United States

Ferromagnetic [Pt/Co]&lt;sub&gt;n&lt;/sub&gt; multilayers that are composed of n stacked [Pt/Co] bilayers have been widely investigated over the past decades, mainly due to the easy tunability of various magnetic properties such as the potentially strong perpendicular magnetic anisotropy (PMA). More recently, it has been demonstrated that the addition of heavy metals (HM) such as Ir or W can lead to the presence of sizeable chiral exchange interactions in [Pt/Co/HM]&lt;sub&gt;n&lt;/sub&gt; systems [1]. As a consequence, topological spin textures (e.g., skyrmions) are commonly reported in these material systems even at room temperature, thus making them promising candidates for future spintronics applications [2]. In the present work, we use additional manganese layers to break the spatial inversion symmetry of conventional [Pt/Co]&lt;sub&gt;n&lt;/sub&gt; stacks and thereby, in combination with spin-orbit interaction, introduce chiral exchange interactions. The investigated [Pt/Co/Mn]&lt;sub&gt;n&lt;/sub&gt; samples were fabricated by magnetron sputtering. Structural characterization of the multilayer stacks was done by performing X-ray reflectometry (XRR) measurements, while magnetic hysteresis curves were acquired in a vibrating sample magnetometer (VSM). In addition, real-time imaging of magnetic domains as a function of the external magnetic field was conducted using a home-built magneto-optical Kerr effect (MOKE) microscope. Our results indicate a complex and sensitive dependence of various magnetic energy terms on the individual layer thicknesses, number of multilayer repetitions as well as on deposition parameters. This is particularly reflected in the shape of hysteresis loops or the types of spin textures seen in our magneto-optical imaging experiments. For instance, we discuss that the presence of defects leads to a very slow dynamics of dendritic-type domain groth in some of the investigated multilayers. Finally, we also elaborate on various approaches towards the possible observation of magnetic skyrmions in [Pt/Co/Mn]&lt;sub&gt;n &lt;/sub&gt;multilayers.&lt;br/&gt;&lt;br/&gt;This work is supported by the Deutsche Forschungsgemeinschaft (DFG) through the research fellowship LO 2584/1-1 and the NSF through the University of Illinois at Urbana-Champaign Materials Research Science and Engineering Center under Grant No. DMR-1720633. .

2022 Joint MMM-INTERMAG

Tuning the Magnetic Properties of Ferromagnetic [Pt/Co/Mn]n Multilayers

#### Welcome to the 67th Annual Conference on Magnetism and Magnetic Materials, MMM 2022!

The Conference was held from October 31 to November 4 and offers both in-person and on-demand content.

MMM 2022 is sponsored jointly by AIP Publishing and the IEEE Magnetics Society. Members of the international scientific and engineering communities interested in recent developments in fundamental and applied magnetism are invited to attend and contribute to the technical sessions. The technical program will include invited and contributed papers in oral and poster sessions, invited symposia, a tutorial, and several special sessions. This Conference provides an outstanding opportunity for worldwide participants to meet their colleagues and collaborators and discuss developments in all areas of magnetism research.

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MMM 2022

This Conference provides an outstanding opportunity for worldwide participants to meet their colleagues and collaborators and discuss developments in all areas of magnetism research.

Ferromagnetic [Pt/Co]n multilayers that are composed of n stacked [Pt/Co] bilayers have been widely investigated over the past decades, mainly due to the easy tunability of various magnetic properties such as the potentially strong perpendicular magnetic anisotropy (PMA). More recently, it has been demonstrated that the addition of heavy metals (HM) such as Ir or W can lead to the presence of sizeable chiral exchange interactions in [Pt/Co/HM]n systems [1]. As a consequence, topological spin textures (e.g., skyrmions) are commonly reported in these material systems even at room temperature, thus making them promising candidates for future spintronics applications [2]. In the present work, we use additional manganese layers to break the spatial inversion symmetry of conventional [Pt/Co]n stacks and thereby, in combination with spin-orbit interaction, introduce chiral exchange interactions. The investigated [Pt/Co/Mn]n samples were fabricated by magnetron sputtering. Structural characterization of the multilayer stacks was done by performing X-ray reflectometry (XRR) measurements, while magnetic hysteresis curves were acquired in a vibrating sample magnetometer (VSM). In addition, real-time imaging of magnetic domains as a function of the external magnetic field was conducted using a home-built magneto-optical Kerr effect (MOKE) microscope. Our results indicate a complex and sensitive dependence of various magnetic energy terms on the individual layer thicknesses, number of multilayer repetitions as well as on deposition parameters. This is particularly reflected in the shape of hysteresis loops or the types of spin textures seen in our magneto-optical imaging experiments. For instance, we discuss that the presence of defects leads to a very slow dynamics of dendritic-type domain groth in some of the investigated multilayers. Finally, we also elaborate on various approaches towards the possible observation of magnetic skyrmions in [Pt/Co/Mn]n multilayers. This work is supported by the Deutsche Forschungsgemeinschaft (DFG) through the research fellowship LO 2584/1-1 and the NSF through the University of Illinois at Urbana-Champaign Materials Research Science and Engineering Center under Grant No. DMR-1720633. .

technical paper

The 15th Joint MMM-INTERMAG Conference (2022 Joint) is sponsored jointly by AIP Publishing and the IEEE Magnetics Society. Members of the international scientific and engineering communities interested in recent developments in fundamental and applied magnetism are invited to attend and contribute to the technical sessions. The technical program will include invited and contributed papers in oral and poster sessions, invited symposia, a plenary session, and an evening session, with about 1500 presentations overall. This Conference provides an outstanding opportunity for worldwide participants to meet their colleagues and collaborators and discuss developments in all areas of magnetism research.

The 2022 Joint Conference will offer both in-person and prerecorded on-demand content.

For tickets to the event, please register at the following link: https://magnetism.org/register

Please register for the Joint MMM-Intermag conference to join the event.

Recently, it has been theoretically and experimentally demonstrated that the effects of inertia of magnetization should be considered in the full description of spin dynamics at pico- and femtosecond timescales [1-8]. The nutation motion of magnetization is a manifestation of inertia of the magnetic moments. A rigorous derivation including inertia in the Landau-Lifshitz-Gilbert equation was carried out by Mondal et al. in the Dirac-Kohn-Sham framework [6,7]. Here, we show that inertia effect in magnetization dynamics results in a new type of spin waves, i.e. nutation surface spin waves, which propagate at terahertz frequencies in in-plane magnetized ferromagnetic thin films. Considering the magnetostatic limit, i.e. neglecting exchange coupling, we calculate dispersion relation. In addition, we find that the nutation surface spin waves are backward spin waves [1]. The phase shift between precessing magnetic moments propagates as a spin wave through the ferromagnet because of dipole-dipole or exchange coupling (Fig. 1(a)). Magnetic inertia effects, which are expected to contribute to dynamics of spin waves, originate from spin-orbit coupling. We find that when taking inertia into account one finds that the deviation of alignment of localized moments will propagate through the spin system in the form of both precession and nutation motions, i.e. in ferromagnetic materials one needs to add to all “conventional” spin wave modes a high frequency wave-like motion with small amplitude caused by inertia. Moreover, a different type of waves having predominantly inertial nature appears in ferromagnetic thin films, which we call here nutation surface spin waves. Since these waves have terahertz frequencies (compared to typically GHz frequencies of other spin wave modes), they can be plotted as a small deviation on top of a “frozen” precession motion (Fig. 1(b)).

![](https://assets.underline.io/uploads/markdown_image/1/image/e702e12d86e64bbc071819e5db941fcf.jpg)

Fig. 1. (a) The precession spin wave without inertia (red curve). The blue arrow indicates the motion of the magnetization M. (b) The nutation surface spin wave (purple curve) with a frequency considerably higher than in (a) plotted with small blue circles on top of the “frozen” precession motion.

Dispersion Relation of Nutation Surface Spin Waves in Ferromagnets

In magnetic thin films, large excitation amplitudes can lead to the onset of the first order Suhl instability, where the driven uniform mode undergoes three magnon scattering to two modes of half the frequency and equal and opposite wavevectors. Although experimental studies of the steady-state behavior are established, a comprehensive study of the nonequilibrium behavior over a large range of excitation powers is lacking. We have developed an experimental technique for sensitive detection of the time evolution of the FMR amplitude over five orders of magnitude in power, which provides a highly comprehensive understanding of the three-magnon scattering process. Applying this technique to patterned 3μm thick YIG thin films, we observe strong agreement with our results from micromagnetic simulations of the Suhl instability. We have developed a semianalytical model to explain the three magnon scattering process. This model shows quantitative agreement with experiment and simulation, including a predicted additional regime corresponding to power-dependent nonlinear oscillatory behavior on the order of 50 MHz. Additional observed effects will also be discussed. This work was supported by SMART, a center funded by nCORE, a SRC program sponsored by NIST, DARPA under Grant W911NF-17-0100, MINT at Minnesota, and the NSF XSEDE through Allocation No. TG-ECS200001. We acknowledge the use of MSI resources.

![](https://assets.underline.io/uploads/markdown_image/1/image/1206326856094257491a60e9c5fd8367.jpg)

Time-resolved Nonlinear Magnetization Dynamics in YIG Thin Films

Time-resolved Nonlinear Magnetization Dynamics in YIG Thin Films

One current goal of spintronics is the development of sustainable information technology based on pure spin currents. One promising way to do this is to use spin waves (SWs) in low damping insulating ferrimagnets like yttrium iron garnet (YIG) where relaxation can be controlled by spin orbit torque (SOT) at a heavy metal interface [1]. However, such metal/insulator hybrid devices exhibit saturation of SW amplification due to nonlinear coupling between modes [2]. Two strategies can be considered to overcome these issues. i) Nanopatterning leads to quantization of SW modes [3], thereby limiting the available nonlinear processes [4]. ii) Tuning the perpendicular magnetic anisotropy (PMA) can be used to control the sign of the nonlinear frequency shift [5]. Recently, the growth of ultra-thin films of bismuth doped YIG (BiYIG) with tunable PMA has been achieved [6], resulting in greatly improved characteristics of SOT emitted SWs [7]. Here, we study the magnetization dynamics in individual nanodisks patterned from such a 30 nm thick BiYIG film with submicron diameters. The static magnetic field is perpendicular to the plane. The in-plane microwave field is produced by an integrated antenna. To detect the FMR, we employ a magnetic resonance force microscope [8]. For the largest disks, the amplitude of the FMR peak quickly saturates as the excitation power is increased, which is accompanied by a strong distortion of the absorption line, that broadens and splits into several peaks (Fig1a). Micromagnetic simulations accurately reproduce these features and reveal that a dynamic instability is responsible for the observed behavior. To experimentally probe this complex dynamics, we apply a second, much weaker excitation field of varying frequency, in addition to the main driving field at high power. The frequency modulation spectrum obtained (Fig1b) reflects the existence of rich low-frequency temporal variations in the magnetization dynamics.

![](https://assets.underline.io/uploads/markdown_image/1/image/0f9922ccb39360e331cfbc33deb7fa05.jpg)

Fig 1. (a) Resonance line in the deeply nonlinear regime. (b) Two-tone spectroscopy performed inside the instability region, at μ0Hz = 165 mT.

Dynamic instabilitiy in high power FMR of BiYIG nanodisks

An interesting phenomenon occurs in submicron, magnetic vortex ground state particles as their thickness is increased, and the vortex becomes a fully-fledged three dimensional object. Although the ground state remains largely homogeneous through the thickness, one but needs to apply the smallest of excitation to see the emergent shearing of the magnetization texture and resonant modes associated with it [1,2]. Using the nanostencil fabrication technique[3] we obtained planar arrays of increasingly thick (up to 350 nm) magnetic particles, going beyond thicknesses studied previously. Not only do we observe the inversion of intensities of the modes, as high order modes become the most intense, we see also the complete disappearance of the homogeneous G0 mode, which marks a transition where the 2D dynamic solutions completely cease their existence, see the spectrum presented on Fig. 1. This new effect also goes toward a significant increase of the speed of dynamics in the system. In the course of study we place a special emphasis on taking the real, dome-like particle profiles into account, which, as we show, influence the spectra for thick particles significantly. The profiles used were attained with a help of atomic force microscopy. The realistic boundaries primarily tune the non-radiative standing spin wave modes[4] which in turn affect gyrational modes through hybridization. We observe this through the detailed, microscopic study of mode distributions such as the one on Fig. 2, by matching experimental spectra, and juxtaposing stationary trajectories (in the time domain).

![](https://assets.underline.io/uploads/markdown_image/1/image/8f782616bbfa5a82e7cffe9fbfba735f.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/fc47f4d3547c1babcc525b8c1162cc50.jpg)

High Order Gyromode Observation in Dome-like Nanoparticles

High Order Gyromode Observation in Dome-like Nanoparticles

All Optical Helicity Independent Switching (AO-HIS) of magnetization, using single femtosecond laser pulses, has been demonstrated in GdFeCo ferrimagnetic alloys for various concentrations [1] as well as in other structures with antiferromagnetic coupling, Gd/Co, [Tb/Co]n/Ta/CoFeB and Mn2RuxGa [2,3,4]. Up to now, AO-HIS has never been observed for ferromagnetic layers. However, it was shown that a single pulse magnetization reversal of a ferromagnet could be observed in a spin-valve structure [5]. The switching is then achieved by the ultrashort spin current pulse generated from the ultrafast demagnetization of GdFeCo [5,6]. In this work, we study Gdx(FeCo)1-x/Cu/FM spin-valve structures, where FM can be different ferromagnetic layers [7] and the composition x of the GdFeCo alloy is also changed [8]. By increasing the Gadolinium concentration x, we aim at increasing the spin current injected in the copper layer [6]. We show that this can reduce the laser fluence threshold required to observe the FM magnetization reversal. In particular, no AO-HIS of the GdFeCo layer is required and the threshold fluence for the FM layer is around 1.6 mJ/cm2 i.e. comparable to GdFeCo and Gd/Co multilayers [1,2] and smaller than what is achieved for Tb/Co/CoFeB [2] and Mn2RuxGa [3]. We also show that by changing the Curie temperature, the laser pulse duration and the Cu/FM interface, one can control the interaction between the spin current and the FM layer and so the laser fluence threshold. Finally, we measured the dynamics of the reversal of the FM layer, which happens in around a picosecond. We show a model, based on a recent theory for the ultrafast magnetization dynamics of ferromagnets [9], that explains this behavior. We thus designed spin-valve structures that could provide technological advantages regarding both speed and energy efficiency of data storage.

Ultrafast Single Pulse All Optical Magnetization Switching of Ferromagnets

Graphene/ferromagnet interfaces have exhibited various unusual spin-orbit coupling(SOC) related effects despite very small SOC strength of graphene[1-3]. Here we have investigated femtosecond laser induced spin dynamics using an all-optical time-resolved magneto-optical Kerr effect(TR-MOKE) magnetometry in sputter-deposited CoFeB thin films on chemical-vapor-deposition grown single-layer graphene(SLG) by varying the thickness of CoFeB from 1.5 to 6 nm[4]. The ultrafast demagnetization time(τm) extracted using three-temperature modelling(Fig. 1(a)) show a monotonic variation with CoFeB thickness(Fig. 1(b)). The Gilbert damping parameter(α) is directly extracted from the decaying amplitude of precessional oscillation(Fig. 1(c)). We have modelled the CoFeB-thickness-dependent α to estimate the effective spin-mixing conductance(Geff) and two-magnon scattering coefficient(βTMS) for SLG/CoFeB interface(Fig. 1(d)) which revealed spin pumping(SP) [4] as the dominant contributor to modulation of α(Fig. 1(e)). Furthermore, we have observed an inverse relationship between τm and α for SLG/CoFeB heterostructures(Fig. 1(f)) due to the dominance of SP-induced nonlocal spin-transport mechanism[4]. To disentangle other possible interface contributions to the damping such as spin memory loss(SML), we have inserted a 1-nm-thick Cu spacer layer between the SLG and CoFeB. Negligible damping modulation by the insertion of Cu spacer between SLG and CoFeB confirms that additional effects like SML are absent in our system. In summary, this study has provided a qualitative understanding of different ultrafast spin manipulation mechanisms in a graphene-based heterostructure, which can lead towards the next-generation graphene-based ultrafast spintronics devices. AB acknowledges the financial assistance from S. N. Bose National Centre for Basic Sciences(SNBNCBS), India under Project SNB/AB/11-12/96 and SNB/AB/18-19/211. SNP, SM, SC and ArB acknowledge SNBNCBS for respective fellowship.

![](https://assets.underline.io/uploads/markdown_image/1/image/2365a212e2a849241df3b94e8286c456.jpg)

Fig. 1(a) Ultrafast demagnetization in SLG/CoFeB(d) (b) Evolution of τm with d (c) Precessional oscillations at H=3.59 kOe (d) Evolution of α fitted with a phenomenological model (e) Variation of 1/τm as a function of α (f) Contributions of SP and TMS to α.

Correlation between Femtosecond Laser Induced Spin Current and Spin Dynamics at the Single Layer Graphene/CoFeB Thin Films

Ultrafast generation of chiral magnetic order is one of the most sought-after technology for its potential application in next generation magnetic memory devices [1]. Recent experimental demonstration of generation of skyrmions with ultrafast laser pulses [2] has opened new horizons regarding the experimental feasibility of achieving this. In spite of such immense experimental achievement, the theoretical understanding of the underlying physics is still not very clear. Most of the existing studies tries to explain this with classical magnetisation dynamics only and thus completely miss the impact of the electronic interactions which plays crucial role in early sub-picosecond regime. More advanced TD-DFT based approaches are quite successful in explaining the fast dynamics in this regime, however, they are not quite fruitful in explaining the slow magnetisation dynamics which can last for several picoseconds. In this presentation we bridge this gap with the help of a quantum-classical hybrid approach which allows us to reveal the physics with a sub-femtosecond resolution and at the same time look at the steady state after several picoseconds [3]. We have successfully identified both the inherent and emergent interactions which drives the intertwined electronic and magnetic interaction leading to a stable chiral configuration and thus can predict their lifetime as well. We show here that the laser assisted dynamics is inherently different from the predictions of phenomenological two/three temperature model which has been widely used in modelling ultrafast demagnetisation. We show that the thermal re-population leads to formation of multiple domains with higher energy and less stability compared to smooth spiral formed by laser excitation. The final chiral configuration can be tuned both with laser and material parameters and formation can sustain at moderate temperature which makes our findings feasible for experimental realisation and thus would be instrumental in revealing the rich physics of ultrafast optical manipulation of the magnetisation.

![](https://assets.underline.io/uploads/markdown_image/1/image/17b5b1fc1f24b7f50457de2d6090ae8f.jpg)

Comparison of magnetisation dynamics excited by laser and thermal repopulation. Thermal excitation forms multiple domain where laser forms a smooth spiral configuration.

Imprinting chirality in collinear magnet with ultrafast laser

The discovery of helicity-independent all-optical switching1 as well as ps current-pulse driven magnetization reversal2 of a ferrimagnetic GdFeCo led to a significant development towards ultrafast magnetization reversal of a magnetic tunnel junction (MTJ) based memory element. Ultrafast switching of Co/Pt multilayers coupled with a GdFeCo has been observed within ~ 7 ps which occurs due to RKKY exchange coupling3. However, GdFeCo isn’t a desirable choice for a MTJ as it does not hold PMA for a patterned dot with a diameter less than a mm4. On the other hand, CoGd ferrimagnet can maintain its PMA down to 200 nm diameter4. In this work, we have experimentally observed the all-optical time-resolved magnetization dynamics of a “CoGd/Pt spacer (1 to 4 nm)/ [Co/Pt] multilayers” heterostructure. The magnetization of CoGd is reversed after 1.5 ps. The Co/Pt multilayer which has slightly higher demagnetization rate, stays demagnetized as the electron temperature reaches its Currie temperature before getting switched ~ 3 ps due to enough angular-momentum transfer from the CoGd sublattice as shown in Fig. 1(a). We rule out the possibility of Co/Pt swithcing triggered by non-local spin current generated from CoGd as Co/Pt switched for both ferromagnetic and anti-ferromagnetic coupling. We performed analytical calculation to simulate the time-resolved dynamics as shown in Fig. 1(b) using an extended microscopic three temperature model (M3TM) proposed by Beans et al5. Considering inter-sublattice, intra-sublattice and indirect RKKY exchange scatterings, we explain the magnetization reversal dynamics of different magnetic components of ferromagnetically and antiferromagnetically coupled as well as decoupled ferromagnet-ferrimagnet heterostructures. We demonstrate that irrespective of the nature of RKKY coupling, ultrafast switching of the Co/Pt multilayers can be achieved, and its switching time strongly depends on the RKKY interaction strength. This work experimentally as well as theoretically establishes the mechanism of all-optical switching in such magnetic heterostructures.

![](https://assets.underline.io/uploads/markdown_image/1/image/17766eb2037f4c3871163c64928d3c26.jpg)

(a) Experimental and (b) theoretical time-resolved magnetization dynamics of a ferromagnetically ([Co/Pt]3/Co/Pt 1 nm/CoGd/cap) coupled stacks.

RKKY exchange coupling mediated ultrafast all-optical switching of a ferromagnet

Single pulse all-optical switching (SP-AOS) using 40 fs light pulses was discovered in films of the amorphous rare earth-transition metal (RE-TM) alloy a-Gd(FeCo)3 [1]. The switching takes less than 5 ps and relies on the different demagnetisation times of the Gd and Fe,Co subnetworks. Replacing Gd by another RE was expected to yield more materials that exhibit ultrafast switching, but it did not happened. Indeed, amorphous RE-TM alloys other than Gd(FeCo)3 have only been switched transiently by a single pulse [2] or slowly using many polarised pulses [3]. Here, we report stable SP-AOS in amorphous Dy-Co and Tb-Co films with perpendicular anisotropy. Room-temperature coercivity is 30-50 mT, and compensation temperatures Tcomp are below 300 K. The example of a-DyCo3 is shown in Fig 1. The behavior is surprising. A single 200 fs pulse creates a non-uniform 40 µm dark spot on a uniformly-magnetized light film. Domain structure on a scale of ~ 3 µm is observed. After two pulses, the darker domains switch back, and the multidomain state will toggle for a few more pulses before leaving the sample in a nonuniform mid-gray state. Images are obtained on a strip of material irradiated with 1-5 pulses, using an off-site Kerr microscope. Other samples show a variety of behavior. The switching of a-TbCo4 shown in Fig. 2 is also granular, but the lighter and darker spots are aggregated into lighter and darker rings with unequal numbers of small dark and light domains. The contrast between rings again disappears after a few pulses, but the small domains persist. This is quite unlike the uniform toggling of large domains, comparable in size to the laser spot, that are seen in SP-AOS of ferrimagnetic a-Gd(FeCo)3 and crystalline Mn2RuxGa. The key difference is probably the random uniaxial anisotropy for the non S-state rare ions and temperature-dependence, which governs that of the coercivity. The influence of stray dipolar fields on a µm scale and possible of radial heat waves in the substrate will be considered in the context of ultra-fast SP-AOS in these a-RE-TM materials.

![](https://assets.underline.io/uploads/markdown_image/1/image/d2f69edc767f147428037a22f4910d14.jpg)

SP-AOS in a 10 nm a-DyCo3 alloy film with perpendicular magnetization. Scale bar 40 μm.

![](https://assets.underline.io/uploads/markdown_image/1/image/952962fa921f2d2bdfcf19a77cdb0149.jpg)

SP-AOS in 20 nm a-TbCo4 with perpendicular magnetic anisotropy.

Single pulse all-optical magnetic switching in amorphous DyCox and TbCox

The ability to control and tune magnetic dissipation is a key concept of emergent spintronic technologies. Magnon-magnon processes constitute a major dissipation channel in nanomagnets [1-3], redefine their response to spin-torques [4], and hold promise for manipulating magnetic states on the quantum level. Controlling these processes [5,6], while being imperative for many spintronic applications [4], has remained difficult to achieve. We identify two avenues to realize this goal: by breaking the symmetry of the static magnetic state or by breaking the symmetry of the magnon modes. Here we focus on the latter approach due its particular technological relevance. As a vehicle for our study, we employ magnetic tunnel junction nanopillars that consist of a free layer and a synthetic antiferromagnet (SAF) [7]. In the normal state of the SAF, its stray field is small at the position of the free layer – the fields from the two constituent layers of the SAF largely cancel out [8]. However, once we trigger SAF’s spin-flop transition, their spins become canted and generate a stray field which is nonuniform at nanoscale – a prerequisite for breaking the symmetry of free layer’s magnons. By controllably switching the SAF between its normal and spin-flop states, we achieve to toggle three-magnon processes in the free layer. We tune the magnon interaction by at least one order of magnitude and thus engineer two distinct dissipative states. Our results open up an avenue for manipulating magnon processes by external stimuli at nanoscale, tuning the nonlinear response in magnetic neuromorphic networks, and controlling large excitation regimes in spin-torque devices. They furthermore show promise for engineering coherent magnon coupling in hybrid quantum information systems. This work was supported by the National Science Foundation through Grant No. ECCS-1810541.

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