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Spin-orbit torque enables electrical control of the magnetic state of ferromagnets or antiferromagnets. The quintessential system exhibiting spin-orbit torque is a bilayer composed of a heavy metal and a ferromagnet. The heterostructure bilayer geometry breaks the inversion symmetry and allows the spin-orbit torque arising from the spin current flow from the heavy metal layer to the ferromagnetic layer. In this work, we consider the intrinsic spin-orbit torque generated in inversion symmetry breaking magnetic materials directly without stacking with other materials.&lt;br/&gt;In the first example of ferromagnetic monolayer Fe3GeTe2, we calculate the intrinsic spin-orbit torque which arises due to the global inversion symmetry breaking. In addition, spin-orbit torque in Fe3GeTe2 has the unique property that the lowest order contribution is fieldlike and time-reversal even because of the C3z rotation symmetry. This is in contrast to the conventional case in which the lowest order is time-reversal odd and fieldlike and the next lowest-order is time-reversal even and dampinglike. We next show that the next lowest-order spin-orbit torque in Fe3GeTe2 is time-reversal odd and dampinglike which can play a more important role in switching the magnetization in the ensuring dynamics, as described by the Landau-Lifshitz-Gilbert equation.&lt;br/&gt;In the second example of antiferromagnetic bilayer CrI3, we find staggered dampinglike (time-reversal even) torque and uniform fieldlike (time-reversal odd) torque due to local inversion symmetry breaking and global inversion plus time-reversal symmetry. This is similar to the previous studies of CuMnAs and Mn2Au, where the Neel order switching is demonstrated using uniform fieldlike torque. However, CrI3 has a unique property in that the anisotropy energies and exchange energies are similar in magnitude. This leads to qualitatively different results in the switching dynamics: the staggered dampinglike torque is the dominant switching mechanism. The primary role of staggered dampinglike torque applies to other antiferromagnets in which the product of Gilbert damping and exchange field is smaller than the anisotropy field.

2022 Joint MMM-INTERMAG

Intrinsic spin-orbit torque in van der Waals magnetic materials

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EMC 2021

Spin-orbit torque enables electrical control of the magnetic state of ferromagnets or antiferromagnets. The quintessential system exhibiting spin-orbit torque is a bilayer composed of a heavy metal and a ferromagnet. The heterostructure bilayer geometry breaks the inversion symmetry and allows the spin-orbit torque arising from the spin current flow from the heavy metal layer to the ferromagnetic layer. In this work, we consider the intrinsic spin-orbit torque generated in inversion symmetry breaking magnetic materials directly without stacking with other materials. In the first example of ferromagnetic monolayer Fe3GeTe2, we calculate the intrinsic spin-orbit torque which arises due to the global inversion symmetry breaking. In addition, spin-orbit torque in Fe3GeTe2 has the unique property that the lowest order contribution is fieldlike and time-reversal even because of the C3z rotation symmetry. This is in contrast to the conventional case in which the lowest order is time-reversal odd and fieldlike and the next lowest-order is time-reversal even and dampinglike. We next show that the next lowest-order spin-orbit torque in Fe3GeTe2 is time-reversal odd and dampinglike which can play a more important role in switching the magnetization in the ensuring dynamics, as described by the Landau-Lifshitz-Gilbert equation. In the second example of antiferromagnetic bilayer CrI3, we find staggered dampinglike (time-reversal even) torque and uniform fieldlike (time-reversal odd) torque due to local inversion symmetry breaking and global inversion plus time-reversal symmetry. This is similar to the previous studies of CuMnAs and Mn2Au, where the Neel order switching is demonstrated using uniform fieldlike torque. However, CrI3 has a unique property in that the anisotropy energies and exchange energies are similar in magnitude. This leads to qualitatively different results in the switching dynamics: the staggered dampinglike torque is the dominant switching mechanism. The primary role of staggered dampinglike torque applies to other antiferromagnets in which the product of Gilbert damping and exchange field is smaller than the anisotropy field.

technical paper

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The frequencies and wave vectors of dipolar dominated spin waves (SW) and surface acoustic waves (SAW) cover the same ranges. Therefore, the propagating waves of both kinds can potentially scatter each other - in other words, the necessary condition for the interaction in a linear regime can be satisfied. The simplest structure in which the magnetoelastic coupling between SW and SAW can be observed is the magnetostrictive layer deposited on the substrate. The confinement of SWs in the magnetic layer is necessary to induce the dipolar interaction and surface localization of SAW ensures the co-existence of both kinds of waves in the magnetostrictive layer deposited on the surface. The strength of the magnetoelastic interaction depends on the orientation of the wave vector concerning the direction of the static magnetic field[1]. Moreover, this interaction is different for different types of SAWs, specifically, Rayleigh-SAWs (R-SAW) and Love-SAWs (L-SAW)[1,4] – see Fig.1. Thus, the coupling is strongly anisotropic and cannot be observed for arbitrary selected SAWs and SWs, even if their frequencies and wave vectors match. This effect is well-known and broadly discussed in the literature[1]. Our study shows an additional factor limiting the interaction between SAWs and SWs. The SAW/SW coupling proves to require an appropriate profile of the elastic wave near the surface of the magnetostrictive structure, at distances much smaller than the wavelength. For R-SAWs the tangential component of displacement ux can have nodes within the magnetic layer, resulting in a reduction of the net strength of magnetoelastic interaction even if the strain εxx is locally significant. In an L-SAW the displacement uy does not have any nodes (uy changes monotonously in the normal direction). We have shown that this additional factor plays a role for some types of surface acoustic waves (R-SAWs), while other types (L-SAWs) are insensitive to it. We think that the studies on magnon-phonon interaction in confined geometries (surfaces, cavities) are very promising and can reveal unusual interaction mechanisms. Sample We studied [Co20Fe60B20/Au]20 multilayer of the thickness 60 nm as a magnetostrictive medium. In Co20Fe60B20 layers (2.1 nm) the magnetization is oriented in-plane and the presence of Au layers (0.9 nm) reduces the SWs’ frequencies due to out-of-plane anisotropy. The multilayer was deposited on top of a 4 nm titanium (Ti) and a 15 nm gold (Au), which buffers the naturally oxidized (001) silicon substrate. Method We measured the dispersion relations of thermally excited SAWs and magnetostatic SWs using a six-pass tandem Brillouin spectrometer (Scientific Instrumentsc©TFP2-HC), which ensures a contrast of 1015. A frequency-stabilized diode-pumped solid-state laser (Coherentc©VERDI V5) operating at λ0= 532 nm was used as a source of incident light. The measurements were performed in the 180o backscattering geometry with crossed (p-s)polarization of the incident and scattered light for SWs and non-crossed (p-p) polarization for SAWs. Using the finite element method in COMSOL Multiphysics©, we solve numerically the coupled equations of motion for magnetization and mechanic displacement. Acknowledgement The authors hereby acknowledge the financial support from the National Science Centre, Poland, project No. UMO-2016/21/B/ST3/00452. S. Mies. would like to additionally acknowledge the support from the National Science Centre, Poland, project No. UMO-2020/36/T/ST3/00542.

![](https://assets.underline.io/uploads/markdown_image/1/image/0d5d93d1592e64189ced2b9a3d060b55.jpg)

Fig.1 (left) - the illustration of the Rayleigh and Love surface acoustic waves (R SAW and L SAW). (right) -the numerically calculated profiles of the strain tensor playing the most significant role for magnetoelastic interaction of spin waves with R SAW (magnetic field applied the 45 deg) and L SAW (magnetic field applied at 0 deg). Please note that the interaction with R SAW can be canceled due to the nodal line.

Conditions for effective coupling between surface acoustic waves and spin waves

Magnetorheological elastomers (MREs) constitute ideal candidates for enabling magnetic control and reconfigurability of soft, integrated interfaces, such as valves for microfluidics, tactile displays for haptics, or actuators for flexible electronics or robotics [1-2]. MREs are composite materials made of a soft elastomeric matrix and magnetic micro- or nanoparticles. Just a few studies have focused on the actuation of MREs, which can undergo very large and rapid deformations upon application of magnetic fields [3–5]. Additionally, prior studies primarily fabricated MREs utilizing relatively large particles with sizes on the micron scale [2–8], which prevent these materials from being utilized to recreate shapes requiring sharp film curvatures in small spaces. We fabricated films with isotropic and anisotropic particle arrangements with different compositions. Anisotropic films present a steeper magnetization curve with larger remanent magnetization than their isotropic counterparts (Fig. 1a). Also, the stiffness of the films increases at a faster rate than the magnetization as a function of nanoparticle content (Fig. 1b). Therefore, for concentrations larger than 6 vol%, even if a film contains more nanoparticles (determining a larger actuation force), the film will not be able to stretch significantly more due to its stiffer nature (Fig. 2). Our isotropic films exhibit drastically higher deflections compared to other studies [3–5], up to 17x the deflections reported in Marchi et al. [5]. Our optimal film is able to deform up to 734 μm upon application of ∼100 mT, and up to 1.59 mm at ∼290 mT (the highest field measured). Finally, we implemented our optimized MRE films in a programmable and real-time reconfigurable tactile display for the visually impaired.

![](https://assets.underline.io/uploads/markdown_image/1/image/c391f5267c8607c19654a83f7fc51124.jpg)

Fig. 1: a) M vs H hysteresis loops for isotropic and anisotropic 6 vol% films and their cross-sectional structure imaged via cryo-SEM. b) Young’s moduli of the isotropic samples along with the respective magnetization values measured in the out-of-plane direction at an applied field of about 100 mT.

![](https://assets.underline.io/uploads/markdown_image/1/image/39e37ca67428400351c22efec8e423f5.jpg)

Fig. 2: Deflection measurements with hysteresis loops for a) isotropic, and b) anisotropic samples at different nanoparticle loadings.

Enhanced Magnetic Actuation of Magnetorheological Elastomers Using Nano-Magnetic Particles

Solid-state refrigeration materials have various thermal effects, among which the hydrostatic pressure is an economical and practical method to drive the barocaloric effect (BCE) of brittle materials[1,2]. The BCE is ubiquitous in first-order phase transition materials, and its packaging technology is not limited to the shape of the materials[3,4]. In the brittle magnetocaloric materials MnCoGe0.99In0.01, there is a low-pressure induced large reversible BCE near room temperature, which avoids part of the refrigeration capacity reduction caused by hysteresis loss[5]. Here, we report the BCE of MnCoGe0.99In0.01 at hydrostatic pressure of 1kbar by variable-pressure calorimetry. Fig.1a shows the temperature dependence of the heat capacity dQ/dT of MnCoGe0.99In0.01 at different hydrostatic pressures after baseline subtraction, it can be found that the thermal hysteresis (ΔThys) at 1bar is 8.8K and the phase transition temperature moves to lower temperature with the increase of pressure. The linear fitting relationship between the transformation temperature shifts with the pressure (dT/dP) is obtained according to the heating and cooling transformation temperature under different pressures, as shown in the inset of Fig. 1b. The dT/dP is -10.6K/kbar in the heating process and is -8.7K/kbar in the cooling process. The entropy curve S(T,P) of MnCoGe0.99In0.01 during heating and cooling process was obtained by the calorimetric curves(Fig. 1a) through the pressure-dependent integrations across the phase transition, as shown in Fig.1b. We evaluated the reversible parts (ΔSrev and ΔTrev) of entropy change ΔS and adiabatic temperature change ΔT at 1kbar from the overlapping of the irreversible ΔS and ΔT during application and removal of pressure, as shown in Fig.1c and 1d, where the shaded areas represent the ΔSrev and ΔTrev, respectively. The relative narrow ΔThys and high driving rate dT/dP under pressure are more conducive to achieve large ΔSrev and ΔTrev. The ΔSrev of 19J/kg K and ΔTrev of 2.9K within a temperature span of 56K at 1kbar have been achieved. The refrigeration capacity of MnCoGe0.99In0.01 at 1kbar is as high as 373J/kg K.

![](https://assets.underline.io/uploads/markdown_image/1/image/f5b2d3fe1b51b27d3f3361529defdc74.jpg)

Fig.1.For MnCoGe0.99In0.01, a)dQ/dT, b)S, c) ΔSrev, d)ΔTrev.

Large room-temperature reversible barocaloric effect in MnCoGe0.99In0.01 alloys at low pressure

Conventional vapor compression refrigeration encounters environmental problems. As an alternative, solid-state refrigeration based on magnetocaloric effect (MCE) or barocaloric effect (BCE) has attracted tremendous attentions for its environmental-friendly and energy-saving superiority. The core of solid-state refrigeration lies in the magnitude of the caloric effect of refrigerants. Increasing the caloric effect as much as possible is a long-term pursuit [1-5]. Here, we report a large enhancement of MCE and BCE by hydrostatic pressure in Co-doped La(Fe,Si)13, which has been regarded to be promising refrigerants since its discovery in 2000[1]. The maximal entropy change SMCE almost doubled under 11.31kbar while the SBCE under 9kbar increases more than three times (Figure 1c and 1d). To disclose the essence from the atomic level, neutron powder diffractions were performed (Figure 1a). The results reveal that hydrostatic pressure sharpens the magnetoelastic transition and enlarges the volume change wherein through impacting the intra-icosahedral Fe-Fe bonds (B1, B2, B3) rather than the inter-icosahedral ones (B4, B5) in the NaZn13-type structure [1]. Such result is distinct from the case introducing chemical pressure by H atoms in the La(Fe,Si)13-based compounds, which can adjust phase transition temperature, but not the sharpness of phase transition and the MCE. To understand the mechanism, first-principles calculations are performed (Figure 1b), which offers a theoretical support for the hydrostatic pressure enhanced magnetovolume effect and the evolution from second-order to first-order transition [1]. The present study proves the enormous potential of enhancing caloric effect through influencing the specific atomic environments by pressure, which is also useful to achieve other pressure-related effects, such as controllable negative thermal expansion.

![](https://assets.underline.io/uploads/markdown_image/1/image/192f971b3efb1d85cc2c7296c0334dc7.jpg)

Hydrostatic Pressure Induced Giant Enhancement of the Solid-state Caloric Effect in the Rare-earth-based Giant Magnetocaloric Materials

Hydrostatic Pressure Induced Giant Enhancement of the Solid-state Caloric Effect in the Rare-earth-based Giant Magnetocaloric Materials

Coupling between lattice degrees of freedom and the spin systems without the use of magnetic fields allows for efficient spintronic devices. A promising alternative to produce large effects uses materials which exhibit a first order structural phase transition (SPT). In particular, for Ni/V2O3 bilayers, changes in the coercive field of up to 500% have been reported due to interfacial proximity to an archetypal Mott insulator V2O3 layer across its SPT [1]. In this work [2], using photoemission electron microscopy (PEEM) combined with X-ray magnetic circular dichroism (XMCD) we find an abrupt temperature-driven reorientation of the Ni magnetic domains. Angular dependent ferromagnetic resonance (FMR) shows a remarkable change in the magnetic anisotropy of the Ni film across the SPT of V2O3. Direct measurements of the lateral correlation length of the Ni domains from XMCD images show an increase of almost one order of magnitude at the SPT compared to room temperature and a broad spatial distribution of the local transition temperatures. Micromagnetic simulations based on these results are in quantitative agreement with the PEEM data, thereby corroborating the phase coexistence of Ni anisotropies caused by the V2O3 SPT. In summary, we show that the rearrangement of the Ni domains is due to the strain induced by the oxide layers’ structural domains across the SPT [2]. Our results illustrate the use of alternative hybrid systems to manipulate magnetic domains at the nanoscale, which allows for engineering of coercive fields for novel data storage architectures. The work was supported by Spanish MCIU and AEI (MAT2015-68772-P; PGC2018-097789-B-I00) and European Union FEDER funds. Some of this work was supported by by DOE-BES grant number DE-FG02-87ER45332.

![](https://assets.underline.io/uploads/markdown_image/1/image/d9e0eb8f03533ad116b494eac4563db7.jpg)

Temperature-driven reorientation of magnetic domains in a thin Ni film across the structural phase transition of a prximity-coupled V2O3 layer, giving rise to large changes in the magnetic anisotropy of the Ni film.

Strain-controlled ferromagnetic domains induced by interfacial proximity to Mott insulator V2O3

The iron-rich alloy Galfenol (Fe1-x-Gax, 10%&lt;x&lt;30%) has been of significant interest for sensor technologies due to the sizeable magnetostriction coefficient found in single-crystal and polycrystalline films. [1,2] However, it is necessary to improve the magnetic softness of the material for many applications. To do so, we have explored the use of Zr and other glass formers and additives, rapid solidification approaches, and subsequent annealing to produce a nanocrystalline (Fe,Ga)-based alloy with the desired magnetostrictive and structural properties. We report studies on a series of 11 melt-spun and annealed (Fe1-x-Gax)92Zr8 alloy ribbons where the Ga concentration (x) has been varied from 15% to 36%. As illustrated in Fig. 1, in contrast to single-crystal and polycrystalline films, the ribbons exhibit the dominant bcc-like phase for Galfenol over a more extensive concentration range with fewer other ordered phases. Analysis of the x-ray peak locations reveals a deviation in lattice parameter from bulk behavior for alloy with similar x, suggesting that the surrounding amorphous phase matrix for the nanocrystallites within the ribbons is Ga-rich. Beginning at x=26%, x-ray diffraction scans exhibit signs of the formation of the ternary ZrFe6Ga6, consistent with CALPHAD-type database calculations. Magnetization measurements reveal a maximum saturation magnetization for the alloy with x=15% and coercivity values increase rapidly on formation of the ternary intermetallic phase. Fig. 2 illustrates the in-plane magnetostriction coefficient for the series of samples, displaying a peak value for x=24-26% which differs from the values observed in single crystalline sample x=18-20%. Acknowledgment: Prepared by LLNL under Contract DE-AC52-07NA2.

![](https://assets.underline.io/uploads/markdown_image/1/image/d0969bacd21d03b76d13d440d0b95364.jpg)

Fig. 1: X-ray diffraction of (Fe1-x-Gax)92Zr8 alloy ribbons for x=15-36% after annealing for 1 hour at 550 oC. (*) peaks indicate the bcc-like phase, with (+) symbols denoting those associated with ZrFe6Ga6.

![](https://assets.underline.io/uploads/markdown_image/1/image/e33e6f18ac454731289f00a2c1bb0a5e.jpg)

Fig. 2: Magnetostriction coefficient vs composition for annealed (Fe1-x-Gax)92Zr8 alloy ribbons for x=15-36%.

Optimizing Magnetostriction in Fe-Ga-Zr Nanocrystalline Alloys

High temperatures and inert atmospheres are required to produce borides due to the covalent character of their chemical bonds and, consequently, their high melting temperatures. Solid and melt state processing of borides from the primary reactants typically results in dense samples, which are crushed, milled, and sieved laboriously into fine powder for further processing. The size reduction process introduces numerous complications that hinder large-scale powder production. Against this backdrop, Molten Salt Infiltration and Encapsulation Method (MSIEM) is a sustainable energy-efficient process that uses no inert gas, relatively low temperatures, and moderately short reaction times to synthesize powders with uniform chemical composition and high-phase purity. In this study, fine particles of the promising magnetocaloric boride AlFe2B2 were prepared by sintering a green compact composed of the constituent elements Al, Fe, and B encapsulated within a layer of KBr molten salt at 1000 °C for 12 hours in the open air. Results indicate that the Al/Fe loading ratio in the precursor compacts strongly influences the phase purity, structural properties, and magnetofunctional response of the samples. It is observed that Curie temperature (Tc), saturation magnetization (Ms), and magnetic entropy change (ΔSmag) of the powders increase with the decrease in the Al/Fe ratio – a feature attributed to the change in the Al/Fe antisite disorder. Powders of nominal composition Al1.2Fe2B2 were found to be nearly single-phase stoichiometric Fe2AlB2 materials containing only 3% Al2O3 as the impurity phase. These powders exhibit an irregular polyhedral morphology with particle sizes in the range 2-5 m and demonstrate a promising magnetocaloric effect corresponding to a ΔSmag = 4.2 J kg−1K−1 at a magnetic field of μ0Happ = 2 T near room temperature, Figure 1. Research efforts centered on 3D printing magnetocaloric structures using the low-cost feedstock AlFe2B2 powders produced via MISEM will be presented and discussed.

![](https://assets.underline.io/uploads/markdown_image/1/image/b241cd2e4bc44d322718a4b672be8b39.jpg)

Fig 1. Magnetic entropy change curves of powders of composition Al1.2Fe2B2 synthesized via MISEM using KBr salt. Inset shows the morphology of the sintered powders.

Low-cost Processing of AlFe2B2 Feedstock Powders for Additive Manufacturing of Magnetocaloric Structures

Gas liquefaction is an essential aspect for gas storage and transport and its demand will significantly increase as the use of gases such as natural gas as well as H2, He, N2, and O2 become prominent in the development of new technologies (e.g. hydrogen based ones). Systems based on the magnetocaloric effect (MCE) are attracting the interest of the scientific community as they can overcome some of the issues of conventional liquefaction systems [1, 2]. In this work, we studied a series of rare-earth rich RE6Co2Ga (RE = Ho, Dy or Gd) compounds, which shows excellent MCE in the range of H2 and N2 liquefaction temperatures [3]. All the samples crystallize in the Ho6Co2Ga-type crystal structure (Immm space group) without significant presence of impurity phases. The nature of the thermomagnetic transition depends on the rare-earth element, showing metamagnetic anti-to-paramagnetic (AF to PM) transitions for Ho and Dy while a ferro-to-paramagnetic (FM to PM) transition is obtained for Gd. Novel MCE field dependence method [4] and conventional Banerjee's criterion have been used for distinguishing the order of the transition: samples with Ho and Dy are found to undergo first-order phase transition whereas a second order phase transition is observed for the one with Gd. Fig.1 depicts the temperature dependence of the isothermal entropy change (ΔSiso) for a magnetic field change of 0-5 T for Ho and Gd samples. The two compounds show significant values of 10.1 and 9.1 J kg-1 K-1 at 26 and 75 K, close to the liquefaction temperatures of H2 and N2, respectively.

![](https://assets.underline.io/uploads/markdown_image/1/image/f4b22391b23280e34c4bc60b9a3ec65c.jpg)

The temperature dependence of isothermal entropy change for Ho6Co2Ga and Gd6Co2Ga compounds whose crystal structures belong to Ho6Co2Ga-type.

Cryogenic magnetocaloric effect and thermomagnetic transitions in RE6Co2Ga (RE = Ho, Dy or Gd) compounds

Materials for magnetocaloric refrigeration near room temperature attract main attention, but compounds exhibiting large magnetocaloric effects (MCE) in the cryogenic regime are also of importance.1,2 In particular, MCE materials that can support liquefaction of certain gases, from hydrogen (boils at 20 K) to natural gas (~110 K), are of interest for diversification of energy supplies.2 Here we report a large MCE in GdNi1-xCox series in the temperature range between 70 and 115 K that can be controlled by varying x(Co) between 0 and 0.15. The compounds undergo second-order magneto-elastic transformations where the transitions from paramagnetic to ferromagnetic states are coupled with anisotropic changes in lattice parameters without significant changes in phase volume.3,4 Lattice symmetry also remains unperturbed across the transitions.3,4 While the transition temperatures increase nearly linearly with x(Co), doping with Co slightly reduces the maximum magnetic entropy changes: from -14 J/ Kg K at 71 K when x(Co) = 0 to -10 J/Kg K at 115 K when x(Co) = 0.15 (all values are quoted for a 50 kOe magnetic field change). The calculated temperature-averaged-entropy changes (TECs), one of the important figures of merit for assessing the potential of magnetic refrigerants,5 are comparable with the best known potential magnetocaloric materials exhibiting second-order phase transition. Our detailed analysis of the magnetic field dependence of the magnetic entropy changes along with critical exponent analysis explore the role of magneto-elastic coupling on the magnetocaloric properties of GdNi1-xCox alloys. Acknowledgement: This work was performed at Ames Laboratory and was supported by the Division of Materials Science and Engineering of the Office of Basic Energy Sciences of the U.S. Department of Energy (DOE). Ames Laboratory is operated for the U.S. DOE by Iowa State University under Contract No. DE-AC02-07CH11358.

Large cryogenic magnetocaloric effect in GdNi1-xCox (0 ≤ x ≤ 0.15)

Long-range ferromagnetic order in the single-layer limit appears to be possible in several chromium-based chalcogenides and halides with layered structure. Ab initio calculations based on the density functional theory of different Cr-based chalcogenides are analyzed approaching the twodimensional limit. The focus will be on magneto-crystalline anisotropy and how to obtain an out-of-plane magnetic polarization that would help circumvent the restrictions of the Mermin-Wagner theorem. This will be studied through various means like strain, pressure, the stability of charge density waves (CDW)[1], stoichiometry and other different structural details. The electronic structure of these compounds will be discussed as an approach to the understanding of the magnetic properties of the transition metal chalcogenide family in general.

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Conditions for effective coupling between surface acoustic waves and spin waves

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Conditions for effective coupling between surface acoustic waves and spin waves

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Deterministic Switching of a Perpendicularly Polarized Magnet Using Unconventional Spin-Orbit Torques in WTe2

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