Anisotropic Magnetostriction 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.

Origin of the metamagnetic transitions in Y0.9Tb0.1Fe2D4.3

Deuterium insertion was used to tune the magnetic properties of Y0.9Tb0.1Fe2 Laves phase towards an itinerant electron metamagnetic (IEM) behavior. The latter is highly sensitive to chemical changes and external parameters. The structural and magnetic properties of Y0.9Tb0.1Fe2D4.3 were investigated using various neutron powder diffraction experiments in addition to magnetic measurements under steady and pulsed high magnetic fields up to 60 T. The deuteride crystallizes in a monoclinic structure (Pc space group) with 4.3 D atoms located in 18 tetrahedral interstitial sites. At zero field, it undergoes a ferrimagnetic-antiferromagnetic (FiM-AFM) transition at TM0 = 90 K, accompanied by an anisotropic magnetostriction and a negative cell volume expansion of 0.6 %. A second AFM-PM transition is observed at 146 K. Under pulsed magnetic field at 4.2 K, the deuteride displays a multistep magnetic behavior from ferrimagnetic to a ferromagnetic state, which can be attributed to a stepwise rotation of the Tb moments. The ZFC-FC magnetization curves at low fields exhibit an irreversibility below 90 K, followed by a sharp decrease in magnetization at the FM-AFM transition. Between 90 K and 130 K, the magnetization curves display an IEM behavior, with the transition field increasing linearly with temperature.

Direct and inverse magnetocaloric effects in magnetostrictive GdMn2Ge2 with field-induced metamagnetic transition

Heavy rare-earth-based ternary intermetallic compounds with the formula RT2X2 have drawn great interest because of their multiple magnetic transitions and various magnetic structures. Here, anisotropic magnetic behaviors, magnetocaloric effects (MCEs), and magnetostriction effects in single-crystalline GdMn2Ge2 are studied in two different directions. Experiments show a magnetic transition characterized by a sudden decrease in magnetization for μ0H//a and a sharp increase for μ0H//c at Tt. The transition is driven by lower temperatures for μ0H//a, contrasting that for μ0H//c with an increase in the magnetic field. An inverse MCE is observed for μ0H//a with a maximum magnetic entropy change (−ΔSMmax) of −7.4 J kg−1 K−1 (μ0ΔH = 6 T), while a direct MCE is obtained for μ0H//c with an −ΔSMmax of 8.0 J kg−1 K−1 under the same magnetic field change. Moreover, a remarkable field-induced metamagnetic transition and a magnetostriction effect are observed simultaneously at Tt, indicating strong magneto-lattice coupling. The T-μ0H phase diagrams are constructed based on the magnetic properties. The coexistence of direct and inverse MCEs is discussed and is due to the spin-flop of Mn and anisotropic magnetic properties under magnetic fields in different directions.

Miniaturized double-wing ∆E-effect magnetic field sensors

Magnetoelastic micro-electromechanical systems (MEMS) are integral elements of sensors, actuators, and other devices utilizing magnetostriction for their functionality. Their sensitivity typically scales with the saturation magnetostriction and inversely with magnetic anisotropy. However, large saturation magnetostriction and small magnetic anisotropy make the magnetoelastic layer highly susceptible to minuscule anisotropic stress. It is inevitably introduced during the release of the mechanical structure during fabrication and severely impairs the device’s reproducibility, performance, and yield. To avoid the transfer of residual stress to the magnetic layer, we use a shadow mask deposition technology. It is combined with a free-free magnetoelectric microresonator design to minimize the influence of magnetic inhomogeneity on device performance. Magnetoelectric resonators are experimentally and theoretically analyzed regarding local stress anisotropy, magnetic anisotropy, and the ΔE-effect sensitivity in several resonance modes. The results demonstrate an exceptionally small device-to-device variation of the resonance frequency < 0.2% with large sensitivities comparable with macroscopic ΔE-effect magnetic field sensors. This development marks a promising step towards highly reproducible magnetoelastic devices and the feasibility of large-scale, integrated arrays.

Energy harvesting using magnetostrictive materials: Effects of material anisotropy and stress multiaxiality

Low-frequency vibrations are common as background noise in urban and industrial environments. They originate from natural or artificial sources: road vehicles, industrial machinery, wind, etc., and constitute a ubiquitous energy source. In the framework of energy harvesting, magnetostrictive materials are an attractive alternative solution to the brittleness and geometrical limitations of piezoelectric materials. While numerous previous works dealt with uniaxial stress on selected materials, the exploration of the effects of multiaxial loadings and material anisotropy has not yet been investigated as a way to improve the performance of low-frequency vibration energy harvesting systems. In this work, we investigated the capability of grain-oriented electrical steel in an energy-harvesting context. This material has been selected as a model material, notably as it is abundant and cost-effective. It shows limited magnetostriction but significant elastic, magnetic, and magnetostrictive anisotropy. We combined experimental and predictive simulation results to discuss the possibility of increasing the levels of harvested energy by playing with the orientation of magnetic and mechanical stimuli. Various orientations of magnetic field and mechanical stress were considered with regard to the rolling direction of the material. Unexpectedly high energy density amounts, up to 10 mJ·cm−3, were obtained, competing with giant magnetostrictive materials like Terfenol-D or Galfenol.

Magnetic order in 2D antiferromagnets revealed by spontaneous anisotropic magnetostriction

The temperature dependent order parameter provides important information on the nature of magnetism. Using traditional methods to study this parameter in two-dimensional (2D) magnets remains difficult, however, particularly for insulating antiferromagnetic (AF) compounds. Here, we show that its temperature dependence in AF MPS3 (M(II) = Fe, Co, Ni) can be probed via the anisotropy in the resonance frequency of rectangular membranes, mediated by a combination of anisotropic magnetostriction and spontaneous staggered magnetization. Density functional calculations followed by a derived orbital-resolved magnetic exchange analysis confirm and unravel the microscopic origin of this magnetization-induced anisotropic strain. We further show that the temperature and thickness dependent order parameter allows to deduce the material’s critical exponents characterising magnetic order. Nanomechanical sensing of magnetic order thus provides a future platform to investigate 2D magnetism down to the single-layer limit.

Non-stoichiometric ErFe2Mnx compounds: Structure, magnetic, magnetoelastic and magnetothermal properties

Crystal structure, magnetostriction, magnetic and magnetothermal properties have been studied for novel non-stoichiometric ErFe2Mnx (0 ≤ x ≤ 0.6) compounds. It has been found that for х ≤ 0.4 the compounds crystallize with MgCu2-type structure. Curie temperature and magnetic moment values decrease with manganese alloying. Molecular field coefficients have been calculated within ferrimagnetic two-sublattice molecular field model. Magnetic and heat capacity measurements have been used to calculate magnetocaloric effect in a wide temperature range. It has been demonstrated that increasing the Mn content in ErFe2Mnx leads to a significant increase (up to 39 %) of anisotropic magnetostriction value at 77 K in magnetic field of 18 kOe. At the same time, the value of effective magnetocrystalline anisotropy decreases. Thus, manganese alloying opens new way for tuning magnetocrystalline anisotropy and magnetostriction in Laves phase compounds.

Giant enhancement of magnetostriction in Pt doped FeGa ribbons

FeGa alloys are among the most promising magnetostrictive materials. How to improve the magnetostriction of FeGa has been a long-term concern. In this work, trace amount of Pt doped FeGa-(Fe0.83Ga0.17)100–xPtx (x = 0, 0.2, 0.4, and 0.6) was fabricated using melt-spinning technique. The magnetostriction, crystal structure, and magnetocrystalline anisotropy of the ribbon samples were studied, revealing that the conforming between the crystal growth direction and the easy magnetization axis, and the enlarged lattice parameter both contribute to the enhancement of magnetostriction, which reached the maximum λ⊥ of −1369 ppm at the optimum composition x = 0.4. Finally, transmission electron microscopy was performed to show that nanoinclusions exist not only in Pt-doped but also in Pt-free samples, demonstrating that the nanoinclusions do not play the dominant role in magnetostriction improvement. This work may accelerate the design of highly magnetostrictive FeGa alloys and other magnetic functional materials, which are required of large magnetostriction.

Structural and magnetostrictive properties of intermetallic (Tb,Ho)(Fe,Co)[formula omitted] compounds

The influence of iron substitution by cobalt on the structural and magnetostrictive characteristics of (Tb,Ho)(Fe, Co)2-type compounds is investigated. It is established that cobalt doping of the Tb0.16Ho0.84Fe2 compound leads to an increase in the Curie temperature and a decrease in the lattice constant. It is shown that the anisotropic magnetostriction of the Tb0.16Ho0.84Fe2−xCox (x≤0.4) compounds significantly exceeds the volumetric one in the moderate (up to 1.2T) magnetic fields. The Tb0.16Ho0.84Fe1.8Co0.2 composition with the highest saturation magnetostriction and magnetostrictive susceptibility is found.

Thermo-Magnetostrictive Effect for Driving Antiferromagnetic Two-Dimensional Material Resonators.

Magnetostrictive coupling has recently attracted interest as a sensitive method for studying magnetism in two-dimensional (2D) materials by mechanical means. However, its application in high-frequency magnetic actuators and transducers requires rapid modulation of the magnetic order, which is difficult to achieve with external magnets, especially when dealing with antiferromagnets. Here, we optothermally modulate the magnetization in antiferromagnetic 2D material membranes of metal phosphor trisulfides (MPS3), to induce a large high-frequency magnetostrictive driving force. From the analysis of the temperature-dependent resonance amplitude, we provide evidence that the force is due to a thermo-magnetostrictive effect, which significantly increases near the Neél temperature, due to the strong temperature dependence of the magnetization. By studying its angle dependence, we find the effect is observed to follow anisotropic magnetostriction of the crystal lattice. The results show that the thermo-magnetostrictive effect results in a strongly enhanced thermal expansion force near the critical temperature of magnetostrictive 2D materials, which can enable more efficient actuation of nano-magnetomechanical devices and can also provide a route for studying the high-frequency coupling among magnetic, mechanical, and thermodynamic degrees of freedom down to the 2D limit.

Microstructures in Iron-rich FeSi Alloys by First-principles Phase Field and Special Quasirandom Structure Methods

Coarse grained phase morphologies of iron-rich region of FeSi alloys at 1050 K are investigated by using first-principles phase field and special quasirandom structure methods without relying on any experimental or empirical information. From the free energy comparison, we find that, for the Si concentration less than 25 at%, a solid-solution-like homogeneous phase is most stable, although a random pattern in nm scale consisting of B2 Fe4–xSix and D03 Fe3Si phases may appear at 12.5 at% Si at somewhat lower temperatures. We make a conjecture that, around 12.5 at% Si, such a random pattern in nm scale is the origin of the zero magnetostriction and low magnetic anisotropy. This solves a long-standing problem of the experimentally observed zero magnetostriction at 6.5 wt% Si. On the other hand, for the Si concentration slightly larger than 25 at%, FeSi alloys prefer two-phase coexistence of the D03 Fe3Si phase and the B2 FeSi phase. All these findings are in good accordance with the available experimental evidence.

Measurement of alternating and rotational magnetostrictions of Non-oriented silicon steel sheets

Extensive numerical analyses and experimental tests have shown that while major regions of magnetic cores in electromagnetic devices, such as transformers and rotating electric machines, are dominated by the alternating magnetic fields, the rotating magnetic fields exist in the corner joints of multi-phase transformers and the yoke area behind the teeth of rotating electric machines. These magnetic fields cause core losses due to hysteresis and eddy currents, mechanical vibration and acoustic noises due to magnetostriction. Many studies have been reported in the literature on alternating and rotational core losses and alternating magnetostriction, but not so much on rotational magnetostriction, especially in non-oriented (NO) silicon steel sheets. The vibration and noise caused by rotational magnetostriction are much higher than those caused by alternating magnetostriction. This paper reports the development of a magnetostriction measurement system consisting of a 2D symmetrical single sheet tester (SST) and resistance strain gauges. The selection considerations of resistance strain gauges are summarized. The alternating and rotational magnetostriction characteristics of a NO silicon steel, B35A300 (0.35 mm), are measured. Because the rotating magnetic field in the stator is not always ideally circular but more often elliptical, the magnetostriction under elliptical magnetizations with different axis ratios is also measured. The magnetostriction anisotropy of the NO steel sheet is observed and analyzed. The elongation and contraction under alternating, circular and elliptical rotating magnetizations with different axis ratios are discussed. The results can provide data support for calculating and designing multi-phase transformers and rotating electric machines under different types of magnetizations. The research can provide theoretical and practical guidance for mitigating mechanical vibration and acoustic noise caused by magnetostriction.

Rhombic skyrmion lattice coupled with orthorhombic structural distortion in EuAl4

The centrosymmetric tetragonal itinerant magnet EuAl$_{4}$ exhibits an intricate magnetic phase diagram including rhombic and square skyrmion-lattice (SkL) phases in the external magnetic field. Here, we report a multi-axis dilatometric investigation of EuAl$_{4}$ by means of a newly designed fiber-Bragg-grating technique complemented by a resonant x-ray scattering experiment, revealing anisotropic magnetostriction and magnetovolume effect associated with successive phase transitions. The rhombic and square SkL phases are found to possess $\sim$0.10% and $\sim$0.03% orthorhombic structural distortion within the $ab$ plane, respectively. We propose that the coupling between the spin system and the lattice deformation should be essential for the structural instability in EuAl$_{4}$, yielding a rich variety of topological spin textures with spontaneous rotational-symmetry breaking as well as a potential controllability of the SkL phases by uniaxial stress or pressure.

Anisotropic magnetic property, magnetostriction, and giant magnetocaloric effect with plateau behavior in TbMn2Ge2 single crystal

The ternary RMn2Ge2 (R = rare earth) intermetallic compounds have attracted great attention due to their interesting magnetic behaviors and magnetotransport responses. Here, we reported our observation of anisotropic magnetic property, magnetostriction, and magnetocaloric effect (MCE) in TbMn2Ge2 single crystal. Below the transition temperature of Tb magnetic sublattices (T_{{text{C}}}^{{{text{Tb}}}} ~ 95 K), strong Ising-like magnetocrystalline anisotropy is observed with an out-of-plane ferromagnetic moments 5.98 μB/f.u. along the easy c axis, which is two orders of magnitude larger than that of field along a axis. Above T_{{text{C}}}^{{{text{Tb}}}}, a field-induced metamagnetic transition is observed from the spin-flip of Mn sublattices. During this transition, remarkable magnetostriction effect is observed, indicating of strong spin–lattice coupling. The responses of Tb and Mn sublattices to the magnetic field generate a giant magnetic entropy change (- Delta S_{M}) and large values of relative cooling power (RCP) and temperature-averaged entropy change (TEC). The calculated maximum magnetic entropy change (- Delta S_{M}^{max }), RCP, and TEC(10) with magnetic field change of 7 T along c axis reach 24.02 J kg−1 K−1, 378.4 J kg−1, and 21.39 J kg−1 K−1 near T_{{text{C}}}^{{{text{Tb}}}}, which is the largest among RMn2Ge2 families. More importantly, this giant MCE shows plateau behavior with wide window temperatures from 93 to 108 K, making it be an attractive candidate for magnetic refrigeration applications.

A New Type of Magnetic Material for Anisotropic Magnetoelectric Effect

Magnetostrictive fiber composites (MFC) based on nickel wires with a diameter of 150 μm, arranged parallel to each other and immersed in a polymer matrix, were fabricated. The field and angular dependences of the MFC magnetostriction have been investigated. Direct magnetoelectric (ME) effect in a two-layered composite structure consisting of a layer of PZT and MFC piezoelectric ceramics has been studied. The frequency, field, and angular dependences of the magnetoelectric (ME) voltage in the PZT-MFC structure are obtained. The highest ME coefficient α1 = 1.7 V/(Oe • cm) was obtained at a frequency of 7.86 kHz with a parallel orientation of the magnetic field relative to the wires. The anisotropy of the ME effect was found. It arises due to the anisotropy of the MFC magnetostriction. It is shown that as a result of the influence of the demagnetizing factor ME voltage decreases with an increase in the angle between the direction of the magnetic field and the axis of the wires. At the same time magnetic field Hm in which ME voltage reaches its maximum increases. A theoretical approach to the change in the ME voltage from the angle between the direction of the magnetic field and the axis of the wires is presented as well.

Anomalous temperature dependence of phonon pumping by ferromagnetic resonance in Co/Pd multilayers with perpendicular anisotropy

We demonstrate the pumping of phonons by ferromagnetic resonance in a series of [Co(0.8 nm)/Pd(1.5 nm)]$_n$ multilayers ($n =$ 6, 11, 15, and 20) with large magnetostriction and perpendicular magnetic anisotropy. The effect is shown using broadband ferromagnetic resonance over a range of temperatures (10 to 300 K), where a resonant damping enhancement is observed at frequencies corresponding to standing wave phonons across the multilayer. The strength of this effect is enhanced by approximately a factor of 4 at 10 K compared to room temperature, which is anomalous in the sense that the temperature dependence of the magnetostriction predicts an enhancement that is less than a factor of 2. Lastly, we demonstrate that the damping enhancement is correlated with a shift in the ferromagnetic resonance field as predicted quantitatively from linear response theory.

Magnetovolume Effect on the First-Order Metamagnetic Transition in UTe2

The link between the metamagnetic transition and novel spin-triplet superconductivity of UTe$_2$ was discussed thermodynamically through magnetostriction measurements in a pulsed-magnetic field. We revealed a discontinuous magnetostriction across the metamagnetic transition at $\mu_0H_{\rm m}\approx 35$~T for the applied magnetic fields along the crystallographic $b$ axis in the orthorhombic structure. The resultanting volume magnetostriction of $\Delta V/V \approx-5.9\times 10^{-4}$ gives the initial pressure dependence of $H_{\rm m}$ by employing the Clausius-Clapeyron's equation, which agrees with previous pressure experiments. Further, significant anisotropic magnetostriction (AMS), derived by subtracting the averaged linear magnetostriction, was revealed. Contrary to the weakly field-dependent AMS along the $a$ axis, those along the $b$ and $c$ axes show strong field dependences with a similar magnitude but with opposite signs, indicating its lattice instability. The relationship between characteristic energy scales of magnetic fields and temperatures was discussed in terms of the Gr\"uneisen parameters compared to the other $f$-electron systems. The volume shrinkage in UTe$_2$ at $H_{\rm m}$, contrary to the volume expansion in typical heavy fermion metamagnets, pushes to invoke the link with the valence instability related to the itinerant-localized dual nature of the U magnetism.

Magnetoelastic coupling anisotropy in the Kitaev material α−RuCl3

In this combined theoretical and experimental research, the authors investigate the anisotropic magnetic and magnetoelastic properties of the quantum spin-liquid candidate $\ensuremath{\alpha}$-RuCl${}_{3}$. They find that the magnetostriction anisotropy is unusually large compared to the anisotropy of the magnetization, which they relate to the strong magnetoelastic \ensuremath{\Gamma}'-type coupling. They also observe nonsymmetric anisotropy for magnetic fields canted out of the honeycomb plane in opposite directions, which they relate to the relative orientation of the magnetic field with respect to the RuCl${}_{6}$ octahedra.

Magnetic Phase Transitions in GdH0.15: Some Peculiarities in the Behavior of Magnetocaloric and Magnetostrictive Effects

The magnetocaloric effect (MCE) and anomalies of magnetostriction behavior were studied at the order-order and order-disorder magnetic phase transitions in hydrided Gd single crystal grown by a modified Czochralski method. The composition GdH_0.15 was obtained using a Sievert-type apparatus. While parent Gd shows an isotropic MCE at the order-disorder phase transition, the effect is anisotropic in GdH_0.15 due to the appearance of local anisotropy. We investigate in detail the temperature variation of the longitudinal, transverse, volume, and anisotropic magnetostriction. Hydrogenation is found to influence both the magnitude and the sign of the magnetostriction constants <inline-formula><tex-math notation="LaTeX">$\lambda_{\rm ij}^{\alpha}$</tex-math></inline-formula>.

Effects of underlayer on structures and magnetic properties of Fe&lt;sub&gt;65&lt;/sub&gt;Co&lt;sub&gt;35&lt;/sub&gt; alloy films

Fe&lt;sub&gt;100-&lt;i&gt;x&lt;/i&gt;&lt;/sub&gt;Co&lt;sub&gt;&lt;i&gt;x&lt;/i&gt;&lt;/sub&gt; (&lt;i&gt;x&lt;/i&gt; = 30–40) alloys have the highest saturation magnetizations, 4π&lt;i&gt;M&lt;/i&gt;&lt;sub&gt;s&lt;/sub&gt; ≥ 24 kG (1 G = 10&lt;sup&gt;–4&lt;/sup&gt; T). Therefore, FeCo thin flms have been widely used in microwave magnetic devices. However, the as-deposited FeCo film has a large coercivity, which is attributed to the large saturation magnetostriction and high magneto-crystalline anisotropy&lt;i&gt;.&lt;/i&gt; On the basis of maintaining high saturation magnetization, adding an appropriate underlayer is a simple and effective method to reduce the coercivity of the film and facilitate the magnetic field-induced in-plane uniaxial magnetic anisotropy. Since these kinds of films are used in a high-frequency environment, the eddy current loss in GHz band must be considered. For a certain film material, the thinner the film, the lower the eddy current loss is. However, at present, the thickness of ferromagnetic layer is generally tens of nanometers or even hundreds of nanometers, which will not help to suppress the eddy current loss at high frequency. In the present study, to obtain FeCo films with good soft magnetic properties and excellent high-frequency characteristics, Fe&lt;sub&gt;65&lt;/sub&gt;Co&lt;sub&gt;35&lt;/sub&gt; alloy films with a thickness of 13 nm and different underlayers (Cu, Co and Ni&lt;sub&gt;80&lt;/sub&gt;Fe&lt;sub&gt;20&lt;/sub&gt;) are prepared by magnetron sputtering. The effects of different underlayer materials and different NiFe underlayer thickness values on the structures and magnetic properties of FeCo films are studied. The results show that the introduction of underlayers can increase the in-plane uniaxial magnetic anisotropies of films, and the soft magnetic properties of films are significantly improved. The reason why the good soft magnetic properties can be achieved is attributed to the grain refinement, the dipolar interaction between layers, and the reduction of surface roughness. For different underlayer materials with the same thickness, NiFe underlayer can obviously improve the soft magnetic properties of FeCo films: the covercivity of easy axis is 23 Oe. By changing the thickness of NiFe underlayer, the dynamic magnetic properties of films can be adjusted. The resonance frequency changes from 3.13 GHz for NiFe(1 nm)/FeCo(13 nm) film to 2.78 GHz for NiFe(9.3 nm)/ FeCo(13 nm) film. For all NiFe/FeCo bilayer films, the real part of the permeability &lt;i&gt;μ′&lt;/i&gt; at low frequency has a large value of 350–450, and the damping coefficient &lt;i&gt;α&lt;/i&gt; shows a small value of 0.01–0.02. In addition, the smaller film thickness can reduce eddy current loss, which contributes to its application in high-frequency microwave magnetic devices.