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Magnonic computing (MC) architectures based on spin waves are increasingly of interest for special-purpose computing applications [1]. MC offers advantages over conventional charge-based computing [2-5], including low power dissipation (magnon propagation does not require charge transfer), and incorporation of phase information in addition to amplitude, reducing the component count needed for certain logic operations [6]. One of the challenges in the realization of most MC concepts is that they require an efficient means for routing magnons in complex networks. In particular, a scalable, nonvolatile, and reconfigurable mechanism to do so is currently lacking [6,7]. Here we address this challenge by utilizing a Néel skyrmion as a programmable scattering center to route magnons. The skyrmion is stabilized by the interfacial Dzyaloshinskii-Moriya Interaction (DMI) and perpendicular magnetic anisotropy (PMA), which itself can be controlled by electric fields via the voltage-controlled magnetic anisotropy (VCMA) effect, making the magnon-skyrmion interaction tunable by voltage. We investigate the interaction of exchange spin waves with wavelength of 26 to 190 nm, with skyrmions having diameters from 9 to 74 nm. Our micromagnetic simulations show that the propagation, scattering angle, and energy transmission of spin waves can be effectively controlled by tuning the ratio of magnon wavelength to the skyrmion diameter, which depends strongly on PMA and DMI. Based on this approach, we propose a new skyrmionic magnon switch (SMS) device, which provides voltage-controlled routing of spin waves in a magnetic wire and can be applied to build basic logic circuits. We simulate the SMS performance using typical material parameters for thin ferromagnetic films supporting skyrmions, and assess the requirements for its experimental realization.References: [1]. Khalili P, Wang K L. IEEE Spectrum, Vol.52(7), p.30-56(2015) [2]. Wang, K.L. and P. Khalili Amiri, SPIN, Vol.02(02), p.1250009(2012) [3]. Khitun, A., D.E. Nikonov, and K.L. Wang, Journal of Applied Physics, Vol.106(12), p.123909(2009) [4]. Dutta, S., et al., Scientific Reports, Vol.5, p.9861(2015) [5]. Cherepov, S., et al., Applied Physics Letters, Vol.104(8), p.082403(2014) [6]. Shabadi, P., et al., SPIN, Vol.02(03), p.1240006(2012) [7]. Vogt, K., et al., Applied Physics Letters, Vol.101(4), p.042410(2012)

MMM 2020

Investigation of spin wave - skyrmion interactions for magnonic information processing

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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technical paper

Manipulation of magnetization precession, namely magnon, with circularly-polarized light has attracted much attention. Many of relevant studies have focused on magnon driven by the inverse Faraday effect in magnetic insulators or semiconductors. However, there have been few reports on metals. Recently Choi et al. reported magnetization precession driven by the circularly-polarized light in ferromagnet/heavy metals bilayers [1]. They proposed new physics, optical spin-torque which is distinct from the traditional inverse Faraday effect. However, the physics of optical spin-torque is not clearly understood yet; thus, it is demanded to deeply understand the physics toward photo-spintronic applications. Here, we observed light-helicity induced magnetization precession in FeCo / Pt bilayers, which is found to be explained by the optical spin-torque. MgO / FeCo / Pt thin film were deposited on thermally oxidized Si substrate by a magnetron sputtering. The pulse width and wavelength of the femtosecond laser pulse used were 120 fs and 800 nm. Figure 1 shows the magnetization precession in FeCo / Pt bilayer with different light helicities, where 2 T in-plane magnetic field is applied. The solid curves in Fig. 1 show the fitting of sinusoidal function to the data. The phase of the magnetization precession has an information of a torque direction. Optical spin-torque is believed to be regarded as a damping-like torque, which is induced by a current of the spin-angular momentum in a nonmagnetic layer transferred from the circularly-polarized light and makes magnetization initailly tilt away from the film surface as shown in Fig. 2. It was found that the magnetization precession is mainly induced by the damping like-torque, however, we also observed field-like torque as a phase shift of the magnetization precession. The detailed discussion of field-like torque as well as its thickness dependence will be discussed in the presentation. This work was partially supported by KAKENHI (19K15430), Advanced Technology Institute Research Grants, and CSRN.References: [1] G. -M. Choi et al. Nat. Commun. 8, 15085 (2017), G. -M. Choi et al. Nat. Commun. 11, 1482 (2020). [2] S. Iihama and S. Mizukami, in-preparation.

Optical spin-torque in FeCo / Pt bilayer thin films

An important aspect of spin-orbitronics is to electrically manipulate the spin degree of freedom in order to achieve spin-based logic and memory functionalities. Spin-orbit torques (SOTs), direct control of the magnetization via spin-orbit interaction of materials by passing an electric current, have been demonstrated in a variety of metallic and insulating ferromagnetic/non-magnetic heavy metal bilayers utilizing both magneto-transport and magneto-optical Kerr effect (MOKE) measurements. Whereas the conventional MOKE measurement successfully expands the detectability of SOTs, an AC current modulation in the SOT devices is required to achieve the desired sensitivity. Here, we show that instead of using the AC current modulation, the SOT-induced effect can be studied by observing static magnetization switching under a DC current excitation taking advantage of the ultrahigh sensitivity of a Sagnac interferometer microscope. Upon the DC current excitation, spatially resolved static magnetization switching in a prototypical SOT device, i.e., NiFe/Pt bilayer is directly measured, by which a current-induced Oersted field, joule-heating, and other parasite artifacts can be well-separated. Our work provides a promising continuous-wave magneto-optical approach to optically characterize the static spin Hall angle in a range of SOT devices without the need for the AC current modulation. This work was supported by NSF-ECCS under grants No. 1933301 and 1933297.

Magneto-Optical Detection of Spin-Orbit Torque Phenomena Using Sagnac Interferometer microscope

Spin Orbit Torque (SOT) is an efficient way to electrically manipulate nanoscale magnetic objects for high-speed, high-density and low power spintronic devices1. However, the high critical current density, jc, required to switch the magnetization of a film is a major bottleneck that limits the practical application of SOT in memory devices2. In this work, we achieve an order of magnitude reduction in jc by irradiating magnetic thin films using a focused helium ion beam. These films consist of Pt(2.0)/Co(1.0)/W(1.5) sandwiches (numbers in nm), chosen to have heavy metals with opposite spin Hall angles (Pt, W)3, and they are sufficiently thin to exhibit perpendicular magnetic anisotropy. The critical current required to switch the magnetic state (±Mz) depends on several parameters including saturation magnetization and magnetic anisotropy, all of which are interface dependent, and can be altered using He+ irradiation4. Our key advance is in-situ monitoring of the evolution of the out-of-plane magnetization under local ion irradiation using the anomalous Hall effect (Fig. 1a). In principle, this allows both precise control of the anisotropy and <~10 nm spatial resolution, while avoiding additional lithography steps needed for patterned broad-beam irradiation. The reduction of the jc is determined via Sot switching experiments (Fig. 1b). This work demonstrates a promising and practical approach for the reduced power consumption in SOT-based spintronic devices which opens the prospect of preferential current driven magnetization switching of predetermined sample areas, limited by the resolution of the ion beam microscope, down to the nanometer scale, while preserving the flat topography of the initial magnetic stack.References: 1 I.M. Miron, K. Garello and G. Gaudin, Nature 476, 189 (2011). 2 R. Ramaswamy, J.M. Lee and K. Cai, Appl. Phys. Rev. 5, 031107 (2018). 3 S. Woo, M. Mann and A.J. Tan, Appl. Phys. Lett. 105, 212404 (2014). 4 C. Chappert, H. Bernas and J. Ferré, Science 280, 1919 (1998).

Helium Ion Microscopy for Reduced Spin Orbit Torque Switching Currents

Recently ferromagnets with antisymmetric exchange (e.g. DMI) interactions have been actively investigated, in part because of the nonreciprocal propagation of spin waves where the frequency for positive and negative wavevectors, i.e. +k or -k, is not the same. This occurs because the DMI interaction leads to an effective field which is proportional to the wavevector k. In contrast, we study a system without DMI, but where the exchange interaction varies linearly as a function of position as shown in Fig. 1. Such a structure could be created by nonuniform lateral doping of Cu into Permalloy for example. [1] We also find an effective field which is linear in k, but the directions of the effective field are different from those found in the DMI systems. Using a simple one-dimensional model and a set of coupled Landau-Lifshitz equations, we set the exchange on the right side to be the value for iron, and it is decreased linearly by a factor of three at the left side. A field of 100 mT is applied perpendicular to the chain. The length of the system is 1 micron, but larger lengths give similar results. We demonstrate a number of interesting features: (1) The eigenstates are strongly asymmetric and can be localized on one side of the sample or the other [2]; (2) Depending on the frequency of excitation, there can be a huge asymmetry in propagation amplitudes for waves going in opposite directions as seen in Fig. 2, and (3) If a wave is excited at the center of a sample, there is a large asymmetry in propagation speed for waves travelling in different directions, where waves travelling in the region where the exchange is larger propagate at a higher speed than waves travelling where the exchange is smaller. We compare our results with analytic calculations, with reasonable agreement. We discuss the potential for applications such as isolators at the end.References: [1] N. Sorensen, R. E. Camley, and Z. Celinski, J. Magn and Magn. Mat. Vol. 477, p 344 (2019) [2] K L Livesey, D C Crew, R L Stamps, Phys. Rev. B Vol. 73, p. 184432 (2006)

Nonreciprocal Behavior in Ferromagnets with Spatially Varying Exchange

Spin waves (or magnons) in a micrometer-sized disk magnetized in the vortex state offer an ideal playground to investigate nonlinear magnetization dynamics. In the past, we demonstrated that the radial spin waves in a vortex, once excited above their instability threshold decay into secondary azimuthal modes due to highly efficient spontaneous three-magnon splitting in a rich variety of scattering channels [1]. Here, we present a combined numerical, theoretical and experimental study on nonlocal stimulated splitting in a magnetic vortex disk. We show that three-magnon splitting can be triggered below the threshold of spontaneous splitting by coupling the magnetic vortex to magnons propagating in an adjacent waveguide. Furthermore, using nonlinear spin-wave theory and time-resolved Brillouin-light-scattering experiments we demonstrate that stimulated scattering can be used to manipulate the time scales of nonlinear magnetization dynamics. We believe that the possibility to actively control three-magnon splitting in confined magnetic elements could provide a way to use magnon-based nonlinear networks as hardware e.g. for neuromorphic computing. Financial support by the Deutsche Forschungsgemeinschaft within programmes SCHU 2922/1-1 and KA 5069/1-1 is gratefully acknowledged.References: [1] K. Schultheiss, et al. PRL 122, 097202 (2019) [2] L. Körber, et al. arXiv:2005.12663 (submitted)

Nonlocal stimulation of three-magnon splitting in a magnetic vortex

Spin waves can be excited by a radio-frequency (rf) real magnetic field or an effective one generated e.g. by a surface acoustic wave (SAW) using magneto-elasticity [1,2]. Thanks to their low attenuation, SAWs in the GHz frequency range are an ideal tool to address remotely magnetic structures and generate or actuate on spin waves quasi-resonantly, which could be implemented in magnonic devices. Although the dynamic strain created by the SAW remains weak (10-5-10-3), non-linear magnetization dynamics is acoustically induced even in moderately magnetostrictive ferromagnetic layers. In order to become of technological interest these non-linearities must be carefully characterized and modeled. Using a time- and spatially-resolved magneto-optical Kerr setup with laser detection synchronized to the SAW rf bursts [3], we evidence clear non-linear effects (frequency and wavevector doubling: f/2f and k/2k components, respectively) in the magnetization dynamics of a GaMnAs ferromagnetic layer [4]. Tuning the spin-wave frequency close to the SAW frequency by magnetic field and temperature the resonance behavior of both the f and 2f dynamical components are obtained. The dependence on these components on the strain amplitude reveals two regimes. In the low-strain regime the f (2f) component has a linear (quadratic) behavior with the SAW amplitude. We show that this regime is well accounted for by an all-analytical perturbative model of two coupled parametric oscillators [5] with SAW-dependent frequency, damping, coupling and force terms while the intrinsic magnetic non-linearities of the Landau-Lifschitz-Gilbert equation can be neglected. With increasing SAW amplitude, the f-component becomes sublinear and the peak of the SAW-induced ferromagnetic resonance curve shifts to lower magnetic field, which are signatures of the rising importance of intrinsic magnetic nonlinearities as shown by our numerical simulations. We thus reach a comprehensive description of the acoustically-driven magnetization dynamics, enabling further development of this magnon-phonon coupling.References: [1] L. Dreher, M. Weiler, M. Pernpeintner et al., Phys. Rev. B 86, 134415 (2012). [2] L. Thevenard, C. Gourdon et al., Phys. Rev. B 90, 094401 (2014). [3] P. Kuszewski, J.-Y. Duquesne, L. Becerra et. al., Phys. Rev. Appl. 10, 034036 (2018). [4] M. Kraimia, P. Kuszewski, J.-Y. Duquesne et al., Phys. Rev. B 101, 144425 (2020). [5] C. L. Chang, A. M. Lomonosov, J. Janusonis et al., Phys. Rev. B 95, 060409 (2017).

Non-linearities Induced by Surface Acoustic Waves in Magnetization Dynamics

Optical frequency combs are powerful tools used for synchronization, stabilization and frequency conversion in both fundamental science and technical applications. In this work, we present experimental observations on the generation of a spin wave frequency comb in a low damping Co25Fe75 conduit measured using Brillouin light scattering microscopy. By driving the magnetization to large precession angles, nonlinear interactions such as four magnon scattering can be observed. When applying two RF signals with independently tunable frequencies and amplitudes to our microstructure, we can actively control the final states that will be populated by these scattering processes. Our results show the generation of a frequency comb, consisting of several spin waves with adjustable frequency spacing and amplitude. We demonstrate that the known effect of frequency mixing for k=0 modes [1] can be extended towards propagating spin waves. This enables simultaneous information transport and processing. This behaviour is studied for different sample geometries, which allow mixing of co-propagating as well as counter-propagating spin waves. Our observations are in qualitative agreement with micro magnetic simulations. The presented data encourage a deeper understanding of the interaction of propagating spin waves in the nonlinear regime and propose utilization of spin wave frequency combs as broadband tunable clocks for information processing. The authors acknowledge financial support from the Deutsche Forschungsgemeinschaft within programs SCHU 2922/1-1, WE5386/4-1 and WE5386/5-1. K. S. acknowledges funding within the Helmholtz Postdoc Programme.References: [1] Marsh, J., & Camley, R. E., Physical Review B - Condensed Matter and Materials Physics, 86(22), 224405 (2012)

Generation and tuning of a spin wave frequency comb

Recently, the formation of a magnon Bose-Einstein Condensate (BEC) triggered by the rapid cooling of magnonic nano-structures was reported [1]. A rapid decrease in the phonon temperature achieved by the application of DC pulses to a nano-sized YIG/Pt sample leads to a non-equilibrium between the phononic and the magnonic system. This results in a redistribution of magnons to the lowest frequencies of the spectrum. Here we report on the application of such a non-equilibrium, showing the possibiltiy to amplify coherently excited spin waves. The structures under investigation (see Fig. 1) consist of a 34 nm thin and 2 µm broad YIG-waveguide. A 3 µm long area is covered with a 7 nm thin layer of platinum, and an antenna allows for the excitation of a propagating spin-wave packet. The magnetization dynamics is investigated using time-resolved micro-focussed Brillouin light scattering spectroscopy. After the applied DC pulse is switched off, a spin wave pulse excited by the antenna is propagating in the waveguide region below the Pt covered area during rapid cooling. Depending on the time-delay between the DC-pulse and the spin-wave package, an amplification of the propagating spin wave is observed (see Fig. 2). This research does not only show the applicability of the phenomenon of rapid cooling to compensate the intrinsic damping in spintronic devices [2], but also gives insight to new physics, namely the interaction of a prepared coherent state with the rapid cooling induced quantum state of the magnon BEC. This research has been supported by ERC StG 678309 MagnonCircuits, ERC ADG 694709 SuperMagnonics and DFU Grant DU 1427/2-1.References: [1] M. Schneider, T. Brächer, D. Breitbach, et. al., Bose-Einstein Condensation of Quasi-Particles by Rapid Cooling, Nat. Nanotechnol. 15, 457–461 (2020) [2] Q. Wang, M. Kewenig, M. Schneider, et. al., Realization of a nanoscale magnonic directional coupler for all-magnon circuits, arXiv:1905.12353

Amplification of Propagating Spin Waves by Rapid Cooling

Current-induced spin-orbit torques (SOT) have attracted great attention for their unique ability to manipulate the magnetization of ferromagnets and antiferromagnets [1]. SOT-induced switching offers speed and reliability comparable to or better than spin transfer torque (STT) switching, as was shown in nanodots [2,3] and magnetic tunnel junctions (MTJ) [4,5]. However, whereas the STT-driven switching dynamics of MTJs has been extensively studied [6-8], less is known about the transient dynamics and actual speed of the magnetization reversal induced by SOT. In this study we investigate the reversal dynamics of SOT switching in 3-terminal MTJs and show how the interplay of voltage control of magnetic anisotropy (VCMA) and STT can be used to optimize the switching efficiency [9,10]. We report real-time measurements of in-field and field-free SOT switching and disentangle the combined impact of SOT, STT, and VCMA on the switching speed and efficiency. We show that the combination of these effects leads to reproducible sub-ns switching with an extremely narrow distribution of the switching times without the aid of an external field. Our 3-terminal devices are fabricated using a fully compatible CMOS process [11] and are based on CoFeB/MgO/CoFeB MTJs grown on a b-W SOT-injection line and patterned into 80 nm pillars (Fig. 1a). The field-free switching functionality is enabled by an in-plane magnet embedded into a hard-mask [12], which provides a symmetry-breaking magnetic field to the magnetization of the free layer (Fig. 1b). Our electrical setup combines after-pulse and real-time detection [13] allowing for the exploration of individual SOT switching events in the time domain as well as of their statistical distributions. The voltage time traces of individual switching events exhibit a finite incubation delay followed by a single-jump reversal, after which the magnetization remains quiescent in the final state (Fig. 1c,d) [13]. Whereas complete magnetization reversal occurs within ≈1 ns, the incubation delay can take a substantial part of the total switching time in close-to-critical conditions. This incubation time, which is not expected for the “instant-on” SOT in perpendicular MTJs, can be minimized by a moderate increase of the SOT current (compare Figs. 1c and 1d), resulting in a very narrow distribution of the switching latency (Fig. 1e) [14]. A similar effect is achieved by increasing the external magnetic field strength or by biasing the MTJ. We attribute the two-steps switching process to the nucleation of a reversed domain and propagation of a domain-wall across the free layer, as supported by micromagnetic simulations (Fig. 1f). The model reveals that a key element to the observed dynamics is the reduction of magnetic anisotropy of the free layer related to the current-induced temperature rise [13]. The results further evidence a significant dependence of the switching speed and reversal onset on the MTJ bias. In Fig. 1g, averaged time traces obtained for different bias conditions clearly show that the bias accelerates the switching process. Finally, from symmetry considerations, we show that the contributions of STT and VCMA can be separated, unraveling their distinct impact on the magnetization dynamics.References: [1] A. Manchon, J. Zelezný, I. M. Miron, et al. Rev. Mod. Phys. 91, 035004 (2019) | [2] K. Garello, C. O. Avci, I. M. Miron, et al. Appl. Phys Lett. 105, 212402 (2014) | [3] M. Baumgartner, K. Garello, J. Mendil, et al. Nat. Nanotech. 12, 980-986 (2017) | [4] S. V. Aradhya, G. E. Rowlands, J. Oh, et al. Nano Lett, 16, 5987-5992 (2016) | [5] M. Cubukcu, O. Boulle, N. Mikuszeit, et al. IEEE Trans. Magn. 54, 9300204 (2018) | [6] Y.-T. Cui, G. Finocchio, C. Wang, et al. Phys. Rev. Lett. 104, 097201 (2010) | [7] C. Hahn, G. Wolf, B. Kardasz, et al. Phys. Rev. B 94, 214432 (2016) | [8] T. Devolder, J.-V. Kim, F. Garcia-Sanchez, et al. Phys Rev. B 93, 024420 (2016) | [9] H. Yoda, H. Sugiyama, T. Inokuchi, et al. IEEE Int. Mem. Wkshp. (2017) | [10] A. van den Brink, S. Cosemans, S. Cornelissen, et al. Apply. Phys. Lett. 104, 012403 (2014) | [11] K. Garello, F. Yasin, S. Couet, et al. IEEE Symp. VLSI Circ., 81-82 (2018) | [12] K. Garello, F. Yasin, H. Hody, et al. IEEE Symp. VLSI Circ., T194-195 (2019) |[13] E. Grimaldi, V. Krizakova, G. Sala, et al. Nat. Nanotech. 15, 111-117 (2020) | [14] V. Krizakova, K. Garello, E. Grimaldi, et al. Appl. Phys. Lett. 116, 232406 (2020)

Real-Time Measurements of Field-Free Spin-Orbit Torque Switching in 3-Terminal Magnetic Tunnel Junctions INVITED

The individual spins associated with nitrogen-vacancy (NV) centers in diamond can serve as exquisite nanoscale magnetic field sensors, enabling (among other things) the measurement of stray fields near YIG [1] and Py [2] films influenced by spin transfer torques. This presentation provides an overview of our latest efforts to (i) reliably fabricate high-quality Py/Pt nanowires on a single-crystal diamond substrate while maintaining the performance of NVs implanted 10's of nanometers below the surface, (ii) develop a Bayesian protocol for optimal estimation of NV spin relaxation, and (iii) estimate thermal time scales in these (and other) nanocircuits while calibrating the applied microwave current. Time permitting, I will also discuss preliminary measurements (microwave transport and NV magnetometry) of driven and thermally populated spin wave modes controlled by spin Hall torques.References: [1] C. Du, T. van der Sar, et al., Science, 357, 195-198 (2017) [2] A. Solyom, Z. Flansberry, et al., Nano Lett., 18, 6494-6499 (2018)

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