Realization of a spin-wave multiplexer

Modulation of Standing Spin Waves in Confined Rectangular Elements

Magnonics is an emerging field within spintronics that focuses on developing novel magnetic devices capable of manipulating information through the modification of spin waves in nanostructures with submicron size. Here, we provide a confined magnetic rectangular element to modulate the standing spin waves, by changing the saturation magnetisation (MS), exchange constant (A), and the aspect ratio of rectangular magnetic elements via micromagnetic simulation. It is found that the bulk mode and the edge mode of the magnetic element form a hybrid with each other. With the decrease in MS, both the Kittel mode and the standing spin waves undergo a shift towards higher frequencies. On the contrary, as A decreases, the frequencies of standing spin waves become smaller, while the Kittel mode is almost unaffected. Moreover, when the length-to-width aspect ratio of the element is increased, standing spin waves along the width and length become split, leading to the observation of additional modes in the magnetic spectra. For each mode, the vibration style is discussed. These spin dynamic modes were further confirmed via FMR experiments, which agree well with the simulation results.

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.

Deeply nonlinear excitation of self-normalized short spin waves

Spin waves are ideal candidates for wave-based computing, but the construction of magnetic circuits is blocked by a lack of an efficient mechanism to excite long-running exchange spin waves with normalized amplitudes. Here, we solve the challenge by exploiting a deeply nonlinear phenomenon for forward volume spin waves in 200-nm-wide nanoscale waveguides and validate our concept using microfocused Brillouin light scattering spectroscopy. An unprecedented nonlinear frequency shift of more than 2 GHz is achieved, corresponding to a magnetization precession angle of 55° and enabling the excitation of spin waves with wavelengths down to 200 nm. The amplitude of the excited spin waves is constant and independent of the input microwave power due to the self-locking nonlinear shift, enabling robust adjustment of the spin-wave amplitudes in future on-chip magnonic integrated circuits.

Dissipative dynamics of optomagnonic nonclassical features via anti-Stokes optical pulses: squeezing, blockade, anti-correlation, and entanglement

We propose a feasible experimental model to investigate the generation and characterization of nonclassical states in a cavity optomagnonic system consisting of a ferromagnetic YIG sphere that simultaneously supports both the magnon mode and two whispering gallery modes of optical photons. The photons undergo the magnon-induced Brillouin light scattering, which is a well-established tool for the cavity-assisted manipulations of magnons as well as magnon spintronics. At first, we derive the desired interaction Hamiltonian under the influence of the anti-Stokes scattering process and then proceed to analyze the dynamical evolution of quantum statistics of photons and magnons as well as their intermodal entanglement. The results show that both photons and magnons generally acquire some nonclassical features, e.g., the strong antibunching and anti-correlation. Interestingly, the system may experience the perfect photon and magnon blockade phenomena, simultaneously. Besides, the nonclassical features may be protected against the unwanted environmental effects for a relatively long time, especially, in the weak driving field regime and when the system is initiated with a small number of particles. However, it should be noted that some fast quantum-classical transitions may occur in-between. Although the unwanted dissipative effects plague the nonclassical features, we show that this system can be adopted to prepare optomagnonic entangled states. The generation of entangled states depends on the initial state of the system and the interaction regime. The intermodal photon-magnon entanglement may be generated and pronounced, especially, if the system is initialized with low intensity even Schrödinger cat state in the strong coupling regime. The cavity-assisted manipulation of magnons is a unique and flexible mechanism that allows an interesting test bed for investigating the interdisciplinary contexts involving quantum optics and spintronics. Moreover, such a hybrid optomagnonic system may be used to design both on-demand single-photon and single-magnon sources and may find potential applications in quantum information processing.

Bias field orientation driven reconfigurable magnonics and magnon-magnon coupling in triangular shaped Ni80Fe20nanodot arrays

Reconfigurable magnonics have attracted intense interest due to their myriad advantages including energy efficiency, easy tunability and miniaturization of on-chip data communication and processing devices. Here, we demonstrate efficient reconfigurability of spin-wave (SW) dynamics as well as SW avoided crossing by varying bias magnetic field orientation in triangular shaped Ni₈₀Fe₂₀nanodot arrays. In particular, for a range of in-plane angles of bias field, we achieve mutual coherence between two lower frequency modes leading to a drastic modification in the ferromagnetic resonance frequency. Significant modification in magnetic stray field distribution is observed at the avoided crossing regime due to anisotropic dipolar interaction between two neighbouring dots. Furthermore, using micromagnetic simulations we demonstrate that the hybrid SW modes propagate longer through an array as opposed to the non-interacting modes present in this system, indicating the possibility of coherent energy transfer of hybrid magnon modes. This result paves the way for the development of integrated on-chip magnonic devices operating in the gigahertz frequency regime.

Tunable interaction between excitons and hybridized magnons in a layered semiconductor

The interaction between distinct excitations in solids is of both fundamental interest and technological importance. One such interaction is the coupling between an exciton, a Coulomb bound electron-hole pair, and a magnon, a collective spin excitation. The recent emergence of van der Waals magnetic semiconductors¹ provides a platform to explore these exciton-magnon interactions and their fundamental properties, such as strong correlation², as well as their photospintronic and quantum transduction³ applications. Here we demonstrate the precise control of coherent exciton-magnon interactions in the layered magnetic semiconductor CrSBr. We varied the direction of an applied magnetic field relative to the crystal axes, and thus the rotational symmetry of the magnetic system⁴. Thereby, we tuned not only the exciton coupling to the bright magnon, but also to an optically dark mode via magnon-magnon hybridization. We further modulated the exciton-magnon coupling and the associated magnon dispersion curves through the application of uniaxial strain. At a critical strain, a dispersionless dark magnon band emerged. Our results demonstrate an unprecedented level of control of the opto-mechanical-magnonic coupling, and a step towards the predictable and controllable implementation of hybrid quantum magnonics^5-11.

{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.

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.

Sensitivity enhancement in magnetic sensor using CoFeB/Y3Fe5O12 resonator

Magnonics, an emerging research field that uses the quanta of spin waves as data carriers, has a potential to dominate the post-CMOS era owing to its intrinsic property of ultra-low power operation. Spin waves can be manipulated by a wide range of parameters; thus, they are suitable for sensing applications in a wide range of physical fields. In this study, we designed a highly sensitive, simple structure, and ultra-low power magnetic sensor using a simple CoFeB/Y₃Fe₅O₁₂ bilayer structure. We demonstrated that the CoFeB/Y₃Fe₅O₁₂ bilayer structure can create a sharp rejection band in its spin-wave transmission spectra. The lowest point of this strong rejection band allows the detection of a small frequency shift owing to the external magnetic field variation. Experimental observations revealed that such a bilayer magnetic sensor exhibits 20 MHz frequency shifts upon the application of an external magnetic field of 0.5 mT. Considering the lowest full width half maximum, which is about 2 MHz, a sensitivity of 10^–2 mT order can be experimentally achieved. Furthermore, the higher sensitivity in the order of 10^–6 T (µT) has been demonstrated using the sharp edge of the rejection band of the CoFeB/Y₃Fe₅O₁₂ bilayer device. A Y-shaped spin waves interference device with two input arms consisting of CoFeB/Y₃Fe₅O₁₂ and Y₃Fe₅O₁₂ has been theoretically investigated. We proposed that such a structure can demonstrate a magnetic sensitivity in the range of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${10}^{-9}$$\end{document}10-9 T (nT) at room temperature. The sensitivity of the sensor can be further enhanced by tuning the width of the CoFeB metal stripe.

Magnonic Metamaterials for Spin-Wave Control with Inhomogeneous Dzyaloshinskii-Moriya Interactions

A magnonic metamaterial in the presence of spatially modulated Dzyaloshinskii-Moriya interaction is theoretically proposed and demonstrated by micromagnetic simulations. By analogy to the fields of photonics, we first establish magnonic Snell's law for spin waves passing through an interface between two media with different dispersion relations due to different Dzyaloshinskii-Moriya interactions. Based on magnonic Snell's law, we find that spin waves can experience total internal reflection. The critical angle of total internal reflection is strongly dependent on the sign and strength of Dzyaloshinskii-Moriya interaction. Furthermore, spin-wave beam fiber and spin-wave lens are designed by utilizing the artificial magnonic metamaterials with inhomogeneous Dzyaloshinskii-Moriya interactions. Our findings open up a rich field of spin waves manipulation for prospective applications in magnonics.

Spin-thermoelectric effects in a quantum dot hybrid system with magnetic insulator

We investigate spin thermoelectric properties of a hybrid system consisting of a single-level quantum dot attached to magnetic insulator and metal electrodes. Magnetic insulator is assumed to be of ferromagnetic type and is a source of magnons, whereas metallic lead is reservoir of electrons. The temperature gradient set between the magnetic insulator and metallic electrodes induces the spin current flowing through the system. The generated spin current of magnonic (electric) type is converted to electric (magnonic) spin current by means of quantum dot. Expanding spin and heat currents flowing through the system, up to linear order, we introduce basic spin thermoelectric coefficients including spin conductance, spin Seebeck and spin Peltier coefficients and heat conductance. We analyse the spin thermoelectric properties of the system in two cases: in the large ondot Coulomb repulsion limit and when these interactions are finite.

Lumped circuit model for inductive antenna spin-wave transducers

We derive a lumped circuit model for inductive antenna spin-wave transducers in the vicinity of a ferromagnetic medium. The model considers the antenna’s Ohmic resistance, its inductance, as well as the additional inductance due to the excitation of ferromagnetic resonance or spin waves in the ferromagnetic medium. As an example, the additional inductance is discussed for a wire antenna on top of a ferromagnetic waveguide, a structure that is characteristic for many magnonic devices and experiments. The model is used to assess the scaling properties and the energy efficiency of inductive antennas. Issues related to scaling antenna transducers to the nanoscale and possible solutions are also addressed.

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.

Reconfigurable Spin-Wave Interferometer at the Nanoscale

Spin waves can transfer information free of electron transport and are promising for wave-based computing technologies with low-power consumption as a solution to severe energy losses in modern electronics. Logic circuits based on the spin-wave interference have been proposed for more than a decade, while it has yet been realized at the nanoscale. Here, we demonstrate the interference of spin waves with wavelengths down to 50 nm in a low-damping magnetic insulator. The constructive and destructive interference of spin waves is detected in the frequency domain using propagating spin-wave spectroscopy, which is further confirmed by the Brillouin light scattering. The interference pattern is found to be highly sensitive to the distance between two magnetic nanowires acting as spin-wave emitters. By controlling the magnetic configurations, one can switch the spin-wave interferometer on and off. Our demonstrations are thus key to the realization of spin-wave computing system based on nonvolatile nanomagnets.

Electric-Field Control of Propagating Spin Waves by Ferroelectric Domain-Wall Motion in a Multiferroic Heterostructure

Magnetoelectric coupling in multiferroic heterostructures offers a promising platform for electric-field control of magnonic devices based on low-power spin-wave transport. Here, electric-field manipulation of the amplitude and phase of propagating spin waves in a ferromagnetic Fe film on top of a ferroelectric BaTiO₃ substrate is demonstrated experimentally. Electric-field effects in this composite material system are mediated by strain coupling between alternating ferroelectric stripe domains with in-plane and perpendicular polarization and fully correlated magnetic anisotropy domains with differing spin-wave transport properties. The propagation of spin waves across the strain-induced magnetic anisotropy domains of the Fe film is directly imaged and it is shown how reversible electric-field-driven motion of ferroelectric domain walls and pinned anisotropy boundaries turns the spin-wave signal on and off. Furthermore, linear electric-field tuning of the spin-wave phase by altering the width of strain-coupled stripe domains is demonstrated. The results provide a new route toward energy-efficient reconfigurable magnonics.

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.

Tunable Damping in Magnetic Nanowires Induced by Chiral Pumping of Spin Waves

Spin-current and spin-wave-based devices have been considered as promising candidates for next-generation information transport and processing and wave-based computing technologies with low-power consumption. Spin pumping has attracted tremendous attention and has led to interesting phenomena, including the line width broadening, which indicates damping enhancement due to energy dissipation. Recently, chiral spin pumping of spin waves has been experimentally realized and theoretically studied in magnetic nanostructures. Here, we experimentally observe by Brillouin light scattering (BLS) microscopy the line width broadening sensitive to magnetization configuration in a hybrid metal-insulator nanostructure consisting of a Co nanowire grating dipolarly coupled to a planar continuous YIG film, consistent with the results of the measured hysteresis loop. Tunable line width broadening has been confirmed independently by propagating spin-wave spectroscopy, where unidirectional spin waves are detected. Position-dependent BLS measurement unravels an oscillating-like behavior of magnon populations in Co nanowire grating, which might result from the magnon trap effect. These results are thus attractive for reconfigurable nanomagnonics devices.

Ballistic Hall Photovoltammetry of Magnetic Resonance in Individual Nanomagnets

We report on ballistic Hall photovoltammetry as a contactless probe of localized spin excitations. Spins resonating in the near field of a two-dimensional electron system are shown to induce a long range electromotive force that we calculate. We use this coupling mechanism to detect the spin wave eigenmodes of a single ferromagnet of sub-100 nm size. The high sensitivity of this detection technique, 380 spins/sqrt[Hz], and its noninvasiveness present advantages for probing magnetization dynamics and spin transport.

Inverse-design magnonic devices

The field of magnonics offers a new type of low-power information processing, in which magnons, the quanta of spin waves, carry and process data instead of electrons. Many magnonic devices were demonstrated recently, but the development of each of them requires specialized investigations and, usually, one device design is suitable for one function only. Here, we introduce the method of inverse-design magnonics, in which any functionality can be specified first, and a feedback-based computational algorithm is used to obtain the device design. We validate this method using the means of micromagnetic simulations. Our proof-of-concept prototype is based on a rectangular ferromagnetic area that can be patterned using square-shaped voids. To demonstrate the universality of this approach, we explore linear, nonlinear and nonreciprocal magnonic functionalities and use the same algorithm to create a magnonic (de-)multiplexer, a nonlinear switch and a circulator. Thus, inverse-design magnonics can be used to develop highly efficient rf applications as well as Boolean and neuromorphic computing building blocks.

Reconfigurable magnonic mode-hybridisation and spectral control in a bicomponent artificial spin ice

Strongly-interacting nanomagnetic arrays are finding increasing use as model host systems for reconfigurable magnonics. The strong inter-element coupling allows for stark spectral differences across a broad microstate space due to shifts in the dipolar field landscape. While these systems have yielded impressive initial results, developing rapid, scaleable means to access a broad range of spectrally-distinct microstates is an open research problem. We present a scheme whereby square artificial spin ice is modified by widening a 'staircase' subset of bars relative to the rest of the array, allowing preparation of any ordered vertex state via simple global-field protocols. Available microstates range from the system ground-state to high-energy 'monopole' states, with rich and distinct microstate-specific magnon spectra observed. Microstate-dependent mode-hybridisation and anticrossings are observed at both remanence and in-field with dynamic coupling strength tunable via microstate-selection. Experimental coupling strengths are found up to g/2π = 0.16 GHz. Microstate control allows fine mode-frequency shifting, gap creation and closing, and active mode number selection.

Time Refraction of Spin Waves

We present an experimental study of time refraction of spin waves (SWs) propagating in microscopic waveguides under the influence of time-varying magnetic fields. Using space- and time-resolved Brillouin light scattering microscopy, we demonstrate that the broken translational symmetry along the time coordinate results in a loss of energy conservation for SWs and thus allows for a broadband and controllable shift of the SW frequency. With an integrated design of SW waveguide and microscopic current line for the generation of strong, nanosecond-long, magnetic field pulses, a conversion efficiency up to 39% of the carrier SW frequency is achieved, significantly larger compared to photonic systems. Given the strength of the magnetic field pulses and its strong impact on the SW dispersion relation, the effect of time refraction can be quantified on a length scale comparable to the SW wavelength. Furthermore, we utilize time refraction to excite SW bursts with pulse durations in the nanosecond range and a frequency shift depending on the pulse polarity.

Emergent Spin Dynamics Enabled by Lattice Interactions in a Bicomponent Artificial Spin Ice

Artificial spin ice (ASI) networks are arrays of nanoscaled magnets that can serve both as models for frustration in atomic spin ice as well as for exploring new spin-wave-based strategies to transmit, process, and store information. Here, we exploit the intricate interplay of the magnetization dynamics of two dissimilar ferromagnetic metals arranged on complementary lattice sites in a square ASI to modulate the spin-wave properties effectively. We show that the interaction between the two sublattices results in unique spectra attributed to each sublattice, and we observe inter- and intralattice dynamics facilitated by the distinct magnetization properties of the two materials. The dynamic properties are systematically studied by angular-dependent broadband ferromagnetic resonance and confirmed by micromagnetic simulations. We show that combining materials with dissimilar magnetic properties enables the realization of a wide range of two-dimensional structures, potentially opening the door to new concepts in nanomagnonics.

Magnonic Bending, Phase Shifting and Interferometry in a 2D Reconfigurable Nanodisk Crystal

Strongly interacting nanomagnetic systems are pivotal across next-generation technologies including reconfigurable magnonics and neuromorphic computation. Controlling magnetization states and local coupling between neighboring nanoelements allows vast reconfigurability and a host of associated functionalities. However, existing designs typically suffer from an inability to tailor interelement coupling post-fabrication and nanoelements restricted to a pair of Ising-like magnetization states. Here, we propose a class of reconfigurable magnonic crystals incorporating nanodisks as the functional element. Ferromagnetic nanodisks are crucially bistable in macrospin and vortex states, allowing interelement coupling to be selectively activated (macrospin) or deactivated (vortex). Through microstate engineering, we leverage the distinct coupling behaviors and magnonic band structures of bistable nanodisks to achieve reprogrammable magnonic waveguiding, bending, gating, and phase-shifting across a 2D network. The potential of nanodisk-based magnonics for wave-based computation is demonstrated via an all-magnon interferometer exhibiting XNOR logic functionality. Local microstate control is achieved here via topological magnetic writing using a magnetic force microscope tip.

Topological Transport of Deconfined Hedgehogs in Magnets

We theoretically investigate the dynamics of magnetic hedgehogs, which are three-dimensional topological spin textures that exist in common magnets, focusing on their transport properties and connections to spintronics. We show that fictitious magnetic monopoles carried by hedgehog textures obey a topological conservation law, based on which a hydrodynamic theory is developed. We propose a nonlocal transport measurement in the disordered phase, where the conservation of the hedgehog flow results in a nonlocal signal decaying inversely proportional to the distance. The bulk-edge correspondence between the hedgehog number and skyrmion number, the fictitious electric charges arising from magnetic dynamics, and the analogy between bound states of hedgehogs in ordered phase and the quark confinement in quantum chromodynamics are also discussed. Our study points to a practical potential in utilizing hedgehog flows for long-range neutral signal propagation or manipulation of skyrmion textures in three-dimensional magnetic materials.

Steering magnonic dynamics and permeability at exceptional points in a parity-time symmetric waveguide

Tuning the magneto optical response and magnetic dynamics are key elements in designing magnetic metamaterials and devices. This theoretical study uncovers a highly effective way of controlling the magnetic permeability via shaping the magnonic properties of coupled magnetic waveguides separated by a nonmagnetic spacer with strong spin–orbit interaction (SOI). We demonstrate how a spacer charge current leads to enhancement of magnetic damping in one waveguide and a decrease in the other, constituting a bias-controlled magnetic parity–time (PT) symmetric system at the verge of the exceptional point where magnetic gains/losses are balanced. We find phenomena inherent to PT-symmetric systems and SOI-driven interfacial structures, including field-controlled magnon power oscillations, nonreciprocal propagation, magnon trapping and enhancement as well as an increased sensitivity to perturbations and abrupt spin reversal. The results point to a new route for designing magnonic waveguides and microstructures with enhanced magnetic response.

The ability to guide and control magnons is central to their potential in future information processing. Here, using a combination of computations and analytical approaches, the authors propose a magnonic waveguide with a unique gain and loss mechanism.

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.

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.

Modal Frustration and Periodicity Breaking in Artificial Spin Ice

Here, an artificial spin ice lattice is introduced that exhibits unique Ising and non-Ising behavior under specific field switching protocols because of the inclusion of coupled nanomagnets into the unit cell. In the Ising regime, a magnetic switching mechanism that generates a uni- or bimodal distribution of states dependent on the alignment of the field is demonstrated with respect to the lattice unit cell. In addition, a method for generating a plethora of randomly distributed energy states across the lattice, consisting of Ising and Landau states, is investigated through magnetic force microscopy and micromagnetic modeling. It is demonstrated that the dispersed energy distribution across the lattice is a result of the intrinsic design and can be finely tuned through control of the incident angle of a critical field. The present manuscript explores a complex frustrated environment beyond the 16-vertex Ising model for the development of novel logic-based technologies.

Distinct handedness of spin wave across the compensation temperatures of ferrimagnets

Antiferromagnetic spin waves have been predicted to offer substantial functionalities for magnonic applications due to the existence of two distinct polarizations, the right-handed and left-handed modes, as well as their ultrafast dynamics. However, experimental investigations have been hampered by the field-immunity of antiferromagnets. Ferrimagnets have been shown to be an alternative platform to study antiferromagnetic spin dynamics. Here we investigate thermally excited spin waves in ferrimagnets across the magnetization compensation and angular momentum compensation temperatures using Brillouin light scattering. Our results show that right-handed and left-handed modes intersect at the angular momentum compensation temperature where pure antiferromagnetic spin waves are expected. A field-induced shift of the mode-crossing point from the angular momentum compensation temperature and the gyromagnetic reversal reveal hitherto unrecognized properties of ferrimagnetic dynamics. We also provide a theoretical understanding of our experimental results. Our work demonstrates important aspects of the physics of ferrimagnetic spin waves and opens up the attractive possibility of ferrimagnet-based magnonic devices.

Propagation of Spin-Wave Packets in Individual Nanosized Yttrium Iron Garnet Magnonic Conduits

Modern-day CMOS-based computation technology is reaching its fundamental limitations. The emerging field of magnonics, which utilizes spin waves for data transport and processing, proposes a promising path to overcome these limitations. Different devices have been demonstrated recently on the macro- and microscale, but the feasibility of the magnonics approach essentially relies on the scalability of the structure feature size down to the extent of a few 10 nm, which are typical sizes for the established CMOS technology. Here, we present a study of propagating spin-wave packets in individual yttrium iron garnet (YIG) conduits with lateral dimensions down to 50 nm. Space and time-resolved microfocused Brillouin-light-scattering (BLS) spectroscopy is used to characterize the YIG nanostructures and measure the spin-wave decay length and group velocity directly. The revealed magnon transport at the scale comparable to the scale of CMOS proves the general feasibility of magnon-based data processing.

Biologically encoded magnonics

Spin wave logic circuits using quantum oscillations of spins (magnons) as carriers of information have been proposed for next generation computing with reduced energy demands and the benefit of easy parallelization. Current realizations of magnonic devices have micrometer sized patterns. Here we demonstrate the feasibility of biogenic nanoparticle chains as the first step to truly nanoscale magnonics at room temperature. Our measurements on magnetosome chains (ca 12 magnetite crystals with 35 nm particle size each), combined with micromagnetic simulations, show that the topology of the magnon bands, namely anisotropy, band deformation, and band gaps are determined by local arrangement and orientation of particles, which in turn depends on the genotype of the bacteria. Our biomagnonic approach offers the exciting prospect of genetically engineering magnonic quantum states in nanoconfined geometries. By connecting mutants of magnetotactic bacteria with different arrangements of magnetite crystals, novel architectures for magnonic computing may be (self-) assembled.

The capability to engineer magnon states in confined geometries is vital to future nano-magnonics. Here the authors demonstrate that the topology of the magnon bands is determined by the local arrangement and orientation of nanoparticles and can be controlled by the genotype of magnetotactic bacteria.

Eigen damping constant of spin waves in ferromagnetic nanostructure

Though varying in nature, all waves share traits in a way that they all follow the superposition principle while also experiencing attenuation as they propagate in space. And thus it is more than common that a comprehensive investigation of one type of wave leads to a discovery that can be extended to all kinds of waves in other fields of research. In the field of magnetism, the wave of interest corresponds to the spin wave (SW). Specifically, there has been a push to use SWs as the next information carriers similar to how electromagnetic waves are used in photonics. At present, the biggest impediment in making SW-based device to be widely adapted is the fact that the SW experiences large attenuation due to the large damping constant. Here, we developed a method to find the SW eigenmodes and show that their respective eigen damping constants can be 40% smaller than the typical material damping constant. From a bigger perspective, this finding means that the attenuation of SW and also other types of waves in general is no more constrained by the material parameters, and it can be controlled by the shape of the waves instead.

Twisted magnon beams carrying orbital angular momentum

Low-energy eigenmode excitations of ferromagnets are spin waves or magnons that can be triggered and guided in magnonic circuits without Ohmic losses and hence are attractive for communicating and processing information. Here we present new types of spin waves that carry a definite and electrically controllable orbital angular momentum (OAM) constituting twisted magnon beams. We show how twisted beams emerge in magnonic waveguides and how to topologically quantify and steer them. A key finding is that the topological charge associated with OAM of a particular beam is tunable externally and protected against magnetic damping. Coupling to an applied electric field via the Aharanov-Casher effect allows for varying the topological charge. This renders possible OAM-based robust, low-energy consuming multiplex magnonic computing, analogously to using photonic OAM in optical communications, and high OAM-based entanglement studies, but here at shorter wavelengths, lower energy consumption, and ready integration in magnonic circuits.

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

Spin waves offer intriguing perspectives for computing and signal processing, because their damping can be lower than the ohmic losses in conventional complementary metal-oxide-semiconductor (CMOS) circuits. Magnetic domain walls show considerable potential as magnonic waveguides for on-chip control of the spatial extent and propagation of spin waves. However, low-loss guidance of spin waves with nanoscale wavelengths and around angled tracks remains to be shown. Here, we demonstrate spin wave control using natural anisotropic features of magnetic order in an interlayer exchange-coupled ferromagnetic bilayer. We employ scanning transmission X-ray microscopy to image the generation of spin waves and their propagation across distances exceeding multiples of the wavelength. Spin waves propagate in extended planar geometries as well as along straight or curved one-dimensional domain walls. We observe wavelengths between 1 μm and 150 nm, with excitation frequencies ranging from 250 MHz to 3 GHz. Our results show routes towards the practical implementation of magnonic waveguides in the form of domain walls in future spin wave logic and computational circuits.

Coherent Excitation of Heterosymmetric Spin Waves with Ultrashort Wavelengths

In the emerging field of magnonics, spin waves are foreseen as signal carriers for future spintronic information processing and communication devices, owing to both the very low power losses and a high device miniaturization potential predicted for short-wavelength spin waves. Yet, the efficient excitation and controlled propagation of nanoscale spin waves remains a severe challenge. Here, we report the observation of high-amplitude, ultrashort dipole-exchange spin waves (down to 80 nm wavelength at 10 GHz frequency) in a ferromagnetic single layer system, coherently excited by the driven dynamics of a spin vortex core. We used time-resolved x-ray microscopy to directly image such propagating spin waves and their excitation over a wide range of frequencies. By further analysis, we found that these waves exhibit a heterosymmetric mode profile, involving regions with anti-Larmor precession sense and purely linear magnetic oscillation. In particular, this mode profile consists of dynamic vortices with laterally alternating helicity, leading to a partial magnetic flux closure over the film thickness, which is explained by a strong and unexpected mode hybridization. This spin-wave phenomenon observed is a general effect inherent to the dynamics of sufficiently thick ferromagnetic single layer films, independent of the specific excitation method employed.

Spin-wave duplexer studied by finite-element micromagnetic simulation

We conceptually designed a robust nano-scale waveguide structure suitable for potential use as a spin-wave duplexer that allows signal propagation only of selected narrow-band frequencies and duplex transmission in a three-port device comprising a receiver, a transmitter, and their common antenna. The waveguide structure combines three different arms and a circular ring, both made of nanostrip waveguides and a single magnetic material for reliably controllable propagations of spin waves. We attribute the observed duplex transmission of spin waves of narrow pass bands to scattering of spin waves by edge solitons placed at contact areas between the arms and the circular ring. This work proposes the first concept of nano-scale magnonic duplexers operating beyond GHz-frequency ranges.

Incoherent Nuclear Resonant Scattering from a Standing Spin Wave

We introduce a method to study the spatial profiles of standing spin waves in ferromagnetic microstructures. The method relies on Nuclear Resonant Scattering of ⁵⁷Fe using a microfocused beam of synchrotron radiation, the transverse coherence length of which is smaller than the length scale of lateral variations in the magnetization dynamics. Using this experimental method, the nuclear resonant scattering signal due to a confined spin wave is determined on the basis of an incoherent superposition model. From the fits of the Nuclear Resonant Scattering time spectra, the precessional amplitude profile across the stripe predicted by an analytical model is reconstructed. Our results pave the way for studying non-homogeneous dynamic spin configurations in microstructured magnetic systems using nuclear resonant scattering of synchrotron light.

Control of Spin-Wave Propagation using Magnetisation Gradients

We report that in an in-plane magnetised magnetic film the in-plane direction of a propagating spin wave can be changed by up to 90 degrees using an externally induced magnetic gradient field. We have achieved this result using a reconfigurable, laser-induced magnetisation gradient created in a conversion area, in which the backward volume and surface spin-wave modes coexist at the same frequency. Shape and orientation of the gradient control the conversion efficiency. Experimental data and numerical calculations agree very well. Our findings open the way to magnonic circuits with in-plane steering of the spin-wave modes.

Spin-Torque Excitation of Perpendicular Standing Spin Waves in Coupled YIG/Co Heterostructures

We investigate yttrium iron garnet (YIG)/cobalt (Co) heterostructures using broadband ferromagnetic resonance (FMR). We observe an efficient excitation of perpendicular standing spin waves (PSSWs) in the YIG layer when the resonance frequencies of the YIG PSSWs and the Co FMR line coincide. Avoided crossings of YIG PSSWs and the Co FMR line are found and modeled using mutual spin pumping and exchange torques. The excitation of PSSWs is suppressed by a thin aluminum oxide interlayer but persists with a copper interlayer, in agreement with the proposed model.

Magnon detection using a ferroic collinear multilayer spin valve

Information transport and processing by pure magnonic spin currents in insulators is a promising alternative to conventional charge-current-driven spintronic devices. The absence of Joule heating and reduced spin wave damping in insulating ferromagnets have been suggested for implementing efficient logic devices. After the successful demonstration of a majority gate based on the superposition of spin waves, further components are required to perform complex logic operations. Here, we report on magnetization orientation-dependent spin current detection signals in collinear magnetic multilayers inspired by the functionality of a conventional spin valve. In Y₃Fe₅O₁₂|CoO|Co, we find that the detection amplitude of spin currents emitted by ferromagnetic resonance spin pumping depends on the relative alignment of the Y₃Fe₅O₁₂ and Co magnetization. This yields a spin valve-like behavior with an amplitude change of 120% in our systems. We demonstrate the reliability of the effect and identify its origin by both temperature-dependent and power-dependent measurements.

Ferromagnetic domain walls as spin wave filters and the interplay between domain walls and spin waves

Spin waves (SW) are low energy excitations of magnetization in magnetic materials. In the promising field of magnonics, fundamental SW modes, magnons, are accessible in magnetic nanostructure waveguides and carry information. The SW propagates in both metals and insulators via magnetization dynamics. Energy dissipation through damping can be low compared to the Joule heating in conventional circuits. We performed simulations in a quasi-one-dimensional ferromagnetic strip and found that the transmission of the propagating SW across the domain wall (DW) depends strongly on the tilt angle of the magnetization at low frequencies. When the SW amplitude is large, the magnetization tilt angle inside the DW changes due to the effective fields. The SW transmission, the DW motion, and the magnetization tilt angle couple to each other, which results in complex DW motion and SW transmission. Both SW filtering and DW motions are key ingredients in magnonics.

Reconfigurable nanoscale spin-wave directional coupler

Spin waves, and their quanta magnons, are prospective data carriers in future signal processing systems because Gilbert damping associated with the spin-wave propagation can be made substantially lower than the Joule heat losses in electronic devices. Although individual spin-wave signal processing devices have been successfully developed, the challenging contemporary problem is the formation of two-dimensional planar integrated spin-wave circuits. Using both micromagnetic modeling and analytical theory, we present an effective solution of this problem based on the dipolar interaction between two laterally adjacent nanoscale spin-wave waveguides. The developed device based on this principle can work as a multifunctional and dynamically reconfigurable signal directional coupler performing the functions of a waveguide crossing element, tunable power splitter, frequency separator, or multiplexer. The proposed design of a spin-wave directional coupler can be used both in digital logic circuits intended for spin-wave computing and in analog microwave signal processing devices.

Detection of Short-Waved Spin Waves in Individual Microscopic Spin-Wave Waveguides Using the Inverse Spin Hall Effect

The miniaturization of complementary metal-oxide-semiconductor (CMOS) devices becomes increasingly difficult due to fundamental limitations and the increase of leakage currents. Large research efforts are devoted to find alternative concepts that allow for a larger data-density and lower power consumption than conventional semiconductor approaches. Spin waves have been identified as a potential technology that can complement and outperform CMOS in complex logic applications, profiting from the fact that these waves enable wave computing on the nanoscale. The practical application of spin waves, however, requires the demonstration of scalable, CMOS compatible spin-wave detection schemes in material systems compatible with standard spintronics as well as semiconductor circuitry. Here, we report on the wave-vector independent detection of short-waved spin waves with wavelengths down to 150 nm by the inverse spin Hall effect in spin-wave waveguides made from ultrathin Ta/Co₈Fe₇₂B₂₀/MgO. These findings open up the path for miniaturized scalable interconnects between spin waves and CMOS and the use of ultrathin films made from standard spintronic materials in magnonics.

Pinned domain wall oscillator as a tuneable direct current spin wave emitter

Local perturbations in the relative orientation of the magnetic moments in a continuous magnetic system can propagate in the form of waves. These so-called spin waves represent a promising candidate as an information carrier for spin-based low-power applications. A localized, energy-efficient excitation of coherent and short-wavelength spin waves is a crucial technological requirement, and alternatives to excitation via the Oersted field of an alternating current must be explored. Here, we show how a domain wall pinned at a geometrical constriction in a perpendicularly magnetized thin nanowire emits spin waves when forced to rotate by the application of a low direct current flowing along the wire. Spin waves are excited by the in-plane stray field of the rotating domain wall and propagate at an odd harmonic of the domain wall rotation frequency in the direction of the electron’s flow. The application of an external field, opposing domain wall depinning induced by the current, breaks the symmetry for spin wave propagation in the two domains, allowing emission in both directions but at different frequencies. The results presented define a new approach to manufacture tuneable high-frequency spin wave emitters of easy fabrication and low power consumption.

Efficient Modulation of Spin Waves in Two-Dimensional Octagonal Magnonic Crystal

Efficient tunability of magnonic spectra is demonstrated in two-dimensional ferromagnetic antidot lattices with different lattice constants arranged in the octagonal lattice which can be considered as quasi-periodic magnonic crystals due to the presence of broken translational symmetry. The precessional dynamics of these samples are investigated in the frequency domain with the help of broadband ferromagnetic resonance spectrometer. A rich variation in the spin wave spectra is observed with the variation of lattice constant as well as the strength and orientation of the bias magnetic field. A broad band of spin wave modes are observed for the denser array, which finally converges to two spin wave modes for the sparsest one. In addition to this, the most intense spin wave frequency shows an 8-fold anisotropy with a superposition of weak 4- and 2-fold anisotropy, which arises due to the angular variation of the magnetostatic field distribution at different regions of the octagonal lattice. Micromagnetic simulations qualitatively reproduce the experimentally observed modes, and the simulated mode profiles reveal the presence of different types of extended and quantized standing spin wave modes in these samples. The observations are important for the tunable and anisotropic propagation of spin waves in magnonic crystal based devices.

Antiferromagnetic domain wall as spin wave polarizer and retarder

As a collective quasiparticle excitation of the magnetic order in magnetic materials, spin wave, or magnon when quantized, can propagate in both conducting and insulating materials. Like the manipulation of its optical counterpart, the ability to manipulate spin wave polarization is not only important but also fundamental for magnonics. With only one type of magnetic lattice, ferromagnets can only accommodate the right-handed circularly polarized spin wave modes, which leaves no freedom for polarization manipulation. In contrast, antiferromagnets, with two opposite magnetic sublattices, have both left and right-circular polarizations, and all linear and elliptical polarizations. Here we demonstrate theoretically and confirm by micromagnetic simulations that, in the presence of Dzyaloshinskii-Moriya interaction, an antiferromagnetic domain wall acts naturally as a spin wave polarizer or a spin wave retarder (waveplate). Our findings provide extremely simple yet flexible routes toward magnonic information processing by harnessing the polarization degree of freedom of spin wave.

Spin waves are promising candidates as carriers for energy-efficient information processing, but they have not yet been fully explored application wise. Here the authors theoretically demonstrate that antiferromagnetic domain walls are naturally spin wave polarizers and retarders, two key components of magnonic devices.

Information processing in patterned magnetic nanostructures with edge spin waves

Low dissipation data processing with spins is one of the promising directions for future information and communication technologies. Despite a significant progress, the available magnonic devices are not broadband yet and have restricted capabilities to redirect spin waves. Here we propose a breakthrough approach to spin wave manipulation in patterned magnetic nanostructures with unmatched characteristics, which exploits a spin wave analogue to edge waves propagating along a water-wall boundary. Using theory, micromagnetic simulations and experiment we investigate spin waves propagating along the edges in magnetic structures, under an in-plane DC magnetic field inclined with respect to the edge. The proposed edge spin waves overcome important challenges faced by previous technologies such as the manipulation of the spin wave propagation direction, and they substantially improve the capability of transmitting information at frequencies exceeding 10 GHz. The concept of the edge spin waves allows to design a broad of logic devices such as splitters, interferometers, or edge spin wave transistors with unprecedented characteristics and a potentially strong impact on information technologies.

Isotropic transmission of magnon spin information without a magnetic field

Spin-wave devices (SWD), which use collective excitations of electronic spins as a carrier of information, are rapidly emerging as potential candidates for post-semiconductor non-charge-based technology. Isotropic in-plane propagating coherent spin waves (magnons), which require magnetization to be out of plane, is desirable in an SWD. However, because of lack of availability of low-damping perpendicular magnetic material, a usually well-known in-plane ferrimagnet yttrium iron garnet (YIG) is used with a large out-of-plane bias magnetic field, which tends to hinder the benefits of isotropic spin waves. We experimentally demonstrate an SWD that eliminates the requirement of external magnetic field to obtain perpendicular magnetization in an otherwise in-plane ferromagnet, Ni₈₀Fe₂₀ or permalloy (Py), a typical choice for spin-wave microconduits. Perpendicular anisotropy in Py, as established by magnetic hysteresis measurements, was induced by the exchange-coupled Co/Pd multilayer. Isotropic propagation of magnon spin information has been experimentally shown in microconduits with three channels patterned at arbitrary angles.