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Traditional inductive methods used for Magnetic Resonance Imaging (MRI) suffer from significant challenges due to the low signal-to-noise ratio (SNR) arising from the weak nuclear magnetic moment of protons when they precess about a large magnetic field at room temperature [1]. In an attempt to amplify the magnetic flux, it has been proposed to use magnetic nanoparticles of various geometrical shapes that are inserted into an NMR inductive coil [1-3]. Thus, the magnetic flux due to the response of the ensemble of proton spins to the RF field can be significantly enhanced as these nanoparticles have high transverse magnetic susceptibility under appropriate DC bias conditions. Prior work did not consider random thermal magnetization fluctuations in such nanomagnets that affect the SNR. In this work, we simulated the magnetization dynamics of a single-domain ellipsoidal nanomagnet driven by an AC field (HAC) along the easy axis for different bias fields (HDC) along the hard axis of the nanomagnet (Fig 1a). Importantly, our simulation also included the effect of room temperature thermal noise as shown in Fig 2. For HDC =hc, the energy profile is nearly flat (Fig 1b) that leads to the maximum magnetization amplification (Fig 1c) in response to the driving AC field that mimics the field due to proton spins precessing at nuclear magnetic resonance (NMR) frequency. However, the flat energy profile also increases the random magnetization fluctuations due to the thermal noise (Fig 2). Nevertheless, the SNRs for h=0, 0.5hc, 0.75hc, 1.0hc and 1.5hc are 0.003, 0.29, 0.63, 0.7 and 0.23 respectively showing h= hc provides the highest SNR. However, these are considering a single nanomagnet only. We will further investigate improvement of NMR detection SNR as a function of the coil-filling factor (millions of magnetic nanoparticles), nanoparticle shape, applied NMR polarizing field, and narrow band filtering to increase the SNR &gt; 1000.References: 1. M. Barbic, A. Scherer, Solid State Nuclear Magnetic Resonance 28, 91 (2005). 2. M. Barbic, H. Elbidweihy, Journal of applied physics 120, 104506 (2016). 3. H.Elbidweihy, R. Smith and M. Barbic, AIP Advances 9, 045031 (2019).

MMM 2020

Signal to Noise Ratio of Single Domain Nanomagnet Amplification of Nuclear Magnetic Resonance Signals at Ambient Temperature

The 65th Annual Conference on Magnetism and Magnetic Materials (MMM 2020) was held in a virtual form. The COVID-19 pandemic, with its associated uncertainty about international travel and the ability to gather in large groups, meant that the Steering Committee decided to cancel the face-to-face meeting that had been planned in Palm Beach, Florida November 2-6, 2020.

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Traditional inductive methods used for Magnetic Resonance Imaging (MRI) suffer from significant challenges due to the low signal-to-noise ratio (SNR) arising from the weak nuclear magnetic moment of protons when they precess about a large magnetic field at room temperature [1]. In an attempt to amplify the magnetic flux, it has been proposed to use magnetic nanoparticles of various geometrical shapes that are inserted into an NMR inductive coil [1-3]. Thus, the magnetic flux due to the response of the ensemble of proton spins to the RF field can be significantly enhanced as these nanoparticles have high transverse magnetic susceptibility under appropriate DC bias conditions. Prior work did not consider random thermal magnetization fluctuations in such nanomagnets that affect the SNR. In this work, we simulated the magnetization dynamics of a single-domain ellipsoidal nanomagnet driven by an AC field (HAC) along the easy axis for different bias fields (HDC) along the hard axis of the nanomagnet (Fig 1a). Importantly, our simulation also included the effect of room temperature thermal noise as shown in Fig 2. For HDC =hc, the energy profile is nearly flat (Fig 1b) that leads to the maximum magnetization amplification (Fig 1c) in response to the driving AC field that mimics the field due to proton spins precessing at nuclear magnetic resonance (NMR) frequency. However, the flat energy profile also increases the random magnetization fluctuations due to the thermal noise (Fig 2). Nevertheless, the SNRs for h=0, 0.5hc, 0.75hc, 1.0hc and 1.5hc are 0.003, 0.29, 0.63, 0.7 and 0.23 respectively showing h= hc provides the highest SNR. However, these are considering a single nanomagnet only. We will further investigate improvement of NMR detection SNR as a function of the coil-filling factor (millions of magnetic nanoparticles), nanoparticle shape, applied NMR polarizing field, and narrow band filtering to increase the SNR > 1000.References: 1. M. Barbic, A. Scherer, Solid State Nuclear Magnetic Resonance 28, 91 (2005). 2. M. Barbic, H. Elbidweihy, Journal of applied physics 120, 104506 (2016). 3. H.Elbidweihy, R. Smith and M. Barbic, AIP Advances 9, 045031 (2019).

technical paper

Magnetic nanoparticles have recently garnered interest for applications as MRI temperature contrast agents for Magnetic Resonance Imaging Thermometry (tMRI)[1]. Magnetic materials which can be used to noninvasively monitor body temperature would be greatly beneficial both for diagnostic purposes as well as MRI guided thermal procedures such as laser ablation of tumors. However, materials studied previously [1,2] are toxic. In this work we present an MRI thermometry study of MgZn ferrite microparticles. Such materials where shown in an earlier study to be less toxic than previously studied ferrites [3]. MgZn ferrites were prepared using a standard ceramic method and size distribution analysis was carried out using Scanning Electron Microscopy (SEM). Proton NMR linewidth, T1, and T2 relaxation times where measured of solutions containing MgZn microparticles ata 3T. T2* weighted images were acquired in a high magnetic field of 3T and low magnetic fieeld of 0.2T scanners (Figure 1) to investigate temperature dependent contrast in images. In addition, tests of particle stability in solution where carried out and Inductively Coupled Plasma Mass Spectroscopy (ICP-MS) was used to determine dissolution of Mg and Fe in aqueous solutions of MgZn particles. results show that MgZn particles are promising compounds for tMRI as images show show strong dependence of image brightness vs temperature. (Figure 2). MgZn compounds have shown a lesserdegree of toxicity putting us closer to the ability to use ferrite particles as tMRI contrast agents in a clinical setting.References: [1] J. Hankiewicz, Z. Celinski, and K. Stupic, Nat. Commun, 7 (2016) [2] J. Hankiewicz, J. Stoll, and J. Stroud, J. Magnet. Magnet. Mater., 469 , pp. 550-557, (2019) [3] N. Alghamdi, J. Stroud, and M. Przybylski, Structural, Magnetic and Toxicity Studies of Ferrite particles for Magnetic Resonance Imaging Thermometry, J. Magnetism and Magnetic Materials. 497 , (2019)

Development of Biocompatible Ferrite Particles for Magnetic Resonance Imaging

Proton magnetic resonance imaging (1H-MRI) is one of the most powerful noninvasive biomedical imaging techniques to date. Conventional 1H-MRI can deliver pictures of exquisite anatomical detail, which is revolutionary in terms of its window into the body. A clear next step would be the delivery of novel MRI methods and molecular imaging probes to enable a window into the physiological chemistry of the body. The chemistry of the body governs nearly all function and dysfunction. Hence, the ability to noninvasively detect said chemistry would revolutionize diagnostic possibilities. We will present two efforts in our lab to develop novel molecular probes for chemical sensitivity. Notably, our efforts focus on magnetic species that are relatively exotic to the commonly used Gd3+ contrast agents: Cobalt-59 nuclear spins and high-spin metal ions (Fig. 1). Our first effort is directed at understanding the temperature-sensitivity of the Cobalt-59 nuclear magnetic resonance (NMR) signal in highly stable Co(III) complexes. Molecules containing the Cobalt-59 nucleus were recognized in 1980 as effective NMR thermometers owing to a highly sensitive chemical shift.1 Indeed, the chemical shifts for Cobalt-59-containing molecules exhibit two orders of magnitude higher sensitivities (on the order of 1-3 ppm/°C) than traditional 1H signals (0.01 ppm/°C).2 If translated into an applicable chemical probe, Cobalt-59 NMR probes could thus facilitate novel imaging techniques for, e.g., monitoring thermal ablation of tumors3 or thermal drug delivery.4 Yet, the exact design parameters to deliver molecular 59Co thermometers with even higher sensitivity (for higher-resolution imaging) are lacking. We will present novel results from our efforts to understand and control temperature sensitivity by molecular design.5,6 A second effort in our group to be presented is developing metal complexes for an imaging scheme that uses the electron analog of nuclear magnetic resonance: electron paramagnetic resonance imaging (EPRI). EPRI is capable of delivering local chemical information, including pH and oxygen content.7 Given the inherent tunability of the chemical properties of unpaired electrons, the potential exists for far more areas of chemical sensitivity relative to nuclei. Hence, merging EPRI with the anatomical detail of 1H-MRI could provide revolutionary new imaging techniques. A key challenge to doing so, however, is the fact that conventional EPRI molecular imaging probes (organic radicals) would use high-frequency microwaves for function in a typical 1.5 T MRI scanner. High-frequency microwaves are absorbed by water, which would heat and injure tissue. Molecules containing high-spin metal ions, owing to a unique electronic feature called zero-field splitting, may surmount this challenge. However, to fully realize this potential, significant insight is necessary in controlling the properties of metal ions under the action of low-frequency microwaves. In the second part of the presentation, we will touch on our efforts in this area.References: [1] G. C. Levy, T. J. Bailey and D. A. Wright, J. Magn. Reson. Vol. 37, p. 353–356 (1980). [2] J. C. Hindman, J. Chem. Phys. Vol. 44, p. 4582–4592 (1966). [3] M. Ahmed, L. Solbiati and C. L. Brace et al., J. Vasc. Interv. Radiol. Vol. 25 , p. 1691-1705.e4 (2014). [4] N. Hijnen, N.; S. Langereis and H. Grüll, Adv. Drug Deliv. Rev. Vol. 72, p. 65–81 (2014). [5] T. M. Ozvat, M. E. Peña and J. M. Zadrozny, Chem. Sci. Vol. 10, p. 6727–6734 (2019). [6] T. M. Ozvat, G. E. Sterbinsky and A. J. Campanella et al., Dalton Trans. Advance Article [DOI: 10.1039/D0DT01391A] (2020). [7] In Vivo EPR (ESR); L. J. Berliner, Ed.; Springer US: Boston, MA (2003).

Controlling Exotic Molecular Spins Toward Next-Generation MRI Probes INVITED

The ground state of nanoscale circular magnetic disks of certain geometric aspect ratios is a spontaneously forming stable vortex configuration with circulating in-plane magnetization and a vortex core pointing out-of-plane. Resonantly exciting the vortex core via either an rf magnetic field or an rf spin-polarized current yields a gyrotropic motion around its equilibrium position, characterised by a specific eigen-frequency, which depends on the material parameters and the disk geometry [1]. Such oscillations, which can be read out via periodic magnetoresistance changes, generate rf signals with high quality factors (>10000) in the sub-GHz bandwidth [2,3]. While all these features make vortex-based nano-oscillators interesting as nanoscale rf sources, the major drawback remains their low frequency tunability associated with the linear characteristics of the gyrotropic mode. Here, we investigate, by micromagnetic simulations, the role of magnetostriction in improving the tunability of vortex nano-oscillators. Specifically, we consider a double-disk structure comprising magnetostrictive (CoFe) and non-magnetostrictive (Py) layers separated vertically by a non-magnetic (NM) spacer. We show that, when the two vortices have different eigen-frequencies and the magnetostatic coupling between them is sufficiently strong, the stress-induced magnetoelastic anisotropy can lead to the synchronized gyration of the two vortex cores (Fig. 1). The stress-induced transition from double-frequency to single-frequency dynamics is mostly controlled by the polarization of the vortices and the magnetostatic coupling strength (i.e. spacer thickness). These findings offer a frequency tunability of vortex-based oscillators via mechanical stress, which can be generated and controlled electrically, for example, using piezoelectric substrates [4]. Funding from the EU Horizon 2020 project No. 737038 (TRANSPIRE) is acknowledged.References: [1] K. Yu. Guslienko, et al, J. Appl. Phys. 91, 8037 (2002). [2] A. Dussaux, et al, Nat. Commun. 1, 1 (2010). [3] N. Locatelli, et al, Appl. Phys. Lett. 98, 062501 (2011). [4] M. Filianina, et al, Appl. Phys. Lett. 115, 062404 (2019).

Stress-Induced Modification of Gyration Eigen-Frequencies in Stacked Double-Vortex Structures

Recent improvements in nanoparticle synthesis have allowed the application of magnetic nanoparticles (MNPs) in many fields where particle size control is key, such as data storage, spintronics or biomedicine, in which drug delivery and cancer treatment using hyperthermia stand out. In MNP systems, shape can trigger magnetostatic anisotropy effects induced by the demagnetizing factor. This feature is most notorious in highly degenerated systems on which shape anisotropy can be induced to alter properties like coercive field and remanence of non-interacting MNPs. In addition, magnetostatic dipolar interactions between MNPs can be tuned in disordered and crystalline structures by adding non-magnetic coatings, which can also control the lattice parameter, in a core-shell scheme, thus affecting the effective anisotropy of the system. This work focuses on the angular study of magnetization reversal processes in quasi-spherical (ε~1) single MNPs with different shapes and magnetic properties. Simulations show different hysteresis loops for different sphericalnesses of the MNPs, which can be related to the presence of different magnetization pinning events at the sharp edges of less spherical MNPs[Fig. 1]. Moreover, the effect of dipolar interactions has been tested out with simulations of the remanent state in MNP superlattices with simple, body-centered and face-centered cubic arrangements[Fig. 2].References: D.L. Huber, small., Vol. 1(5), p.482-501 (2005) D. Kim et al., Journal of Magnetism and Magnetic Materials., Vol. 320(19), p.2390-2396 (2008) Q. Li et al., Scientific Reports., Vol. 7, p.9894 (2017) D. Peddis et al., Chemistry of Materials., Vol. 25(10), p.2005-2013 (2013) A. Vansteenkiste et al., AIP Advances, Vol. 4, p.107133 (2014)

Shape-related Effects on Ferromagnetic Nanoparticles: A Micromagnetic Approach for Highly Diluted and Highly Ordered Systems

Inhomogeneous magnetic phases like magnetic vortex are expected to open up a wide range of opportunities both from a fundamental and technological perspective. Asymmetric nanostructures offer alternative data storage possibilities by suggesting a control over the vortex formation and thereby chirality [1-3]. Asymmetry introduced in the geometry also has a strong impact on magnetization reversal. Increased coercivity, remanence, and switching field distribution with the degree of asymmetry establishes the existence of an induced anisotropy, which in turn could even destabilize the magnetic vortex depending on the degree of asymmetry in a particular geometry [4]. Following these ideas, in this work, we investigate how the asymmetry modifies the magnetization reversal in hemispherical shells. We address this issue by breaking the symmetry of non-interacting hemispherical cap structures through a thickness modulation inclined at an angle with the symmetry plane and by analyzing the magnetization reversal mechanism for varying thicknesses. Micromagnetic simulations indicate that the asymmetric nanocaps reverse through the propagation of a curling state, while in the symmetric caps, magnetization reversal happens via coherent rotation. With an increase in thickness, the field at which curling state nucleates, shifts towards a higher applied field. The non-uniform magnetization reversal is apparently due to the altered energy contributions resulting from the asymmetry introduced in the nanocaps.References: [1] M. Schneider, H. Hoffmann, and J. Zweck, Appl. Phys. Lett., Vol. 79, p.3113 (2001) [2] D. B. Gopman, Y. P. Kabanov, J. Cui, et al., Appl. Phys. Lett., Vol. 109, p.082407 (2016) [3] J. Rothman, M. Kläui, L. Lopez-Diaz, et al., Phys. Rev. Lett., Vol. 86, p.1098 (2001) [4] K. M. Wu, J. F. Wang, Y. H. Wu, et al., J. Appl. Phys., Vol. 103, p.07F314 (2008)

Asymmetry Induced Inhomogeneous Magnetization Reversal in Hemispherical Shells

Achieving a strong perpendicular magnetic anisotropy is of great importance for materials intended for use in spintronics devices. Perpendicular anisotropy in magnetic multilayers arises from the broken symmetry at the interfaces due to the enhanced orbital and spin moments relative to the bulk system1. In order to accurately describe the quasi-static properties of these materials using a macrospin approach, the inclusion of both second-order (K2) fourth-order (K4) uniaxial anisotropies is essential. Beik Mohammadi et al2 have shown that lateral inhomogeneities of the second-order uniaxial anisotropy in thin films with perpendicular uniaxial anisotropy can give rise to higher-order anisotropy contributions. Here, we report on the study of the layer to layer variation of the second-order perpendicular anisotropy in magnetic bilayers and its influence on the quasi-static properties. We analyze the results of micromagnetic simulations3 in magnetic bilayers using a macrospin model. We show that in order to describe the micromagnetic simulation data using macrospin model, one requires a fourth-order uniaxial anisotropy contribution although the underlaying micromagnetic model does not include such term. Quasi-static calculations show that the fourth-order uniaxial anisotropy is caused by the deviation of the magnetization from the applied field direction.References: 1. J. M. Shaw, H. T. Nembach and T. J. Silva, Physical Review B 87 (5), 054416 (2013). 2. J. Mohammadi, K. Cole, T. Mewes and C. Mewes, Physical Review B 97 (1), 014434 (2018). 3. T. Mewes, C. Mewes, MATLAB based micromagnetics code M3, (2018). URL http://magneticslab.ua.edu/micromagnetics-code.html

Micromagnetic Simulations of the Quasi-static Properties of Dissimilar Bilayers

Two-dimensional (2D) magnetic materials, such as chromium trihalides and manganese dichalcogenides, have recently drawn immense attention of both theoretical and experimental research, due to both fundamental significance and promising technological applications. Particularly, some chromium trihalides have been shown able to host terahertz spin-waves (SW) [1] and are promising candidates for ultra-fast information transport and processing based on magnons. In this work we investigated the spin-wave propagation in the presence of strategically-placed defects (halide vacancies) in the honeycomb structure of chromium trihalides. We performed Density Functional Theory (DFT) calculations to obtain the magnetic parameters of the considered structures, followed by spin-dynamics simulations of the SW propagation. We reveal that the lattice defects host strong Dzyaloshinskii–Moriya interaction (DMI), so that a designed pattern of defects can serve as a spin-wave guide. We show the spectra of spin-waves propagating across periodic defect lines that prove such structures can work as a magnonic crystal [2] for terahertz SWs, exhibiting key features such as band gaps where SWs are not allowed to propagate. Such broad degree of manipulations available in 2D materials therefore suggests these systems as a front-runner for terahertz magnonics, applicable in cutting-edge devices.References: [1] W. Jin, H. Kim, Z. Ye, et al. Nature communications, 9, 5122 (2018). [2] A. V. Chumak, A. A. Serga, and B. Hillebrands. Journal of Physics D: Applied Physics, 50, 244001 (2017).

Terahertz Magnonics in 2D Chromium Trihalides with Atomically-Engineered Dzyaloshinskii–Moriya Interaction

Square Artificial Spin Ices (S-ASI)1-3 are the 2-dimensional realization of the standard 3-dimensional spin ice material of the type Dy2Ti2O7 (pyrochlore compound), with the alluring possibility of studying geometric frustration in a controlled way. In addition to the frustration, these kinds of structures enable the investigation of a variety of fascinating phenomena such as frustration, emergent magnetic monopoles, collective magnetization dynamics of interacting spins, and phase transition, etc. Recently, there is a focus on the understanding of dynamical behavior of spins or spin wave (sw) modes in such dipolar coupled systems. Detailed understanding of such behavior may be of importance to the applications in magnonics4,5. Here, we have investigated the sw modes of strongly dipolar coupled, highly anisotropic nanoislands forming S-ASI system using micro-magnetic simulation in MUMAX3 in combination with MATLAB coding. For the same, we have systematically scrutinized the sw spectra of the building block of S-ASI which is a square ring-like structure of highly shape anisotropic nanoislands of permalloy6,7. The evolution of the spectra as a function of no. of rings of up to four rings forming a S-ASI with closed edges exhibit a direct relation between the sw modes and the micro-states of the system. The study reveals that a single ring-type structure can alone be adequately used to understand the sw modes of S-ASI as well as it’s behavior in the presence of an external bias field. All the ring-type structures studied show ubiquitous switching identifier mode at approximately 14 GHz. Detailed analysis of the spin wave propagation modes in the building block as well as individual vertices of S-ASI structure will be discussed in this work.References: [1] P.W. Anderson, Phys. Rev., Vol. 102, p.1008 (1956). [2] C. Castelnovo et al., Nature, Vol. 451, p.42–45 (2008). [3] L. Balents, Nature Vol. 464, p.199–208 (2010). [4] E. Iacocca et al., Phys. Rev. B, Vol. 93, p.134420 (2016). [5] S. Mamica et al., Adv. Cond. Matter Phys., Vol. 2012 (2012). [6] N. Keswani and P. Das, AIP Adv., Vol. 8, p.101501 (2018). [7] N. Keswani et al., Appl. Phys. Lett., Vol 116, p. 102401 (2020).

Spin Wave Spectral Probing of Possible Micro-states in building block of Macroscopically Degenerate Artificial Spin Ice

Non-linear parametric excitation phenomena of magnons, with their interesting properties, can be utilized to realize magnonic devices for futuristic computation [1,2] and processing of microwave signals [3]. However, for robust device-design, much more remains to be understood regarding the effects of noise on magnons. The modification of the parametric resonance effects, in the presence of an additional signal, is a problem of both theoretical as well as practical interest. We use micromagnetics to model an yttrium iron garnet film of dimensions 5.1 μm x 100 μm x 1250 μm, employing 128x128x1 cells. A parallel-pumping configuration that scatters magnons largely in a plane perpendicular to the bias-field is used, allowing the use of a 2D simulation paradigm [3]. Saturation magnetization of 145 emu/cm3, exchange constant 3.77e-7 ergs/cm, and intrinsic-damping 0.0007 along with 2D periodic boundary conditions and thermal-fields (300 K) are used. A bias field of 200 Oe and a primary frequency of 6 GHz are used. The secondary signal is polarized parallel to the bias-field. Introduction of a secondary signal is found to limit the non-linearity by increasing the threshold-field. This effect, as shown in Fig. 1, is found to dominate at a frequency that corresponds to the relaxation rate of the longitudinal magnetization. Oscillatory behavior of the threshold with secondary frequency is noticeable especially for higher frequencies. These features have been explained analytically and are physically brought about by the modification of the relative phase of the magnons with respect to the microwave photons. The magnon modes that are dominant differ from the original 3 GHz modes by integer multiples of half the secondary frequency. The variation in the number of such modes w.r.t secondary frequency is also studied. We also examine phase noise and find that it affects the magnon instability by reducing the non-linearity and growth rate of magnons as shown in Fig. 2.References: 1. A. Chumak, A. Serga, B. Hillebrands, Nat. Comm. 5, 4700, 2014. 2. A. Khitun, M. Bao, K. L. Wang, J. Phys. D: Appl. Phys. 43, 264005, 2010. 3. A. Venugopal, T. Qu and R. H. Victora, IEEE Trans. Microw. Theory and Techn., vol. 68, no. 2, pp. 602-610, Feb. 2020.

Modification of Magnon Threshold and Characteristics Using a Secondary Signal and Phase Noise

New fascinating phenomena involving coupled spin waves and phonons are observed at the magneto-elastic resonance: magnetic field dependent spin Seebeck effect [1], acoustically-assisted spin pumping [2, 3] and magnetization swiching [4, 5]. In this context, it has been shown that an efficient mean to excite phonons is by surface acoustic waves (SAW). The integration of SAW-FMR (ferromagnetic resonance) mechanism in spintronic and magnonic devices are claimed to operate with very low power. However, most ferromagnetic materials have precession frequencies well above 5 GHz, i.e. above the highest frequency reached by today's SAW technologies. This restricts the research on SAW-FMR to low magnetization and/or low magnetic anisotropy materials, such as (Ga,Mn)As or (GaMn)(As,P), Ni, and YIG. Here, we show that thin films of Fe epitaxially grown on GaAs(001), a spintronic and magnonic compatible magnetoelastic and piezoelectric heterostucture, give the opportunity to obtain SAW-FMR, at room temperature, below 1 GHz despite the high Fe magnetization. This is obtained by exploiting the softening of the magnetic stiffness when the field is applied along a hard axis, at moderate intensity (60 mT). Slight variations of the magnetic field direction, less than 0.1 deg off, increase dramatically magnetization precession frequency leading to off-resonance interaction and suppressing SAW attenuation. The observed phenomena are described by adopting a very simple magnetization dynamics model that catches the physics of the interaction. The observation of resonant, low frequency and highly directional magnetoelastic coupling in Fe suggests that SAW mature technology offers the opportunity to magnonics and spintronics to handle magnetization precession in a remote way, without using any dissipative electron current. [6]References: [1] Takashi Kikkawa, et al., Phys. Rev. Lett. 117, 207203, (2016) [2] M. Weiler, et al. Phys. Rev. Lett. 108, 176601, (2012) [3] Ken ichi Uchida, et al., Solid State Communications 198, 26, (2014) [4] L. Thevenard,et al. Phys. Rev. B 93, 134430, (2016) [5] P. Kuszewski, et al. Journal of Physics: Condensed Matter 30, 244003 (2018) [6] J.-Y. Duquesne, P. Rovillain, et al. Phys. Rev. Appl. 12, 024042 (2019)

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