Magnetoelastic Stress Research Articles

Enhanced magnetic properties of strontium ferrites through constructing magnetoelastic stress

Strontium ferrites, which exhibit large remanence, high coercivity (Hc), are fascinating for applications in motors and high-frequency microwave devices. Here we demonstrate the strontium ferrites (Sr0.34Ca0.25La0.41Fe11.4Co0.19O19-δ) sintered at 1150 °C with enhanced magnetic properties through constructing magnetoelastic stress. The effects of applied pressure (Pc-axis) of 0–16 kPa during the sintering process on phase compositions, morphologies, magnetic and microwave properties are investigated in detail. We note that the Pc-axis could contribute to enhanced c-axis preferred orientation. This mechanism of enhancement has been also discussed according to the magnetoelastic theory. By applying an external pressure of 8 kPa, intrinsic coercivity (Hcj) of 4657 Oe and magnetic coercivity (Hcb) of 3781 Oe are obtained. The increments are 8.1% and 18.0% for Hcj and Hcb, respectively, compared to the sample with Pc-axis of 0 kPa. However, the enhancement of Hc by the Pc-axis is seen to be limited above 8 kPa, which can be attributed to the enlarged grain size and porosity observed. In addition, the ferromagnetic resonance frequency (fr) is also increased by the increased Pc-axis.

Crack-Inclusion Problem in a Superconducting Cylinder with Exponential Distribution of Critical Current Density

In this paper, the crack-inclusion interaction considering the exponential distribution of critical current density is carried out for a functionally graded superconducting cylinder during the zero-field cooling (ZFC) process. By determining the stress intensity factors (SIFs) at the crack tips and performing magnetoelastic stress analysis, the result indicates that the increase of the gradient parameter of critical current density could effectively reduce the stress intensity factors based on the effect of the gradient parameter on the elastic constants ratio of inclusion/matrix, sizes of the inclusion and crack, and the distance between them upon electromagnetic force.

Magnetoelastic deformation of a circular membrane: Wrinkling and limit point instabilities

We study the inflation of a weakly magnetizable isotropic incompressible circular membrane in the presence of magnetic field generated by a magnetic dipole. Following the approach in recent papers by Reddy and Saxena (Int. J. Sol. Struct. 136, 203–219, 2018; Int. J. Non-Lin. Mech. 95, 248–263, 2017) we start with a variational formulation, solving the resulting governing equations to determine the equilibria and checking the second variation condition for stability. Conjecture of possibility of multiple equilibria under a single coupled load, and attaining elastic and magnetic limit points made in the above two papers is confirmed in the present work for a circular membrane. Another main focus of this work is on the determination of wrinkling instability in the membrane due to magnetoelastic stresses. Wrinkles along one or both in-plane directions of membrane appear in a majority of loading scenarios due to compressive Maxwell stresses. Our computations demonstrate that wrinkles arise in the central region when dipole and inflation are in the same direction and in the annular region close to the edges when the dipole and inflation are in opposite directions.

Beyond a phenomenological description of magnetostriction

Magnetostriction, the strain induced by a change in magnetization, is a universal effect in magnetic materials. Owing to the difficulty in unraveling its microscopic origin, it has been largely treated phenomenologically. Here, we show how the source of magnetostriction—the underlying magnetoelastic stress—can be separated in the time domain, opening the door for an atomistic understanding. X-ray and electron diffraction are used to separate the sub-picosecond spin and lattice responses of FePt nanoparticles. Following excitation with a 50-fs laser pulse, time-resolved X-ray diffraction demonstrates that magnetic order is lost within the nanoparticles with a time constant of 146 fs. Ultrafast electron diffraction reveals that this demagnetization is followed by an anisotropic, three-dimensional lattice motion. Analysis of the size, speed, and symmetry of the lattice motion, together with ab initio calculations accounting for the stresses due to electrons and phonons, allow us to reveal the magnetoelastic stress generated by demagnetization.

Analysis of a kinked crack in soft ferromagnetic and paramagnetic elastic materials subjected to uniform magnetic field intensity

A kinked crack initiating from an initial crack in an infinite plate of a soft ferromagnetic and paramagnetic elastic materials is analyzed. Uniform magnetic field intensity applies at the remote area in the plate. Paramagnetic and soft ferromagnetic elastic materials can be belonged to the linear magneto-elastic material. Three ways analyzing this magneto-elastic stress problem are stated, which use ferromagnetic field intensity, paramagnetic field intensity and stress field derived from Faraday’s law of magnetic force line (uniform pure shear stress state), respectively. These three ways give the same result which is a uniform pure shear stress state.The kinked crack angles θ just after the crack initiation are achieved for any direction δ of the magnetic field intensity. The directions for 0⩽δ⩽360° are considered. The following three criteria for the crack initiation are considered; (1) The kinked crack initiates in the direction taking maximum value of the Mode I stress intensity factor just after the crack initiation under the additional condition that the Mode I stress intensity factor is positive; (2) The kinked crack initiates in the direction satisfying Mode II stress intensity factor is zero; (3) The kinked crack initiates in the direction taking the maximum value of the strain energy release rate under the additional condition that the Mode I stress intensity factor is positive. It is found that the initiating angles exist in the range of -150°⩽θ⩽150°. It is stated that these criteria give the same results for the kinked crack angles. The distributions of the magnetic field intensity and the stress are investigated for some kinked crack angles and directions of magnetic field intensity. The stress intensity factors for some directions of magnetic field intensity are also investigated versus the crack length for some kinked crack angles.

Magnetoelastic Effect-Based Transmissive Stress Detection for Steel Strips: Theory and Experiment

For the deficiencies of traditional stress detection methods for steel strips in industrial production, this paper proposes a non-contact stress detection scheme based on the magnetoelastic effect. The theoretical model of the transmission-type stress detection is established, in which the output voltage and the tested stress obey a linear relation. Then, a stress detection device is built for the experiment, and Q235 steel under uniaxial tension is tested as an example. The result shows that the output voltage rises linearly with the increase of the tensile stress, consistent with the theoretical prediction. To ensure the accuracy of the stress detection method in actual application, the temperature compensation, magnetic shielding and some other key technologies are investigated to reduce the interference of the external factors, such as environment temperature and surrounding magnetic field. The present research develops the theoretical and experimental foundations for the magnetic stress detection system, which can be used for online non-contact monitoring of strip flatness-related stress (tension distribution or longitudinal residual stress) in the steel strip rolling process, the quality evaluation of strip flatness after rolling, the life and safety assessment of metal construction and other industrial production links.

A versatile platform for magnetostriction measurements in thin films

We present a versatile nanomechanical sensing platform for the investigation of magnetostriction in thin films. It is based on a doubly clamped silicon nitride nanobeam resonator covered with a thin magnetostrictive film. Changing the magnetization direction within the film plane by an applied magnetic field generates a magnetoelastic stress and thus changes the resonance frequency of the nanobeam. A measurement of the resulting resonance frequency shift, e.g., by optical interferometry, allows to quantitatively determine the magnetostriction constants of the thin film. In a proof-of-principle experiment, we determine the magnetostriction constants of a 10 nm thick polycrystalline cobalt film, showing very good agreement with literature values. The presented technique aims, in particular, for the precise measurement of magnetostriction in a variety of (conducting and insulating) thin films, which can be deposited by, e.g., electron beam deposition, thermal evaporation, or sputtering.

Effects of magnetic field and pressure in magnetoelastic stress reconfigurable thin film resonators

Free-standing CoFe thin-film doubly clamped stress reconfigurable resonators were investigated as a function of magnetic field and pressure. A large uniaxial anisotropy resulting from residual uniaxial tensile stress, as revealed from magnetic hysteresis loops, leads to an easy magnetization axis aligned along the length of the beams. The quality factor of the driven resonator beams under vacuum is increased by 30 times, leading to an enhanced signal-to-noise ratio and a predicted reduction in the intrinsic magnetic noise by a factor of 6, potentially reaching as low as ∼25 pT/√Hz at 1 Torr. Stress reconfigurable sensors operating under vacuum could thus further improve the limit of detection and advance development of magnetic field sensing technology.

Analysis of Nonlinear Stresses and Strains in a Thin Current-Carrying Elastic Plate

Two-dimensional magnetoelastic problems of a thin current-carrying plate under the interaction of an unsteady electromagnetic field and a mechanical field are studied. The nonlinear magnetoelastic kinetic equations, geometric equations, physical equations, electrodynamics equations, and expressions for the Lorentz force of a thin current-carrying plate under the action of a coupled field are given. The normal Cauchy form nonlinear differential equations, which include ten basic unknown functions in all, are obtained by the variable replacement method. Using the difference and quasi-linearization methods, the nonlinear magnetoelastic equations are reduced to a sequence of quasilinear differential equations, which can be solved by the discrete-orthogonalization method. Numerical solutions for the magnetoelastic stresses and strains in a thin current-carrying elastic plate are obtained by considering a specific example. The results that the stresses and strains in the thin current-carrying elastic plate change with variation of the electromagnetic parameters are discussed. The results show that the stress–strain state in thin plates can be controlled by changing the electromagnetic parameters. This provides a method of theoretical analysis and numerical calculation for changing the service conditions and intensity research of thin plates of engineering structures in the electromagnetic field

Magnetization and magnetoelastic behavior of a functionally graded rectangular superconductor slab

The magnetoelastic stress and magnetostriction induced by flux-pinning in a functionally graded rectangular superconductor slab are investigated analytically. Two material graded indexes α and β are introduced for indicating the critical current state and the elastic property of the inhomogeneous superconductor. Based on an extended exponent model, the magnetic field distributions are analytically obtained under the zero-field cooling process. The magnetoelastic strain/stress state and the magnetostriction behavior induced by flux-pinning forces are then evaluated, and the maximum stress variation inside the superconductor slab is highlighted. Results show that the maximum flux-pinning stress is increased with the superconductor inhomogeneity, and the maximum magnetostriction of the slab is independent on the maximum applied magnetic field after the slab is completely trapped. The inhomogeneity of the material is a considerable factor to affect the electromagnetic properties and its mechanical behavior significantly for the graded superconductor slab.

Influence of the film thickness and additional elements (Al, O, and N) on the properties of FeCo film structures

The magnetic properties and domain structure of FeCoAlON thin films with thicknesses varying from 55 to 550 nm have been studied, and conditions favoring preparation of FeCoAlON films with uniaxial anisotropy in the direction normal to the film plane, which is required for designing “perpendicular” super-high-density information recording, have been established. In FeCoAlON films with a thickness up to 300 nm, the domain structure consists of cross-linked domain walls, because strong demagnetizing field suppresses formation of stripe domains. After the film thickness has reached 320 nm, cross-linked domain walls transform into stripe domains, with uniaxial anisotropy in the film plane disappearing, to become replaced by uniaxial anisotropy in the direction normal to the film plane, which can be assigned to magnetoelastic stresses induced by nitrogen atoms filling up interstitial space in the (110) plane. A further increase in the film thickness (up to 550 nm) leads to a rotational anisotropy due to the increase of nitrogen concentration in interstitials and the increase of magnetoelastic stresses.

Entanglement between nitrogen vacancy spins in diamond controlled by a nanomechanical resonator

One of the main challenges in spin qubits' studies associated with nitrogen vacancy impurities in diamond is to increase the coupling strength between the spins. With this task in mind we suggest a new type of a hybrid magneto-nano-electromechanical resonator, the functionality of which is based on a magnetic-field-induced deflection of an appropriate cantilever that oscillates between nitrogen vacancy (NV) spins in diamond. Specifically, we consider a $\mathrm{Si}(100)$ cantilever coated with a thin magnetic $\mathrm{Ni}$ film. As a new aspect of this study we utilize magnetoelastic stress and magnetic-field-induced torque to induce a controlled cantilever deflection. It is shown that, depending on the value of the system parameters, the induced asymmetry of the cantilever deflection substantially modifies the characteristics of the system. In particular, the coupling strength between the NV spins and the degree of entanglement can be controlled through magnetoelastic stress and magnetic-field-induced torque effects. Our theoretical proposal can be implemented experimentally with the potential of increasing several times the coupling strength between the NV spins. It finds that the coupling strength achieved by using our proposal enhances several times the maximal coupling strength reported before by Rabl et al. [P. Rabl, P. Cappellaro, M. V. Gurudev Dutt, L. Jiang, J. R. Maze, and M. D. Lukin, Phys. Rev. B 79, 041302(R) (2009)].

Transient response of carbon nanotubes with inhomogeneous coating under radial impact loading and magnetic field

An analytical method is presented to solve magnetoelastic dynamic stress responses and perturbation of the magnetic field vector in carbon nanotubes with inhomogeneous costing subjected to radial internal pressure shock and axial magnetic field. By utilizing finite Hankle transforms and Laplace transforms, the analytical solution for magnetodynamic stress response and perturbation of an axial magnetic field vector in the carbon nanotubes with inhomogeneous coating are obtained. From example calculations both magnetodynamic stress and perturbation of the axial magnetic field vector in carbon nanotubes with inhomogeneous coating are described and discussed.

Uniaxial magnetic anisotropy in Fe/GaAs(001): Role of magnetoelastic interactions

The origin of the in-plane uniaxial magnetic anisotropy of epitaxial $\mathrm{Fe}(001)$ films on $\mathrm{GaAs}(001)$ has been controversially attributed either to a magnetoelastic interaction or to oriented interface bonds. In order to check the relevance of magnetoelastic contributions we performed magneto-optic Kerr effect (MOKE) and magnetoelastic stress measurements on $\mathrm{Fe}(001)$ and ${\mathrm{Fe}}_{32}{\mathrm{Co}}_{68}(001)$ bcc epitaxial films on $\mathrm{GaAs}(001)$ in a thickness range from several monolayers (ML) up to 100 ML. The magnetoelastic coupling coefficient ${B}_{2}$ of 30 ML films is $+(8.4\ifmmode\pm\else\textpm\fi{}1.4)\phantom{\rule{0.16em}{0ex}}{\mathit{MJ}/\mathrm{m}}^{3}$ for $\mathrm{Fe}(001)$ and $\ensuremath{-}(23.2\ifmmode\pm\else\textpm\fi{}3.7)\phantom{\rule{0.16em}{0ex}}{\mathit{MJ}/\mathrm{m}}^{3}$ for ${\mathrm{Fe}}_{32}{\mathrm{Co}}_{68}(001)$, respectively. In spite of the opposite sign of ${B}_{2}$ for $\mathrm{Fe}$ and ${\mathrm{Fe}}_{32}{\mathrm{Co}}_{68}$, the same sign of the uniaxial anisotropy constant ${K}_{U}^{\mathrm{eff}}$ is experimentally observed. It is concluded that the magnetoelastic interaction is not the dominating contribution to the uniaxial magnetic anisotropy in these systems.

Magnetoactive feature of in-situ polymerised polyaniline film developed on the surface of manganese–zinc ferrite

A polyaniline film exhibits magnetoactive properties when deposited on the surface of multidomain particles of manganese–zinc ferrite during in-situ polymerisation of aniline. This is reflected in the increased coercivity and thermomagnetic stability of an in-situ prepared composite compared with bare ferrite and its mixed composite with polyaniline. In addition, the deposition of a polyaniline film results in a shift of the complex-permeability dispersion region towards ultrahigh frequency band. These changes in the magnetic properties of polyaniline-coated ferrite are attributed to the increased value of the inner demagnetisation factor, which results from stress-induced magnetic anisotropy due to the pinning of domain walls appearing on the surface of ferrite. This study is focused on the mechanism of pinning of domain walls and its influence on the magnetic properties of in-situ prepared composites in terms of the molecular mechanism of oxidative polymerisation of aniline. Ferrite stimulates the propagation of polyaniline chains, which start to grow on the domain walls on the ferrite surface. It leads to the pinning of domain walls and restricts their mobility in a magnetic field. The further increase in the coercivity and the resonance frequency of polyaniline-coated ferrite due to film shrinkage after deprotonation of polyaniline makes it obvious that polyaniline coating induces elastic stresses in a ferrite particle that stimulate the growth of the effective magnetic anisotropy. Stress-induced magnetic anisotropy contributes to the reorientation of the magnetisation vectors in domains with respect to the new directions of easy magnetisation, given by magnetoelastic stresses, which leads to complex changes in the magnetic properties of in-situ prepared composites.

Chiral modulations and reorientation effects in MnSi thin films

We present an experimental and theoretical investigation of the influence of a uniaxial magnetocrystalline anisotropy on the magnetic textures that are formed in a chiral magnetic system. We show that the epitaxially induced tensile stress in MnSi thin films grown on Si(111) creates an easy-plane uniaxial anisotropy. The magnetoelastic shear stress coefficient is derived from SQUID magnetometry measurements in combination with transmission electron microscopy and x-ray diffraction data. Density functional calculations of the magnetoelastic coefficient support the conclusion that the uniaxial anisotropy originates from the magnetoelastic coupling. Theoretical calculations based on a Dzyaloshinskii model that includes an easy-plane anisotropy predict a variety of modulations to the magnetic order that are not observed in bulk MnSi crystals. Evidence for these states is found in the magnetic hysteresis and polarized neutron reflectometry measurements.

Magneto stress analysis of a strip with a semi elliptical notch under uniform magnetic field

Two dimensional solutions of the magnetic field and magneto elastic stress are presented for a magnetic material of a thin strip with a semi-elliptical notch subjected to uniform magnetic field. The strip is a finite plate of a simply connected region. A linear constitutive equation is used for the stress analysis. According to the electro-magneto theory, only Maxwell stress is caused as a body force in a plate. Therefore, the magneto elastic stress is analyzed using Maxwell stress. In the present problem, as a result, the plane stress state does not arise, and the σ z in the direction of the plate thickness and the shear deflection (anti-plane shear stress) arise for soft ferromagnetic material. The stress σ z in the plate is strong compressive stress for a soft ferromagnetic material. A rational mapping function is used for the stress analysis, and the each solution is obtained as a closed form. No further assumption of the plane stress state that the plate is thin is made for the stress analysis, though Maxwell stress components are expressed by nonlinear terms. The rigorous boundary condition is completely satisfied without any linear assumptions on the boundary. The anti-plane shear stress causes Mode III stress intensity factor when the notch is a crack. Stress concentration values are investigated for a notch problem, of which expression is given. Figures of the anti-plane shear stress distribution, Mode III stress intensity factor, and stress concentration values are shown.

Colossal magnetodielectric effect in SmFe3(BO3)4 multiferroic

The colossal (more than threefold) decrease in the dielectric constant ɛ in the easy-plane SmFe3(BO3)4 ferroborate in a magnetic field of ∼5 kOe applied in the basal ab plane of the crystal has been found. A close relation of this effect to anomalies in the field dependence of the electric polarization has been established. It has been shown that this magnetodielectric effect is due to the contribution to ɛ from the electric susceptibility, which is related to the rotation of spins in the ab plane, arises in the region of the antiferromagnetic ordering T < TN = 33 K, and is suppressed by the magnetic field. A theoretical model describing the main features of the behavior of ɛ and electric polarization in the magnetic field has been proposed, taking into account the additional anisotropy in the basal plane induced by the magnetoelastic stresses.

Magneto elastic stress subjected to uniform magnetic field over a thin infinite plate containing an elliptical hole with an edge crack

Two dimensional solutions of the magnetic field and magneto elastic stress are presented for a magnetic material of a thin infinite plate containing an elliptical hole with an edge crack subjected to uniform magnetic field. Using a rational mapping function, each solution is obtained as a closed form. The linear constitutive equation is used for these analyses. According to the electro-magneto theory, only Maxwell stress is caused as a body force in a plate. In the present paper, it raises a plane stress state for a thin plate, the deformation of the plate thickness and the shear deflection. Therefore the magneto elastic stress is analyzed using Maxwell stress. No further assumption of the plane stress state that the plate is thin is made for the stress analysis, though Maxwell stress components are expressed by nonlinear terms. The rigorous boundary condition expressed by Maxwell stress components is completely satisfied without any linear assumptions on the boundary. First, magnetic field and stress analyses for soft ferromagnetic material are carried out and then those analyses for paramagnetic and diamagnetic materials are carried out. It is stated that those plane stress components are expressed by the same expressions for those materials and the difference is only the magnitude of the permeability, though the magnetic fields H x , H y are different each other in the plates. If the analysis of magnetic field of paramagnetic material is easier than that of soft ferromagnetic material, the stress analysis may be carried out using the magnetic field for paramagnetic material to analyze the stress field, and the results may be applied for a soft ferromagnetic material. It is stated that the stress state for the magnetic field H x , H y is the same as the pure shear stress state. Solutions of the magneto elastic stress are nonlinear for the direction of uniform magnetic field. Stresses in the direction of the plate thickness and shear deflection are caused and the solutions are also obtained. Figures of the magnetic field and stress distribution are shown. Stress intensity factors are also derived and investigated for the crack length.

Magnetic field and magneto elastic stress in an infinite plate containing an elliptical hole with an edge crack under uniform electric current

Two-dimensional solutions of the electric current, magnetic field and magneto elastic stress are presented for a magnetic material of a thin infinite plate containing an elliptical hole with an edge crack under uniform electric current. Using a rational mapping function, the each solution is obtained as a closed form. The linear constitutive equation is used for the magnetic field and the stress analyses. According to the electro-magneto theory, only Maxwell stress is caused as a body force in a plate which raises a plane stress state for a thin plate and the deformation of the plate thickness. Therefore the magneto elastic stress is analyzed using Maxwell stress. No further assumption of the plane stress state that the plate is thin is made for the stress analysis, though Maxwell stress components are expressed by nonlinear terms. The rigorous boundary condition expressed by Maxwell stress components is completely satisfied without any linear assumptions on the boundary. First, electric current, magnetic field and stress analyses for soft ferromagnetic material are carried out and then those analyses for paramagnetic and diamagnetic materials are carried out. It is stated that the stress components are expressed by the same expressions for those materials and the difference is only the magnitude of the permeability, though the magnetic fields H x , H y are different each other in the plates. If the analysis of magnetic field of paramagnetic material is easier than that of soft ferromagnetic material, the stress analysis may be carried out using the magnetic field for paramagnetic material to analyze the stress field, and the results may be applied for a soft ferromagnetic material. It is stated that the stress state for the magnetic field H x , H y is the same as the pure shear stress state. Solving the present magneto elastic stress problem, dislocation and rotation terms appear, which makes the present problem complicate. Solutions of the magneto elastic stress are nonlinear for the direction of electric current. Stresses in the direction of the plate thickness are caused and the solution is also obtained. Figures of the magnetic field and stress distribution are shown. Stress intensity factors are also derived and investigated for the crack length and the electric current direction.