Magnetoelastic Coupling Constants Research Articles

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.

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.

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.

Coupling of fully symmetric As phonon to magnetism in Ba(Fe1−xAux)2As2

We used polarization-resolved Raman scattering to study magneto-elastic coupling in Ba(Fe$_{1-x}$Au$_{x}$)$_2$As$_2$ crystals as a function of light Au-doping, materials for which temperatures of the structural transition ($T_S$) and of the magnetic ordering transition ($T_N$) split. We study the appearance of the $A_g$(As)phonon intensity in the $XY$ scattering geometry that is very weak just below $T_S$, but for which the intensity is significantly enhanced below $T_N$. In addition, the $A_g$(As) phonon shows an asymmetric line shape below $T_N$ and an anomalous linewidth broadening upon Au-doping in the magnetic phase. We demonstrate that the anomalous behavior of the $A_g$(As) phonon mode in the $XY$ scattering geometry can be consistently described by a Fano model involving the $A_g$(As) phonon mode interacting with the $B_{2g}$ symmetry-like magnetic continuum in which the magneto-elastic coupling constant is proportional to the magnetic order parameter.

Extended x-ray absorption fine structure spectroscopy of stretched magnetic films on flexible substrate

This study investigates element-specific atomic distances and strains in ferromagnetic (FM) nano-thin films deposited on a flexible substrate, which can be modulated by stretching the substrate. Extended x-ray absorption fine structure (EXAFS) spectroscopy was used for the experiments. Both in-plane tensile and out-of-plane compressive strains were investigated by applying %-order tensile strains to the substrate. The atomic distance changes induced by stretching the substrate were quantitatively discussed by considering the Poisson compression, crystalline orientations of the FM metals, and polarization in the EXAFS measurement. Consequently, the ratio of strain transfer from the flexible substrate to the FM layers was estimated to be about 30% and 60% in Co and Fe nano-thin films, respectively. The strain transfer in Co films with different Co or Pt underlayer thicknesses was also measured. The results are compared with the thickness dependence of the effective magnetoelastic coupling constant, which represents the magnitude of the inverse magnetostriction effect. Although the strain transfer partially contributes to the thickness dependence, the difference in the Co lattice constant is suggested to have a significant influence on the effective magnetoelastic coupling constant.

Pressure Dependence of Magnetic Properties in La(Fe,Si)13 : Multistimulus Responsiveness of Caloric Effects by Modeling and Experiment

For a better understanding of multistimuli-responsive caloric materials with a first-order transition and for optimization of their functional properties, it is necessary to predict the behavior of the material under changes of both magnetic field and pressure. Here, we design and build a special device that can provide a self-consistent set of parameters needed for the comprehensive characterization of multistimuli-responsive functional magnetic materials. Using this scientific instrument, a data set of simultaneously measured magnetization, ${M(T)}_{H}$, and volume magnetostriction, $\ensuremath{\omega}(T{)}_{H}$, values are obtained for ${\mathrm{LaFe}}_{11.4}{\mathrm{Si}}_{1.6}$ with a first-order transition. Furthermore, based on simultaneously measured M(T) and \ensuremath{\omega}(T) dependencies obtained at ambient pressure, we develop an approach that allows the behavior of magnetization under different pressures, ${M(T)}_{P}$, to be described analytically. Additional parameters, such as compressibility, \ensuremath{\kappa}(T); thermal expansion coefficient, \ensuremath{\alpha}(T); and magnetoelastic interaction or effective magnetovolume coupling constant, ${C}_{MV}$, are determined. For verification of our developed model, direct measurements of magnetization under external pressure (up to P = 1 GPa) are carried out on the same sample as that used for simultaneous measurement of magnetization and magnetovolume effect. A comparison of simulated ${M(T)}_{P}$ dependencies with experimental $M(T{)}_{P}$ confirms that our approach provides a more realistic behavior of transition temperature under pressure, ${T}_{C}(P)$, than that of the ${T}_{C}(P)$ predicted by the Bean-Rodbell model; thus, this approach is more suitable for predicting the behavior of multistimuli-responsive caloric materials with first-order transitions under changes of both magnetic field and pressure.

Magneto‐Structural Properties of the Layered Quasi‐2D Triangular‐Lattice Antiferromagnets Cs2CuCl4−xBrx for x = 0, 1, 2, and 4

A study of the magnetic susceptibility under variable hydrostatic (He gas) pressure on single crystals of Cs2CuCl4−xBrx is presented. This work includes the border compounds x = 0 and 4, known as good realizations of the distorted triangular‐lattice spin‐1/2 Heisenberg antiferromagnet, as well as the recently discovered well‐ordered isostructural systems Cs2CuCl3Br1 and Cs2CuCl2Br2. For the determination of the exchange coupling constants J and J′ of their anisotropic triangular lattice, the susceptibility data are fitted by the recently proposed J–J′ model [Schmidt and Thalmeier, New J. Phys. 2015, 17, 073025]. Its application on magnetic susceptibility data, validated for the border compounds, yields a degree of frustration J′/J = 0.47 for Cs2CuCl3Br1 and J′/J ≃ 0.63–0.78 for Cs2CuCl2Br2, making these systems particular interesting representatives of this family. From the evolution of the magnetic susceptibility under pressure up to about 0.4 GPa, the maximum pressure applied, two observations were made for all the compounds investigated here. First, it has been found that the overall energy scale, given by Jc = (J2 + J′2)1/2, increases under pressure, whereas the ratio J′/J remains unchanged in this pressure range. These experimental observations are in accordance with the results of DFT calculations performed for these materials. Secondly, for the magnetoelastic coupling constants, extraordinarily small values are obtained, about two orders of magnitude smaller compared to other Cu‐based quantum magnets. These observations have been assigned to a structural peculiarity of this class of materials, consisting of well‐isolated magnetic units not sharing any common coordination element.

Magnetic and Elastic Vibrations in Manganese–Zinc Spinel Crystals as the Functions of Anisotropy Constant

The amplitudes of magnetic and elastic vibrations for Mn0.61Zn0.35Fe2.04O4 spinel crystalline slab are calculated by solving the equations describing the magnetic and elastic dynamics. The anisotropy constants, magnetization, second-order elastic constants and magnetoelastic coupling constants for a studied crystal are expressed as the functions of temperature. The magnetization vector and elastic shear components are found as the functions of the first magnetic anisotropy constant at different values of an external constant magnetic field greater than a saturation field. The procession patterns for normally and tangentially magnetized slabs are displayed for two values of the first anisotropy constant. High absolute values of the first anisotropy constant are shown to refer to reorientation of the magnetization vector.

Магнитные и упругие колебания в кристаллах марганец-цинковой шпинели в зависимости от константы анизотропии

AbstractThe amplitudes of magnetic and elastic vibrations for Mn_0.61Zn_0.35Fe_2.04O_4 spinel crystalline slab are calculated by solving the equations describing the magnetic and elastic dynamics. The anisotropy constants, magnetization, second-order elastic constants and magnetoelastic coupling constants for a studied crystal are expressed as the functions of temperature. The magnetization vector and elastic shear components are found as the functions of the first magnetic anisotropy constant at different values of an external constant magnetic field greater than a saturation field. The procession patterns for normally and tangentially magnetized slabs are displayed for two values of the first anisotropy constant. High absolute values of the first anisotropy constant are shown to refer to reorientation of the magnetization vector.

Effect of single-particle magnetostriction on the shear modulus of compliant magnetoactive elastomers.

The influence of an external magnetic field on the static shear strain and the effective shear modulus of a magnetoactive elastomer (MAE) is studied theoretically in the framework of a recently introduced approach to the single-particle magnetostriction mechanism [V. M. Kalita et al., Phys. Rev. E 93, 062503 (2016)10.1103/PhysRevE.93.062503]. The planar problem of magnetostriction in an MAE with magnetically soft inclusions in the form of a thin disk (platelet) having the magnetic anisotropy in the plane of this disk is solved analytically. An external magnetic field acts with torques on magnetic filler particles, creates mechanical stresses in the vicinity of inclusions, induces shear strain, and increases the effective shear modulus of these composite materials. It is shown that the largest effect of the magnetic field on the effective shear modulus should be expected in MAEs with soft elastomer matrices, where the shear modulus of the matrix is less than the magnetic anisotropy constant of inclusions. It is derived that the effective shear modulus is nonlinearly dependent on the external magnetic field and approaches the saturation value in magnetic fields exceeding the field of particle anisotropy. It is shown that model calculations of the effective shear modulus correspond to a phenomenological definition of effective elastic moduli and magnetoelastic coupling constants. The obtained theoretical results compare well with known experimental data. Determination of effective elastic coefficients in MAEs and their dependence on magnetic field is discussed. The concentration dependence of the effective shear modulus at higher filler concentrations has been estimated using the method of Padé approximants, which predicts that both the absolute and relative changes of the magnetic-field-dependent effective shear modulus will significantly increase with the growing concentration of filler particles.

Stress-induced large anisotropy field modulation in Ni films deposited on a flexible substrate

A tensile strain on the order of a few percent was created in Ni thin films deposited on a flexible polyethylene naphthalate substrate, and the strain-induced change in the magnetic anisotropy was investigated. The magnetic easy axis was reversibly switched by 90° by the application of the stress. The easy axis was orthogonal to the applied stress. The in-plane saturation magnetic field or the uniaxial magnetic anisotropy energy changed linearly in reaction to the applied tensile strain up to a strain of 2.3%. Moreover, a large difference in the saturation magnetic field up to ∼0.3 T, which corresponds to a change in the magnetic anisotropy energy of ∼7 × 104 J/m3, was realized. The effective magnetoelastic coupling constant was almost independent of the thickness of Ni.

Magnetovolume effects and effect of pressure on the temperature dependence of sublattice magnetization in Ho(Co0.9Ga0.1)2 compounds

The temperature dependence of the magnetic moments of cobalt and holmium ions in the temperature range of 5–300 K at pressures of P = 0 and 5 kbar was determined based on neutron diffraction data on Ho(Co0.9Ga0.1)2 intermetallide. The temperature dependence of the lattice parameter was established, and the spontaneous bulk magnetostriction was determined. These quantities were calculated using the exchange striction model of a ferrimagnet, and good agreement with the experiment was obtained. The parameters of the exchange interaction between pairs of atoms of this compound and the magnetoelastic coupling constant were estimated. An original interpretation of the nature of the first-order magnetic phase transition in HoCo2 is proposed.

Magnetoelastic coupling in A2FeReO6 (A = Ba and Ca) probed by elastic constants and magnetostriction measurements

Double perovskites A2FeReO6 (A = Ba, Ca) have been synthesized and studied using a combination of resonant ultrasound spectroscopy, magnetization, and magnetostriction measurements. A large softening in C44 over a wide temperature range is observed for Ba2FeReO6 below its Curie temperature (TC ≈ 311 K), which is indicative of a structural distortion. This softening is partially suppressed upon application of a low magnetic field. For Ca2FeReO6, both the longitudinal and shear moduli show a softening starting at T ≈ 160 K. In addition, magnetoelastic coupling constants have been estimated from elastic constants and magnetostriction data, which provide direct evidence of pronounced coupling between magnetism and the lattice degrees of freedom present in both compounds.

Effects of Zn additions to highly magnetoelastic FeGa alloys

Fe1−xMx (M = Ga, Ge, Si, Al, Mo and x ∼ 0.18) alloys offer an extraordinary combination of magnetoelasticity and mechanical properties. They are rare-earth-free, can be processed using conventional deformation techniques, have high magnetic permeability, low hysteresis, and low magnetic saturation fields, making them attractive for device applications such as actuators and energy harvesters. Starting with Fe-Ga as a reference and using a rigid-band-filling argument, Zhang et al. predicted that lowering the Fermi level by reducing the total number of electrons could enhance magnetoelasticity. To provide a direct experimental validation for Zhang's hypothesis, elemental additions with lower-than-Ga valence are needed. Of the possible candidates, only Be and Zn have sufficient solubility. Single crystals of bcc Fe-Ga-Zn have been grown with up to 4.6 at. % Zn in a Bridgman furnace under elevated pressure (15 bars) in order to overcome the high vapor pressure of Zn and obtain homogeneous crystals. Single-crystal measurements of magnetostriction and elastic constants allow for the direct comparison of the magnetoelastic coupling constants of Fe-Ga-Zn with those of other magnetoelastic alloys in its class. The partial substitution of Ga with Zn yields values for the magnetoelastic coupling factor, −b1, comparable to those of the binary Fe-Ga alloy.

Tetragonal magnetostriction and magnetoelastic coupling in Fe-Al, Fe-Ga, Fe-Ge, Fe-Si, Fe-Ga-Al, and Fe-Ga-Ge alloys

This paper presents a comparative study on the tetragonal magnetostriction constant, λγ,2, [ = (3/2)λ100] and magnetoelastic coupling, b1, of binary Fe100-xZx (0 < x < 35, Z = Al, Ga, Ge, and Si) and ternary Fe-Ga-Al and Fe-Ga-Ge alloys. The quantities are corrected for magnetostrains due to sample geometry (the magnetostrictive form effect). Recently published elastic constant data along with magnetization measurements at both room temperature and 77 K make these corrections possible. The form effect correction lowers the magnetostriction by ∼10 ppm for high-modulus alloys and by as much as 30 ppm for low-modulus alloys. The elastic constants are also used to determine the values of the magnetoelastic coupling constant, b1. With the new magnetostriction data on the Fe-Al-Ga alloy, it is possible to show how the double peak magnetostriction feature of the binary Fe-Ga alloy flows into the single peak binary Fe-Al alloy. The corrected magnetostriction and magnetoelastic coupling data for the various alloys are also compared using the electron-per-atom ratio, e/a, as the common variable. The Hume-Rothery rules link the e/a ratio to the regions of phase stability, which appear to be intimately related to the magnetostriction versus the solute concentration curve in these alloys. Using e/a as the abscissa tends to align the peaks in the magnetostriction and magnetoelastic coupling for the Fe-Ga, Fe-Ge, Fe-Al, Fe-Ga-Al, and Fe-Ga-Ge alloys, but not for the Fe-Si alloys for which the larger atomic size difference may play a greater role in phase stabilization. Corrections for the form effect are also presented for the rhombohedral magnetostriction, λɛ,2, and the magnetoelastic coupling, b2, of Fe100-xGax (0 < x < 35) alloys.

Magnetoelastic properties of Nd 6Fe 13Cu intermetallic compound

Magnetoelastic properties of Nd 6Fe 13Cu intermetallic compound are reported. To study the magnetoelastic behaviour of this compound, the thermal expansion as well as the longitudinal ( λ l) and transverse ( λ t) magnetostriction were measured by using the strain gauge method in the selected temperature range of 80–500 K under applied magnetic fields up to 1.5 T. An anomaly and invar-type effects are observed in the linear thermal expansion and α( T) curves at the Néel temperature. The linear spontaneous magnetostriction decreases sharply by approaching the Néel temperature and also shows the short-range magnetic ordering effects when antiferromagnetic–paramagnetic transition occurs. In the low field region, the absolute values of the anisotropic magnetostriction are small and then start to increase with applied magnetic field. Each isofield curve of the anisotropic magnetostriction passes through a minimum and then approaches to zero with increasing temperature. This magnetostriction compensation arises from the difference in the magnetoelastic coupling constants of the sublattices in this compound.

Magnetostrictive and elastic properties of Fe100−xMox (2<x<12) single crystals

In this paper we investigate the magnetostrictive [(3/2)λ100 and (3/2)λ111] and elastic (c′ and c44) behavior of single crystalline alloys Fe100−xMox for 2<x<12; the magnetoelastic coupling constants (−b1 and −b2) are computed from the measurements. Similar to other Fe–X (X=Al, Ga, and Ge) alloys, the tetragonal magnetostriction (3/2)λ100 increases monotonically from ∼70×10−6 at ∼2.5 at. % Mo to a maximum of either ∼100×10−6 at ∼8 at. % Mo for the slow cooled crystals or ∼125×10−6 at ∼11 at. % Mo for quenched crystals. A sharp decrease after the peak is observed for the slow cooled crystals due to the formation of a second phase. The rhombohedral magnetostriction (3/2)λ111 of the Fe–Mo alloys is found to be insensitive to the Mo content. This behavior is distinctly different from other Fe–X (X=Al, Ga, and Ge) alloys where a slight decrease in magnitude and a sign reversal upon chemical ordering was observed for (3/2)λ111. Both shear elastic constants (c′ and c44) for Fe–Mo are remarkably insensitive to the Mo content, which is also distinct from the other Fe-based alloys used in the comparison. The two magnetoelastic coupling constants −b1=3λ100c′ (with values from 7.15 to 9.77 MJ/m3) and −b2=3λ111c44 (with values from −4.96 to −5.81 MJ/m3) were calculated and compared with those of other Fe–X (X=Al, Ga, and Ge) alloys.

Magnetism and anomalous properties of plutonium

It is shown that because of their high magnetic susceptibility δ plutonium and its alloys are close to magnetic instabilities; dynamic effects of short-range magnetic order which are associated with the fluctuating magnetization density of electrons – spin fluctuations – play a large role in them. Long-range ferro- and antiferromagnetic order is suppressed. A model is developed for the spin fluctuations in plutonium. In this model, because of strong magneto-elastic coupling the spin-fluctuation energy depends on the volume of the crystal and is independent of temperature and spatial dispersion. It is shown that the contribution of the zero-point quantum spin-fluctuations is largely temperature-independent, as a result of which saturation of local magnetic moments is absent, the Curie–Weiss law for the magnetic susceptibility breaks down, and below the melting temperature plutonium is a strongly quantum system. An explanation is given for the thermal expansion anomalies of the δ phase of plutonium and its alloys on the basis of the theory of magneto-volume effect with a negative magneto-elastic coupling constant.

Magnetoelasticity of Fe$_{100-x}$Ge$_{x}(5 ≪ x ≪ 18)$ Single Crystals From 81 K to 300 K

Temperature dependent magnetoelastic properties of Fe 100 - xGex(5 < x < 18) single crystals have been measured. Tetragonal magnetostriction (3/2) lambda100 measurements at x = 5.7, 12.1, 14.9, and 17.7 were performed between 78 K and 426 K and resonant ultrasound spectroscopy measurements were used to determine the shear elastic constant c' from 5 K to 300 K for x = 6.4, 7.2, 10.8, 14.6, 17.7 , and 17.9 . A clear distinction was observed between the temperature dependencies of lambda100 for the A2 and D03 phases of Fe100-xGex . The elastic constant c' displays a monotonic decrease with concentration through the different phases (6 < x < 18) and at all temperatures. Experimental values of the tetragonal magnetoelastic coupling constant -b 1 at 81 K were remarkably consistent with theoretical values determined by density functional calculations at 0 K.

Magnetoelastic coupling in Fe100−xGex single crystals with 4&amp;lt;x&amp;lt;18

In this paper we examine the elastic (c′ and c44) and magnetostrictive (λ100 and λ111) behaviors of Fe100−xGex for 4&amp;lt;x&amp;lt;18, quantities used further to find the fundamental magnetoelastic coupling constants b1 and b2 at room temperature. The x dependence of b1 and b2 for Fe100−xGex is contrasted to those of Fe100−xGax and Fe100−xAlx. While the rhombohedral shear elastic constant c44 is almost insensitive to the type and amount of solute, the tetragonal shear constant c′ shows a pronounced and rapid softening with increasing x for all three alloys but with different decreasing slopes. Similarly, while the rhombohedral magnetostriction λ111 behavior is analogous for all three alloy systems, showing a sign change from negative to positive at the onset of chemical order, the tetragonal magnetostriction λ100 behavior differs. For the Ga and Al alloys, λ100 maintains positive values over the entire x range, both curves showing large peak values, whereas λ100 of Fe100−xGex exhibits a moderate positive peak followed by a negative dip, both of comparable magnitude. Finally the tetragonal coupling constant −b1 of Fe–Ge shows a marked, sharp decrease as chemical order occurs at x∼12 at. % Ge. The decline continues until the ordered D03 phase is fully established at x∼18 at. % Ge. The peak value of |b1| for Fe–Ge is approximately half of those for Fe–Ga and Fe–Al. This smaller value of |b1|, obtained for the higher electron concentration Ge alloy, is consistent with predictions based on band structure calculations. The rhombohedral coupling constant −b2 shows a consistent sign change at the occurrence of chemical ordering in both Fe–Ga and Fe–Ge.