Magnetoelastic Contribution Research Articles

Thermal expansion, quasi-metamagnetism and spin-reorientation in Fe7Se8 substituted with chromium

The properties of the selenide compound Fe7Se8 with a layered crystal structure of the NiAs type are strongly influenced by substitutions and the distribution of vacancies. The Cr-substituted compound Fe6.5Cr0.5Se8 was obtained in single-crystalline form and studied by x-ray diffraction, energy-dispersive x-ray spectroscopy, thermal expansion and magnetization measurements. It was observed that the partial replacement of iron with chromium led to a twofold decrease in spontaneous volume magnetostriction due to changes in competing magnetoelastic contributions to thermal expansion along and perpendicular to the c axis of the crystal. The replacement of iron with chromium slightly decreases the Néel temperature (from 440 to 435 K) and significantly enhances the critical temperature of spin reorientation transition Tsr (from 115 to 160 K), apparently due to a change in the crystal electric field. Below 160 K, the Fe6.5Cr0.5Se crystal is found to exhibit metamagnetic-like behavior of the magnetization when the magnetic field is applied along the c axis. A jump-like change of the magnetization at a critical field up to ∼10 kOe is attributed to the presence of pinning centers of domain walls presumably due the ordering of chromium atoms substituting iron in cationic layers.

Energy and Structure of the Terbium Domain Wall

The domain wall energy is calculated by the balance between exchange, magnetocrystalline anisotropy and magnetoelastic energy contributions. The described method is theoretical and is based on experimental measurements of neutron inelastic scattering. The domain wall energy is determined by both finding the minimum of energy and deriving the energy and setting it to zero. The determination was undertaken for the discrete case, and this means that the calculation was performed for each plane or atomic layer. This is in contrast with the Bloch wall, which assumes continuum mean. The energy of the Lilley domain wall was discussed. Most of the energy of the Bloch wall was comprised inside the Lilley distance (above 99.9% of the energy). Antiferromagnetic interactions strongly decreased the domain wall energy. The negative terms due to antiferromagnetism must be considered in the Hamiltonian describing the exchange energy terms. The domain wall energy and width of terbium were reassessed. The values varied between 83.7 and 95.2 Kelvin (10.3 to 11.2 ergs/cm2). The domain width was estimated to be 57 Angstroms. It was found that a significant part of the total domain wall energy was concentrated on the planes at the center of the domain wall.

Generation of imprinted strain gradients for spintronics

In this work, we propose and evaluate an inexpensive and CMOS-compatible method to locally apply strain on a Si/SiOx substrate. Due to high growth temperatures and different thermal expansion coefficients, a SiN passivation layer exerts a compressive stress when deposited on a commercial silicon wafer. Removing selected areas of the passivation layer alters the strain on the micrometer range, leading to changes in the local magnetic anisotropy of a magnetic material through magnetoelastic interactions. Using Kerr microscopy, we experimentally demonstrate how the magnetoelastic energy landscape, created by a pair of openings, enables in a magnetic nanowire the creation of pinning sites for in-plane vortex walls that propagate in a magnetic racetrack. We report substantial pinning fields up to 15 mT for device-relevant ferromagnetic materials with positive magnetostriction. We support our experimental results with finite element simulations for the induced strain, micromagnetic simulations, and 1D model calculations using the realistic strain profile to identify the depinning mechanism. All the observations above are due to the magnetoelastic energy contribution in the system, which creates local energy minima for the domain wall at the desired location. By controlling domain walls with strain, we realize the prototype of a true power-on magnetic sensor that can measure discrete magnetic fields or Oersted currents. This utilizes a technology that does not require piezoelectric substrates or high-resolution lithography, thus enabling wafer-level production.

The Magnetoelastic Contribution to the Steel Internal Damping.

In this paper, the steel internal damping due to both the thermoelastic and the magnetoelastic phenomena has been investigated through a formulation based on thermodynamical potential joints with a hysteretic damping model. With the aim of focusing on the temperature transient in the solid, a first configuration has been considered, which is characterized by a steel rod with an imposed alternating pure shear strain in which only the thermoelastic contribution was studied. The magnetoelastic contribution was then introduced in a further configuration, in which a steel rod in free motion was subjected to torsion on its ends in the presence of a constant magnetic field. A quantitative assessment of the influence of the magnetoelastic dissipation in steel has been computed according to the Sablik-Jiles model by giving a comparison between the thermoelastic and the prevailing magnetoelastic damping coefficients.

Temperature dependence of magnetic anisotropy and magnetoelasticity from classical spin-lattice calculations

We present a classical molecular-spin dynamics (MSD) methodology that enables accurate computations of the temperature dependence of the magnetocrystalline anisotropy as well as magnetoelastic properties of magnetic materials. The nonmagnetic interactions are accounted for by a spectral neighbor analysis potential (SNAP) machine-learned interatomic potential, whereas the magnetoelastic contributions are accounted for using a combination of an extended Heisenberg Hamiltonian and a N\'eel pair interaction model, representing both the exchange interaction and spin-orbit-coupling effects, respectively. All magnetoelastic potential components are parameterized using a combination of first-principles and experimental data. Our framework is applied to the $\ensuremath{\alpha}$ phase of iron. Initial testing of our MSD model is done using a 0 K parametrization of the N\'eel interaction model. After this, we examine how individual N\'eel parameters impact the ${B}_{1}$ and ${B}_{2}$ magnetostrictive coefficients using a moment-independent $\ensuremath{\delta}$ sensitivity analysis. The results from this study are then used to initialize a genetic algorithm optimization which explores the N\'eel parameter phase space and tries to minimize the error in the ${B}_{1}$ and ${B}_{2}$ magnetostrictive coefficients in the range of 0--1200 K. Our results show that while both the 0 K and genetic algorithm optimized parametrization provide good experimental agreement for ${B}_{1}$ and ${B}_{2}$, only the genetic algorithm optimized results can capture the second peak in the ${B}_{1}$ magnetostrictive coefficient which occurs near approximately 800 K.

Influence of substrate on interfacial Dzyaloshinskii-Moriya interaction in epitaxial Tm3Fe5O12 films

The interfacial Dzyaloshinskii-Moriya interaction (iDMI) promotes homochiral magnetic structures such as N\'eel-type domain walls (DWs) and skyrmions. iDMI as well as chiral magnetic structures have been demonstrated in metal/garnet heterostructures offering desirable properties for spintronic applications compared to their metallic counterparts. By measuring the motion of DWs as a function of current and in-plane magnetic field, we show that for 6.6 nm thick epitaxial thulium iron garnet films with perpendicular magnetic anisotropy grown on gallium garnet substrates, the iDMI and the DW width depend on the substrate but do not scale linearly with lattice mismatch strain. The largest iDMI was $0.007 \mathrm{mJ} {\mathrm{m}}^{\ensuremath{-}2}$, obtained for three substrates of different compositions. The total anisotropy, however, does increase linearly with lattice parameter, indicating a dominant magnetoelastic anisotropy contribution. The sensitivity of iDMI and anisotropy to substrate composition provides opportunities for engineering homochiral magnetic structures and their dynamics.

A strain-controlled magnetostrictive pseudo spin valve

Electric-field control of magnetism via an inverse magnetostrictive effect is an alternative path toward improving energy-efficient storage and sensing devices based on a giant magnetoresistance effect. In this Letter, we report on lateral electric-field driven strain-mediated modulation of magnetotransport properties in a Co/Cu/Py pseudo spin valve grown on a ferroelectric 0.7Pb[Mg1/3Nb2/3)]O3–0.3PbTiO3 substrate. We show a decrease in the giant magnetoresistance ratio of the pseudo spin valve with the increase in the electric field, which is attributed to the deviation of the Co layer magnetization from the initial direction due to strain-induced magnetoelastic anisotropy contribution. Additionally, we demonstrate that strain-induced magnetic anisotropy effectively shifts the switching field of the magnetostrictive Co layer, while keeping the switching field of the nearly zero-magnetostrictive Py layer unaffected due to its negligible magnetostriction. We argue that magnetostrictively optimized magnetic films in properly engineered multilayered structures can offer a path to enhancing the selective magnetic switching in spintronic devices.

Voltage modulated magnetic anisotropy of rare earth iron garnet thin films on a piezoelectric substrate

Voltage-tuning of magnetic anisotropy is demonstrated in ferrimagnetic insulating rare earth iron garnets on a piezoelectric substrate, (011)-oriented PMN-PT. A 42 nm thick yttrium-substituted dysprosium iron garnet (YDyIG) film is grown via pulsed laser deposition followed by a rapid thermal anneal to crystallize the garnet into ≈5 μm diameter grains. The annealed polycrystalline film is magnetically isotropic in the film plane with total anisotropy dominated by shape and magnetoelastic contributions. Application of an electric field perpendicular to the substrate breaks the in-plane easy axis along [01[Formula: see text]] and an intermediate axis along [100]. The results are explained in terms of the piezoelectric remanent strain caused by poling the substrate, which is transferred to the YDyIG and modulates the magnetoelastic anisotropy.

Third harmonic characterization of antiferromagnetic heterostructures

Electrical switching of antiferromagnets is an exciting recent development in spintronics, which promises active antiferromagnetic devices with high speed and low energy cost. In this emerging field, there is an active debate about the mechanisms of current-driven switching of antiferromagnets. For heavy-metal/ferromagnet systems, harmonic characterization is a powerful tool to quantify current-induced spin-orbit torques and spin Seebeck effect and elucidate current-induced switching. However, harmonic measurement of spin-orbit torques has never been verified in antiferromagnetic heterostructures. Here, we report harmonic measurements in Pt/α-Fe2O3 bilayers, which are explained by our modeling of higher-order harmonic voltages. As compared with ferromagnetic heterostructures where all current-induced effects appear in the second harmonic signals, the damping-like torque and thermally-induced magnetoelastic effect contributions in Pt/α-Fe2O3 emerge in the third harmonic voltage. Our results provide a new path to probe the current-induced magnetization dynamics in antiferromagnets, promoting the application of antiferromagnetic spintronic devices.

Annealing Temperature and Thickness Dependencies of Perpendicular Magnetic Anisotropy and Dzyaloshinskii– Moriya Interaction of Pt/Co/MgO Thin Films

Effects of the ferromagnetic layer thickness and annealing temperature were studied in Pt-/Co-/MgO-based systems grown on thermally oxidized Si substrates using magnetron sputtering system. The Co thicknesses were varied in the range of 1–6 nm and the samples were annealed <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ex situ</i> at 200 °C, 300 °C, and 400 °C. Vibrating sample magnetometry was used to determine the magnetization at saturation and the magnetic dead layer thickness that were found to be insignificantly affected by the annealing. Brillouin light scattering, in Damon–Eshbach configuration, was used to measure the thermally excited spin wave (SW) frequencies versus the in-plane applied magnetic field and the SW vector which were used to investigate the perpendicular magnetic anisotropy (PMA) and interfacial Dzyaloshinskii–Moriya interaction (iDMI), respectively. The Co effective thickness dependence of the effective magnetization ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M_{\mathrm {eff}}$ </tex-math></inline-formula> ), which provides information on the PMA constants, shows the existence of two linear regimes with different slopes due to misfit strain-induced magnetoelastic anisotropy contributions to volume and surface terms. The volume magnetocrystalline anisotropy constant increases monotonously with annealing temperature, whereas the pure surface (Néel type) constant increases with annealing up to 300 °C and degrades at 400 °C. The surface iDMI constant decreases with increasing annealing temperature and no obvious correlation with interface PMA constant has been found, suggesting different interfaces contribution to PMA and iDMI.

Influence of ferromagnetic layer thickness on the Gilbert damping and magnetocrystalline anisotropy in PLD grown epitaxial Co2FeSi Heusler alloy thin films

In the present work, full Heusler alloy (FHA) Co2FeSi (CFS) epitaxial thin films with thickness (tCFS) ranging from 5–25 nm were grown by Pulse laser deposition (PLD) on MgO (001) substrates at an optimized deposition temperature of 600°C. Dynamic magnetization response of PLD-grown CFS thin films was systematically investigated as a function of tCFS. Thickness-dependent structural and magnetic correlation exhibit a non-monotonic variation in Gilbert damping parameter, α. The ferromagnetic resonance (FMR) investigation revealed that the presence of lattice strain and a lower degree of atomic ordering in the thinner FHA CFS films, results in additional enhancement of α. The lowest α value of 4×10−3 is obtained from the theoretical fit of experimental data in a 20 nm thick film. This low value of α is suitable in magnonic devices, such as spin-transfer torque magnetic random-access memories (STT-MRAMs) where an efficient spin injecting source from a FHA ferromagnet to a non-magnetic interface is required. Further, in-plane angle-dependent (φ-variation) FMR measurements of the sample yield an intrinsic four-fold magnetocrystalline anisotropy (MCA) along with the presence of uniaxial anisotropy that has non-monotonicity with tCFS. A significant value of cubic anisotropy constant of 5.16×105erg/cm3 has been obtained in the film with a thickness of around 15nm. Further investigation suggests that uniaxial anisotropy in the CFS/MgO film is a combination of strain-induced magneto-elastic and interface-related contribution that is intrinsic in nature. The experimental observations have been verified by using micromagnetic simulations run on the epitaxial crystal structure. FMR mode position and linewidth of varied thickness CFS films are generated by micromagnetic simulations utilizing the Landau–Lifshitz–Gilbert formalism.

Magnetoelastic Gilbert damping in magnetostrictive Fe0.7Ga0.3 thin films

We report an enhanced magnetoelastic contribution to the Gilbert damping in highly magnetostrictive Fe$_{0.7}$Ga$_{0.3}$ thin films. This effect is mitigated for perpendicular-to-plane fields, leading to a large anisotropy of the Gilbert damping in all of the films (up to a factor of 10 at room temperature). These claims are supported by broadband measurements of the ferromagnetic resonance linewidths over a range of temperatures (5 to 400 K), which serve to elucidate the effect of both the magnetostriction and phonon relaxation on the magnetoelastic Gilbert damping.

Magnetocrystalline origin of the perpendicular magnetic anisotropy in Ga-poor FeGa thin films

In this work we have investigated the influence of Ar sputtering pressure (PAr) in the magnetic properties of polycrystalline sputtered Fe0.89Ga0.11 thin films. The structural characterization shows that the samples are composed by several fiber-like crystallographic textures in which the fiber axis is always along the growth direction, whereas their portion weights evolve with PAr during the sputtering deposition. Magnetometry and ferromagnetic resonance (FMR) experiments evidence the existence of a perpendicular magnetic anisotropy (PMA) that increases systematically for increasing PAr. By proposing a model that takes into account the interfacial, magnetoelastic and magnetocrystalline contributions to the magnetic free energy, we find that the magnetocrystalline one appears as the main responsible of the increasing PMA. The PMA values estimated from the model predict satisfactorily the experimental values obtained from FMR.

High-frequency power loss mechanisms in ultra-thin amorphous ribbons

Soft magnetic amorphous materials with ultra-low power loss are highly desirable for high-frequency drive applications. The present work demonstrates the high-frequency power loss performance and underlying loss mechanisms in ultra-thin amorphous alloys. This is achieved by rapid-quenching amorphous alloys of Co-, CoFe- and Fe-rich systems, investigating their amorphous atomic structure, quantifying the saturation magnetostriction constants (λs), imaging magnetic domains at remanent magnetization, analyzing magnetization reversal from various magnetization levels, and finally, investigating the material loss performance over a broad frequency range (f = 50 kHz–2 MHz) at various excitation levels (Bm = 25–100 mT). The ultra-high performance of ultra-thin Co-rich amorphous ribbons, as compared to CoFe- and Fe-rich alloys, was attributed to the significantly low eddy current loss, due to the reduced thickness, and a minimal amount of excess loss, owning to minimal magnetoelastic contributions and magnetization reversal by rotation. The underlying loss mechanisms were analyzed by decomposing material loss into primary components and identifying the magnetization reversal mechanisms using minor hysteresis loops. In the Co-rich amorphous alloys, we suggest that magnetization reversal by rotation dominates, at least at low excitations, while in CoFe- and Fe-rich alloys domain wall displacement prevails and contributes significantly to the excess loss up to the MHz frequency range. Magnetization reversal by rotation in Co-rich alloys could be attributed to the zero/near-zero λs, and eventually low residual stress, leading to a homogeneous magnetic domain structure, as compared to the inhomogeneous “fingerprint-like” complex domains in highly magnetostrictive CoFe-rich alloys.

The magneto-elastic and optical properties of multiferroic GaFeO3-δ

Temperature-dependent Raman spectroscopy, X-ray absorption near-edge spectroscopy (XANES), optical absorption spectroscopy (OAS) and ac-susceptibility measurements have been carried out on GaFeO3 samples to understand the effect of sintering temperature (TS) on optical and magneto-elastic properties. The temperature-dependent ac-susceptibility measurements suggest the systematic scaling in the values of ferri-magnetic transition temperature (TC) with TS. The observed variation has been understood in terms of enhancement in the Goodenough-Kanamori-Anderson coupling. Instead of expected anharmonic behavior in Raman spectra around TC, several vibrational modes of rigid FeO6 units were found to show anomalous behavior, which suggests the significant magneto-elastic coupling contributions to phonon frequencies. The strength of magneto-elastic coupling has been quantified by using the phonon renormalization function (Δw) and is found to scale systematically with TS. Further, optical absorption study demonstrates the increase in intensity and red shift in charge-neutral d-d transitions, which infers the increase in oxygen non-stoichiometry with TS. The oxygen non-stoichiometry has been further quantified by the XANES measurements. The present investigations on GaFeO3 samples reveal that TC can be tuned by varying the oxygen stoichiometry and can be very beneficial for spintronic devices applications.

Anomalous magnetorheological effect in unstructured magnetoisotropic magnetoactive elastomers

It was found that the anomalous magnetorheological effect observed in initially unstructured magnetoisotropic magnetoactive elastomers, i.e., the growth of their effective shear modulus in an external magnetic field by almost two orders of magnitude, is a result of the uniaxial magnetic anisotropy induced by the magnetic field. An additional magnetoelastic contribution to the mechanical stress created by the induced magnetic anisotropy counteracts the shear and increases the effective shear modulus of the magnetoactive elastomer when the latter is magnetized. Numerical estimates made for the magnitude of magnetorheological effect are in good agreement with known experimental data.

Novel Fe-based amorphous and nanocrystalline powder cores for high-frequency power conversion

The present work demonstrates the high-frequency core loss performance of Fe-based amorphous and nanocrystalline powder cores, initially produced by gas atomised powder, consolidated using sieved particles ≤20 µm, and isolated by a precise insulating layer of polymer to limit the inter- and intra-particle eddy currents to attain enhanced performance. The large glass forming ability (GFA) of the gas atomised powder, reflected by different glass forming instruments, such as the supercooled region (ΔTX = 54 °C) and the reduced glass transition temperature (Trg = 0.56), is consistent with the substantial amorphisation capability of the alloy. To the best of our knowledge, this is the first-ever report to reveal a large ΔTX in the Finemet-type alloy powders, an essential parameter to gas-atomise the amorphous powders with significantly lower cooling rates compared to the melt-spun ribbons. Further, subsequent annealing of the amorphous powders, between the exothermic events guided by differential scanning calorimetry (DSC), lead to the growth of a fine nanocrystalline structure of grains ≤15 nm, thanks to the positive enthalpy of mixing of Cu with the constituents to act as a nucleation agent, to retain the excellent soft magnetic properties. The DC soft magnetic properties of the powders were significantly improved on thermal annealing, confirmed by hysteretic loops, quantified by reduced coercivity HC <1 Oe of annealed powders at <575 °C, and attributed to the reduced magnetoelastic contribution due to zero/near-zero magnetostriction anisotropy, attained due to the homogenous nanocrystalline structure. The amorphous and nanocrystalline powder cores, consolidated by compression moulding, show ultra-high loss performance, due to the ultra-low coercivity attained on nanocrystallisation, and negligible eddy currents loss, owning to efficient insulation of small particles, for high-frequency power conversion applications, such as voltage regulator (VR), and resonant converters, in automotive industry and data storage centres.

Role of magnetostrictive effect in magnetization dynamics of SmFe thin films

Laser induced magnetization dynamic behaviors of SmxFe1–x thin films with tunable x (0.25 ≤ x ≤ 0.5) are investigated by the time-resolved magneto-optical Kerr effect. It is found that the demagnetization process is accomplished by a two-stage process, the demagnetization time of stage I is within 1.0 ps (t1) for all the samples with different x, while it increases from 0 to 16 ps at stage II (t2) due to the reduced exchange coupling. By introducing an additional magneto-elastic energy contribution, the dispersion relation of precession frequency is deduced, by which the field-dependent frequency curves are well fitted.

Anomalous Nernst effect in stressed magnetostrictive film grown onto flexible substrate

The anomalous Nernst effect in nanostructured magnetic materials is a key phenomenon to optimally control and employ the internal energy dissipated in electronic devices, being dependent on, for instance, the magnetic anisotropy of the active element. Thereby, here, we report a theoretical and experimental investigation of the magnetic properties and anomalous Nernst effect in a flexible magnetostrictive film with induced uniaxial magnetic anisotropy and under external stress. Specifically, we calculate the magnetization behavior and the thermoelectric voltage response from a theoretical approach for a planar geometry, with magnetic free energy density that takes into account the induced uniaxial and magnetoelastic anisotropy contributions. Experimentally, we verify modifications of the effective magnetic anisotropy by changing the external stress, and explore the anomalous Nernst effect, a powerful tool to investigate the magnetic properties of magnetostrictive materials. We find quantitative agreement between experiment and numerical calculations, thus elucidating the magnetic behavior and thermoelectric voltage response. Besides, we provide evidence to confirm the validity of the theoretical approach to describe the magnetic properties and anomalous Nernst effect in ferromagnetic magnetostrictive films having uniaxial magnetic anisotropy and submitted to external stress. Hence, the results place flexible magnetostrictive systems as promising candidates for active elements in functionalized touch electronic devices.

Critical phenomena in the double-exchange ferromagnet La0.8Na0.2Mn1-xNixO3 around the critical temperature

The research results of magnetocaloric effect and critical properties of La0.8Na0.2Mn1-xNixO3 (0 ≤ x ≤ 0.06) manganite are reported. Using the Banerjee's criteria, Franco method and Landau theory, we proved the second order ferromagnetic-paramagnetic phase transition for all samples. The critical exponents values β, γ and δ are determined using modified Arrott plot (MAP), Kouvel Fisher technique and the critical isotherm. Indeed, comparing our determined exponent values with those of standards model, there is a shifting tendency from the mean field model for the compositions La0.8Na0.2MnO3 and La0.8Na0.2Mn0.97Ni0.03O3 to those of the 3D-Ising model for La0.8Na0.2Mn0.94Ni0.06O3 sample. Thus, reflect that the magnetic coupling tends to change from the long-range to the short-range interaction as increasing Ni content. Particularly, by performing the Landau theory we suggest that the magnetoelastic contribution and the electron interaction should be associated with the Jahn Teller interaction in the determination of ΔSM magnetic entropy change effect in our compounds.