Magnetoelastic Constants Research Articles

Large magnetocrystalline anisotropic energy and its impact on magnetostriction of L10-FePt

Abstract The origin of magnetocrystalline anisotropic energy (MAE) guided by spin–orbit coupling in the L10-FePt alloy was analyzed. Correlation of MAE with the calculated magnetoelastic constants in the single and polycrystal model was determined by means of first-principles calculations using density functional theory (DFT). More specifically, a systematic analysis of the large MAE and magnetostriction coefficients (λ’s) were done by means of post-processing of eigenvalues (orbital energies) and eigenfunctions (orbital occupancies). Our numerical analysis includes the convolution of the projected wave-function (density of states) of each orbital of the Fe and Pt sub-lattices into their orbital energies, which in principle should be valid for any solid regardless of the strength of the MAE. The determined anisotropic magnetostriction coefficients are of the λ ∼ 10 − 4 –10–3 order for several crystallographic directions; which is in accord to the known experimental data. However, the polycrystalline model based on the uniform stress approximation leads to a decrease of the λ by two orders in the overall magnetostrictive behavior ( λ ∼ 10 − 5 ). Such a large difference is not unexpected as the magnetostriction for polycrystalline FePt thin films were recorded as very low, thus validating the robustness of the current theoretical proposition of analyzing MAE.

Spin-Mechanical Coupling in 2D Antiferromagnet CrSBr.

Spin-mechanical coupling is vital in diverse fields including spintronics, sensing, and quantum transduction. Two-dimensional (2D) magnetic materials provide a unique platform for investigating spin-mechanical coupling, attributed to their mechanical flexibility and novel spin orderings. However, studying their spin-mechanical coupling presents challenges in probing mechanical deformation and thermodynamic property changes at the nanoscale. Here we use nano-optoelectromechanical interferometry to mechanically detect the phase transition and magnetostriction effect in multilayer CrSBr, an air-stable antiferromagnet with large magnon-exciton coupling. The transitions among antiferromagnetism, spin-canted ferromagnetism, and paramagnetism are visualized. Nontrivial magnetostriction coefficient 2.3 × 10-5 and magnetoelastic coupling strength on the order of 106 J/m3 have been found. Moreover, we demonstrate the substantial tunability of the magnetoelastic constant by nearly 50% via gate-induced strain. Our findings demonstrate the strong spin-mechanical coupling in CrSBr and pave the way for developing sensitive magnetic sensing and efficient quantum transduction at the atomically thin limit.

Finite deformation modeling of wrinkling in thin magnetoelastic sheets

This paper presents an asymptotic two-dimensional (2D) finite-deformation theory for a thin magnetoelastic sheet starting from a three-dimensional (3D) variational form. This theory is used to model wrinkling phenomena under applied traction and external magnetic field. The resulting 2D potential energy is specialized to an isotropic, in compressible material, and the expressions for material constants, i.e., elasticity tensor, magnetoelastic coupling constant, and permeability, are obtained as a function of the applied magnetic field. The formulation is further simplified assuming reflection symmetry about the mid-surface of the sheet. Strong form of the resulting 2D governing equations are obtained by setting the first variation of potential energy functional to zero. The resulting governing equations are used to analyze wrinkling in a stretched rectangular sheet placed in a uniform magnetic field. Approximate analytical solutions are obtained by linearizing the 2D plate equation for small slopes. The effect of magnetic field and applied stretch on onset of wrinkling and amplitude of wrinkles is studied.

Ударное возбуждение магнитоупругой системы периодической последовательностью сверхкоротких импульсов поля

The nonlinear magnetization precession in normal magnetized ferrite film which has magnetic, elastic and magnetoelastic properties is investigated. The excitation field is presented as a vibration on resonance frequency which is modulated by short pulses which frequency is more lower than resonance frequency. It is proposed the formation procedure of periodic succession of ultra-short pulses by the involution to even degree of modulation signal sine. It is found two different cases of excitation: first when modulate pulse duration is larger than initial signal period and second when modulate pulse duration is smaller than initial signal period. In the first case the modulated signal has the form of main frequency vibrations tandem and in the second case the modulated signal has the form of unit sign-variation pulse. It is investigated the time development of magnetic and elastic vibrations whish are firmed by excitation field. It is shown that in the first case the magnetization vibrations at first hat sharp jump to upward and after this decreases by exponent. In this case the elastic vibrations after the same jump at first increases and then decreases by exponent. The elastic vibrations behaviour is interpret as energy pump from magnetic system to elastic system. In the second case the initial jump both vibrations is absent. It is investigated the degree modulation index influence to excited vibrations. It is shown that by increasing of this index the amplitude of magnetic and elastic vibrations decreases. It is investigated the magnetization excited vibrations character by different degree of magnetoelastic connection. It is introduced the coefficient multiple of magnetoelastic constant which is equal to ratio of considered constant to value of magnetoelastic constant of yttrium iron garnet. It is shown that by increasing of multiple coefficient the magnetization vibrations period is increased. It is found the sharp increasing the period by determined value of multiple coefficient which has a threshold character. It is investigated the excitation of magnetization in large time interval when the multiple coefficient is above the threshold value. It is found the principle difference between two cases when pulse duration is large or smaller as alternating field period. It is shown that in the first case the magnetization vibrations has the character of equilibrium position precession in conditions of orientational transition. In the second case the magnetization vibrations has the form of periodic re-orientational jumps from one equilibrium position to another. It is mentioned some properties of observed phenomena and proposed some recommendations for further investigations.

Вторичный магнитоупругий резонанс в структуре: тонкая магнитная пленка – толстая упругая подложка

The task about excitation of connected magnetic and elastic vibrations in flat-parallel structure consisted of normal magnetized thin magnetic film applied on thick nonmagnetic substrate is considered. As a result of estimated task solution the amplitude-frequency characteristics of magnetic and elastic vibrations are found. It is shown that in conditions when the ferromagnetic resonance frequency is higher then own elastic vibration of the structure on the amplitude-frequency characteristics of magnetic vibrations applied the equidistance net of elastic resonances of structure. For the interpretation of observed resonance net it is proposed the model of phase synchronization between initial excitation and elastic wave which experience two passages along the thickness of structure. It is shown that the frequency of maximum elastic vibrations rounding exceeds frequency of maximum magnetization characteristic. The existence of own rounding elastic vibrations characteristic is named the second elastic system resonance. It is investigated the dependence of maximum second resonance characteristic from value of magnetoelastic interaction constant. It is shown that by increasing of this constant the frequency distance between both characteristic maxima increases. As a hypothesis of this increasing it is proposed the analogy with splitting of amplitude-frequency characteristic of system consisted of two connected resonators. It is investigated the amplitude-frequency characteristics magnetic and elastic vibrations in wide frequency region. On the equidistance elastic resonances net amplitude-frequency characteristic it is found the narrow equidistance disposed resonance depressions which are correspond to decreasing of amplitude more then two orders of value. It is shown that the frequency interval between neighbouring depressions is back proportional to distance between point of elastic vibrations registration and surface of substrate opposite to magnetic film. For the interpretation of depressions formation it is proposed the model which takes into account the phase opposition in registration point between wave which goes out of the excitation point and wave which is reflected from the opposite end of structure. Briefly noted some physical analogies of investigated phenomena.

On-chip all-electrical determination of the magnetoelastic coupling constant of magnetic heterostructures

We have developed an approach to determine the magnetoelastic coupling constant of magnetic layers in thin film heterostructures. The film is formed on a piezoelectric substrate between two interdigital transducers (IDTs), a platform often used to construct a surface acoustic wave device. With the substrate piezoelectricity, strain is induced into the film by applying a dc voltage to the IDTs. The strain causes changes in the magnetization direction of the magnetic layer, which is probed by measuring changes, if any, in the transverse resistance of the heterostructure. We find that the extracted magnetoelastic coupling constant of the magnetic layer (CoFeB) depends on the film stacking. Such change can be accounted for provided that the elastic properties of the layers that constitute the heterostructures are taken into account. The on-chip all-electrical approach described here provides a versatile means to quantitatively assess the magnetoelastic coupling constant of thin film heterostructures.

Giant magnetoelectric effect of Ni–Mn-Ga/piezopolymer composites tailored by a martensitic transformation

Polymer-based magnetoelectric (ME) composites, composed of magnetostrictive and piezoelectric phases, in addition to exhibiting an effective coupling between the magnetic and electric orders of the matter, also offer important advantages for the Internet-of-Things, digitalization, and 4.0 revolution environments: light weight, flexibility, wearability, environmental friendliness, printability, and biocompatibility. Nevertheless, their successful implementation on applications such as sensors, actuators, energy harvesters, biomedical devices and spintronics strongly depends on the increase of its ME voltage response.This work explores, both experimentally and theoretically, the magnetostrictive Ni–Mn-Ga's martensite ‒ austenite phase transformation to shift/tailor/design the ME resonance peak exhibited by Ni–Mn-Ga/P(VDF-TrFE) piezoelectric composites. In the austenite phase, the determined peak value of the ME coefficient of 18.1 V cm−1 Oe−1 was much higher than the value of 6.05 V cm−1 Oe−1 obtained for the martensite phase, whereas the estimated theoretically value of magnetoelastic constant in the austenite is much smaller. The ways to further increase the magnetically induced ME response are also outlined.

Structural and magnetic transitions in the Bi2Fe4O9/BiFeO3 composite

A Bi2Fe4O9/BiFeO3 composite with a percentage ratio of 67/33 has been synthesized, its morphological analysis has been carried out. The average crystallite sizes for each phase have been determined. The magnetization hysteresis has been established and the temperature of its disappearance has been found. Using the infrared absorption spectra, temperatures of the magnetic phase transitions in each phase have been determined from the magnetic susceptibility, magnetostriction constant, ultrasound damping coefficient, and phonon mode softening. The change of magnetostriction constant sign observed in the vicinity of the spin reorientation transition and antiferromagnetic transition in mullite has been attributed to the change of the sign of the magnetoelastic constants. The interaction between the phases in the composite and the correlation of its structural and magnetic properties have been established.

Automated calculations of exchange magnetostriction

We present a methodology based on deformations of the unit cell that allows to compute the isotropic magnetoelastic constants, isotropic magnetostrictive coefficients and spontaneous volume magnetostriction associated to the exchange magnetostriction. This method is implemented in the python package MAELAS (v3.0), so that it can be used to obtain these quantities by first–principles calculations and classical spin–lattice models in an automated way. We show that the required reference state to obtain the spontaneous volume magnetostriction combines the equilibrium volume of the paramagnetic state and magnetic order of the ground state. In the framework of a classical spin–lattice model, we find that the analysis of volume dependence of this method jointly to the knowledge of the spatial derivative of the exchange interactions can reveal the equilibrium volume of the paramagnetic state and spontaneous volume magnetostriction unambiguously without involving any calculation of the paramagnetic state. We identify an error in the theoretical expression of the isotropic magnetostrictive coefficient λα1,0 for uniaxial crystals given in previous publications, which is corrected in this work. The presented computational tool may be helpful to provide a better understanding and characterization of the relationship between the exchange interaction and magnetoelasticity.

Microwave switching in the magnetic and elastic subsystems of a three-layer magnetic structure

Three modes of magnetic and elastic vibrations of the layers were revealed when a three-layer planar magnetic structure was excited by a microwave magnetic field. These modes are: microwave switching, low-frequency oscillations, microwave sinusoidal oscillations. Each mode of oscillation of the layers in a certain range of amplitudes of the alternating field is observed depending on the dc magnetic field and the magnetoelastic constant of the layer.

Magnetic skyrmion dynamics induced by surface acoustic waves

Magnetic skyrmions are promising information carriers for high-density memories. The dynamical motion of magnetic skyrmions have been extensively investigated in the development of magnetic racetracks. In this study, a surface acoustic wave (SAW) is theoretically investigated to drive skyrmions by using micromagnetic simulations. The in-plane type and out-of-plane particle displacement components of SAWs generate different magnetoelastic effective fields. The shear horizontal (SH) wave mode SAW drives skyrmions flow movement by the magnetoelastic coupling effect. Increasing the acoustic wave amplitude and magnetoelastic coupling constants, as well as a reduced wavelength, are beneficial for an enhanced skyrmion motion velocity. The skyrmion motion trajectory can be controlled by designing the geometry of magnetic films. Interestingly, in a circular magnetic film, the skyrmions driven by SH waves show clockwise or counterclockwise movement trajectories depending on the sign of topological charges. Our results provide an energy efficient approach to drive skyrmion dynamics including rotational motion, thus paving the way for low-power spintronics.

Anisotropy of magnetoelastic properties in epitaxial Co2FexMn1−xSi Heusler alloy thin films

A strain modulated ferromagnetic resonance technique was applied to determine two cubic magnetoelastic constants of the epitaxially grown 30-nm-thick ${\mathrm{Co}}_{2}{\mathrm{Fe}}_{x}{\mathrm{Mn}}_{1\ensuremath{-}x}\mathrm{Si}$ magnetic layers with different Fe and Mn contents, which were deposited on a MgO substrate with a 20-nm-thick Cr buffer layer---MgO (001) $\ensuremath{\parallel}$ Cr(001) $\ensuremath{\parallel} {\mathrm{Co}}_{2}{\mathrm{Fe}}_{x}{\mathrm{Mn}}_{1\ensuremath{-}x}\mathrm{Si}$ (001). It was found that, for the samples with the Fe content $x=0.4$ or higher, the magnitudes of the two cubic magnetoelastic constants are clearly different, showing that the magnetoelastic properties of these samples are different than in the case of isotropic samples for which these two constants are expected to be equal. The magnitude of the cubic magnetocrystalline anisotropy constant reveals an evident maximum at the composition of $x=0.4$, which corresponds to the minimum of the minor spin density of states, and thus the correlation between the cubic magnetocrystalline anisotropy and the electronic band structure. For all the investigated samples, a large perpendicular component of the magnetocrystalline anisotropy was observed as well as inhomogeneous broadening of the ferromagnetic resonance linewidth.

Effect of magnetoelastic interaction on the thermal expansion of the trigonal crystal FeBO3

Iron borate FeBO3 – a trigonal antiferromagnet with weak ferromagnetism – was used as a model object for experimental and theoretical studies of thermal expansion. X-ray diffraction analysis indicated that the character of the thermal expansion changes significantly when passing through the Néel point. In the magnetically ordered state below the phase transition temperature, the thermal changes in the crystal lattice parameters are additionally affected by magnetostrictive deformations. A theoretical model was developed that allows interpreting experimental data and determining the magnetoelastic constants using X-ray diffraction analysis. Temperature dependences of some of the magnetoelastic constants of iron borate were determined, and the hitherto unknown constants were found. These data are essential to describe various phenomena associated with magnetoelastic interactions in magnetically ordered materials.

Magnetoelastic constant of thin films determined by a four-point bending apparatus

We have developed a method to variably induce lattice strains and to quantitatively evaluate the induced magnetic anisotropy. Both tensile and compressive strains were introduced into epitaxial films of cobalt ferrite (CFO) grown on a single crystal MgO(001) substrate using a four-point bending apparatus made of a plastic material fabricated by a 3D printer. The change in magnetic anisotropy due to bending strain can be measured quantitatively by using the conventional magneto-torque meter. The strain-induced magnetic anisotropy increased with the tensile strain and decreased with the compressive strain as expected from a phenomenological magnetoelastic theory. The magnetoelastic constant obtained from the changes in bending strains shows quantitatively good agreement with that of the CFO films with a uniaxial epitaxial strain. This signifies that the magnetoelastic constant can be evaluated by measuring only one film sample with strains applied by using the bending apparatus.

A comparative study on energy-based fatigue criteria for lifetime calculation of magnetorheological elastomers under multiaxial loading

Predicting fatigue life of magnetorheological elastomers (MREs) containing, different volumes of carbonyl iron particles (CIPs) with various external magnetic fields has been investigated. Unlike many studies on fatigue behavior of MREs, representing experimental models, a novel three-dimensional constitutive magneto-hyper-viscoelastic semi-coupling model based on strain energy density function (3DSED) is derived, analyzing the fatigue of structures enhanced by MRE experimentally and numerically. In this 3DSED model, to obtain the best predicting MREs’ fatigue life, three different hyper-elastic functions, including Neo-Hookean, Mooney-Rivlin, and Yeoh are utilized. Using some uniaxial compression, such as loading phase, relaxation, and loading/unloading phases tests, hyper-elastic, magneto-elastic, and viscoelastic constants are determined. In addition, multi-axial fatigue tests are performed to define the number of cycles to failure. These tests have been induced by the magnetic fields of 0, 0.27, and 0.4 T. The fatigue tests re-performed with the magnetic field of 0.3 T to compare the predicted results using the proposed fatigue models. The results show that the 3DSED model can be used for the prediction of MREs fatigue life when subjected to complex and repetitive loading. For all CIP contents, the Mooney-Rivlin fatigue predictor has more accurate results. The Yeoh fatigue predictor indicates better results for MREs with higher CIP contents, while the Neo-Hookean fatigue predictor doesn’t show acceptable results for any CIP contents.

Second-order magnetoelastic effects: From the Dirac equation to the magnetic properties of ultrathin epitaxial films for magnetic thin-film applications

Abstract It has always been the endeavour of Professor Kronmüller to combine various methods in order to attain a comprehensive understanding of a physical phenomenon on all relevant scales. In this spirit, we combine the phenomenological nonlinear theory of magnetoelasticity with the relativistic density functional electron theory to describe the magnetoelastic behaviour of epitaxial films. We explain the two already performed cantilever bending beam experiments on the magnetoelasticity and underpin the assumption that second-order magnetoelastic effects are very important for epitaxial Fe films. A complete set of six cantilever experiments is introduced which allows to calculate the intrinsic first- and second-order magnetoelastic constants for cubic materials, and these constants are calculated ab initio for Fe, face-centred cubic Co, Ni, Ni3Fe and CsCl-type CoFe.

WITHDRAWN: Effect of magnetostrictive coupling on the magnetic properties of TbFe2: ab initio study

• Elastic and magnetoelastic constants governing the amorphous TbFe 2 have been computed, and strains on crystal lattice have been studied. • Ferromagnetic interaction between Tb atoms has been found and the 111-direction is revealed to be the easy axis of the magnetization. • XMCD and XAS spectra show a large sensitivity on magnetic and elastic properties. Density functional theory (DFT) within the GGA approach is applied to investigate the electronic, elastic and magnetic properties of the amorphous TbFe 2 alloy. We found that TbFe 2 exhibits a trigonal R3̅m structure at T=0 K with lattice constants a = b = c = 5.15 Å, and α = β = γ = 60.14°. This structure can undergo elastic deformations that affect the TbFe 2 properties. The electronic properties analysis revealed a magnetic behavior and a metallic character. Therefore, to investigate the elastic and magnetic properties of TbFe 2 , the elastic and magnetoelastic constants governing the system are determined before studying the effects of applied strains on the crystal lattice. The results reveal a redistribution of Tb and Fe magnetic moments along the a-and c-axis. Moreover, a ferromagnetic interaction between the Tb atoms is found, and the [111] direction is the easy axis of the magnetization. Furthermore, the XMCD and XAS spectra of TbFe 2 in normal and deformed cases show significant magnetic and elastic properties sensitivity.

Ultra-high anisotropic magneto-mechanical damping in Fe-18at.%Ga single crystals

An ultra-high anisotropic magneto-mechanical hysteresis-type damping (MMHD) with temperature and frequency insensitivity was found in Fe-18at.%Ga single crystals. The [111]-orientated Fe-Ga single crystal exhibits a damping value up to 0.13 (Q−1, equivalent to a special damping capacity SDC of 0.82) in the wide temperature range of −100–150 °C, much higher than that of the conventional ferromagnetic high damping alloys (Fe-Cr/Al based alloys). For the [001]-orientated single crystal however, the MMHD value is almost zero despite the large magnetostrictive coefficient along [001] direction. Through magnetic domain analysis, it is demonstrated that MMHD originates from the stress-induced irreversible movement of 90° domain walls. The MMHD of Fe-Ga single crystals depends positively on the orientation factor, and the ultra-high relaxation strength is closely related to the magnetostriction in the [001] direction and the tetragonal magnetoelastic coupling constant.

Magnetostriction of the Fe-=SUB=-75-=/SUB=-Ga-=SUB=-25-x-=/SUB=-Z-=SUB=-x-=/SUB=- (Z=Al, Ge, Si) alloys: calculation by the magnetic torque method

This work presents an ab initio study of the effect of a small addition of the third element of III and IV groups on the elastic and magnetoelastic properties of Fe75Ga25 alloy. The dependencies of the tetragonal elastic modulus C', magnetoelastic constant -b1, and the tetragonal magnetostrictive constant λ001 on the concentration of the Z-element in the cubic crystal structures A2 and D03 were obtained with the help of the density functional theory and the magnetic torque method in Fe75Ga25-xZx (Z=Al, Ge, Si) alloys (0≤ x≤6 at.%). It is shown that the addition of Al and Si atoms leads to an increase in the tetragonal elastic modulus compared to the Fe75Ga25 binary alloy. A correlation was established in the dependence equilibrium lattice constants a0(x) and λ001(x) in the studied ternary alloys for the A2 structure. Keywords: tetragonal magnetostriction constant, magnetoelastic constant, tetragonal shear modulus, magnetic torque method.

Magnetostriction of the Fe-=SUB=-75-=/SUB=-Ga-=SUB=-25-x-=/SUB=-Z-=SUB=-x-=/SUB=- (Z=Al, Ge, Si) alloys: calculation by the magnetic torque method

This work presents an ab initio study of the effect of a small addition of the third element of III and IV groups on the elastic and magnetoelastic properties of Fe75Ga25 alloy. The dependencies of the tetragonal elastic modulus C', magnetoelastic constant -b1, and the tetragonal magnetostrictive constant λ001 on the concentration of the Z-element in the cubic crystal structures A2 and D03 were obtained with the help of the density functional theory and the magnetic torque method in Fe75Ga25-xZx (Z=Al, Ge, Si) alloys (0≤ x≤6 at.%). It is shown that the addition of Al and Si atoms leads to an increase in the tetragonal elastic modulus compared to the Fe75Ga25 binary alloy. A correlation was established in the dependence equilibrium lattice constants a0(x) and λ001(x) in the studied ternary alloys for the A2 structure. Keywords: tetragonal magnetostriction constant, magnetoelastic constant, tetragonal shear modulus, magnetic torque method.