Emission and propagation of 1D and 2D spin waves with nanoscale wavelengths in anisotropic spin textures

High data rate spin-wave transmitter

Spin-wave devices have recently become a strong competitor in computing and information processing owing to their excellent energy efficiency. Researchers have explored magnons, the quanta of spin-waves, as an information carrier and significant progress has occurred in both excitation and computation. However, most transmission designs remain immature in terms of data rate and information complexity as they only utilize simple spin-wave pulses and suffer from signal distortion. In this work, using micromagnetic simulations, we demonstrate a spin-wave transmitter that operates reliably at a data rate of 4 Gbps over significant (multi-micron) distances with error rates as low as 10-14. Spin-wave amplitude is used to encode information. Carrier frequency and data rate are carefully chosen to restrict dispersion spreading, which is the main reason for signal distortion. We show that this device can be integrated into either pure-magnonic circuits or modern electronic networks. Our study reveals the potential for achieving an even higher data rate of 10 Gbps and also offers a comprehensive and logical methodology for performance tuning.

Steerable current-driven emission of spin waves in magnetic vortex pairs

The efficient excitation of spin waves is a key challenge in the realization of magnonic devices. We demonstrate current-driven generation of spin waves in antiferromagnetically coupled magnetic vortices. We use time-resolved x-ray microscopy to directly image the emission of spin waves upon the application of alternating currents flowing directly through the magnetic stack. Micromagnetic simulations allow us to identify the current-driven Oersted field as the main origin of excitation, in contrast to spin-transfer torques. In our case, these internal Oersted fields have an orders of magnitude higher spin-wave excitation efficiency than commonly used stripline antennas. For magnetostrictive materials, we furthermore demonstrate that the direction of magnon propagation can be steered by increasing the excitation amplitude, which modifies the underlying magnetization profile through an additional anisotropy. The demonstrated methods allow for the efficient and tunable excitation of spin waves, marking a substantial advance concerning the design of magnonic devices.

Microscopic evaluation of spin and orbital moment in ferromagnetic resonance

Time-resolved X-ray magnetic circular dichroism under the effects of ferromagnetic resonance (FMR), known as X-ray ferromagnetic resonance (XFMR) measurements, enables direct detection of precession dynamics of magnetic moment. Here we demonstrated XFMR measurements and Bayesian analyses as a quantitative probe for the precession of spin and orbital magnetic moments under the FMR effect. Magnetization precessions in two different Pt/Ni-Fe thin film samples were directly detected. Furthermore, the ratio of dynamical spin and orbital magnetic moments was evaluated quantitatively by Bayesian analyses for XFMR energy spectra around the Ni L 2 , 3 absorption edges. Our study paves the way for a microscopic investigation of the contribution of the orbital magnetic moment to magnetization dynamics.

Asymmetric Magnon Frequency Comb

We theoretically show the asymmetric spin wave transmission in a coupled waveguide-skyrmion structure, where the skyrmion acts as an effective nanocavity allowing the whispering gallery modes for magnons. The asymmetry originates from the chiral spin wave mode localized in the circular skyrmion wall. By inputting two-tone excitations and mixing them in the skyrmion wall, we observe a unidirectional output magnon frequency comb propagating in the waveguide with a record number of teeth (>50). This coupled waveguide-cavity structure turns out to be a universal paradigm for generating asymmetric magnon frequency combs, where the cavity can be generalized to other magnetic structures that support the whispering gallery mode of magnons. Our results advance the understanding of the nonlinear interaction between magnons and magnetic textures and open a new pathway to exploring the asymmetric spin wave transmission and to steering the magnon frequency comb.

Topological Spin Textures in an Insulating van der Waals Ferromagnet

Generation and control of topological spin textures constitutes one of the most exciting challenges of modern spintronics given their potential applications in information storage technologies. Of particular interest are magnetic insulators, which due to low damping, absence of Joule heating and reduced dissipation can provide energy-efficient spin-textures platform. Here, it is demonstrated that the interplay between sample thickness, external magnetic fields, and optical excitations can generate a prolific paramount of spin textures, and their coexistence in insulating CrBr3 van der Waals (vdW) ferromagnets. Using high-resolution magnetic force microscopy and large-scale micromagnetic simulation methods, the existence of a large region in T-B phase diagram is demonstrated where different stripe domains, skyrmion crystals, and magnetic domains exist and can be intrinsically selected or transformed to each-other via a phase-switch mechanism. Lorentz transmission electron microscopy unveils the mixed chirality of the magnetic textures that are of Bloch-type at given conditions but can be further manipulated into Néel-type or hybrid-type via thickness-engineering. The topological phase transformation between the different magnetic objects can be further inspected by standard photoluminescence optical probes resolved by circular polarization indicative of an existence of exciton-skyrmion coupling mechanism. The findings identify vdW magnetic insulators as a promising framework of materials for the manipulation and generation of highly ordered skyrmion lattices relevant for device integration at the atomic level.

Three-dimensional spin-wave dynamics, localization and interference in a synthetic antiferromagnet

Spin waves are collective perturbations in the orientation of the magnetic moments in magnetically ordered materials. Their rich phenomenology is intrinsically three-dimensional; however, the three-dimensional imaging of spin waves has so far not been possible. Here, we image the three-dimensional dynamics of spin waves excited in a synthetic antiferromagnet, with nanoscale spatial resolution and sub-ns temporal resolution, using time-resolved magnetic laminography. In this way, we map the distribution of the spin-wave modes throughout the volume of the structure, revealing unexpected depth-dependent profiles originating from the interlayer dipolar interaction. We experimentally demonstrate the existence of complex three-dimensional interference patterns and analyze them via micromagnetic modelling. We find that these patterns are generated by the superposition of spin waves with non-uniform amplitude profiles, and that their features can be controlled by tuning the composition and structure of the magnetic system. Our results open unforeseen possibilities for the study and manipulation of complex spin-wave modes within nanostructures and magnonic devices.

High-resolution imaging of 3D stray-field components with a Fe3O4 nanoparticle sensor

Despite rapid advances in magnetic domain imaging techniques, high-resolution imaging of 3D magnetic field components remains a great challenge. Magnetic force microscopy has been utilized to observe the 1D magnetic field component from the sample surface; however, the 1D stray-field component lacks sufficient conditions to clarify the nature of nanomagnetism. Herein, we propose a method for the detection of 3D stray-field components by using a Fe3O4-nanoparticle sensor. We employed this Fe3O4-nanoparticle sensor to detect nanoscale magnetic domains, domain walls, and magnetic vortices (resolution ∼5 nm), and our findings demonstrate its potential in imaging both out-of-plane and in-plane magnetic-field components. Our technique overcomes the limitations of 3D stray-field detection and high-resolution imaging and provides the possibility of observing both out-of-plane and in-plane magnetic field components with a 5 nm resolution, thereby paving the way for the development of future spin-based devices.

Twisted van der Waals Quantum Materials: Fundamentals, Tunability, and Applications

Twisted van der Waals (vdW) quantum materials have emerged as a rapidly developing field of two-dimensional (2D) semiconductors. These materials establish a new central research area and provide a promising platform for studying quantum phenomena and investigating the engineering of novel optoelectronic properties such as single photon emission, nonlinear optical response, magnon physics, and topological superconductivity. These captivating electronic and optical properties result from, and can be tailored by, the interlayer coupling using moiré patterns formed by vertically stacking atomic layers with controlled angle misorientation or lattice mismatch. Their outstanding properties and the high degree of tunability position them as compelling building blocks for both compact quantum-enabled devices and classical optoelectronics. This paper offers a comprehensive review of recent advancements in the understanding and manipulation of twisted van der Waals structures and presents a survey of the state-of-the-art research on moiré superlattices, encompassing interdisciplinary interests. It delves into fundamental theories, synthesis and fabrication, and visualization techniques, and the wide range of novel physical phenomena exhibited by these structures, with a focus on their potential for practical device integration in applications ranging from quantum information to biosensors, and including classical optoelectronics such as modulators, light emitting diodes, lasers, and photodetectors. It highlights the unique ability of moiré superlattices to connect multiple disciplines, covering chemistry, electronics, optics, photonics, magnetism, topological and quantum physics. This comprehensive review provides a valuable resource for researchers interested in moiré superlattices, shedding light on their fundamental characteristics and their potential for transformative applications in various fields.

Resonant generation of propagating second-harmonic spin waves in nano-waveguides

Generation of second-harmonic waves is one of the universal nonlinear phenomena that have found numerous technical applications in many modern technologies, in particular, in photonics. This phenomenon also has great potential in the field of magnonics, which considers the use of spin waves in magnetic nanostructures to implement wave-based signal processing and computing. However, due to the strong frequency dependence of the phase velocity of spin waves, resonant phase-matched generation of second-harmonic spin waves has not yet been achieved in practice. Here, we show experimentally that such a process can be realized using a combination of different modes of nano-sized spin-wave waveguides based on low-damping magnetic insulators. We demonstrate that our approach enables efficient spatially-extended energy transfer between interacting waves, which can be controlled by the intensity of the initial wave and the static magnetic field.

True amplification of spin waves in magnonic nano-waveguides

Magnonic nano-devices exploit magnons - quanta of spin waves - to transmit and process information within a single integrated platform that has the potential to outperform traditional semiconductor-based electronics. The main missing cornerstone of this information nanotechnology is an efficient scheme for the amplification of propagating spin waves. The recent discovery of spin-orbit torque provided an elegant mechanism for propagation losses compensation. While partial compensation of the spin-wave losses has been achieved, true amplification - the exponential increase in the spin-wave intensity during propagation - has so far remained elusive. Here we evidence the operating conditions to achieve unambiguous amplification using clocked nanoseconds-long spin-orbit torque pulses in magnonic nano-waveguides, where the effective magnetization has been engineered to be close to zero to suppress the detrimental magnon scattering. We achieve an exponential increase in the intensity of propagating spin waves up to 500% at a propagation distance of several micrometers.

Coherent Magnons with Giant Nonreciprocity at Nanoscale Wavelengths

Nonreciprocal wave propagation arises in systems with broken time-reversal symmetry and is key to the functionality of devices, such as isolators or circulators, in microwave, photonic, and acoustic applications. In magnetic systems, collective wave excitations known as magnon quasiparticles have so far yielded moderate nonreciprocities, mainly observed by means of incoherent thermal magnon spectra, while their occurrence as coherent spin waves (magnon ensembles with identical phase) is yet to be demonstrated. Here, we report the direct observation of strongly nonreciprocal propagating coherent spin waves in a patterned element of a ferromagnetic bilayer stack with antiparallel magnetic orientations. We use time-resolved scanning transmission X-ray microscopy (TR-STXM) to directly image the layer-collective dynamics of spin waves with wavelengths ranging from 5 μm down to 100 nm emergent at frequencies between 500 MHz and 5 GHz. The experimentally observed nonreciprocity factor of these counter-propagating waves is greater than 10 with respect to both group velocities and specific wavelengths. Our experimental findings are supported by the results from an analytic theory, and their peculiarities are further discussed in terms of caustic spin-wave focusing.

Probing spin waves in Co3O4 nanoparticles for magnonics applications

The magnetic properties of spinel nanoparticles can be controlled by synthesizing particles of a specific shape and size. The synthesized nanorods, nanodots and cubic nanoparticles have different crystal planes selectively exposed on the surface. The surface effects on the static magnetic properties are well documented, while their influence on spin waves dispersion is still being debated. Our ability to manipulate spin waves using surface and defect engineering in magnetic nanoparticles is the key to designing magnonic devices. We synthesized cubic and spherical nanoparticles of a classical antiferromagnetic material Co3O4 to study the shape and size effects on their static and dynamic magnetic proprieties. Using a combination of experimental methods, we probed the magnetic and crystal structures of our samples and directly measured spin wave dispersions using inelastic neutron scattering. We found a weak, but unquestionable, increase in exchange interactions for the cubic nanoparticles as compared to spherical nanoparticle and bulk powder reference samples. Interestingly, the exchange interactions in spherical nanoparticles have bulk-like properties, despite a ferromagnetic contribution from canted surface spins.

Zero-Field Spin Waves in YIG Nanowaveguides

Spin-wave-based transmission and processing of information is a promising emerging nanotechnology that can help overcome limitations of traditional electronics based on the transfer of electrical charge. Among the most important challenges for this technology is the implementation of spin-wave devices that can operate without the need for an external bias magnetic field. Here we experimentally demonstrate that this can be achieved using submicrometer wide spin-wave waveguides fabricated from ultrathin films of a low-loss magnetic insulator, yttrium iron garnet (YIG). We show that these waveguides exhibit a highly stable single-domain static magnetic configuration at zero field and support long-range propagation of spin waves with gigahertz frequencies. The experimental results are supported by micromagnetic simulations, which additionally provide information for the optimization of zero-field guiding structures. Our findings create the basis for the development of energy-efficient zero-field spin-wave devices and circuits.

Spontaneous periodic polarization wave in helielectric fluids

By analogy with spin waves in ferromagnetic systems, the polarization (or dipole) wave is the electric counterpart that remains elusive. Here, we discover that the helielectricity, i.e. a polarization field with helicoidal helices that corresponds to a quasi-layered chiral nematic environment, causes a spontaneous formation of large-scale polarization waves in the form of the sinusoidal function. Both experimental and theoretical analyses reveal that the polarization ordering over a threshold polarization strength violates the inherent periodicity of the polarization helices, thus penalizing the compression energy. It drives a second-order structural transition to a periodically modulated polarization wave state. The roles of chirality and confinement condition are discussed.

Long-Distance Coherent Propagation of High-Velocity Antiferromagnetic Spin Waves

We report on coherent propagation of antiferromagnetic (AFM) spin waves over a long distance (∼10  μm) at room temperature in a canted AFM α-Fe_{2}O_{3} owing to the Dzyaloshinskii-Moriya interaction (DMI). Unprecedented high group velocities (up to 22.5  km/s) are characterized by microwave transmission using all-electrical spin wave spectroscopy. We derive analytically AFM spin-wave dispersion in the presence of the DMI which accounts for our experimental results. The AFM spin waves excited by nanometric coplanar waveguides have large wave vectors in the exchange regime and follow a quasilinear dispersion relation. Fitting of experimental data with our theoretical model yields an AFM exchange stiffness length of 1.7  Å. Our results provide key insights on AFM spin dynamics and demonstrate high-speed functionality for AFM magnonics.

Influence of Dzyaloshinskii-Moriya interaction and perpendicular anisotropy on spin waves propagation in stripe domain patterns and spin spirals

Texture-based magnonics focuses on the utilization of spin waves in magnetization textures to process information. Using micromagnetic simulations, we study how (1) the dynamic magnetic susceptibility, (2) dispersion relations, and (3) the equilibrium magnetic configurations in periodic magnetization textures in a ultrathin ferromagnetic film in remanence depend on the values of the Dzyaloshinskii-Moriya interaction and the perpendicular magnetocrystalline anisotropy. We observe that for large Dzyaloshinskii-Moriya interaction values, spin spirals with periods of tens of nanometers are the preferred state; for small Dzyaloshinskii-Moriya interaction values and large anisotropies, stripe domain patterns with over a thousand times larger period are preferable. We observe and explain the selectivity of the excitation of resonant modes by a linearly polarized microwave field. We study the propagation of spin waves along and perpendicular to the direction of the periodicity. For propagation along the direction of the periodicity, we observe a bandgap that closes and reopens, which is accompanied by a swap in the order of the bands. For waves propagating in the perpendicular direction, some modes can be used for unidirectional channeling of spin waves. Overall, our findings are promising in sensing and signal processing applications and explain the fundamental properties of periodic magnetization textures.

Electrically Active Domain Wall Magnons in Layered van der Waals Antiferromagnets

We study, theoretically, domain wall (DW) magnons-elementary collective excitations of magnetic DWs-in easy-axis layered van der Waals (vdW) antiferromagnets, where they behave as normal modes of coupled spin superfluids. We uncover that, due to spin-charge coupling in vdW magnets, such DW magnons can be activated by voltage-induced torques, thereby providing a path for their low-dissipation and nanoscale excitation. Moreover, the electrical activation and the number of DW magnons at a frequency can be controlled by applying symmetry-breaking static magnetic field, adding tunability of signal transmission by them. Our results highlight that domain walls in vdW magnets provide a promising platform to route coherent spin information for a broad range of explorations in spintronics and magnetism.

Filtering and Imaging of Frequency-Degenerate Spin Waves Using Nanopositioning of a Single-Spin Sensor

Nitrogen-vacancy (NV) magnetometry is a new technique for imaging spin waves in magnetic materials. It detects spin waves by their microwave magnetic stray fields, which decay evanescently on the scale of the spin-wavelength. Here, we use nanoscale control of a single-NV sensor as a wavelength filter to characterize frequency-degenerate spin waves excited by a microstrip in a thin-film magnetic insulator. With the NV probe in contact with the magnet, we observe an incoherent mixture of thermal and microwave-driven spin waves. By retracting the tip, we progressively suppress the small-wavelength modes until a single coherent mode emerges from the mixture. In-contact scans at low drive power surprisingly show occupation of the entire isofrequency contour of the two-dimensional spin-wave dispersion despite our one-dimensional microstrip geometry. Our distance-tunable filter sheds light on the spin-wave band occupation under microwave excitation and opens opportunities for imaging magnon condensates and other coherent spin-wave modes.

Element-specific visualization of dynamic magnetic coupling in a Co/Py bilayer microstructure

We present the element-specific and time resolved visualization of uniform ferromagnetic resonance excitations of a Permalloy (Py) disk-Cobalt (Co) stripe bilayer microstructure. The transverse high frequency component of the resonantly excited magnetization is sampled in the ps regime by a combination of ferromagnetic resonance (FMR) and scanning transmission X-ray microscopy (STXM-FMR) recording snapshots of the local magnetization precession of Py and Co with nanometer spatial resolution. The approach allows us to individually image the resonant dynamic response of each element, and we find that angular momentum is transferred from the Py disk to the Co stripe and vice versa at their respective resonances. The integral (cavity) FMR spectrum of our sample shows an unexpected additional third resonance. This resonance is observed in the STXM-FMR experiments as well. Our microscopic findings suggest that it is governed by magnetic exchange between Py and Co, showing for the Co stripe a difference in relative phase of the magnetization due to stray field influence.

Omnidirectional flat bands in chiral magnonic crystals

The magnonic band structure of two-dimensional chiral magnonic crystals is theoretically investigated. The proposed metamaterial involves a three-dimensional architecture, where a thin ferromagnetic layer is in contact with a two-dimensional periodic array of heavy-metal square islands. When these two materials are in contact, an anti-symmetric exchange coupling known as the Dzyaloshinskii–Moriya interaction (DMI) arises, which generates nonreciprocal spin waves and chiral magnetic order. The Landau–Lifshitz equation and the plane-wave method are employed to study the dynamic magnetic behavior. A systematic variation of geometric parameters, the DMI constant, and the filling fraction allows the examination of spin-wave propagation features, such as the spatial profiles of the dynamic magnetization, the isofrequency contours, and group velocities. In this study, it is found that omnidirectional flat magnonic bands are induced by a sufficiently strong Dzyaloshinskii–Moriya interaction underneath the heavy-metal islands, where the spin excitations are active. The theoretical results were substantiated by micromagnetic simulations. These findings are relevant for envisioning applications associated with spin-wave-based logic devices, where the nonreciprocity and channeling of the spin waves are of fundamental and practical scientific interest.

Reconfigurable Magnonic Crystals Based on Imprinted Magnetization Textures in Hard and Soft Dipolar-Coupled Bilayers

Reconfigurable magnetization textures offer control of spin waves with promising properties for future low-power beyond-CMOS systems. However, materials with perpendicular magnetic anisotropy (PMA) suitable for stable magnetization-texture formation are characterized by high damping, which limits their applicability in magnonic devices. Here, we propose to overcome this limitation by using hybrid structures, i.e., a PMA layer magnetostatically coupled to a low-damping soft ferromagnetic film. We experimentally show that a periodic stripe-domain texture from a PMA layer is imprinted upon the soft layer and induces a nonreciprocal dispersion relation of the spin waves confined to the low-damping film. Moreover, an asymmetric bandgap features the spin-wave band diagram, which is a clear demonstration of collective spin-wave dynamics, a property characteristic for magnonic crystals with broken time-reversal symmetry. The composite character of the hybrid structure allows for stabilization of two magnetic states at remanence, with parallel and antiparallel orientation of net magnetization in hard and soft layers. The states can be switched using a low external magnetic field; therefore, the proposed system obtains an additional functionality of state reconfigurability. This study offers a link between reconfigurable magnetization textures and low-damping spin-wave dynamics, providing an opportunity to create miniaturized, programmable, and energy-efficient signal processing devices operating at high frequencies.

Spin-Wave Channeling in Magnetization-Graded Nanostrips

Magnetization-graded ferromagnetic nanostrips are proposed as potential prospects to channel spin waves. Here, a controlled reduction of the saturation magnetization enables the localization of the propagating magnetic excitations in the same way that light is controlled in an optical fiber with a varying refraction index. The theoretical approach is based on the dynamic matrix method, where the magnetic nanostrip is divided into small sub-strips. The dipolar and exchange interactions between sub-strips have been considered to reproduce the spin-wave dynamics of the magnonic fiber. The transition from one strip to an infinite thin film is presented for the Damon-Eshbach geometry, where the nature of the spin-wave modes is discussed. An in-depth analysis of the spin-wave transport as a function of the saturation magnetization profile is provided. It is predicted that it is feasible to induce a remarkable channeling of the spin waves along the zones with a reduced saturation magnetization, even when such a reduction is tiny. The results are compared with micromagnetic simulations, where a good agreement is observed between both methods. The findings have relevance for envisioned future spin-wave-based magnonic devices operating at the nanometer scale.

{ScnGdn} Heterometallic Rings: Tunable Ring Topology for Spin-Wave Excitations

Data carriers using spin waves in spintronic and magnonic logic devices offer operation at low power consumption and free of Joule heating yet requiring noncollinear spin structures of small sizes. Heterometallic rings can provide such an opportunity due to the controlled spin-wave transmission within such a confined space. Here, we present a series of {Sc_nGd_n} (n = 4, 6, 8) heterometallic rings, which are the first Sc-Ln clusters to date, with tunable magnetic interactions for spin-wave excitations. By means of time- and temperature-dependent spin dynamics simulations, we are able to predict distinct spin-wave excitations at finite temperatures for Sc₄Gd₄, Sc₆Gd₆, and Sc₈Gd₈. Such a new model is previously unexploited, especially due to the interplay of antiferromagnetic exchange, dipole-dipole interaction, and ring topology at low temperatures, rendering the importance of the latter to spin-wave excitations.

TimeMaxyne: A Shot-Noise Limited, Time-Resolved Pump-and-Probe Acquisition System Capable of 50 GHz Frequencies for Synchrotron-Based X-ray Microscopy

With the advent of modern synchrotron sources, X-ray microscopy was developed as a vigorous tool for imaging material structures with element-specific, structural, chemical and magnetic sensitivity at resolutions down to 25 nm and below. Moreover, the X-ray time structure emitted from the synchrotron source (short bunches of less than 100 ps width) provides a unique possibility to combine high spatial resolution with high temporal resolution for periodic processes by means of pump-and-probe measurements. To that end, TimeMaxyne was developed as a time-resolved acquisition setup for the scanning X-ray microscope MAXYMUS at the BESSY II synchrotron in order to perform high precision, high throughput pump-and-probe imaging. The setup combines a highly sensitive single photon detector, a real time photon sorting system and a dedicated synchronization scheme for aligning various types of sample excitations of up to 50 GHz bandwidth to the photon probe. Hence, TimeMaxyne has been demonstrated to be capable of shot-noise limited, time-resolved imaging, at time resolutions of 50 ps and below, only limited by the X-ray pulse widths of the synchrotron.

Imaging mesoscopic antiferromagnetic spin textures in the dilute limit from single-geometry resonant coherent x-ray diffraction

The detection and manipulation of antiferromagnetic domains and topological antiferromagnetic textures are of central interest to solid-state physics. A fundamental step is identifying tools to probe the mesoscopic texture of an antiferromagnetic order parameter. In this work, we demonstrate that Bragg coherent diffractive imaging can be extended to study the mesoscopic texture of an antiferromagnetic order parameter using resonant magnetic x-ray scattering. We study the onset of the antiferromagnet transition in PrNiO₃, focusing on a temperature regime in which the antiferromagnetic domains are dilute in the beam spot and the coherent diffraction pattern modulating the antiferromagnetic peak is greatly simplified. We demonstrate that it is possible to extract the arrangements and sizes of these domains from single diffraction patterns and show that the approach could be extended to a time-structured light source to study the motion of dilute domains or the motion of topological defects in an antiferromagnetic spin texture.

Low-Loss Nanoscopic Spin-Wave Guiding in Continuous Yttrium Iron Garnet Films

Long-distance transport and control of spin waves through nanochannels is essential for integrated magnonic technology. Current strategies relying on the patterning of single-layer nano-waveguides suffer from a decline of the spin-wave decay length upon downscaling or require large magnetic bias field. Here, we introduce a new waveguiding structure based on low-damping continuous yttrium iron garnet (YIG) films. Rather than patterning the YIG film, we define nanoscopic spin-wave transporting channels within YIG by dipolar coupling to ferromagnetic metal nanostripes. The hybrid material structure offers long-distance transport of spin waves with a decay length of ∼20 μm in 160 nm wide waveguides over a broad frequency range at small bias field. We further evidence that spin waves can be redirected easily by stray-field-induced bends in continuous YIG films. The combination of low-loss spin-wave guiding and straightforward nanofabrication highlights a new approach toward the implementation of magnonic integrated circuits for spin-wave computing.

Edge spin wave transmission through a vertex domain wall in triangular dots

Spin waves (SWs), being usually reflected by domain walls (DWs), could also be channeled along them. Edge SWs yield the interesting, and potentially applicable to real devices property of broadband spin wave confinement to the edges of the structure. Here, we investigate through numerical simulations the propagation of quasi one-dimensional spin waves in triangle-shaped amorphous YIG (Y3Fe5O12) micron sized ferromagnets as a function of the angle aperture. The edge spin waves (ESWs) have been propagated over the corner in triangles of 2 microns side with a fixed thickness of 85 nm. Parameters such as superior vertex angle (in the range of 40$$^\circ $$ ∘ –75$$^\circ $$ ∘ ) and applied magnetic field have been optimized in order to obtain a higher transmission coefficient of the ESWs over the triangle vertex. We observed that for a certain aperture angle for which dominated ESW frequency coincides with one of the localized DW modes, the transmission is maximized near one and the phase shift drops to $$\pi /2$$ π / 2 indicating resonant transmission of ESWs through the upper corner. We compare the obtained results with existing theoretical models. These results could contribute to the development of novel basic elements for spin wave computing.

New Dimension in Magnetism and Superconductivity: 3D and Curvilinear Nanoarchitectures

Traditionally, the primary field, where curvature has been at the heart of research, is the theory of general relativity. In recent studies, however, the impact of curvilinear geometry enters various disciplines, ranging from solid-state physics over soft-matter physics, chemistry, and biology to mathematics, giving rise to a plethora of emerging domains such as curvilinear nematics, curvilinear studies of cell biology, curvilinear semiconductors, superfluidity, optics, 2D van der Waals materials, plasmonics, magnetism, and superconductivity. Here, the state of the art is summarized and prospects for future research in curvilinear solid-state systems exhibiting such fundamental cooperative phenomena as ferromagnetism, antiferromagnetism, and superconductivity are outlined. Highlighting the recent developments and current challenges in theory, fabrication, and characterization of curvilinear micro- and nanostructures, special attention is paid to perspective research directions entailing new physics and to their strong application potential. Overall, the perspective is aimed at crossing the boundaries between the magnetism and superconductivity communities and drawing attention to the conceptual aspects of how extension of structures into the third dimension and curvilinear geometry can modify existing and aid launching novel functionalities. In addition, the perspective should stimulate the development and dissemination of research and development oriented techniques to facilitate rapid transitions from laboratory demonstrations to industry-ready prototypes and eventual products.

Probing Magnetic Defects in Ultra-Scaled Nanowires with Optically Detected Spin Resonance in Nitrogen-Vacancy Center in Diamond

Magnetic nanowires (NWs) are essential building blocks of spintronics devices as they offer tunable magnetic properties and anisotropy through their geometry. While the synthesis and compositional control of NWs have seen major improvements, considerable challenges remain for the characterization of local magnetic features at the nanoscale. Here, we demonstrate nonperturbative field distribution mapping in ultrascaled magnetic nanowires with diameters down to 6 nm by scanning nitrogen-vacancy magnetometry. This enables localized, minimally invasive magnetic imaging with sensitivity down to 3 μT Hz^-1/2. The imaging reveals the presence of weak magnetic inhomogeneities inside in-plane magnetized nanowires that are largely undetectable with standard metrology and can be related to local fluctuations of the NWs' saturation magnetization. In addition, the strong magnetic field confinement in the nanowires allows for the study of the interaction between the stray magnetic field and the nitrogen-vacancy sensor, thus clarifying the contrasting formation mechanisms for technologically relevant magnetic nanostructures.

Creating Ferroic Micropatterns through Geometrical Transformation

The functionality of a ferroic device is intimately coupled to the configuration of domains, domain boundaries, and the possibility for tailoring them. Exemplified with a ferromagnetic system, we present a novel approach which allows the creation of new, metastable multidomain patterns with tailored wall configurations through a self-assembled geometrical transformation. By preparing a magnetic layer system on a polymeric platform including swelling layer, a repeated self-assembled rolling into a multiwinding tubular structure and unrolling of the functional membrane is obtained. When polarizing the rolled-up 3D structure in a simple homogeneous magnetic field, the imprinted configuration translates into a regularly arranged multidomain configuration once the tubular structure is unwound. The process is linked to the employed magnetic anisotropy with respect to the surface normal, and the geometrical transformation connects the angular with the lateral degrees of freedom. This combination offers unparalleled possibilities for designing new magnetic or other ferroic micropatterns.

Applications of nanomagnets as dynamical systems: II

In Part I of this topical review, we discussed dynamical phenomena in nanomagnets, focusing primarily on magnetization reversal with an eye to digital applications. In this part, we address mostly wave-like phenomena in nanomagnets, with emphasis on spin waves in myriad nanomagnetic systems and methods of controlling magnetization dynamics in nanomagnet arrays which may have analog applications. We conclude with a discussion of some interesting spintronic phenomena that undergird the rich physics exhibited by nanomagnet assemblies.

The 2021 Magnonics Roadmap

Magnonics is a budding research field in nanomagnetism and nanoscience that addresses the use of spin waves (magnons) to transmit, store, and process information. The rapid advancements of this field during last one decade in terms of upsurge in research papers, review articles, citations, proposals of devices as well as introduction of new sub-topics prompted us to present the first roadmap on magnonics. This is a collection of 22 sections written by leading experts in this field who review and discuss the current status besides presenting their vision of future perspectives. Today, the principal challenges in applied magnonics are the excitation of sub-100 nm wavelength magnons, their manipulation on the nanoscale and the creation of sub-micrometre devices using low-Gilbert damping magnetic materials and its interconnections to standard electronics. To this end, magnonics offers lower energy consumption, easier integrability and compatibility with CMOS structure, reprogrammability, shorter wavelength, smaller device features, anisotropic properties, negative group velocity, non-reciprocity and efficient tunability by various external stimuli to name a few. Hence, despite being a young research field, magnonics has come a long way since its early inception. This roadmap asserts a milestone for future emerging research directions in magnonics, and hopefully, it will inspire a series of exciting new articles on the same topic in the coming years.

Propagation of Spin Waves in a 2D Vortex Network

Efficient propagation of spin waves in a magnetically coupled vortex is crucial to the development of future magnonic devices. Thus far, only a double vortex can serve as spin-wave emitter or oscillator; the propagation of spin waves in the higher-order vortex is still lacking. Here, we experimentally realize a higher-order vortex (2D vortex network) by a designed nanostructure, containing four cross-type chiral substructures. We employ this vortex network as a waveguide to propagate short-wavelength spin waves (∼100 nm) and demonstrate the possibility of guiding spin waves from one vortex to the network. It is observed that the spin waves can propagate into the network through the nanochannels formed by the Bloch-Néel-type domain walls, with a propagation decay length of several micrometers. This technique paves the way for the development of low-energy, reprogrammable, and miniaturized magnonic devices.

Chiral Emission of Exchange Spin Waves by Magnetic Skyrmions

Spin waves or their quanta magnons raise the prospect to act as information carriers in the absence of Joule heating. The challenge to excite spin waves with nanoscale wavelengths free of nanolithography becomes a critical bottleneck for the application of nanomagnonics. Magnetic skyrmions are chiral magnetic textures at the nanoscale. In this work, short-wavelength exchange spin waves are demonstrated to be chirally emitted in a low damping magnetic insulating thin film by magnetic skyrmions. The spin-wave chirality originates from the chiral spin pumping effect and is determined by the cross product of the magnetization orientation and the film normal direction. The Halbach effect explains the enhancement or attenuation of the spin-wave amplitude with a reversed sign of the Dyzaloshinskii-Moriya interaction. Controllable spin-wave propagation is demonstrated by rotating a moderate applied field. Our findings are key for building compact low-power nanomagnonic devices based on intrinsic nanoscale magnetic textures.

Spin-Wave Emission from Vortex Cores under Static Magnetic Bias Fields

We studied the influence of a static in-plane magnetic field on the alternating-field-driven emission of nanoscale spin waves from magnetic vortex cores. Time-resolved scanning transmission X-ray microscopy was used to image spin waves in disk structures of synthetic ferrimagnets and single ferromagnetic layers. For both systems, it was found that an increasing magnetic bias field continuously displaces the wave-emitting vortex core from the center of the disk toward its edge without noticeably altering the spin-wave dispersion relation. In the case of the single-layer disk, an anisotropic lateral expansion of the core occurs at higher magnetic fields, which leads to a directional rather than radial-isotropic emission and propagation of waves. Micromagnetic simulations confirm these findings and further show that focusing effects occur in such systems, depending on the shape of the core and controlled by the static magnetic bias field.

Imaging non-collinear antiferromagnetic textures via single spin relaxometry

Antiferromagnetic materials are promising platforms for next-generation spintronics owing to their fast dynamics and high robustness against parasitic magnetic fields. However, nanoscale imaging of the magnetic order in such materials with zero net magnetization remains a major experimental challenge. Here we show that non-collinear antiferromagnetic spin textures can be imaged by probing the magnetic noise they locally produce via thermal populations of magnons. To this end, we perform nanoscale, all-optical relaxometry with a scanning quantum sensor based on a single nitrogen-vacancy (NV) defect in diamond. Magnetic noise is detected through an increase of the spin relaxation rate of the NV defect, which results in an overall reduction of its photoluminescence signal under continuous laser illumination. As a proof-of-concept, the efficiency of the method is demonstrated by imaging various spin textures in synthetic antiferromagnets, including domain walls, spin spirals and antiferromagnetic skyrmions. This imaging procedure could be extended to a large class of intrinsic antiferromagnets and opens up new opportunities for studying the physics of localized spin wave modes for magnonics.

Magnetic resonance imaging of spin-wave transport and interference in a magnetic insulator

Spin waves-the elementary excitations of magnetic materials-are prime candidate signal carriers for low-dissipation information processing. Being able to image coherent spin-wave transport is crucial for developing interference-based spin-wave devices. We introduce magnetic resonance imaging of the microwave magnetic stray fields that are generated by spin waves as a new approach for imaging coherent spin-wave transport. We realize this approach using a dense layer of electronic sensor spins in a diamond chip, which combines the ability to detect small magnetic fields with a sensitivity to their polarization. Focusing on a thin-film magnetic insulator, we quantify spin-wave amplitudes, visualize spin-wave dispersion and interference, and demonstrate time-domain measurements of spin-wave packets. We theoretically explain the observed anisotropic spin-wave patterns in terms of chiral spin-wave excitation and stray-field coupling to the sensor spins. Our results pave the way for probing spin waves in atomically thin magnets, even when embedded between opaque materials.

Spin-wave spectroscopy of individual ferromagnetic nanodisks

The increasing demand for nanoscale magnetic devices requires development of 3D magnetic nanostructures. In this regard, focused electron beam induced deposition (FEBID) is a technique of choice for direct-writing of complex nano-architectures with applications in nanomagnetism, magnon spintronics, and superconducting electronics. However, intrinsic properties of nanomagnets are often poorly known and can hardly be assessed by local optical probe techniques. Here, an original spatially resolved approach is demonstrated for spin-wave spectroscopy of individual circular magnetic elements with sample volumes down to about 10-3 μm3. The key component of the setup is a coplanar waveguide whose microsized central part is placed over a movable substrate with well-separated CoFe-FEBID nanodisks which exhibit standing spin-wave resonances. The circular symmetry of the disks allows for the deduction of the saturation magnetization and the exchange stiffness of the material using an analytical theory. A good correspondence between the results of analytical calculations and micromagnetic simulations is revealed, indicating a validity of the used analytical model going beyond the initial thin-disk approximation used in the theoretical derivation. The presented approach is especially valuable for the characterization of direct-write magnetic elements opening new horizons for 3D nanomagnetism and magnonics.

Helium Ion Microscopy for Reduced Spin Orbit Torque Switching Currents

Spin orbit torque driven switching is a favorable way to manipulate nanoscale magnetic objects for both memory and wireless communication devices. The critical current required to switch from one magnetic state to another depends on the geometry and the intrinsic properties of the materials used, which are difficult to control locally. Here, we demonstrate how focused helium ion beam irradiation can modulate the local magnetic anisotropy of a Co thin film at the microscopic scale. Real-time in situ characterization using the anomalous Hall effect showed up to an order of magnitude reduction of the magnetic anisotropy under irradiation, with multilevel switching demonstrated. The result is that spin-switching current densities, down to 800 kA cm^-2, can be achieved on predetermined areas of the film, without the need for lithography. The ability to vary critical currents spatially has implications not only for storage elements but also neuromorphic and probabilistic computing.

Nanoimaging of Ultrashort Magnon Emission by Ferromagnetic Grating Couplers at GHz Frequencies

On-chip signal processing at microwave frequencies is key for modern mobile communication. When one aims at small footprints, low power consumption, reprogrammable filters, and delay lines, magnons in low-damping ferrimagnets offer great promise. Ferromagnetic grating couplers have been reported to be specifically useful as microwave-to-magnon transducers. However, their interconversion efficiency is unknown and real-space measurements of the emitted magnon wavelengths have not yet been accomplished. Here, we image with subwavelength spatial resolution the magnon emission process into ferrimagnetic yttrium iron garnet (YIG) at frequencies up to 8 GHz. We evidence propagating magnons of a wavelength of 98.7 nm underneath the gratings, which enter the YIG without a phase jump. Counterintuitively, the magnons exhibit an even increased amplitude in YIG, which is unexpected and due to a further wavelength conversion process. Our results are of key importance for magnonic components, which efficiently control microwave signals on the nanoscale.

Tunable Magnon-Magnon Coupling Mediated by Dynamic Dipolar Interaction in Synthetic Antiferromagnets

We report an experimental observation of magnon-magnon coupling in interlayer exchange coupled synthetic antiferromagnets of FeCoB/Ru/FeCoB layers. An anticrossing gap of spin-wave resonance between acoustic and optic modes appears when the external magnetic field points to the direction tilted from the spin-wave propagation. The magnitude of the gap (i.e., coupling strength) can be controlled by changing the direction of the in-plane magnetic field and also enhanced by increasing the wave number of excited spin waves. We find that the coupling strength under the specified conditions is larger than the dissipation rates of both the resonance modes, indicating that a strong coupling regime is satisfied. A theoretical analysis based on the Landau-Lifshitz equation shows quantitative agreement with the experiments and indicates that the anticrossing gap appears when the exchange symmetry of two magnetizations is broken by the spin-wave excitation.

Chiral Magnonics: Reprogrammable Nanoscale Spin Wave Networks Based on Chiral Domain Walls

Spin waves offer promising perspectives as information carriers for future computational architectures beyond conventional complementary metal-oxide-semiconductor (CMOS) technology, owing to their benefits for device minimizations and low-ohmic losses. Although plenty of magnonic devices have been proposed previously, scalable nanoscale networks based on spin waves are still missing. Here, we demonstrate a reprogrammable two-dimensional spin wave network by combining the chiral exchange spin waves and chiral domain walls. The spin-wave network can be extended to two dimensions and offers unprecedented control of exchange spin waves. Each cell in the network can excite, transmit, and detect spin waves independently in the chiral domain wall, and spin-wave logics are also demonstrated. Our results open up perspectives for integrating spin waves into future logic and computing circuits and networks.

Switchable giant nonreciprocal frequency shift of propagating spin waves in synthetic antiferromagnets

The nonreciprocity of propagating spin waves, i.e., the difference in amplitude and/or frequency depending on the propagation direction, is essential for the realization of spin wave-based logic circuits. However, the nonreciprocal frequency shifts demonstrated so far are not large enough for applications because they originate from interfacial effects. In addition, switching of the spin wave nonreciprocity in the electrical way remains a challenging issue. Here, we show a switchable giant nonreciprocal frequency shift of propagating spin waves in interlayer exchange-coupled synthetic antiferromagnets. The observed frequency shift is attributed to large asymmetric spin wave dispersion caused by a mutual dipolar interaction between two magnetic layers. Furthermore, we find that the sign of the frequency shift depends on relative configuration of two magnetizations, based on which we demonstrate an electrical switching of the nonreciprocity. Our findings provide a route for switchable and highly nonreciprocal spin wave-based applications.

Efficient wavelength conversion of exchange magnons below 100 nm by magnetic coplanar waveguides

Exchange magnons are essential for unprecedented miniaturization of GHz electronics and magnon-based logic. However, their efficient excitation via microwave fields is still a challenge. Current methods including nanocontacts and grating couplers require advanced nanofabrication tools which limit the broad usage. Here, we report efficient emission and detection of exchange magnons using micron-sized coplanar waveguides (CPWs) into which we integrated ferromagnetic (m) layers. We excited magnons in a broad frequency band with wavelengths λ down to 100 nm propagating over macroscopic distances in thin yttrium iron garnet. Applying time- and spatially resolved Brillouin light scattering as well as micromagnetic simulations we evidence a significant wavelength conversion process near mCPWs via tunable inhomogeneous fields. We show how optimized mCPWs can form microwave-to-magnon transducers providing phase-coherent exchange magnons with λ of 37 nm. Without any nanofabrication they allow one to harvest the advantages of nanomagnonics by antenna designs exploited in conventional microwave circuits.

Optically Inspired Nanomagnonics with Nonreciprocal Spin Waves in Synthetic Antiferromagnets

Integrated optically inspired wave-based processing is envisioned to outperform digital architectures in specific tasks, such as image processing and speech recognition. In this view, spin waves represent a promising route due to their nanoscale wavelength in the gigahertz frequency range and rich phenomenology. Here, a versatile, optically inspired platform using spin waves is realized, demonstrating the wavefront engineering, focusing, and robust interference of spin waves with nanoscale wavelength. In particular, magnonic nanoantennas based on tailored spin textures are used for launching spatially shaped coherent wavefronts, diffraction-limited spin-wave beams, and generating robust multi-beam interference patterns, which spatially extend for several times the spin-wave wavelength. Furthermore, it is shown that intriguing features, such as resilience to back reflection, naturally arise from the spin-wave nonreciprocity in synthetic antiferromagnets, preserving the high quality of the interference patterns from spurious counterpropagating modes. This work represents a fundamental step toward the realization of nanoscale optically inspired devices based on spin waves.

Temperature Dependence of the Magnetic Properties of IrMn/CoFeB/Ru/CoFeB Exchange Biased Synthetic Antiferromagnets

Synthetic antiferromagnets (SAF) are widely used for a plethora of applications among which data storage, computing, and in the emerging field of magnonics. In this framework, controlling the magnetic properties of SAFs via localized thermal treatments represents a promising route for building novel magnonic materials. In this paper, we study via vibration sample magnetometry the temperature dependence of the magnetic properties of sputtered exchange bias SAFs grown via magnetron sputtering varying the ferromagnetic layers and spacer thickness. Interestingly, we observe a strong, reversible modulation of the exchange field, saturation field, and coupling strength upon heating up to 250 °C. These results suggest that exchange bias SAFs represent promising systems for developing novel artificial magnetic nanomaterials via localized thermal treatment.

Mode-Resolved Detection of Magnetization Dynamics Using X-ray Diffractive Ferromagnetic Resonance

Collective spin excitations of ordered magnetic structures offer great potential for the development of novel spintronic devices. The present approach relies on micromagnetic models to explain the origins of dynamic modes observed by ferromagnetic resonance (FMR) studies, since experimental tools to directly reveal the origins of the complex dynamic behavior are lacking. Here we demonstrate a new approach which combines resonant magnetic X-ray diffraction with FMR, thereby allowing for a reconstruction of the real-space spin dynamics of the system. This new diffractive FMR technique builds on X-ray detected FMR that allows for element-selective dynamic studies, giving unique access to specific wave components of static and dynamic coupling in magnetic heterostructures. In combination with diffraction, FMR is elevated to the level of a modal spectroscopy technique, potentially opening new pathways for the development of spintronic devices.

Magnetization dynamics in artificial spin ice

In this topical review, we present key results of studies on magnetization dynamics in artificial spin ice (ASI), which are arrays of magnetically interacting nanostructures. Recent experimental and theoretical progress in this emerging area, which is at the boundary between research on frustrated magnetism and high-frequency studies of artificially created nanomagnets, is reviewed. The exploration of ASI structures has revealed fascinating discoveries in correlated spin systems. Artificially created spin ice lattices offer unique advantages as they allow for a control of the interactions between the elements by their geometric properties and arrangement. Magnonics, on the other hand, is a field that explores spin dynamics in the gigahertz frequency range in magnetic micro- and nanostructures. In this context, magnonic crystals are particularly important as they allow the modification of spin-wave properties and the observation of band gaps in the resonance spectra. Very recently, there has been considerable progress, experimentally and theoretically, in combining aspects of both fields-artificial spin ice and magnonics-enabling new functionalities in magnonic and spintronic applications using ASI, as well as providing a deeper understanding of geometrical frustration in the gigahertz range. Different approaches for the realization of ASI structures and their experimental characterization in the high-frequency range are described and the appropriate theoretical models and simulations are reviewed. Special attention is devoted to linking these findings to the quasi-static behavior of ASI and dynamic investigations in magnonics in an effort to bridge the gap between both areas further and to stimulate new research endeavors.