Spin-wave emission with current-controlled frequency by a PMA-based spin-Hall oscillator

Spin wave emission and propagation in magnonic waveguides represent a highly promising alternative for beyond-CMOS computing. It is therefore all the more important to fully understand the underlying physics of the emission process. Here, we use time-resolved scanning transmission x-ray microscopy to directly image the formation process of the globally excited local emission of spin waves in a permalloy waveguide at the nanoscale. Thereby, we observe spin wave emission from the corner of the waveguide as well as from a local oscillation of a domain-wall-like structure within the waveguide. Additionally, an isofrequency contour analysis is used to fully explain the origin of quasicylindrical spin wave excitation from the corner and its concurrent nonreflection and nonrefraction at the domain interface. This study is complemented by micromagnetic simulations which perfectly fit the experimental findings. Thus, we clarify the fundamental question of the emission mechanisms in magnonic waveguides which lay the basis for future magnonic operations.

Iron garnets as an important type of low-damping magnetic insulator can provide an ideal platform for the field of magnonics. In this work, we study the propagation of spin waves in a 60 nm-thick TmIG film with perpendicular magnetic anisotropy using all-electrical spin wave spectroscopy. The magnetostatic forward volume mode spin waves show a fully reciprocal propagation. By sweeping out-of-plane magnetic fields in the low-field regime, spin textures are created and observed; meanwhile, the spin wave mode vanishes, which indicates that propagating spin waves are filtered by the spin textures. By applying a large in-plane field, spin wave propagation in a Damon–Eshbach configuration is studied. Our findings provide a potential method to explore reconfigurable magnonic devices.

Spin waves are collective excitations of a spin system, where the magnetic moments precess with a spatially periodic phase shift that determines the wavelength [1]. From a technological point of view, the use of spin waves as signal carriers in future spintronic logic and memory devices has the advantages of a potentially lower power consumption and improved miniaturization prospects compared to the present charge-based CMOS technology [2]. For achieving nanoscale integration, topological spin textures such as magnetic vortex cores can be driven by alternating magnetic fields to excite coherent spin waves with short, sub-micrometer wavelengths, as shown recently for both synthetic ferrimagnetic systems and single ferromagnetic layers [3, 4]. In this contribution, we will demonstrate the versatility of this excitation mechanism by showing that the application of a static magnetic bias field makes the vortex core a manipulable spin-wave source that can be continuously translated in space without altering the resulting spin-wave dispersion relation [5]. We employ time-resolved scanning transmission x-ray microscopy (TR-STXM) to directly image vortex-core spin textures as well as the emission and propagation of spin waves from them.By applying a static in-plane magnetic bias field, we can continuously displace the vortex core from its equilibrium position in the center of a structured element. For a synthetic ferrimagnet (Co/Ru/Ni81Fe19), it is possible to shift the core relatively close to the edge while maintaining a radial, isotropic spin-wave emission pattern (see Figure 1). The wavelengths of the excited spin waves are not noticeably changed by the applied magnetic bias field, but remain tunable by the driving frequency in the same way as without bias field.For a single Ni81Fe19 layer with a thickness of the order of 100 nm, we observe a similar behavior for relatively small magnetic bias fields but when the vortex core approaches the edge of the disk, it also expands (see Figure 2). This expansion can be seen as a transformation from a zero-dimensional point source to a one-dimensional curved object where its shape and extent is controlled by the magnitude of the applied magnetic bias field. Such an expansion leads to a directional emission of the spin waves that propagate away from the core in mainly two opposite directions rather than radially as observed for non-expanded cores. For certain combinations of magnetic bias fields and driving frequencies, focusing effects appear. Such effects provide promising means for a controlled and directional propagation of spin waves without the need for additional patterning or waveguides. **

Nanocontact spin-torque oscillators are devices in which the generation of propagating spin waves can be sustained by spin transfer torque. In the present paper, we perform combined electrical and optical measurements in a single experimental setup to systematically investigate the excitation of spin waves by a nanocontact spin-torque oscillator and their propagation in a Ni80Fe20 extended layer. By using microfocused Brillouin light scattering we observe an anisotropic emission of spin waves, due to the broken symmetry imposed by the inhomogeneous Oersted field generated by the injected current. In particular, spin waves propagate on the side of the nanocontact where the Oersted field and the in-plane component of the applied magnetic field are antiparallel, while propagation is inhibited on the opposite side. Moreover, propagating spin waves are efficiently excited only in a limited frequency range corresponding to wavevectors inversely proportional to the size of the nanocontact. This frequency range obeys the dispersion relation for exchange-dominated spin waves in the far field, as confirmed by micromagnetic simulations of similar devices. The present results have direct consequences for spin wave based applications, such as synchronization, computation, and magnonics.

Magnonic holographic memory is a type of memory that uses spin waves for magnetic bit read-in and read-out. Its operation is based on the interaction between magnets and propagating spin waves where the phase and the amplitude of the spin wave are sensitive to the magnetic field produced by the magnet. Memory states 0 and 1 are associated with the presence/absence of the magnet in a specific location. In this work, we present experimental data showing the feasibility of magnetic bit location using spin waves. The testbed consists of four micro-antennas covered by Y3Fe2(FeO4)3 yttrium iron garnet (YIG) film. A constant in-plane bias magnetic field is provided by NdFeB permanent magnet. The magnetic bit is made of strips of magnetic steel to maximize interaction with propagating spin waves. In the first set of experiments, the position of the bit was concluded by the change produced in the transmittance between two antennas. The minima appear at different frequencies and show different depths for different positions of the bit. In the second set of experiments, two input spin waves were generated, where the phase difference between the waves is controlled by the phase shifter. The minima in the transmitted spectra appear at different phases for different positions of magnetic bit. The utilization of the structured bit enhances its interaction with propagating spin waves and improves recognition fidelity compared to a regular-shaped bit. The recognition accuracy is further improved by exploiting spin wave interference. The depth of the transmission minima corresponding to different magnet positions may exceed 30 dB. All experiments are accomplished at room temperature. Overall, the presented data demonstrate the practical feasibility of using spin waves for magnetic bit red-out. The practical challenges are also discussed.

Multifrequency Spin Wave Device for Parallel Data Processing using Micro Structured Yttrium Iron Garnet Thin Films

Directional spin-wave propagation in the skyrmion chain

Spin-wave propagation and spin-wave induced domain wall motion in nanostrips with a Néel wall are studied by micromagnetic simulations. It is found that the reflection of spin waves by the wall can be resonantly excited due to the interaction between spin waves and domain-wall normal modes. With the decrease of the saturation magnetization Ms (and the consequent increase of the wall width), the reflection is diminished and complete transmission can occur. The domain wall motion induced by spin waves is closely related to the spin-wave reflectivity of the wall, and may exhibit different types of behavior. The reflected spin waves (or magnons) give rise to a magnonic linear momentum-transfer torque, which drives the wall to move along the spin wave propagation direction. The maximal velocity of the domain wall motion corresponds to the resonance reflection of the spin waves. The transmitted spin waves (or magnons) lead to a magnonic spin-transfer torque, which drags the wall to move backwardly. The complicated domain wall motion can be described qualitatively by a one-dimensional model incorporating both the magnonic linear momentum-transfer torque and the magnonic spin-transfer torque. The results obtained here may find use in designing magnonic nanodevices.

Magnetic materials are at the hearts of billions of high frequency communication devices and on-chip integration of magnetic microwave devices is of paramount importance for efficient utilization of the huge electromagnetic (EM) spectrum beyond 5G. Magnonics – a sub-field of spintronics – employs magnetic waves and oscillations in magnetic thin films and patterned nanostructures for processing GHz to sub-THz EM signal [1-2]. Magnetic ferrites are conventionally used in such magnetic microwave devices. However, due to the need for external bias magnetic field and incompatibility with complementary metal oxide semiconductor (CMOS) process, ferrites are not suitable for miniaturized microwave components. On the other hand, metallic magnetic thin films and nanostructures have great potential for efficient engineering of microwaves. Although, the need for bias field remains a bottleneck. We have been working on solutions where the requirement of the bias-field is absent. We have successfully demonstrated several strategies for achieving such device architecture by utilizing self-biased nanomagnets with reprogrammable remanent states which are associated with distinct magnetization dynamics [2-11].To illustrate reconfigurable microwave properties, we have shown in Fig 1 as an example, a pair of dipolarly coupled rhomboid nanomagnets (RNMs). Two different remanent states (↑↑ and ↑↓) are obtained by utilizing a simple field initialization (HI) scheme: applying a saturating field along short and long axes of the RNMs with subsequent removal of the field (Fig. 1(a)). Due to different distributions of the stray fields for the two remanent states, the effective fields (Fig. 1(b)) are different which manifest in the shift of the microwave spectra for the two remanent states. Measurement of microwave properties from a single isolated nanomagnetic pair was obtained by using micro-focused Brillouin light scattering (micro-BLS) experiment (Fig. 1(c)) and the micro-BLS spectra are shown in Fig. 1(d). This strategy for reconfigurable magnonic responses is expanded to 2D arrays of the RNMs for different magnetic configurations: antiferromagnetic-type and ferrimagnetic-type artificial magnonic crystals. The maximum amount of the shift in the microwave responses is achieved by using multilayer isolated as well as dipolar-coupled networks of RNMs. Beyond, RNM shape, we have also demonstrated reconfigurable microwave operation based on other strategic shapes with multiple remanent states, such as arrow-, C-, L- and S-type nanomagnets and zigzag nanowires.Furthermore, we emphasize that such self-biased nanomagnets are also suitable for magnonic device applications where the propagation and gating of magnons – quanta for spin waves – are of primary interest. Conventionally, a large bias magnetic field is used in order to satisfy an orthogonal orientation between spin wave propagation and magnetization direction for efficient transmission characteristics (known as surface geometry or Damon-Eshbach mode). The need of such bias field hinders device integration on-chip for magnonic waveguides. Therefore, we have proposed and demonstrated a self-biased magnonic waveguide based on dipolar-coupled but physically separated chain of RNMs (Fig. 2). A prototype of such magnonic devices is shown in Fig. 2(a) where a microwave antenna (input) excites the spin waves and the spin waves are detected using micro-BLS technique with a focused laser spot (output). In order to gate the spin wave propagation, we have flipped a RNM in the waveguide and it is marked as ‘gate’ in the scanning electron microscopy (SEM) image (Fig. 2(b)). Such waveguide design enables one to have two different remanent states: ferromagnetically ordered (FO) and FO with a defect (FO*) when field initialized (same scheme as mentioned above) along the width and the length of the waveguide, respectively. FO and FO* remanent magnetic states are shown in Fig. 2(b) using magnetic force microscopy (MFM) images. Gating of the spin wave propagation has been shown by plotting 2D spatial profiles of the spin wave intensities using micro-BLS technique which clearly indicate gated magnon flow for the FO* state in comparison to the FO state. Thus, one can also achieve binary gating of output signal amplitude using such self-biased nanomagnetic waveguide which is remarkable as it also eliminates the need for bias field.In this presentation, we would like to emphasize the need for bias-free reconfigurable magnonics along with recent developments and future roadmap. **

Objectives. Nonreciprocal spin wave effects can manifest themselves in metalized films of ferrite garnets. By studying the dynamics of spin waves in micro- and nano-scale magnetic films, the possibility of using multilayer dielectric films of yttrium iron garnet (YIG) to ensure the manifestation of the nonreciprocity effect is demonstrated. This approach offers advantages compared to the use of a layered YIG/metal structure due to significantly lower spin-wave losses in the two-layer YIG film consisting of layers with different values of magnetization. Such films can be used in logical elements to create controllable Mach-Zehnder interferometers based on magnonic principles. The purpose of this work is to reconcile the concept of nonreciprocal spin-wave propagation of a signal with the simultaneous manifestation of the effects arising from the propagation of spin waves in microwave guides formed by finite-width YIG films.Methods. We used an experimental microwave spectroscopy method based on a vector network analyzer along with a finite difference method to perform a numerical simulation of the dispersion characteristics of spin waves in two-layer magnonic microwave guides. An analytical model was also used to obtain a dispersion equation based on the magnetostatic approximation.Results. Based on measurements of the amplitude and phase responses, the possible coexistence of two frequency ranges for the propagation of a spin-wave signal in a two-layer magnon microwave guide based on a YIG film formed by two layers with different values of saturation magnetization was demonstrated. Regimes of nonreciprocal propagation of a spin-wave signal were revealed. A numerical model was using to study the formation mechanisms of spin wave modes in the spectrum of a two-layer structure formed due to the finite dimensions of the microwave guide. An analytical model was used to evaluate the transformation of the mode spectrum. The experimental data are in good agreement with the results of the proposed numerical and analytical models.Conclusions. The possibility of frequency-selective propagation of spin waves in a magnon microwaveguide consisting of two layers with different saturation magnetization values is demonstrated. Multimode propagation of spin waves can occur inside a two-layer structure in two frequency ranges. At the same time, this process is accompanied by a strong nonreciprocity of spin-wave signal propagation, which manifests itself in a change in the amplitude and phase responses when the direction of the external magnetic field is reversed. The proposed two-layer spin-wave waveguide concept can be used in the manufacture of magnon interconnects and magnon interferometers with the support of multiband regimes of operation.

Spin waves are promising candidates to carry, transport, and process information. Controlling the propagation characteristics of spin waves in magnetic materials is an essential ingredient for designing spin-wave based computing architectures. Here, we study the influence of surface inhomogeneities on the spin-wave signals transmitted through thin films. We use micromagnetic simulations to study the spin-wave dynamics in an in-plane magnetized yttrium iron garnet thin film with a thickness in the nanometre range in the presence of surface defects in the form of locally introduced uniaxial anisotropies. These defects are used to demonstrate that the Backward Volume Magnetostatic Spin Waves (BVMSW) are more responsive to backscattering in comparison to Magnetostatic Surface Spin Waves (MSSWs). For this particular defect type, the reason for this behavior can be quantitatively related to the difference in the magnon band structures for the two types of spin waves. To demonstrate this, we develop a quasi-analytical theory for the scattering process. It shows an excellent agreement with the micromagnetic simulations, sheds light on the backscattering processes and provides a new way to analyze the spin-wave transmission rates in the presence of surface inhomogeneities in sufficiently thin films, for which the role of exchange energy in the spin-wave dynamics is significant. Our study paves the way to designing magnonic logic devices for data processing which rely on a designed control of the spin-wave transmission.

The motion of magnetic skyrmions driven by propagating spin waves (SWs) in a skyrmion-based magnetic nanotrack is investigated by means of micromagnetic simulation. It is found that the propagating SWs can drive the skyrmion into a stream motion. The velocity of the skyrmion motion is controlled by the changes of SWs frequency and exciting field amplitude, which is sensitive to the size of skyrmion.

We investigated the dynamics of spin waves in micro-patterned Permalloy thin films using time-resolved magneto-optic Kerr effect microscopy (TR-MOKE). By applying an external magnetic field, we observe the field dependence of spin wave signals with picosecond resolution. Fourier transform analysis of the signals confirms their agreement with the dispersion relation, demonstrating the successful detection of propagating spin waves using the MOKE technique. Furthermore, we perform dynamic measurements of interfering spin waves generated by a V-shaped antenna. The experimental results reveal differences in spin wave amplitude at each detection point. In combination with simulation analysis based on wave propagation from the V-shaped antenna, we reproduced the experimental results and revealed the existence of a protective zone.

The Landau-Lifshitz equation with a scalar damping constant predicts that the damping of spin waves propagating in an infinite homogeneous magnetic medium does not depend on the direction of propagation. This is not the case in materials with a periodic arrangement of magnetic constituents (known as magnonic crystals). In this paper, the plane wave method is extended to include damping in the calculation of the dispersion and relaxation of spin waves in three-dimensional magnonic crystals. A model material system is introduced and calculations are then presented for magnonic crystals realized in the direct and inverted structure and for two different filling fractions. The ability of magnonic crystals to support the propagation of spin waves is characterized in terms of a figure of merit, defined as the ratio of the spin wave frequency to the decay constant. The calculations reveal that in magnonic crystals with a modulated value of the relaxation constant, the figure of merit depends strongly on the frequency and wave vector of the spin waves, with the dependence determined by the spatial distribution of the spin wave amplitude within the unit cell of the magnonic crystal. Bands and directions of exceptionally long spin wave propagation have been identified. The results are also discussed in terms of the use of magnonic crystals as metamaterials with designed magnetic permeability.

One current goal of spintronics is the development of a sustainable information technology based on the transport of pure spin currents. One promising way to do this is to use spin waves (SWs), the elementary excitations of magnetically ordered materials: by collective precession of magnetic moments, they can transport angular momentum. SW information processing also offers interesting alternatives to conventional microelectronics [1]. For this, yttrium iron garnet (YIG), an insulating ferrimagnet, is the ideal material because it has the lowest magnetic damping. Furthermore, thanks to the spin orbit torque (SOT), it is possible to control the relaxation time of SWs in YIG by an electric current injected into an adjacent platinum layer [2]. However, such metal/insulator hybrid devices presently have certain limitations, as a sudden drop in the amplitude of the main mode beyond a certain excitation threshold, which originates from nonlinear coupling with other SW modes [2].Different strategies can be considered to overcome these issues. In nanopatterned samples the available SW modes become quantized, which severely limits the available nonlinear processes. As a result, nonlinear saturation thresholds are postponed, which allows to reach much higher amplitudes of single mode dynamics [3]. The perpendicular magnetic anisotropy (PMA) can also be used to control the sign of the nonlinear frequency shift. Recently, the growth of ultra-thin films of Bismuth doped YIG (BiYIG) with tunable PMA has been achieved while preserving a high dynamic quality [4]. It was shown that the emission characteristics of SWs emitted by SOT in thin BiYIG films where PMA compensates the in-plane shape anisotropy are greatly improved [5].Here, we study the magnetization dynamics in individual nanodisks patterned from such a 30 nm thick BiYIG film, with diameters ranging from 1 µm down to 200 nm. The static magnetic field is applied perpendicularly to the sample plane. To excite the ferromagnetic resonance (FMR) of the BiYIG nanodisks, we use the spatially uniform in-plane microwave field produced by an antenna integrated on top. To detect it, we employ a magnetic resonance force microscope [6] in which a cobalt nanosphere grown at the tip of a soft cantilever [7] is dipolarly coupled to the longitudinal component of the magnetization of the nanodisk positioned underneath (Fig. 1).By studying the SW spectra of these BiYIG nanodisks in the linear regime, we find that their effective anisotropy field is weakly dependent of the diameter and negative, about -10 mT, which means that the PMA slightly overcompensates the shape anisotropy. The damping parameter is found to increase as the diameter is decreased and lies in the high 10-4 – low 10-3 range for all disks.We then perform measurement of the main resonance line, corresponding to the quasi-uniform mode, as a function of the microwave power injected into the antenna, which is varied by up to four orders of magnitude (excitation field ranging from 0.03 mT to 3 mT at 5 GHz). For all the disks, we observe a distortion of the resonance line at intermediate excitation power, corresponding to the onset of foldover. As expected, due to the negative effective anisotropy field, the resonance line shifts towards higher magnetic field as the precession angle increases, which is opposite to the behavior reported on undoped YIG nanodisks [3]. For the largest BiYIG disks, the dynamics witnessed at higher power is quite more complex and interesting, as shown in Fig. 2 for the 700 nm diameter nanodisk. We observe a rapid saturation of the peak amplitude, corresponding to average precession angles of the order of 10° to 20°, accompanied with a broadening of the line towards both lower and higher magnetic field. To understand this behavior, we perform extensive micromagnetic simulations. Using the magnetic parameters extracted in the linear regime and the nominal geometry of the nanodisks, these simulations reproduce the main characteristics of the measured FMR lines in the strongly nonlinear regime. They reveal that a dynamic instability is responsible of the observed behavior: as the amplitude of the quasi-uniform mode increases with the driving field, its precession profile gets more and more localized at the center of the disk, which eventually leads to the formation of a dynamic soliton similar to a wave bullet [8]. Moreover, this soliton is not stable over time, resulting in a rich temporal dynamics, which, depending on the exact driving conditions, can be quasi-periodic or intermittent. To experimentally access this complex temporal dynamics, we use the method introduced in [3], which consists in applying a second, much weaker excitation field of varying frequency, in addition to the main driving field at high power. The obtained frequency modulation spectra indeed reflect the existence of rich low-frequency temporal variations in the dynamics of the magnetization, as suggested by the simulations. **