Realization of a spin-wave multiplexer

Spin-wave propagation in cubic anisotropy materials

The information carrier of modern technologies is the electron charge whose transport inevitably generates Joule heating. Spin-waves, the collective precessional motion of electron spins, do not involve moving charges and thus avoid Joule heating [1-3]. In this respect, magnonic devices in which the information is carried by spin-waves attract interest for low-power computing. However implementation of magnonic devices for practical use suffers from low spin-wave signal and on/off ratio. Here we demonstrate that cubic anisotropy materials can enhance spin-wave signals by improving spin-wave amplitude as well as group velocity and attenuation length. Furthermore, cubic anisotropy material shows an enhanced on/off ratio through a laterally localized edge mode, which closely mimics the gate-controlled conducting channel in traditional field-effect transistors. These attractive features of cubic anisotropy materials will invigorate magnonics research towards wave-based functional devices.

Overcoming thermal noise in non-volatile spin wave logic

Spin waves are propagating disturbances in magnetically ordered materials, analogous to lattice waves in solid systems and are often described from a quasiparticle point of view as magnons. The attractive advantages of Joule-heat-free transmission of information, utilization of the phase of the wave as an additional degree of freedom and lower footprint area compared to conventional charge-based devices have made spin waves or magnon spintronics a promising candidate for beyond-CMOS wave-based computation. However, any practical realization of an all-magnon based computing system must undergo the essential steps of a careful selection of materials and demonstrate robustness with respect to thermal noise or variability. Here, we aim at identifying suitable materials and theoretically demonstrate the possibility of achieving error-free clocked non-volatile spin wave logic device, even in the presence of thermal noise and clock jitter or clock skew.

Brillouin light scattering studies of 2D magnonic crystals

Magnonic crystals, materials with periodic modulation of their magnetic properties, represent the magnetic counterpart of photonic, phononic and plasmonic crystals, and have been largely investigated in recent years because of the possibility of using spin waves as a new means for carrying and processing information over a very large frequency bandwidth. Here, we review recent Brillouin light scattering studies of 2D magnonic crystals consisting of single- and bi-component arrays of interacting magnetic dots or antidot lattices. In particular, we discuss the principal properties of the magnonic band diagram of such systems, with emphasis given to its dependence on both magnetic and the geometrical parameters. Thanks to the possibility of tailoring their band structure by means of several degrees of freedom, planar magnonic crystals offer a good opportunity to design an innovative class of nanoscale microwave devices.

Guided magnonic Michelson interferometer

Magnonics is an emerging field with potential applications in classical and quantum information processing. Freely propagating magnons in two-dimensional media are subject to dispersion, which limits their effective range and utility as information carriers. We show the design of a confining magnonic waveguide created by two surface current carrying wires placed above a spin-sheet, which can be used as a primitive for reconfigurable magnonic circuitry. We theoretically demonstrate the ability of such guides to counter the transverse dispersion of the magnon in a spin-sheet, thus extending the range of the magnon. A design of a magnonic directional coupler and controllable Michelson interferometer is shown, demonstrating its utility for information processing tasks.

Phase-to-intensity conversion of magnonic spin currents and application to the design of a majority gate

Magnonic spin currents in the form of spin waves and their quanta, magnons, are a promising candidate for a new generation of wave-based logic devices beyond CMOS, where information is encoded in the phase of travelling spin-wave packets. The direct readout of this phase on a chip is of vital importance to couple magnonic circuits to conventional CMOS electronics. Here, we present the conversion of the spin-wave phase into a spin-wave intensity by local non-adiabatic parallel pumping in a microstructure. This conversion takes place within the spin-wave system itself and the resulting spin-wave intensity can be conveniently transformed into a DC voltage. We also demonstrate how the phase-to-intensity conversion can be used to extract the majority information from an all-magnonic majority gate. This conversion method promises a convenient readout of the magnon phase in future magnon-based devices.

Curvature-Induced Asymmetric Spin-Wave Dispersion

In magnonics, spin waves are conceived of as electron-charge-free information carriers. Their wave behavior has established them as the key elements to achieve low power consumption, fast operative rates, and good packaging in magnon-based computational technologies. Hence, knowing alternative ways that reveal certain properties of their undulatory motion is an important task. Here, we show using micromagnetic simulations and analytical calculations that spin-wave propagation in ferromagnetic nanotubes is fundamentally different than in thin films. The dispersion relation is asymmetric regarding the sign of the wave vector. It is a purely curvature-induced effect and its fundamental origin is identified to be the classical dipole-dipole interaction. The analytical expression of the dispersion relation has the same mathematical form as in thin films with the Dzyalonshiinsky-Moriya interaction. Therefore, this curvature-induced effect can be seen as a "dipole-induced Dzyalonshiinsky-Moriya-like" effect.

Magnetic vortex cores as tunable spin-wave emitters

The use of spin waves as information carriers in spintronic devices can substantially reduce energy losses by eliminating the ohmic heating associated with electron transport. Yet, the excitation of short-wavelength spin waves in nanoscale magnetic systems remains a significant challenge. Here, we propose a method for their coherent generation in a heterostructure composed of antiferromagnetically coupled magnetic layers. The driven dynamics of naturally formed nanosized stacked pairs of magnetic vortex cores is used to achieve this aim. The resulting spin-wave propagation is directly imaged by time-resolved scanning transmission X-ray microscopy. We show that the dipole-exchange spin waves excited in this system have a linear, non-reciprocal dispersion and that their wavelength can be tuned by changing the driving frequency.

Spin-wave propagation steered by electric field modulated exchange interaction

Combined ab initio and micromagnetic simulations are carried out to demonstrate the feasibility on the electrical manipulation of spin-wave propagation in ultrathin Fe films. It is discovered that the exchange interaction can be substantially weakened under the influence of electric field applied perpendicular to the magnetic film surface. Furthermore, we demonstrate that the electric field modified exchange constant could effectively control the propagation of spin waves. To be specific, an external applied electric field of 5 V/nm can effectively weaken exchange interaction by 80% and is sufficient to induce nearly twofold change of the wavenumber. This discovery may open a door to energy-efficient local manipulation of the spin wave propagation utilizing electric fields, which is crucial for both fundamental research and spin wave based logic applications.

Snell's Law for Spin Waves

We report the experimental observation of Snell's law for magnetostatic spin waves in thin ferromagnetic Permalloy films by imaging incident, refracted, and reflected waves. We use a thickness step as the interface between two media with different dispersion relations. Since the dispersion relation for magnetostatic waves in thin ferromagnetic films is anisotropic, deviations from the isotropic Snell's law known in optics are observed for incidence angles larger than 25° with respect to the interface normal between the two magnetic media. Furthermore, we can show that the thickness step modifies the wavelength and the amplitude of the incident waves. Our findings open up a new way of spin wave steering for magnonic applications.

Giant nonreciprocal emission of spin waves in Ta/Py bilayers

Spin waves are propagating disturbances in the magnetization of magnetic materials. One of their interesting properties is nonreciprocity, exhibiting that their amplitude depends on the magnetization direction. Nonreciprocity in spin waves is of great interest in both fundamental science and applications because it offers an extra knob to control the flow of waves for the technological fields of logics and switch applications. We show a high nonreciprocity in spin waves from Ta/Py bilayer systems with out-of-plane magnetic fields. The nonreciprocity depends on the thickness of Ta underlayer, which is found to induce an interfacial anisotropy. The origin of observed high nonreciprocity is twofold: different polarities of the in-plane magnetization due to different angles of canted out-of-plane anisotropy and the spin pumping effect at the Ta/Py interface. Our findings provide an opportunity to engineer highly efficient, nonreciprocal spin wave-based applications, such as nonreciprocal microwave devices, magnonic logic gates, and information transports.

Nanopatterning reconfigurable magnetic landscapes via thermally assisted scanning probe lithography

The search for novel tools to control magnetism at the nanoscale is crucial for the development of new paradigms in optics, electronics and spintronics. So far, the fabrication of magnetic nanostructures has been achieved mainly through irreversible structural or chemical modifications. Here, we propose a new concept for creating reconfigurable magnetic nanopatterns by crafting, at the nanoscale, the magnetic anisotropy landscape of a ferromagnetic layer exchange-coupled to an antiferromagnetic layer. By performing localized field cooling with the hot tip of a scanning probe microscope, magnetic structures, with arbitrarily oriented magnetization and tunable unidirectional anisotropy, are reversibly patterned without modifying the film chemistry and topography. This opens unforeseen possibilities for the development of novel metamaterials with finely tuned magnetic properties, such as reconfigurable magneto-plasmonic and magnonic crystals. In this context, we experimentally demonstrate spatially controlled spin wave excitation and propagation in magnetic structures patterned with the proposed method.

A reconfigurable waveguide for energy-efficient transmission and local manipulation of information in a nanomagnetic device

Spin-wave-based devices promise to usher in an era of low-power computing where information is carried by the precession of the electrons' spin instead of dissipative translation of their charge. This potential is, however, undermined by the need for a bias magnetic field, which must remain powered on to maintain an anisotropic device characteristic. Here, we propose a reconfigurable waveguide design that can transmit and locally manipulate spin waves without the need for any external bias field once initialized. We experimentally demonstrate the transmission of spin waves in straight as well as curved waveguides without a bias field, which has been elusive so far. Furthermore, we experimentally show a binary gating of the spin-wave signal by controlled switching of the magnetization, locally, in the waveguide. The results have potential implications in high-density integration and energy-efficient operation of nanomagnetic devices at room temperature.

Magnetic domain walls as reconfigurable spin-wave nanochannels

In the research field of magnonics, it is envisaged that spin waves will be used as information carriers, promoting operation based on their wave properties. However, the field still faces major challenges. To become fully competitive, novel schemes for energy-efficient control of spin-wave propagation in two dimensions have to be realized on much smaller length scales than used before. In this Letter, we address these challenges with the experimental realization of a novel approach to guide spin waves in reconfigurable, nano-sized magnonic waveguides. For this purpose, we make use of two inherent characteristics of magnetism: the non-volatility of magnetic remanence states and the nanometre dimensions of domain walls formed within these magnetic configurations. We present the experimental observation and micromagnetic simulations of spin-wave propagation inside nano-sized domain walls and realize a first step towards a reconfigurable domain-wall-based magnonic nanocircuitry.

Phase-shift-controlled logic gates in Y-shaped nonlinearly coupled chains

We introduce a model system composed of two input discrete chains nonlinearly coupled to a single output chain which mimics the geometry of Y-shaped carbon nanotubes, photonic crystal wave guides, and DNA junctions. We explore the capability of the proposed system to perform logic gate operations based on the transmission of phase-shifted harmonic incoming waves. Within a tight-binding approach, we determine the exact transmission spectrum which exhibits a nonlinear induced bistability. Using a digitalization scheme of the output signal based on amplitude modulation, we show that AND, OR, and XOR logic operations can be achieved. Nonlinearity strongly favors the realization of logic operations in the regime of large wavelengths, while phase shifting is required for the OR logic gate to be realizable. A detailed analysis of the contrast ratio shows that optimal operation of the AND and OR logic gates takes place when the nonlinear response is the predominant physical property distinguishing the coupling and regular sites. These results point towards the possibility of Y-branched junctions to perform logic operations based on the transmission of traveling waves.

Microwave excitation of spin wave beams in thin ferromagnetic films

An inherent element of research and applications in photonics is a beam of light. In magnonics, which is the magnetic counterpart of photonics, where spin waves are used instead of electromagnetic waves to transmit and process information, the lack of a beam source limits exploration. Here, we present an approach enabling generation of narrow spin wave beams in thin homogeneous nanosized ferromagnetic films by microwave current. We show that the desired beam-type behavior can be achieved with the aid of a properly designed coplanar waveguide transducer generating a nonuniform microwave magnetic field. We test this idea using micromagnetic simulations, confirming numerically that the resulting spin wave beams propagate over distances of several micrometers. The proposed approach requires neither inhomogeneity of the ferromagnetic film nor nonuniformity of the biasing magnetic field. It can be generalized to different magnetization configurations and yield multiple spin wave beams of different width at the same frequency.

Direct observation of isolated Damon-Eshbach and backward volume spin-wave packets in ferromagnetic microstripes

The analysis of isolated spin-wave packets is crucial for the understanding of magnetic transport phenomena and is particularly interesting for applications in spintronic and magnonic devices, where isolated spin-wave packets implement an information processing scheme with negligible residual heat loss. We have captured microscale magnetization dynamics of single spin-wave packets in metallic ferromagnets in space and time. Using an optically driven high-current picosecond pulse source in combination with time-resolved scanning Kerr microscopy probed by femtosecond laser pulses, we demonstrate phase-sensitive real-space observation of spin-wave packets in confined permalloy (Ni80Fe20) microstripes. Impulsive excitation permits extraction of the dynamical parameters, i.e. phase- and group velocities, frequencies and wave vectors. In addition to well-established Damon-Eshbach modes our study reveals waves with counterpropagating group- and phase-velocities. Such unusual spin-wave motion is expected for backward volume modes where the phase fronts approach the excitation volume rather than emerging out of it due to the negative slope of the dispersion relation. These modes are difficult to excite and observe directly but feature analogies to negative refractive index materials, thus enabling model studies of wave propagation inside metamaterials.

Tunable short-wavelength spin wave excitation from pinned magnetic domain walls

Miniaturization of magnonic devices for wave-like computing requires emission of short-wavelength spin waves, a key feature that cannot be achieved with microwave antennas. In this paper, we propose a tunable source of short-wavelength spin waves based on highly localized and strongly pinned magnetic domain walls in ferroelectric-ferromagnetic bilayers. When driven into oscillation by a microwave spin-polarized current, the magnetic domain walls emit spin waves with the same frequency as the excitation current. The amplitude of the emitted spin waves and the range of attainable excitation frequencies depend on the availability of domain wall resonance modes. In this respect, pinned domain walls in magnetic nanowires are particularly attractive. In this geometry, spin wave confinement perpendicular to the nanowire axis produces a multitude of domain wall resonances enabling efficient spin wave emission at frequencies up to 100 GHz and wavelengths down to 20 nm. At high frequency, the emission of spin waves in magnetic nanowires becomes monochromatic. Moreover, pinning of magnetic domain wall oscillators onto the same ferroelectric domain boundary in parallel nanowires guarantees good coherency between spin wave sources, which opens perspectives towards the realization of Mach-Zehnder type logic devices and sensors.

Direct Depth- and Lateral- Imaging of Nanoscale Magnets Generated by Ion Impact

Nanomagnets form the building blocks for a variety of spin-transport, spin-wave and data storage devices. In this work we generated nanoscale magnets by exploiting the phenomenon of disorder-induced ferromagnetism; disorder was induced locally on a chemically ordered, initially non-ferromagnetic, Fe60Al40 precursor film using  nm diameter beam of Ne(+) ions at 25 keV energy. The beam of energetic ions randomized the atomic arrangement locally, leading to the formation of ferromagnetism in the ion-affected regime. The interaction of a penetrating ion with host atoms is known to be spatially inhomogeneous, raising questions on the magnetic homogeneity of nanostructures caused by ion-induced collision cascades. Direct holographic observations of the flux-lines emergent from the disorder-induced magnetic nanostructures were made in order to measure the depth- and lateral- magnetization variation at ferromagnetic/non-ferromagnetic interfaces. Our results suggest that high-resolution nanomagnets of practically any desired 2-dimensional geometry can be directly written onto selected alloy thin films using a nano-focussed ion-beam stylus, thus enabling the rapid prototyping and testing of novel magnetization configurations for their magneto-coupling and spin-wave properties.

Realization of a micrometre-scale spin-wave interferometer

The recent development of spin dynamics opens perspectives for various applications based on spin waves, including logic devices. The first important step in the realization of spin-wave-based logics is the manipulation of spin-wave interference. Here, we present the experimental realization of a micrometre-scale spin-wave interferometer consisting of two parallel spin-wave waveguides. The spin waves propagate through the waveguides and the superposition or interference of the electrical signals corresponding to the spin waves is measured. A direct current flowing through a metal wire underneath one of the spin-wave waveguides affects the propagation properties of the corresponding spin wave. The signal of constructive or destructive interference depends on the magnitude and direction of the applied direct current. Thus, the present work demonstrates a unique manipulation of spin-wave interference.

Non-volatile Clocked Spin Wave Interconnect for Beyond-CMOS Nanomagnet Pipelines

The possibility of using spin waves for information transmission and processing has been an area of active research due to the unique ability to manipulate the amplitude and phase of the spin waves for building complex logic circuits with less physical resources and low power consumption. Previous proposals on spin wave logic circuits have suggested the idea of utilizing the magneto-electric effect for spin wave amplification and amplitude- or phase-dependent switching of magneto-electric cells. Here, we propose a comprehensive scheme for building a clocked non-volatile spin wave device by introducing a charge-to-spin converter that translates information from electrical domain to spin domain, magneto-electric spin wave repeaters that operate in three different regimes - spin wave transmitter, non-volatile memory and spin wave detector, and a novel clocking scheme that ensures sequential transmission of information and non-reciprocity. The proposed device satisfies the five essential requirements for logic application: nonlinearity, amplification, concatenability, feedback prevention, and complete set of Boolean operations.

Magnetic skyrmion logic gates: conversion, duplication and merging of skyrmions

Magnetic skyrmions, which are topological particle-like excitations in ferromagnets, have attracted a lot of attention recently. Skyrmionics is an attempt to use magnetic skyrmions as information carriers in next generation spintronic devices. Proposals of manipulations and operations of skyrmions are highly desired. Here, we show that the conversion, duplication and merging of isolated skyrmions with different chirality and topology are possible all in one system. We also demonstrate the conversion of a skyrmion into another form of a skyrmion, i.e., a bimeron. We design spin logic gates such as the AND and OR gates based on manipulations of skyrmions. These results provide important guidelines for utilizing the topology of nanoscale spin textures as information carriers in novel magnetic sensors and spin logic devices.