that the demagnetization process is accomplished by a two-stage process, the demagnetization time of stage I is within 1.0 ps (t1) for all the samples with different x, while it increases from 0 to 16 ps at stage II (t2) due to the reduced exchange coupling. By introducing an additional magneto-elastic energy contribution, the dispersion relation of precession frequency is deduced, by which the field-dependent frequency curves are well fitted.

Room temperature giant magnetostriction in single-crystal nickel nanowires

Magnetostriction is the emergence of a mechanical deformation induced by an external magnetic field. The conversion of magnetic energy into mechanical energy via magnetostriction at the nanoscale is the basis of many electromechanical systems such as sensors, transducers, actuators, and energy harvesters. However, cryogenic temperatures and large magnetic fields are often required to drive the magnetostriction in such systems, rendering this approach energetically inefficient and impractical for room-temperature device applications. Here, we report the experimental observation of giant magnetostriction in single-crystal nickel nanowires at room temperature. We determined the average values of the magnetostrictive constants of a Ni nanowire from the shifts of the measured diffraction patterns using the 002 and 111 Bragg reflections. At an applied magnetic field of 600 Oe, the magnetostrictive constants have values of λ100 = −0.161% and λ111 = −0.067%, two orders of magnitude larger than those in bulk nickel. Using Bragg coherent diffraction imaging (BCDI), we obtained the three-dimensional strain distribution inside the Ni nanowire, revealing nucleation of local strain fields at two different values of the external magnetic field. Our analysis indicates that the enhancement of the magnetostriction coefficients is mainly due to the increases in the shape, surface-induced, and stress-induced anisotropies, which facilitate magnetization along the nanowire axis and increase the total magnetoelastic energy of the system.

Development of residual stress and uniaxial magnetic anisotropy during growth of polycrystalline Co film

Growth of e-beam evaporated Co films on Si (001)/SiO2 substrate has been studied using real-time multi-beam optical stress sensor (MOSS), four probe resistivity (FPR) and in-situ magneto-optic Kerr effect (MOKE) measurements. While MOSS and FPR provide information about internal stress and film morphology, MOKE provides information about magnetic properties, thus making it possible to correlate the evolution of film stress and morphology with that of uniaxial magnetic anisotropy (UMA) in the film. Film grows via Volmer–Weber mechanism, where islands grow larger to impinge with other islands and eventually coalesce into a continuous film at around 10 nm thickness. Development of tensile stress in the film is found to be associated with the island coalescence process. The film exhibits a well-defined UMA, which varies synchronously with internal tensile stress developed during growth, suggesting that the observed UMA originates from minimization of magnetoelastic and morphological anisotropic energies in the presence of internal stress. Absence of UMA in Co film having Ag underlayer in the form of islands is understood in terms of random short-range stress in the film caused by arbitrary pinning by the Ag islands.

Thin film rare earth iron garnets with perpendicular magnetic anisotropy for spintronic applications

Perpendicular magnetic anisotropy (PMA) in garnet thin films is important for achieving numerous spintronic applications including spin-orbit switching. In this study, we computationally investigated how to control PMA by tuning substrate strain in Holmium Iron Garnet (HoIG) films grown on five different (111) single crystal garnet substrates of Gadolinium Gallium Garnet (GGG, Gd3Ga5O12), Yttrium Aluminum Garnet (YAG, Y3Al5O12), Terbium Gallium Garnet (TGG, Tb3Ga5O12), Substituted Gadolinium Gallium Garnet (sGGG, Gd3Sc2Ga3O12), and Neodymium Gallium Garnet (NGG, Nd3Ga5O12). The negative sign of effective anisotropy energy density, Keff < 0, and anisotropy field, Ha < 0, determines the easy magnetization axis of the film to be perpendicular to the film surface. Here, we show that magnetoelastic anisotropy energy density determines the sign of the total anisotropy and it can be manipulated by altering the lattice parameter mismatch of the film and its substrate. Based on this study, HoIG is predicted to have PMA when grown on GGG, TGG and YAG among all five substrates mentioned. Moreover, the saturation field magnitude is calculated as an order of several hundreds of Oersteds, which is feasible in practical applications to saturate rare earth iron garnets with perpendicular magnetic anisotropy.

Computational study on microstructure evolution and magnetic property of laser additively manufactured magnetic materials

Additive manufacturing (AM) offers an unprecedented opportunity for the quick production of complex shaped parts directly from a powder precursor. But its application to functional materials in general and magnetic materials in particular is still at the very beginning. Here we present the first attempt to computationally study the microstructure evolution and magnetic properties of magnetic materials (e.g. Fe-Ni alloys) processed by selective laser melting (SLM). SLM process induced thermal history and thus the residual stress distribution in Fe-Ni alloys are calculated by finite element analysis (FEA). The evolution and distribution of the $\gamma$-Fe-Ni and FeNi$_3$ phase fractions were predicted by using the temperature information from FEA and the output from CALculation of PHAse Diagrams (CALPHAD). Based on the relation between residual stress and magnetoelastic energy, magnetic properties of SLM processed Fe-Ni alloys (magnetic coercivity, remanent magnetization, and magnetic domain structure) are examined by micromagnetic simulations. The calculated coercivity is found to be in line with the experimentally measured values of SLM-processed Fe-Ni alloys. This computation study demonstrates a feasible approach for the simulation of additively manufactured magnetic materials by integrating FEA, CALPHAD, and micromagnetics.

High magnetic-dielectric tunability in Ni nanocrystals embedded BaTiO3 films

A large lattice mismatch (>10%) system was designed, consisting of epitaxial BaTiO3 matrix and Ni nanocrystals (NCs). The interfacial stress was fully released by the formation of three-dimensional islands Ni NCs with a preferred (111) orientation. We further demonstrated that the elastic energy of (111) was much smaller than the (100) planes. The remarkable dielectric tunability of 0.41 at 100 Oe was obtained, attributing to the large magnetoelastic energy ΔH = 0.096 eV. Due to the smaller magnetoelastic energy density (2.32 × 106 J/m3) relative to the magnetocrystalline anisotropy energy densities, magnetically polarized Ni NCs could overcome the anisotropy field and diamagnetism of the BaTiO3 matrix, resulting in the easily tunable dielectric properties with a weak magnetic field. These discoveries represent great potential for magnetoelectric devices.

Increased mechanical robustness of piezoelectric magnetoelastic vibrational energy harvesters

This work presents a cantilever based broadband piezoelectric magnetoelastic vibration energy harvester with increased mechanical robustness. The energy harvester is fabricated using KOH etching to define the cantilever and the proof mass is made using micromachined Fe foils which together with a pair of miniature magnets provides the magnetoelastic properties. KOH etching leads to very sharp corners at the anchoring point of the cantilever which makes the cantilever fragile. The mechanical robustness of the energy harvesters is increased using a lithography-free two-step fabrication process where a thermal oxidation is used for corner rounding. The corner rounding at the anchoring point lowers the stress concentration and thereby increases the robustness of the device. The radius of curvature for the corner depends linearly on the thickness of the oxide. Both enhanced and non-enhanced beams are excited at increasing frame accelerations. The conventional beams break at frame accelerations of around 3 g while the enhanced break at almost twice as much, 5.7 g. The devices are characterized electrically by impedance measurements in both their linear and non linear regime. The magnetoelastic behaviour can be adjusted by varying the beam-magnet distance which allows for both spring softening and spring hardening.