A spin-wave logic gate based on a width-modulated dynamic magnonic crystal
Andrey A. Nikitin, Alexey B. Ustinov, Alexander A. Semenov, Andrii V. Chumak, Alexander A. Serga, Vitaliy I. Vasyuchka, Erkki Lähderanta, Boris A. Kalinikos, Burkard Hillebrands
An electric current controlled spin-wave logic gate based on a width-modulated dynamic magnonic crystal is realized. The device utilizes a spin-wave waveguide fabricated from a single-crystal Yttrium Iron Garnet film and two conducting wires attached to the film surface. Application of electric currents to the wires provides a means for dynamic control of the effective geometry of the waveguide and results in a suppression of the magnonic band gap. The performance of the magnonic crystal as an AND logic gate is demonstrated.
In Ref. [PRL 102, 127202 (2009)] Lee et al. reported the existence of large magnonic bandgaps in one-dimensional width-modulated Permalloy nanostripe waveguides based on OOMMF simulations. However, as the symmetry of the magnetic field pulse they applied to excite the spin waves (SWs) was not general, the entire set of SW branches with A symmetry was omitted from the magnonic band structures (see below). This omission has unfortunately led to misleading conclusions of, for instance, the number, width and position of the bandgaps. We present here the full band structure based on three different…
A design of a magnonic phase shifter operating without an external bias magnetic field is proposed. The phase shifter uses a localized collective spin wave mode propagating along a domain wall "waveguide" in a dipolarly-coupled magnetic dot array existing in a chessboard antiferromagnetic (CAFM) ground state. It is demonstrated numerically that remagnetization of a single magnetic dot adjacent to the domain wall waveguide introduces a controllable phase shift in the propagating spin wave mode without significant change of the mode amplitude. It is also demonstrated that a logic XOR gate can be…
Circuit elements within magnonic computers generally operate using signals that are either amplitude or phase modulated (AM or PM). We propose a simple all-magnon circuit element capable of converting between these two types of encoding. We highlight the potential of our technique to augment existing devices and propose a novel schematic for an 'equality' gate and XNOR gate.
Reprogrammable magnonic logic in a multiferroic heterostructure via magnetoelectric coupling
Laboratoire Albert Fert, CNRS, Thales, Université Paris-Saclay（阿尔伯特·费尔特实验室，法国国家科学研究中心，泰雷兹集团，巴黎萨克雷大学）；Faculty of Information Technology and Bionics, Pázmány Peter Catholic University（帕兹马尼·彼得天主教大学信息与仿生技术学院）；Centre de Nanosciences et de Nanotechnologies, CNRS, Université Paris-Saclay（纳米科学与工程中心，法国国家科学研究中心，巴黎萨克雷大学）；Laboratoire de Physique des Solides, CNRS, Université Paris-Saclay（固体物理实验室，法国国家科学研究中心，巴黎萨克雷大学）；Institute of Applied Physics, University of Münster（明斯特大学应用物理研究所）
Magnonic crystals with locally alternating properties and specific periodicities exhibit interesting effects, such as a multitude of different spin-wave states and large band gaps. This work aims for demonstrating and understanding the key role of local demagnetizing fields in such systems. To achieve this, hybrid structures are investigated consisting of a continuous thin film with a stripe modulation on top favorable due to the adjustability of the magnonic effects with the modulation size. For a direct access to the spin dynamics, a magnonic crystal was reconstructed from `bottom-up', i.e.,…
We investigated a possible use of the magnonic interferometric switches in multi-valued logic circuits. The switch is a three-terminal device consisting of two spin channels where input, control, and output signals are spin waves. Signal modulation is achieved via the interference between the source and gate spin waves. We report experimental data on a micrometer scale prototype based on Y3Fe2(FeO4)3 structure. The output characteristics are measured at different angles of the bias magnetic field. The On/Off ratio of the prototype exceeds 36 dB at room temperature. Experimental data is complem…
We have experimentally and numerically investigated the dispersion of collective spin waves prop-agating through arrays of longitudinally magnetized nanowires with periodically modulated width. Two nanowire arrays with single-side modulation and different periodicity of modulation were studied and compared to the nanowires with homogeneous width. The spin-wave dispersion, meas-ured up to the third Brillouin zone of the reciprocal space, revealed the presence of two dispersive modes for the width-modulated NWs, whose amplitude of magnonic band depends on the modula-tion periodicity, and a set o…
We present a minimal one-dimensional model of collective spin excitations in itinerant ferromagnetic superlattices within the regime of parabolic spin-carrier dispersion. We discuss the cases of weakly and strongly modulated magnetic profiles finding evidences of antiferromagnetic correlations for long-wave magnons (especially significant in layered systems), with an insight into the ground state properties. In addition, the presence of local minima in the magnonic dispersion suggests the possibility of (thermal) excitation of spin waves with a relatively well controlled wave length. Some of t…
We study the effect of surface-induced Dzyaloshinskii-Moriya interaction (DMI) on the ferromagnetic resonance (FMR) spectrum of thickness-modulated one-dimensional magnonic crystals and isolated stripes. The DMI is found to substantially increases the intensity of absorption peaks and shifts the frequencies of the laterally quantized modes. The role of the DMI is determined by analyzing the amplitude and phase distributions of dynamic magnetic excitations calculated with frequency- and time-domain calculation methods. We propose experimentally realizable magnonic crystals and confined structur…
We propose and develop a concept of magnonic logic gates enabling reversible computing. The gates consist of passive elements: waveguides, cross-junctions and phase shifters. Logical 0 and 1 are encoded in the relative phase of the propagating spin wave packets (0 or π). The gates contain several possible trajectories for each packet to propagate from the input to the output. Re-direction of the spin wave packets among the possible trajectories is due to the interference in the magnetic cross-junctions. Two wave packets coming to the cross-junction in-phase propagate through the junction witho…
Wave-based data processing by spin waves and their quanta, magnons, is a promising technique to overcome the challenges which CMOS-based logic networks are facing nowadays. The advantage of these quasi-particles lies in their potential for the realization of energy efficient devices on the micro- to nanometer scale due to their charge-less propagation in magnetic materials. In this paper, the frequency dependence of the propagation direction of caustic-like spin-wave beams in microstructured ferromagnets is studied by micromagnetic simulations. Based on the observed alteration of the propagati…
Huazhong University of Science and Technology（华中科技大学）；University of Vienna（维也纳大学）；V. G. Baryakhtar Institute of Magnetism of the NAS of Ukraine（乌克兰国家科学院V.G.巴里亚赫塔尔磁学研究所）；INNOVENT e.V.（INNOVENT协会）；Hubei University（湖北大学）；Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology（华中科技大学武汉国家强磁场中心）；Rheinland-Pfälzische Technische Universität Kaiserslautern-Landau（凯泽斯劳滕-兰道莱茵兰-普法尔茨技术大学）
We investigate the reflection coefficient of spin waves propagating in an ultra-thin ferromagnetic film with regions where saturation magnetization is modulated. We find analytically and using micromagnetic simulations that there are transmission resonances that depend on the width of the regions and on the energy of excitation. Our results resemble the quantum mechanical Ramsauer-Townsend effect in which an electron with certain energies can propagate above a potential field without scattering. Our findings are useful for reconfigurable magnonic devices where the saturation magnetization can …
The emerging field of nano-magnonics utilizes high-frequency waves of magnetization - the spin waves - for the transmission and processing of information on the nanoscale. The advent of spin-transfer torque has spurred significant advances in nano-magnonics, by enabling highly efficient local spin-wave generation in magnonic nanodevices. Furthermore, the recent emergence of spin-orbitronics, which utilizes spin-orbit interaction as the source of spin torque, has provided a unique ability to exert spin torque over spatially extended areas of magnonic structures, enabling enhanced spin-wave tran…
Multiferroics offer an elegant means to implement voltage-control and on the fly reconfigurability in microscopic, nanoscaled systems based on ferromagnetic materials. These properties are particularly interesting for the field of magnonics, where spin waves are used to perform advanced logical or analogue functions. Recently, the emergence of nano-magnonics {\color{black} is expected to} eventually lead to the large-scale integration of magnonic devices. However, a compact voltage-controlled, on demand reconfigurable magnonic system has yet to be shown. Here, we introduce the combination of m…
Strongly-interacting nanomagnetic systems are pivotal across next-generation technologies including reconfigurable magnonics and neuromorphic computation. Controlling magnetisation state and local coupling between neighbouring nanoelements allows vast reconfigurable functionality and a host of associated functionalities. However, existing designs typically suffer from an inability to tailor inter-element coupling post-fabrication and nanoelements restricted to a pair of Ising-like magnetisation states. Here, we propose a new class of reconfigurable magnonic crystal incorporating nanodisks as t…
Strongly-interacting nanomagnetic arrays are crucial across an ever-growing suite of technologies. Spanning neuromorphic computing, control over superconducting vortices and reconfigurable magnonics, the utility and appeal of these arrays lies in their vast range of distinct, stable magnetisation states. Different states exhibit different functional behaviours, making precise, reconfigurable state control an essential cornerstone of such systems. However, few existing methodologies may reverse an arbitrary array element, and even fewer may do so under electrical control, vital for device integ…
Hybrid dynamic systems have recently gained interests with respect to both fundamental physics and device applications, particularly with their potential for coherent information processing. In this perspective, we will focus on the recent rapid developments of magnon-based hybrid systems, which seek to combine magnonic excitations with diverse excitations for transformative applications in devices, circuits and information processing. Key to their promising potentials is that magnons are highly tunable excitations and can be easily engineered to couple with various dynamic media and platforms…
We have investigated surface spin wave states in one-dimensional planar bi-component magnonic crystals, localized on the surfaces resulting from the breaking of the periodic structure. The two systems have been considered: the magnonic crystal with periodic changes of the anisotropy field in exchange regime and the magnonic crystal composed of Fe and Ni stripes in dipolar regime with exchange interactions included. We chose the symmetric unit cell for both systems to implement the symmetry related criteria for existence of the surface states. We investigated also the surface states induced by …
We present the results of a systematic micromagnetic study of the effect of the Dzyaloshinskii-Moriya interaction (DMI) on the spin wave band structure of two one-dimensional magnonic crystals (MCs), both with the same periodicity p=300 nm, but different implementation of the DMI modulation. In the first system the artificial periodicity was achieved by modulating the interfacial DMI constant D, while in the second system also the sample morphology was modulated. Due to the folding property of the band structure in the dispersion relations of the magnonic crystals it is possible to extend the …
Using Brillouin light scattering spectroscopy and dynamical matrix method calculations, we study collective spin waves in dense arrays of periodically double-side width-modulated Permalloy nanowires. Width modulation is achieved by creating a sequence of triangular notches on the two parallel nanowire sides, with a periodicity of p=1000 nm, and tunable relative displacement (D) of the notches sequence on the two lateral sides. Both symmetric (D=0) and asymmetric (D= 250 and 500 nm) width-modulated nanowires were investigated. We have found that the detected modes have Bloch-type character and …
Over the past few years, the study of magnetization dynamics in artificial spin ices has become a vibrant field of study. Artificial spin ices are ensembles of geometrically arranged, interacting magnetic nanoislands, which display frustration by design. These were initially created to mimic the behavior in rare earth pyrochlore materials and to study emergent behavior and frustration using two-dimensional magnetic measurement techniques. Recently, it has become clear that it is possible to create artificial spin ices, which can potentially be used as functional materials. In this Perspective,…
The research feld of magnonics proposes a low-energy wave-logic computation technology based on spin waves to complement the established CMOS technology and provide a basis for emerging unconventional computation architectures. However, magnetic damping is a limiting factor for all-magnonic logic circuits and multi-device networks, ultimately rendering mechanisms to effciently manipulate and amplify spin waves a necessity. In this regard, parallel pumping is a versatile tool since it allows to selectively generate and amplify spin waves. While extensively studied in microscopic systems, nano-s…
The outlook for producing useful practical devices within the paradigm of magnonics rests on our ability to emit, control and detect coherent exchange spin waves on the nanoscale. Here, we argue that all these key functionalities can be delivered by chiral magnonic resonators - soft magnetic elements chirally coupled, via magneto-dipole interaction, to magnonic media nearby. Starting from the basic principles of chiral coupling, we outline how they could be used to construct devices and explore underpinning physics, ranging from basic logic gates to field programmable gate arrays, in-memory co…
This article presents theoretical results for the dynamic response of periodically surface-modulated ferromagnetic thin films. For such system, the role of the periodic dipolar field induced by the modulation is addressed by using the plane-wave method. By controlling the geometry of the modulated volumes within the film, the frequency modes and spatial profiles of spin waves can be manipulated. The angular dependence of the frequency band-gaps unveils the influence of both dynamic and static magnetic charges, which reside in the edges of the etching periodic zones, and it is stablished that b…
Spin-wave modes are studied under the gradual transition from a flat thin film to a 'full' (one-dimensional) magnonic crystal. For this purpose, the surface of a pre-patterned 36.8 nm thin permalloy film was sequentially ion milled resulting in magnonic hybrid structures, referred to as surface-modulated magnonic crystals, with increasing modulation depth. After each etching step, ferromagnetic resonance measurements were performed yielding the spin-wave resonance modes in backward-volume and Damon-Eshbach geometry. The spin-wave spectra of these hybrid systems reveal an even larger variety of…
Spin torque nano-oscillator has been extensively studied both theoretically and experimentally in recent decades due to its potential applications in future microwave communication technology and neuromorphic computing. In this work, we present a skyrmion-based spin torque nano-oscillator driven by a spatially uniform direct current, where the skyrmion is confined by two pinning sites. Different from other skyrmion-based oscillators that arise from the circular motion or the breathing mode of a skyrmion, the steady-state oscillatory motions are produced by the periodic deformation of an elonga…
Magnons, the quanta of spin waves, could be used to encode information in beyond-Moore computing applications, and magnonic device components, including logic gates, transistors, and units for non-Boolean computing, have already been developed. Magnonic directional couplers, which can function as circuit building blocks, have also been explored, but have been impractical because of their millimetre dimensions and multi-mode spectra. Here, we report a magnonic directional coupler based on yttrium iron garnet single-mode waveguides of 350 nm width. We use the amplitude of a spin-wave to encode i…
Artificial spin ices are ensembles of geometrically-arranged, interacting nanomagnets which have shown promising potential for the realization of reconfigurable magnonic crystals. Such systems allow for the manipulation of spin waves on the nanoscale and their potential use as information carriers. However, there are presently two general obstacles to the realization of artificial spin ice-based magnonic crystals: the magnetic state of artificial spin ices is difficult to reconfigure and the magnetostatic interactions between the nanoislands are often weak, preventing mode coupling. We demonst…
We report the development of a hybrid numerical / analytical model capable of mapping the spatially-varying distributions of the local ferromagnetic resonance (FMR) frequency and dynamic magnetic susceptibility in a wide class of patterned and compositionally modulated magnetic structures. Starting from the numerically simulated static micromagnetic state, the magnetization is deliberately deflected orthogonally to its equilibrium orientation, and the magnetic fields generated in response to this deflection are evaluated using micromagnetic software. This allows us to calculate the elements of…
We present a semiclassical formalism for antiferromagnetic (AFM) magnonics which promotes the central ingredient of spin wave chirality, encoded in a quantity called magnonic isospin, to a first-class citizen of the theory. We use this formalism to unify results of interest from the field under a single chirality-centric formulation. Our main result is that the isospin is governed by unitary time evolution, through a Hamiltonian projected down from the full spin wave dynamics. Because isospin is SU(2)-valued, its dynamics on the Bloch sphere are precisely rotations - which, in general, do not …
Spin-wave phase modulation using magnetic domain walls in dipolarly coupled structures for non-volatile magnonic computation
Rheinland-Pfälzische Technische Universität Kaiserslautern-Landau（莱茵兰-普法尔茨技术大学凯泽斯劳滕-兰道）；Université Paris-Saclay, Centre de Nanosciences et de Nanotechnologies, CNRS（巴黎萨克雷大学，纳米科学中心，法国国家科学研究中心）
Magnonics is a research field complementary to spintronics, in which the quanta of spin waves (magnons) replace electrons as information carriers, promising less energy dissipation. The development of ultrafast nanoscale magnonic logic circuits calls for new tools and materials to generate coherent spin waves with frequencies as high, and wavelengths as short, as possible. Antiferromagnets can host spin waves at THz frequencies and are therefore seen as a future platform for the fastest and the least dissipative transfer of information. However, the generation of short-wavelength coherent prop…
Electrostatic gating confines and controls the transport of electrons in integrated circuits. Magnons, the quanta of spin waves of the magnetic order, are promising alternative information carriers, but difficult to gate. Here we report that superconducting strips on top of thin magnetic films can totally reflect magnons by its diamagnetic response to the magnon stray fields. The induced large frequency shifts unidirectionally blocks the magnons propagating normal to the magnetization. Two superconducting gates parallel to the magnetization create a magnonic cavity. The option to gate coherent…
Local modification of magnetic properties of nanoelements is a key to design future-generation magnonic devices, in which information is carried and processed via spin waves. One of the biggest challenges here is to fabricate simple and miniature phase-controlling elements with broad tunability. Here, we successfully realize such spin-wave phase shifter upon a single nanogroove milled by focused ion beam in a Co-Fe microsized magnonic waveguide. By varying the groove depth and the in-plane bias magnetic field we continuously tune the spin-wave phase and experimentally evidence a complete phase…
Magnonics, which employs spin-waves to transmit and process information, is a promising venue for low-power data processing. One of the major challenges is the local control of the spin-wave propagation path. Here, we introduce the concept of writable magnonics by taking advantage of the highly flexible reconfigurability and rewritability of artificial spin ice systems. Using micromagnetic simulations, we show that globally switchable spin-wave propagation and the locally writable spin-wave nanochannels can be realized in a ferromagnetic thin film underlying an artificial pinwheel spin ice. Th…
We report broadband spectroscopy and numerical analysis by which we explore propagating spin waves in a magnetic bilayer consisting of a 23 nm thick permalloy film deposited on 130 nm thick $Y_{3}Fe_{5}O_{12}$. In the bilayer, we observe a characteristic mode that exhibits a considerably larger group velocity at small in-plane magnetic field than both the magnetostatic and perpendicular standing spin waves. Using the finite element method, we confirm the observations by simulating the mode profiles and dispersion relations. They illustrate the hybridization of spin wave modes due to exchange c…
Magnonics is a rapidly developing subfield of spintronics, which deals with devices and circuits that utilize spin currents carried by magnons - quanta of spin waves. Magnon current, i.e. spin waves, can be used for information processing, sensing, and other applications. A possibility of using the amplitude and phase of magnons for sending signals via electrical insulators creates conditions for avoiding Ohmic losses, and achieving ultra-low power dissipation. Most of the envisioned magnonic logic devices are based on spin wave interference, where the minimum energy per operation is limited b…
Tuning the low-energy magnetic dynamics is a key element in designing novel magnetic metamaterials, spintronic devices and magnonic logic circuits. This study uncovers a new, highly effective way of controlling the magnetic permeability via shaping the magnonic properties in coupled magnetic waveguides separated by current carrying spacer with strong spin-orbit coupling. The spin-orbit torques exerted on the waveguides leads to an externally tunable enhancement of magnetic damping in one waveguide and a decreased damping in the other, constituting so a magnetic parity-time (PT) symmetric syste…
Spin-wave technology (magnonics) has the potential to further reduce the size and energy consumption of information processing devices. In the submicrometer regime (exchange spin waves), topological defects such as domain walls may constitute active elements to manipulate spin waves and perform logic operations. We predict that spin waves that pass through a domain wall in an ultrathin perpendicular-anisotropy film experience a phase shift that depends on the orientation of the domain wall (chirality). The effect, which is absent in bulk materials, originates from the interfacial Dzyaloshinski…
Determining the prime factors of a given number N is a problem, which requires super-polynomial time for conventional digital computers. A polynomial-time algorithm was invented by P. Shor for quantum computers. However, the realization of quantum computers is associated with significant technological challenges in achieving and preserving quantum entanglement. Prime factorization can be also solved by using classical wave interference without quantum entanglement. In this work, we present experimental data showing prime factorization by utilizing spin wave interference. The prime factorizatio…
Magnonics and magnon spintronics aim at the utilization of spin waves and magnons, their quanta, for the construction of wave-based logic networks via the generation of pure all-magnon spin currents and their interfacing with electrical charge transport. The promise of efficient parallel data processing and low power consumption renders this field one of the most promising research areas in spintronics. In this context, the process of parallel parametric amplification, i.e., the conversion of microwave photons into magnons at one half of the microwave frequency, has proven to be a versatile to…
Using analysis of iso-frequency contours of the spin-wave dispersion relation, supported by micromagnetic simulations, we study the propagation of spin-wave (SW) beams in thin ferromagnetic films through the areas of the inhomogeneous refractive index. We compare the transmission and reflection of SWs in areas with gradual and step variation of the SW refractive index. In particular, we show the mirage effect for SWs with narrowing SW beam width, and an application of the gradual modulation of the SWs refractive index as a diverging lens. Furthermore, we study the propagation of SWs in ferroma…
Artificial spin ice systems have seen burgeoning interest due to their intriguing physics and potential applications in reprogrammable memory, logic and magnonics. Integration of artificial spin ice with functional magnonics is a relatively recent research direction, with a host of promising results. As the field progresses, direct in-depth comparisons of distinct artificial spin systems are crucial to advancing the field. While studies have investigated the effects of different lattice geometries, little comparison exists between systems comprising continuously connected nanostructures, where…
Spin waves offer intriguing novel perspectives for computing and signal processing, since their damping can be lower than the Ohmic losses in conventional CMOS circuits. For controlling the spatial extent and propagation of spin waves on the actual chip, magnetic domain walls show considerable potential as magnonic waveguides. However, low-loss guidance of spin waves with nanoscale wavelengths, in particular around angled tracks, remains to be shown. Here we experimentally demonstrate that such advanced control of propagating spin waves can be obtained using natural features of magnetic order …
The interplay between spin, charge, and orbital degrees of freedom has led to the development of spintronic devices like spin-torque oscillators, spin-logic devices, and spin-transfer torque magnetic random-access memories. In this development spin pumping, the process where pure spin-currents are generated from magnetisation precession, has proved to be a powerful method for probing spin physics and magnetisation dynamics. The effect originates from direct conversion of low energy quantised spin-waves in the magnet, known as magnons, into a flow of spins from the precessing magnet to adjacent…
We show that an inhomogeneity in the spin-transfer torques in a metallic ferromagnet under suitable conditions strongly amplifies incoming spin waves. Moreover, at nonzero temperatures the incoming thermally occupied spin waves will be amplified such that the region with inhomogeneous spin transfer torques emits spin waves spontaneously, thus constituting a spin-wave laser. We determine the spin-wave scattering amplitudes for a simplified model and set-up, and show under which conditions the amplification and lasing occurs. Our results are interpreted in terms of a so-called black-hole laser, …
1D spin-wave conduits are envisioned as nanoscale components of magnonics-based logic and computing schemes for future generation electronics. `A-la-carte methods of versatile control of the local magnetization dynamics in such nanochannels are highly desired for efficient steering of the spin waves in magnonic devices. Here, we present a study of localized dynamical modes in 1-$μ$m-wide Permalloy conduits probed by microresonator ferromagnetic resonance technique. We clearly observe the lowest-energy edge mode in the microstrip after its edges were finely trimmed by means of focused Ne$^+$ io…
We model the operation and readout sensitivity of two current-modulated magnetoplasmonic devices which exploit spin Hall effect-like behavior as a function of their device and material parameters. In both devices, current pulses are applied to an electrically-isolated stack, containing an active layer (either a metal with large spin orbit coupling or a topological insulator) embedded within a plasmonic metal (Au). The first device, composed of a ferromagnet and the active layer, illustrates a plasmonic readout scheme for detecting magnetic reorientation driven by current-induced spin transfer …
In magnonics, an emerging branch of wave physics characterized by low-energy consumption, it is highly desirable to realize circuit elements within the scope of spin-wave computing. Here, based on numerical simulations, we demonstrate the functionality of the spin-wave diode and the circulator to steer and manipulate spin waves over a wide range of frequency in the GHz regime. They take advantage of the unidirectional coupling induced by the interfacial Dzyaloshinskii-Moriya interaction to transfer the spin wave between thin ferromagnetic layers in only one direction of propagation. Using the …
