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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).

MMM 2020

Non-linearities Induced by Surface Acoustic Waves in Magnetization Dynamics

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

Magnetic transition-metal silicides and germanides, crystallizing in the B20 cubic structure with broken inversion symmetry, have attracted much attention in the context of Dzyaloshinskii-Moriya interactions, helical spin structures, and magnetic skyrmions [1, 2]. Finding skyrmions in confined geometries such as nanoparticles and nanowires is particularly intriguing from the viewpoints of fundamental science and practical applications [3]. Such low-dimensional structures also often show size-induced magnetic properties as compared to corresponding bulk alloys [4]. We have used density-functional-theory (DFT) calculations and cluster-deposition experiments to investigate the size dependence of magnetic properties in equiatomic CoSi; the average particle size d of the clusters varies from about 0.6 nm to 11.6 nm. In sharp contrast to bulk CoSi, which is nonmagnetic down to liquid helium temperature, the nanoclusters order magnetically with a net low-temperature magnetic moment from 0.69 to 0.21 μB/Co as d varies from 0.6 to 11.6 nm. The fast Fourier transform (FFT) of the HRTEM image (Fig. 1a) and x-ray diffraction pattern (not shown here) of the sample having d = 11.6 nm confirm the cubic B20 structure. The corresponding DC susceptibility curves display anomalies in limited field (about 20 – 200 Oe) and temperature (100 K – 300 K) ranges (Fig. 1b), which are similar to the signature of helical or skyrmion-like spin structures. DC susceptibility and anomalous Hall resistivity data are used to determine a field-temperature magnetic phase diagram that includes a skyrmionic region and to discuss the confinement effect on skyrmions within the small diameter of CoSi nanoclusters.This research is supported by the US DOE/BES (DE-FG02-04ER46152) and performed in part in the Nebraska Nanoscale Facility and the NCMN, which are supported by the U.S. NSF (NNCI -1542182), and the Nebraska Research Initiative (NRI).References: [1] N. Nagaosa and Y. Tokura, Nature Nanotech. 8, 899 (2013). [2] B. Balasubramanian, P. Manchanda, R. Pahari, Z. Chen, W. Zhang, S.R. Valloppilly, X. Li, A. Sarella, L. Yue, A. Ullah, P. Dev, D. A. Muller, R. Skomski, G. C. Hadjipanayis, and D.J. Sellmyer, Phys. Rev. Lett. 124, 057201 (2020). [3] B. Das, B. Balasubramanian, R. Skomski, P. Mukherjee, S.R. Valloppilly, G.C. Hadjipanayis, and D.J. Sellmyer, Nanoscale. 10, 9504 (2018). [4] B. Balasubramanian, M. Sakurai, C.-Z. Wang, X. Xu, K.-M. Ho, J. R. Chelikowsky and D. J. Sellmyer, Mol. Syst. Des. Eng. DOI: 10.1039/d0me00050g (2020).

Size-Dependent Magnetism and Skyrmionic Properties in CoSi Nanoclusters

This work shows that Co-rich microwires (MWs) with nearly zero magnetostriction have colossal heating efficiency under radiofrequency fields.[1] MWs of 31 µm diameter and 5 mm length show a specific loss power (SLP) of 3000 W/g at 36 Oe and 625 kHz. The SLP varies with the MWs length and number. The role of length lies on the magnetic domains that change from radial to axial when the length is reduced, as deduced from the hysteresis curve shapes, and makes SLP to decrease by a factor of 10 when the length switch from 5 to 15 mm, see Fig. 1. The number of MWs sets side by side determine the magnetostatic interactions which affect to the remanence (Mr) and susceptibility: Mr = 80% for 2 to 6 MWs and then decreases to Mr = 50% for 10 MWs, suggesting the formation of closure domains that diminish the magnetostatic energy. This change of the hysteresis loop shapes also influences the SLP. In this work, it is assumed that this colossal heating efficiency is dominated by the eddy-currents, although a small contribution from hysteresis losses cannot be ruled out. The eddy currents are generated by electromagnetic induction and lead to Joule heating of the material. The eddy–currents in Co-rich MWs are enhanced by the magnetization reversal and, thus, the magnetic susceptibility becomes a key factor for the heating efficiency. This magnetic susceptibility is given by the change of the magnetic domain with the length, with the circumferential domains playing probable the main role at high frequency. Therefore, short MWs with nearly zero magnetostriction are key candidates to show colossal heating efficiencyReferences: [1] I. Morales, D. Archilla, P. de la Presa, et al., Sc. Report 10, 602 (2020).

Colossal heating efficiency for nearly zero magnetostrictive amorphous microwires via eddy currents at radiofrequency fields.

Fe3O4 (FeF), MnxFe3-xO4 (Mn1, Mn3, Mn5 for x = 0.1, 0.3, 0.5) and CoxFe3-xO4 (Co1, Co3, Co5 for x = 0.1, 0.3, 0.5) nanoparticles (NPs) were synthesized using co-precipitation technique to study the effect of factors that influence the effective specific absorption rate (ESAR). The samples were characterized using XRD, TEM, VSM, TMA and ESR. The heating efficiency was probed employing infrared thermography at ac field of 4 kA/m and frequency 500 kHz [1, 2]. The particle sizes are in the range of 10-13 nm, except Co5 which is 40 nm. The saturation magnetization (Ms) of the samples at 300 K is between 55-66 emu/g. The coercivity (Hc) of the Mn-doped samples is below 33 Oe where it increased up to 548 Oe with Co-doping. The low-temperature (15 K) hysteresis show a decrease in Hc with Mn-doping and enhancement with Co from 326 to 180 and 4345 Oe, respectively. Fig. 1 shows the ESR spectra from which the effective magnetic anisotropy (Keff) was computed. While the values are between 15.3-16.5 kJ/m3 for the Mn-doped samples, an increase in Keff of 20.9 (Co1) and 31.3 kJ/m3 (Co3) is observed with Co-doping reflecting the effect of particle size and doping. ESAR vs. magnetic anisotropy energy (KeffV) was theoretically and experimentally estimated (Fig. 2), where V is the volume of the particle. The highest and lowest ESAR (theoretical) of 1124 and 89 × 10-9 Wg-1Oe-2Hz-1 was obtained for Mn5 and Mn3, respectively. In contrast, the experimental ESAR (right axis) was the highest for Mn3 with a value of 21 × 10-9 Wg-1Oe-2Hz-1 and decreased with KeffV. The ESAR of FeF is 20 × 10-9 Wg-1Oe-2Hz-1. The deviation in the experimental from the theoretical values of the Mn-doped samples is mainly due to the distribution in particle sizes, whereas the decrease in ESAR with Co-doping from 20 to 18 × 10-9 Wg-1Oe-2Hz1 was as per the linear response theory (LRT) [3]. Our superparamagnetic NPs produce heat in accordance with LRT. The decreasing trend in ESAR with Co-doping in Fe3O4 is correlated with anisotropy, whereas with Mn-doping, particle size distribution plays a significant role rather than anisotropy.References: [1] J.S. Anandhi, G.A. Jacob and R.J. Joseyphus, Mater. Res. Express, 6, 015045 (2019) [2] J.S. Anandhi, G.A. Jacob and R.J. Joseyphus, J. Magn. Magn. Mater., 512, 166992 (2020) [3] J. Carrey, B. Mehdaoui and M. Respaud, J. Appl. Phys., 109, 083921 (2011)

Insights on the Heating Characteristics of Mn and Co-doped Fe3O4

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

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)

Non-linearities Induced by Surface Acoustic Waves in Magnetization Dynamics

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