Magnetoelastic Field Research Articles

Magnetoelectric coupling in Ba:Pb(Zr,Ti)O3/Co40Fe40B20 nanoscale waveguides studied by propagating spin-wave spectroscopy

In this study, we report on the characterization of the magnetoelectric coupling coefficient in Ba-substituted Pb(Zr, Ti)O3/Co40Fe40B20 (BPZT/CoFeB) nanoscaled waveguides with lateral dimensions of 700 nm using propagating spin-wave spectroscopy. The characterization was conducted in a Damon–Eshbach configuration to maximize the magnetoelastic coupling strength, as predicted by strain distribution calculations using finite element simulations. The spin-wave resonance frequency is controlled by applying bias voltages on the magnetoelectric waveguide. The magnitude of the frequency shift was correlated with the strength of the magnetoelastic field, which reached a maximum value of 5.71 mT in our experiments. In addition, the results demonstrated that the coupling coefficient behavior is associated with the hysteretic ferroelectric nature of BPZT, reaching a maximum value of 1.69 mT/V.

Direct-Current Electrical Detection of Surface-Acoustic-Wave-Driven Ferromagnetic Resonance.

Surface acoustic waves (SAW) provide a promising platform to study spin-phonon coupling, which can be achieved by SAW-driven ferromagnetic resonance (FMR) for efficient acoustic manipulation of spin. Although the magneto-elastic effective field model has achieved great success in describing SAW-driven FMR, the magnitude of the effective field acting on the magnetization induced by SAW still remains hard to access. Here, by integrating ferromagnetic stripes with SAW devices, direct-current detection for SAW-driven FMR based on electrical rectification is reported. By analyzing FMR rectified voltage, the effective fields are straightforwardly characterized and extracted, which exhibitsthe advantages of better integration compatibility and lower cost than traditional methods such as vector-network analyzer-based techniques. A large nonreciprocal rectified voltage is obtained, which is attributed to the coexistence of in-plane and out-of-plane effective fields. The effective fields can be modulated by controlling the longitudinal and shear strains within the films to achieve almost 100% nonreciprocity ratio, demonstrating the potential for electrical switches. Besides its fundamental significance, this finding provides a unique opportunity for a designable spin acousto-electronic device and its convenient signal readout.

Transverse domain wall dynamics in hybrid piezoelectric/ferromagnetic devices

This work investigates the static and dynamic features of transverse domain walls in a magnetostrictive, linear elastic isotropic ferromagnetic material under the action of magnetic field (axial and transverse) and electric current. The investigation is done in the framework of the extended Landau–Lifshitz–Gilbert equation by taking into account the effects of stresses induced by a piezoelectric actuator and Rashba spin‐orbit torque caused by structural inversion asymmetry. First, we obtain the expression of magnetization orientation into the two faraway domains, then characterize the static magnetization profile under the action of magnetoelastic and transverse magnetic fields. Next, we introduce a trial function (Schryer and Walker type). After that, by adopting the small angle approximation formalism, we derive the explicit expression of key quantities such as propagating transverse domain wall profile, excitation angle, transverse domain wall velocity, mobility, and displacement. Finally, we present the numerical illustrations of derived analytical results and find that they are in qualitatively good agreement with the recent numerical simulations and experimental observations.

Enhanced magnetic modulation at a border of magnetic ordering in La1−xSrxMnO3/BaTiO3(100) heterostructure

In La1−xSrxMnO3 (LSMO)/BaTiO3 (BTO) heterostructures with a multiferroic interface, an artificial modulation of the magnetic structure is observed. The saturation magnetization of La1−xSrxMnO3 changes discontinuously due to in-plane distortions caused by a structural phase transition of a BaTiO3 substrate. Polarity reversal of the external electric field also causes a reversible switching in the magnetization. The magnitude of both magnetic modulations, due to the magnetoelastic and electric field effects, is concomitantly enhanced at a critical composition xc∼0.55, locating at a border of the magnetic phase transition. The polarity-dependent change in magnetization is possibly attributed to a change in the concentration of oxygen ions at the LSMO/BTO interface, indicating that the exchange interaction is reciprocally driven from being ferromagnetic to antiferromagnetic by the electric field polarity.

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.

Magnetic properties of 09G2S steel, manufactured by selective laser melting and cyclically deformed by tension

Low-cycle fatigue tests in the elastic-plastic strain region of 09G2S steel specimens manufactured with a laser 3D printer by selective laser melting method (SLS steel) were carried out. The major hysteresis loops and field dependences of the reversible magnetic permeability were measured. It has been established that normalization at 980 °C (1 hour) reduces the ultimate strength of steel 09G2S in 2 times (502 MPa) and increases the relative elongation almost 6 times (34.6%), bringing this steel closer to cast steel 09G2S. The magnetic properties (Нс, Br, µmax) of cast and SLM normalized steel before and after cyclic tests are similar. The main changes in these properties of both cast and SLM steel are observed at the initial stage of low-cycle tests, a further increase in the number of cycles (up to the destruction of the tested samples) does not lead to their significant change. The nature of the change in the magnetoelastic field Hσ, determined from the experimental field dependences of the reversible magnetic permeability, during low-cycle tests for cast and SLM steels is radically different: for cast 09G2S steel the magnetoelastic field Hσ practically does not change with increasing number of cycles, whereas for SLM 09G2S steel a sharp increase of Hσ value by 30% is observed during the first test cycles, which is most likely associated with an increase in residual mechanical stresses.

Influence of the bi-nonlinearity on the characterization of mode I fracture parameter [formula omitted] for a cracked giant magnetostrictive material in the coupled magneto-elastic field: An experimental and numerical study

Terfenol-D, a giant magnetostrictive material exhibits bi-nonlinear stress-strain relationship in coupled magneto-elastic field. A novel hyperbolic vector generalized magneto-elastic constitutive model is employed to describe this bi-nonlinear stress-strain behaviour. Some physics-based experiments for magnetization and magnetostriction hysteresis loops and mechanical compression tests under the applied magnetic field are conducted. The general HM and stress-strain relationships are programmed in C language to define the coupled field constitutive material model. Coupled magneto-elastic response from the performed finite element analyses are compared with experiments to optimize the material parameters. Fracture experiments employing single edge notch bend (SENB) specimens are conducted with and without external magnetic field as per ASTM E399. The digital image correlation technique is used to capture the load line and crack opening displacement variation with peak fracture load data. Two parameter Weibull statistical theory of strength has been utilised to forecast the mean peak fracture load. The Weibull modulus and goodness of fit are assessed using linear regression analysis (LIN2), biased and unbiased maximum likelihood estimation (MLE2-B & MLE2-U) approach. Finite element crack propagation model based on the optimized nonlinear constitutive relations is built concerning to magnetization and stress dependent elasticity problem of Terfenol-D fracture. Three-dimensional J-integral is formulated considering the effects of magneto-elastic fields, which is subsequently used to characterize the crack front singularity near the fracture process zone. Critical strain energy release rate JIc was calculated using the mean peak fracture load in both absence and presence of the external magnetic field. Finally, the influence of bi-nonlinear modularity and applied external magnetic field on the fracture behaviour of the Terfenol-D SENB fracture specimen were compared with the unimodular experimental results and substantial differences were reported. The stipulation and importance of considering the bi-nonlinear critical strain energy release rate JIc in the context of a coupled magneto-elastic field was discussed certifying the observations.

Design of Reconfigurable Spin-Wave Nanochannels Based on Strain-Mediated Multiferroic Heterostructures and Logic Device Applications

A method based on the magnetoelectric effect present in multiferroic heterostructures was used to design a reconfigurable waveguide (WG) channel for spin wave (SW) transmission. The multiferroic heterostructures consisted of a piezoelectric (PZT) layer and an adjacent ferromagnetic (CoFeB) layer within the WG region. By applying voltage to the PZT layer, a piezostrain would be generated and transferred to the ferromagnetic layer, leading to a magnetoelastic field in the latter, which could modulate SW dispersion, including propagation frequency and SW vector. Two applications based on these piezostrain-modulated SW dispersion parameters were explored. A piezostrain-modulated, multiple-shaped WG channel was first proposed to allow specific-frequency SW propagation via control of the applied strain. Then, piezostrain was used to perform a phase shift modulation in the multiferroic SW channel. A <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\pi }$ </tex-math></inline-formula> -phase shift in the propagation of SW was obtained by customizing the length of strain operation for a given frequency. A phase shifter was designed to build an interferometer to fulfill the destruct and construct logic functions based on strain-controlled SWs. These simulation results highlight the considerable potential of strain engineering to control logical and computational reconfigurable SW devices.

Influence of the Anisotropy of Magnetic Films on the Detection of Magnetoelastic Fields upon Excitation by an Amplitude-Modulated Magnetic Field

Influence of the Anisotropy of Magnetic Films on the Detection of Magnetoelastic Fields upon Excitation by an Amplitude-Modulated Magnetic Field

Estimation of residual stresses in plastically deformed eutectoid steel with different perlite morphology via magnetic parameters

Measurements of magnetic properties, as well as microscopic and X-ray diffraction investigations, of eutectoid steels with the structure of spheroidized and of coarse lamellar pearlite after cold plastic deformation by tension have been carried out. The steel with the coarse lamellar pearlite was unexpectedly found to have a lower coercivity than the steel with the spheroidized pearlite. With growing elongation, the coercivity of the steels with various pearlite morphologies grows, whereas the remanence and maximal magnetic permeability decrease. At an elongation more than 0.7%, the remanence and maximum magnetic permeability become almost equal. The difference in the coercivity of eutectoid steel with various pearlite morphology raises with elongation growth. The main changes in magnetic properties occur prior to elongations of 2–4%. The magnetoelastic fields Hσ were calculated from the field dependences of the magnetic incremental permeability and the residual compressive stresses, estimated. It is found that the average residual stresses are −222 MPa for steel with the spheroidized pearlite and −349 MPa for steel with the lamellar pearlite. According to the results of X-ray diffraction analysis, the values of residual stresses are −251 MPa and –342 MPa for steels with the spheroidized and lamellar pearlite, respectively.

Differentiated Strain-Control of Localized Magnetic Modes in Antidot Arrays.

The control of localized magnetic modes has been obtained in Ni60Fe40 square lattice (600 nm) antidot arrays. This has been performed by tailoring the magnetoelastic field at the scale of the antidot primitive cell. The corresponding heterogeneous strain field distributions have been generated by a PZT substrate and enhanced by the incorporation of a supporting compliant layer. It has been highlighted by a differentiated variation of magnetic energy directly due to the local magnetoelastic field felt by each magnetic mode, probed by ferromagnetic resonance spectroscopy. A modeling, involving micromagnetic simulations (to locate the magnetic modes), full-field simulations (to evaluate the strain field distributions), and an analytical model generally dedicated to continuous film that we have extended to those magnetic modes, shows a good agreement with the experimental data. This approach is very promising to develop multichannel systems with simultaneous and differentiated controlled frequencies in magnetic devices.

Optimized Voltage-Induced Control of Magnetic Domain-Wall Propagation in Hybrid Piezoelectric/Magnetostrictive Devices

A theory of voltage-induced control of magnetic domain walls propagating along the major axis of a magnetostrictive nanostrip, tightly coupled with a ceramic piezoelectric, is developed in the framework of the Landau–Lifshitz–Gilbert equation. It is assumed that the strains undergone by the piezoelectric actuator, subject to an electric field generated by a dc bias voltage applied through a couple of lateral electrodes, are fully transferred to the magnetostrictive layer. Taking into account these piezo-induced strains and considering a magnetostrictive linear elastic material belonging to the cubic crystal class, the magnetoelastic field is analytically determined. Therefore, by using the classical traveling-wave formalism, the explicit expressions of the most important features characterizing the two dynamical regimes of domain-wall propagation have been deduced, and their dependence on the electric field strength has been highlighted. Moreover, some strategies to optimize such a voltage-induced control, based on the choice of the ceramic piezoelectric material and the orientation of dielectric poling and electric field with respect to the reference axes, have been proposed.

Effects of Heterogeneous Strain on the Magnetization Processes in Magnetic Nanomembranes

The realization of mechanically compliant spintronic elements relies on magnetic thin films prepared on flexible polymeric foils. Due to the strong difference in the mechanical properties of the magnetic thin film and the polymeric support, strong effects of heterogeneous strain emerge, which govern the magnetic response of the magnetic nanomembrane. Herein, the effect of the heterogeneous strain in a prototypical magnetic nanomembrane of Ni on the application‐relevant polyimide foil is studied. The distribution of the magnetoelastic field in the case of the heterogeneous strain is taken into account and compared with the case of the free‐standing Ni thin film. It is shown that the reversal process is strongly influenced by the heterogeneity at the early stages. Indeed, the reversal is characterized by two modes in the heterogeneous case, due to the strain localization in the nanomembrane, whereas the homogeneous case is characterized by a single mode. In contrast, the strain heterogeneity does not change significantly the postreversal oscillations as well as the equilibrium configuration for a given mean strain. These results are strongly relevant for a broad magnetism community working in the field of curvilinear magnetism, shapeable magnetoelectronics, and straintronics.

Thermodynamics of magnetic emergent crystals under coupled magnetoelastic fields

Magnetic fields and mechanical forces can change the deformation and stability of magnetic emergent crystals (MECs) such as Bloch skyrmion crystal (SkX), Néel SkX and Anti-SkX. Due to the tensor nature of strains, mechanical loads provide more fruitful ways to manipulate the MECs, while their effect on MECs other than the Bloch SkX is hitherto unclear. We construct a thermodynamic model for noncentrosymmetric ferromagnets in all possible point groups when subjected to coupled magnetoelastic fields. Compared with classic theories, we include terms coupling the elastic strains, the magnetization, and its derivatives in the free energy, which lead to strain-induced Dzyaloshinskii–Moriya interaction anisotropy. For epitaxial thin films in three types of point groups (T, C 3v , D 2d ) hosting Bloch SkX, Néel SkX and Anti-SkX, we find the newly added terms always deform the MECs and eventually lead to their instability as the misfit strains increase. Specifically, for Bloch SkX in group T materials and Néel SkX in group C 3v materials, a novel magnetic phase called paired-skyrmion crystal (pSkX) appears. Our theory lays the path to study deformation and phase transitions of different MECs, and to explore novel states of MECs in chiral magnets when subjected to magnetoelastic fields.

Interference of co-propagating Rayleigh and Sezawa waves observed with micro-focused Brillouin light scattering spectroscopy

We use micro-focused Brillouin light scattering spectroscopy (BLS) to investigate surface acoustic waves (SAWs) in a GaN layer on a Si substrate at GHz frequencies. Furthermore, we discuss the concept of BLS for SAWs and show that the crucial parameters of SAW excitation and propagation can be measured. We investigate a broad range of excitation parameters and observe that Rayleigh and Sezawa waves are excited simultaneously at the same frequency. Spatially resolved measurements of these co-propagating waves show a periodic pattern, which proves their coherent interference. From the periodicity of the spatial phonon patterns, the wavevector difference between the two waves has been identified and compared to the dispersion relation. The appearance of Sezawa waves related to the finite thickness of the piezoelectric substrate leads to acoustic fields with a time-independent spatial variation similar to the situations realized using counter-propagating waves. This periodicity can have an influence on experimental results in angular momentum conversion experiments, for example, via magneto-elastic fields in hybrid-SAW-structures with additional magnetic layers.

Excitation and propagation of spin waves in non-uniformly magnetized waveguides

The characteristics of spin waves in ferromagnetic waveguides with non-uniform magnetization have been investigated for situations where the shape anisotropy field of the waveguide is comparable to the external bias field. Spin-wave generation was realized by the magnetoelastic effect by applying normal and shear strain components, as well as by the Oersted field emitted by an inductive antenna. The magnetoelastic excitation field has a non-uniform profile over the width of the waveguide because of the non-uniform magnetization orientation, whereas the Oersted field remains uniform. Using micromagnetic simulations, we indicate that both types of excitation fields generate quantised width modes with both odd and even mode numbers as well as tilted phase fronts. We demonstrate that these effects originate from the average magnetization orientation with respect to the main axes of the magnetic waveguide. Furthermore, it is indicated that the excitation efficiency of the second-order mode generally surpasses that of the first-order mode due to their symmetry. The relative intensity of the excited modes can be controlled by the strain state as well as by tuning the dimensions of the excitation area. Finally, we demonstrate that the nonreciprocity of spin-wave radiation due to the chirality of an Oersted field generated by an inductive antenna is absent for magnetoelastic spin-wave excitation.

Laser-Induced Magnetization Precession in Individual Magnetoelastic Domains of a Multiferroic Co40Fe40B20/BaTiO3 Composite

Using a magneto-optical pump-probe technique with micrometer spatial resolution we show that magnetization precession can be launched in individual magnetic domains imprinted in a Co$_{40}$Fe$_{40}$B$_{20}$ (CoFeB) layer by elastic coupling to ferroelectric domains in a BaTiO$_{3}$ substrate. The dependence of the precession parameters on external magnetic field strength and orientation reveal that by laser-induced ultrafast partial quenching of the magnetoelastic coupling parameter of CoFeB by $\approx$27% along with 10% ultrafast demagnetization trigger the magnetization precession. The relation between the laser-induced reduction of the magnetoelastic coupling and the demagnetization is approximated by the $n(n+1)/2$-law with n$\approx$2. This correspondence confirms the thermal origin of the laser-induced anisotropy change. Based on the analysis and modeling of the excited precession we find signatures of laser-induced precessional switching, which occurs when the magnetic field is applied along the hard magnetization axis and its value is close to the effective magnetoelastic anisotropy field. The precession excitation process in an individual magnetoelastic domain is found to be unaffected by neighboring domains. This makes laser-induced changes of magnetoelastic anisotropy a promising tool for driving magnetization dynamics and switching in composite multiferroics with spatial selectivity.

Strain-mediated propagation of magnetic domain-walls in cubic magnetostrictive materials

The role played by magnetoelastic effects on the properties exhibited by magnetic domain walls propagating along the major axis of a thin magnetostrictive nanostrip, coupled mechanically with a thick piezoelectric actuator, is theoretically investigated. The magnetostrictive layer is assumed to be a linear elastic material belonging to the cubic crystal classes $$\bar{4}$$3m, 432 and m$$\bar{3}$$m and to undergo isochoric magnetostrictive deformations. The analysis is carried out in the framework of the extended Landau–Lifshitz–Gilbert equation, which allows to describe, at the mesoscale, the spatio-temporal evolution of the local magnetization vector driven by magnetic fields and electric currents, in the presence of magnetoelastic and magnetocrystalline anisotropy fields. Through the traveling-wave transformation, the explicit expression of the key features involved in both steady and precessional regimes is provided and a qualitative comparison with data from the literature is also presented.

Magnetic non-destructive testing of residual stresses in low carbon steels

A new calibration-free magnetic method and a measuring system for residual stresses monitoring in low carbon steels have been developed. The method is based on the fact that during the action of compressive stresses in the material an “easy plane” magnetic texture appears. Magnetic texture affects the processes of magnetization reversal of the testing object in such a way that two or three maxima on the curves of differential μd(H) or reversible μrev(H) magnetic permeabilities appear. The fields of the maxima are associated with the magnetoelastic field and residual stresses. To increase the reliability of testing results and simplify the evaluation of residual stresses in testing objects, it was proposed to use the method of subtracting experimental μd(H) curves measured in the zones of action of compressive stresses and in the object under test without stresses. The method can also be used to estimate residual tensile stresses that are the most dangerous for steel structures.

Multilevel nonvolatile memory based on the hysteretic giant magnetoimpedance effect of heterogeneous magnetic laminate

This work investigates the asymmetric and hysteretic GMI effect of two-phase heterogeneous magnetic laminate consisting of Ni/Fe30Ni45Co18Si2B5/micro-planar coil/Fe30Ni45Co18Si2B5/Ni for nonvolatile memory application. Since the magnetostrictive Ni ribbon produces the remanent magnetoelastic and magnetostatic fields to the neighboring soft amorphous magnetic alloy (Fe30Ni45Co18Si2B5) when the external dc magnetic field is removed, the proposed laminate manifests multi-level remanent impedances depending on the previously applied magnetic field. And the maximum nonvolatile GMI ratio of 130% is obtained at 400 kHz frequency. Furthermore the laminate can function as multilevel nonvolatile memory, which consumes zero standby power without losing data.