Review and prospects of magnonic crystals and devices with reprogrammable band structure

Tunable magnonic crystal in a hybrid superconductor-ferrimagnet nanostructure

One of the most intriguing properties of magnonic systems is their reconfigurability, where an external magnetic field alters the static magnetic configuration to influence magnetization dynamics. In this paper, we present an alternative approach to tunable magnonic systems. We studied theoretically and numerically a magnonic crystal induced within a uniform magnetic layer by a periodic magnetic field pattern created by the sequence of superconducting strips. We showed that the spin-wave spectrum can be tuned by the inhomogeneous stray field of the superconductor in response to a small uniform external magnetic field. Additionally, we demonstrated that modifying the width of superconducting strips and separation between them leads to the changes in the internal field which are unprecedented in conventional magnonic structures. The paper presents the results of semi-analytical calculations for realistic structures, which are verified by finite-element method computations.

Temperature-Dependent Surface Anisotropy in (110) Epitaxial Rare Earth Iron Garnet Films

Ferrimagnetic oxide thin films are important material platforms for spintronic devices. Films grown on low symmetry orientations such as (110) exhibit complex anisotropy landscapes that can provide insight into novel phenomena such as spin-torque auto-oscillation and spin superfluidity. Using spin-Hall magnetoresistance measurements, the in-plane (IP) and out-of-plane (OOP) uniaxial anisotropy energies are determined for a thickness series (5-50 nm) of europium iron garnet (EuIG) and thulium iron garnet (TmIG) films epitaxially grown on a gadolinium gallium substrate with (110) orientation and capped with Pt. Pt/EuIG/GGG exhibits an (001) easy plane of magnetization perpendicular to the substrate, whereas Pt/TmIG/GGG exhibits an (001) hard plane of magnetization perpendicular to the substrate with an IP easy axis. Both IP and OOP surface anisotropy energies comparable in magnitude to the bulk anisotropy are observed. The temperature dependence of the surface anisotropies is consistent with first-order predictions of a simplified Néel surface anisotropy model. By taking advantage of the thickness and temperature dependence demonstrated in these ferrimagnetic oxides grown on the low symmetry (110) orientations, the complex anisotropy landscapes can be tuned to act as a platform to explore rich spin textures and dynamics.

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

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

Magnetization dynamics in quasiperiodic magnonic crystals

Quasiperiodic magnonic crystals, in contrast to their periodic counterparts, lack strict periodicity which gives rise to complex and localised spin wave spectra characterized by numerous band gaps and fractal features. Despite their intrinsic structural complexity, quasiperiodic nature of these magnonic crystals enables better tunability of spin wave spectra over their periodic counterparts and therefore holds promise for the applications in reprogrammable magnonic devices. In this article, we provide an overview of magnetization reversal and precessional magnetization dynamics studied so far in various quasiperiodic magnonic crystals, illustrating how their quasiperiodic nature gives rise to tailored band structure, enabling unparalleled control over spin waves. The review is concluded by highlighting the possible potential applications of these quasiperiodic magnonic crystals, exploring potential avenues for future exploration followed by a brief summary.

Investigation of phonons and magnons in [Ni80Fe20/Au/Co/Au]Nmultilayers

The interaction between phonons and magnons is a rapidly developing area of research, particularly in the field of acoustic spintronics. To discuss this interaction, it is necessary to observe two different waves (acoustic and spin waves) with the same frequency and wavelength. In the Ni80Fe20/Au/Co/Au system deposited on a silicon substrate, we observe the interaction between spin waves and surface acoustic waves using Brillouin light scattering spectroscopy. As a result, we can selectively control (activate or deactivate) the magnetoelastic interaction between the fundamental spin wave mode and surface acoustic waves. This is achieved by adjusting the magnetostrictive layer thickness in the multilayer. We demonstrate that by adjusting the number of layers in a multilayer structure, it is possible to precisely control the dispersion of surface acoustic waves while having minimal impact on the fundamental spin wave mode.

The role of non-uniform magnetization texture for magnon-magnon coupling in an antidot lattice

We numerically study the spin-wave dynamics in an antidot lattice based on a Co/Pd multilayer structure with reduced perpendicular magnetic anisotropy at the edges of the antidots. This structure forms a magnonic crystal with a periodic antidot pattern and a periodic magnetization configuration consisting of out-of-plane magnetized bulk and in-plane magnetized rims. Our results show a different behavior of spin waves in the bulk and in the rims under varying out-of-plane external magnetic field strength, revealing complex spin-wave spectra and hybridizations between the modes of these two subsystems. A particularly strong magnon-magnon coupling, due to exchange interactions, is found between the fundamental bulk spin-wave mode and the second-order radial rim modes. However, the dynamical coupling between the spin-wave modes at low frequencies, involving the first-order radial rim modes, is masked by the changes in the static magnetization at the bulk-rim interface with magnetic field changes. The study expands the horizons of magnonic-crystal research by combining periodic structural patterning and non-collinear magnetization texture to achieve strong magnon-magnon coupling, highlighting the significant role of exchange interactions in the hybridization.

Magnon-Skyrmion Hybrid Quantum Systems: Tailoring Interactions via Magnons

Coherent and dissipative interactions between different quantum systems are essential for the construction of hybrid quantum systems and the investigation of novel quantum phenomena. Here, we propose and analyze a magnon-skyrmion hybrid quantum system, consisting of a micromagnet and nearby magnetic skyrmions. We predict a strong-coupling mechanism between the magnonic mode of the micromagnet and the quantized helicity degree of freedom of the skyrmion. We show that with this hybrid setup it is possible to induce magnon-mediated nonreciprocal interactions and responses between distant skyrmion qubits or between skyrmion qubits and other quantum systems like superconducting qubits. This work provides a quantum platform for the investigation of diverse quantum effects and quantum information processing with magnetic microstructures.

Collective Spin-Wave Dynamics in Gyroid Ferromagnetic Nanostructures

Expanding upon the burgeoning discipline of magnonics, this research elucidates the intricate dynamics of spin waves (SWs) within three-dimensional nanoenvironments. It marks a shift from traditionally used planar systems to exploration of magnetization configurations and the resulting dynamics within 3D nanostructures. This study deploys micromagnetic simulations alongside ferromagnetic resonance measurements to scrutinize magnetic gyroids, periodic chiral configurations composed of chiral triple junctions with a period in nanoscale. Our findings uncover distinctive attributes intrinsic to the gyroid network, most notably the localization of collective SW excitations and the sensitivity of the gyroid's ferromagnetic response to the orientation of the static magnetic field, a correlation closely tied to the crystallographic alignment of the structure. Furthermore, we show that for the ferromagnetic resonance, multidomain gyroid films can be treated as a magnonic material with effective magnetization scaled by its filling factor. The implications of our research carry the potential for practical uses such as an effective, metamaterial-like substitute for ferromagnetic parts and lay the groundwork for radio frequency filters. The growing areas of 3D magnonics and spintronics present exciting opportunities to investigate and utilize gyroid nanostructures for signal processing purposes.

Compact localized states in magnonic Lieb lattices

Lieb lattice is one of the simplest bipartite lattices, where compact localized states (CLS) are observed. This type of localization is induced by the peculiar topology of the unit cell, where the modes are localized only on selected sublattices due to the destructive interference of partial waves. We demonstrate the possibility of magnonic Lieb lattice realization, where flat bands and CLS can be observed in the planar structure of sub-micron in-plane sizes. Using forward volume configuration, the Ga-doped YIG layer with cylindrical inclusions (without Ga content) arranged in a Lieb lattice with 250 nm period was investigated numerically (finite-element method). The structure was tailored to observe, for a lowest magnonic bands, the oscillatory and evanescent spin waves in inclusions and matrix, respectively. Such a design reproduces the Lieb lattice of nodes (inclusions) coupled to each other by the matrix with the CLS in flat bands.

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

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

Tailoring crosstalk between localized 1D spin-wave nanochannels using focused ion beams

1D spin-wave conduits are envisioned as nanoscale components of magnonics-based logic and computing schemes for future generation electronics. À-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-[Formula: see text]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[Formula: see text] ion irradiation. Furthermore, after milling the microstrip along its long axis by focused ion beams, creating consecutively [Formula: see text]50 and [Formula: see text]100 nm gaps, additional resonances emerge and are attributed to modes localized at the inner edges of the separated strips. To visualize the mode distribution, spatially resolved Brillouin light scattering microscopy was used showing an excellent agreement with the ferromagnetic resonance data and confirming the mode localization at the outer/inner edges of the strips depending on the magnitude of the applied magnetic field. Micromagnetic simulations confirm that the lowest-energy modes are localized within [Formula: see text]15-nm-wide regions at the edges of the strips and their frequencies can be tuned in a wide range (up to 5 GHz) by changing the magnetostatic coupling (i.e., spatial separation) between the microstrips.

Magnetic patterning of Co/Ni layered systems by plasma oxidation

We studied the structural, chemical, and magnetic properties of Ti/Au/Co/Ni layered systems subjected to plasma oxidation. The process results in the formation of NiO at the expense of metallic Ni, as clearly evidenced by X-ray photoelectron spectroscopy, while not affecting the surface roughness and grain size of the Co/Ni bilayers. Since the decrease of the thickness of the Ni layer and the formation of NiO increase the perpendicular magnetic anisotropy, oxidation may be locally applied for magnetic patterning. Using this approach, we created 2D heterostructures characterized by different combinations of magnetic properties in areas modified by plasma oxidation and in the regions protected from oxidation. As plasma oxidation is an easy to use, low cost, and commonly utilized technique in industrial applications, it may constitute an improvement over other magnetic patterning methods.

Engineering the Exchange Spin Waves in Graded Thin Ferromagnetic Films

The results of experimental and theoretical studies of standing spin waves in a series of epitaxial films of the ferromagnetic Pd1−xFex alloy (0.02 < x < 0.11) with different distributions of the magnetic properties across the thickness are presented. Films with linear and stepwise, as well as more complex Lorentzian, sine and cosine profiles of iron concentration in the alloy, and thicknesses from 20 to 400 nm are considered. A crucial influence of the magnetic properties profile on the spectrum of spin wave resonances is demonstrated. A capability of engineering the standing spin waves in graded ferromagnetic films for applications in magnonics is discussed.

Shaping the spin wave spectra of planar 1D magnonic crystals by the geometrical constraints

We present experimental and numerical studies demonstrating the influence of geometrical parameters on the fundamental spin-wave mode in planar 1D magnonic crystals. The investigated magnonic crystals consist of flat stripes separated by air gaps. The adjustment of geometrical parameters allows tailoring of the spin-wave frequencies. The width of stripes and the width of gaps between them affect spin-wave frequencies in two ways. First, directly by geometrical constraints confining the spin waves inside the stripes. Second, indirectly by spin-wave pinning, freeing the spin waves to a different extent on the edges of stripes. Experimentally, the fundamental spin-wave mode frequencies are measured using an all-optical pump-probe time-resolved magneto-optical Kerr-effect setup. Our studies address the problem of spin-wave confinement and spin-wave dipolar pinning in an array of coupled stripes. We show that the frequency of fundamental mode can be tuned to a large extent by adjusting the width of the stripes and the width of gaps between them.

Omnidirectional flat bands in chiral magnonic crystals

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

Resonance behavior of embedded and freestanding microscale ferromagnets

The ferromagnetic resonance of a disordered A2 Fe60Al40 ferromagnetic stripe, of dimensions 5 µm × 1 µm × 32 nm, has been observed in two vastly differing surroundings: in the first case, the ferromagnetic region was surrounded by ordered B2 Fe60Al40, and in the second case it was free standing, adhering only to the oxide substrate. The embedded ferromagnet possesses a periodic magnetic domain structure, which transforms to a single domain structure in the freestanding case. The two cases differ in their dynamic response, for instance, the resonance field for the uniform (k = 0) mode at ~ 14 GHz excitation displays a shift from 209 to 194 mT, respectively for the embedded and freestanding cases, with the external magnetic field applied along the long axis. The resonant behavior of a microscopic ferromagnet can thus be finely tailored via control of its near-interfacial surrounding.

Spin-Wave Channeling in Magnetization-Graded Nanostrips

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

Interface modes in planar one-dimensional magnonic crystals

We present the concept of Zak phase for spin waves in planar magnonic crystals and discuss the existence condition of interface modes localized on the boundary between two magnonic crystals with centrosymmetric unit cells. Using the symmetry criterion and analyzing the logarithmic derivative of the Bloch function, we study the interface modes and demonstrate the bulk-to-edge correspondence. Our theoretical results are verified numerically and extended to the case in which one of the magnonic crystals has a non-centrosymmetric unit cells. We show that by shifting the unit cell, the interface modes can traverse between the band gap edges. Our work also investigate the role of the dipolar interaction, by comparison the systems both with exchange interaction only and combined dipolar-exchange interactions.

Accumulation and control of spin waves in magnonic dielectric microresonators by a comb of ultrashort laser pulses

Spin waves in magnetic microresonators are at the core of modern magnonics. Here we demonstrate a new method of tunable excitation of different spin wave modes in magnetic microdisks by using a train of laser pulses coming at a repetition rate higher than the decay rate of spin precession. The microdisks are etched in a transparent bismuth iron garnet film and the light pulses influence the spins nonthermally through the inverse Faraday effect. The high repetition rate of the laser stimulus of 10 GHz establishes an interplay between the spin wave resonances in the frequency and momentum domains. As a result, scanning of the focused laser spot near the disk boarder changes interference pattern of the magnons and leads to a resonant dependence of the spin wave amplitude on the external magnetic field. Apart from that, we achieved a switching between volume and surface spin waves by a small variation of the external magnetic field.

Intrinsic topological magnons in arrays of magnetic dipoles

We study a simple magnetic system composed of periodically modulated magnetic dipoles with an easy axis. Upon adjusting the geometric modulation amplitude alone, chains and two-dimensional stacked chains exhibit a rich magnon spectrum where frequency gaps and magnon speeds are easily manipulable. The blend of anisotropy due to dipolar interactions between magnets and geometrical modulation induces a magnetic phase with fractional Zak number in infinite chains and end states in open one-dimensional systems. In two dimensions it gives rise to topological modes at the edges of stripes. Tuning the amplitude in two-dimensional lattices causes a band touching, which triggers the exchange of the Chern numbers of the volume bands and switches the sign of the thermal conductivity.

Nanoimprinted and Anodized Templates for Large-Scale and Low-Cost Nanopatterning

Nanopatterning to fabricate advanced nanostructured materials is a widely employed technology in a broad spectrum of applications going from spintronics and nanoelectronics to nanophotonics. This work reports on an easy route for nanopatterning making use of ordered porous templates with geometries ranging from straight lines to square, triangular or rhombohedral lattices, to be employed for the designed growth of sputtered materials with engineered properties. The procedure is based on large-scale nanoimprinting using patterned low-cost commercial disks, as 1-D grating stamps, followed by a single electrochemical process that allows one to obtain 1-D ordered porous anodic templates. Multiple imprinting steps at different angles enable more complex 2-D patterned templates. Subsequently, sputtering facilitates the growth of ferromagnetic antidot thin films (e.g., from 20 to 100 nm Co thick layers) with designed symmetries. This technique constitutes a non-expensive method for massive mold production and pattern generation avoiding standard lithographical techniques. In addition, it overcomes current challenges of the two-stage electrochemical porous anodic alumina templates: (i) allowing the patterning of large areas with high ordering and/or complex antidot geometries, and (ii) being less-time consuming.

Applications of nanomagnets as dynamical systems: II

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

Magnonic Crystal with Strips of Magnetic Nanoparticles: Modeling and Experimental Realization via a Dip-Coating Technique

In this article, we describe a magnonic crystal formed by magnetite nanoparticles. The periodic strip-like structure of the nanoparticles was fabricated on the surface of thin yttrium iron garnet single-crystal film grown on a gallium–gadolinium garnet substrate via dip-coating techniques. It was shown that such periodic structure induces the formation of the bandgaps in the transmission spectra of magnetostatic surface spin-waves (MSSW). The structure was simulated by the transfer matrix method. Spin-wave detection has been carried out by using a pair of microwave antennas and a vector network analyzer.

Eigenmodes of a disordered FeCo magnonic crystal at finite temperatures

In this report we present a systematic study of the magnonic modes in the disordered Fe_0.5Co_0.5alloy based on the Heisenberg Hamiltonian using two complementary approaches. In order to account for substitutional disorder, on the one hand we directly average the transverse magnetic susceptibility in real space over different disorder configurations and on the other hand we use the coherent potential approximation (CPA). While the method of direct averaging is numerically exact, it is computationally expensive and limited by the maximal size of the supercell which can be simulated on a computer. On the contrary the CPA does not suffer from this drawback and yields a cheap numerical scheme. Therefore, we additionally compare the results of these two approaches and show that the CPA gives very good results for most of the magnetic properties considered in this report, including the magnon energies and the spatial shape of the eigenmodes. However, it turns out that while reproducing the general trend, the CPA systematically underestimates the disorder induced damping of the magnons. This provides evidence that the physics of impurity scattering in this system is governed by non-local effects missing in the CPA. Finally, we study the real space eigenmodes of the system, including their spatial shapes, and analyze their temperature dependence within the random phase approximation.

Voltage-Controlled Reconfigurable Magnonic Crystal at the Sub-micrometer Scale

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 nanomagnonics 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 multiferroics with ferromagnets in a fully epitaxial heterostructure to achieve such voltage-controlled and reconfigurable magnonic systems. Imprinting a remnant electrical polarization in thin multiferroic BiFeO₃ with a periodicity of 500 nm yields a modulation of the effective magnetic field in the micrometer-scale, ferromagnetic La_2/3Sr_1/3MnO₃ magnonic waveguide. We evidence the magnetoelectric coupling by characterizing the spin wave propagation spectrum in this artificial, voltage induced, magnonic crystal and demonstrate the occurrence of a robust magnonic band gap with >20 dB rejection.

Observation of Coherent Spin Waves in a Three-Dimensional Artificial Spin Ice Structure

Harnessing high-frequency spin dynamics in three-dimensional (3D) nanostructures may lead to paradigm-shifting, next-generation devices including high density spintronics and neuromorphic systems. Despite remarkable progress in fabrication, the measurement and interpretation of spin dynamics in complex 3D structures remain exceptionally challenging. Here, we take a first step and measure coherent spin waves within a 3D artificial spin ice (ASI) structure using Brillouin light scattering. The 3D-ASI was fabricated by using a combination of two-photon lithography and thermal evaporation. Two spin-wave modes were observed in the experiment whose frequencies showed nearly monotonic variation with the applied field strength. Numerical simulations qualitatively reproduced the observed modes. The simulated mode profiles revealed the collective nature of the modes extending throughout the complex network of nanowires while showing spatial quantization with varying mode quantization numbers. The study shows a well-defined means to explore high-frequency spin dynamics in complex 3D spintronic and magnonic structures.

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.

Nanoscale magnonic Fabry-Pérot resonator for low-loss spin-wave manipulation

Active control of propagating spin waves on the nanoscale is essential for beyond-CMOS magnonic computing. Here, we experimentally demonstrate reconfigurable spin-wave transport in a hybrid YIG-based material structure that operates as a Fabry-Pérot nanoresonator. The magnonic resonator is formed by a local frequency downshift of the spin-wave dispersion relation in a continuous YIG film caused by dynamic dipolar coupling to a ferromagnetic metal nanostripe. Drastic downscaling of the spin-wave wavelength within the bilayer region enables programmable control of propagating spin waves on a length scale that is only a fraction of their wavelength. Depending on the stripe width, the device structure offers full nonreciprocity, tunable spin-wave filtering, and nearly zero transmission loss at allowed frequencies. Our results provide a practical route for the implementation of low-loss YIG-based magnonic devices with controllable transport properties.

Spin-Wave Dynamics and Symmetry Breaking in an Artificial Spin Ice

Artificial spin ices are periodic arrangements of interacting nanomagnets which allow investigating emergent phenomena in the presence of geometric frustration. Recently, it has been shown that artificial spin ices can be used as building blocks for creating functional materials, such as magnonic crystals. We investigate the magnetization dynamics in a system exhibiting anisotropic magnetostatic interactions owing to locally broken structural inversion symmetry. We find a rich spin-wave spectrum and investigate its evolution in an external magnetic field. We determine the evolution of individual modes, from building blocks up to larger arrays, highlighting the role of symmetry breaking in defining the mode profiles. Moreover, we demonstrate that the mode spectra exhibit signatures of long-range interactions in the system. These results contribute to the understanding of magnetization dynamics in spin ices beyond the kagome and square ice geometries and are relevant for the realization of reconfigurable magnonic crystals based on spin ices.

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.

Resonant subwavelength control of the phase of spin waves reflected from a Gires-Tournois interferometer

Subwavelength resonant elements are essential building blocks of metamaterials and metasurfaces, which have revolutionized photonics. Despite similarities between different wave phenomena, other types of interactions can make subwavelength coupling significantly distinct; its investigation in their context is therefore of interest both from the physics and applications perspective. In this work, we demonstrate a fully magnonic Gires–Tournois interferometer based on a subwavelength resonator made of a narrow ferromagnetic stripe lying above the edge of a ferromagnetic film. The bilayer formed by the stripe and the film underneath supports two propagative spin-wave modes, one strongly coupled with spin waves propagating in the rest of the film and another almost completely reflected at the ends of the bilayer. When the Fabry–Perot resonance conditions for this mode are satisfied, the weak coupling between both modes is sufficient to achieve high sensitivity of the phase of waves reflected from the resonator to the stripe width and, more interestingly, also to the stripe-film separation. Such spin-wave phase manipulation capabilities are a prerequisite for the design of spin-wave metasurfaces and may stimulate development of magnonic logic devices and sensors detecting magnetic nanoparticles.

Real-Space Observation of Magnon Interaction with Driven Space-Time Crystals

The concept of space-time crystals (STC), i.e., translational symmetry breaking in time and space, was recently proposed and experimentally demonstrated for quantum systems. Here, we transfer this concept to magnons and experimentally demonstrate a driven STC at room temperature. The STC is realized by strong homogeneous microwave pumping of a micron-sized permalloy (Py) stripe and is directly imaged by scanning transmission x-ray microscopy (STXM). For a fundamental understanding of the formation of the STC, micromagnetic simulations are carefully adapted to model the experimental findings. Beyond the mere generation of a STC, we observe the formation of a magnonic band structure due to back folding of modes at the STC's Brillouin zone boundaries. We show interactions of magnons with the STC that appear as lattice scattering, which results in the generation of ultrashort spin waves (SW) down to 100-nm wavelengths that cannot be described by classical dispersion relations for linear SW excitation. We expect that room-temperature STCs will be useful to investigate nonlinear wave physics, as they can be easily generated and manipulated to control their spatial and temporal band structures.

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.

Building Blocks for Magnon Optics: Emission and Conversion of Short Spin Waves

Magnons have proven to be a promising candidate for low-power wave-based computing. The ability to encode information not only in amplitude but also in phase allows for increased data transmission rates. However, efficiently exciting nanoscale spin waves for a functional device requires sophisticated lithography techniques and therefore, remains a challenge. Here, we report on a method to measure the full spin wave isofrequency contour for a given frequency and field. A single antidot within a continuous thin film excites wave vectors along all directions within a single excitation geometry. Varying structural parameters or introducing Dzyaloshinskii-Moriya interaction allows the manipulation and control of the isofrequency contour, which is desirable for the fabrication of future magnonic devices. Additionally, the same antidot structure is utilized as a multipurpose spin wave device. Depending on its position with respect to the microstrip antenna, it can either be an emitter for short spin waves or a directional converter for incoming plane waves. Using simulations we show that such a converter structure is capable of generating a coherent spin wave beam. By introducing a short wavelength spin wave beam into existing magnonic gate logic, it is conceivable to reduce the size of devices to the micrometer scale. This method gives access to short wavelength spin waves to a broad range of magnonic devices without the need for refined sample preparation techniques. The presented toolbox for spin wave manipulation, emission, and conversion is a crucial step for spin wave optics and gate logic.

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.

Voltage controlled on-demand magnonic nanochannels

Development of energy-efficient on-demand magnonic nanochannels (MNCs) can revolutionize on-chip data communication and processing. We have developed a dynamic MNC array by periodically tailoring perpendicular magnetic anisotropy using the electric field. Brillouin light scattering spectroscopy is used to probe the spin wave (SW) dispersion of MNCs formed by applying a static electric field at the CoFeB/MgO interface through the one-dimensional stripe-like array of indium tin oxide electrodes placed on top of Ta/CoFeB/MgO/Al2O3 heterostructures. Magnonic bands, consisting of two SW frequency modes, appear with a bandgap under the application of moderate gate voltage, which can be switched off by withdrawing the voltage. The experimental results are reproduced by plane wave method-based numerical calculations, and simulated SW mode profiles show propagating SWs through nanochannels with different magnetic properties. The anticrossing between these two modes gives rise to the observed magnonic bandgap.

Magnon Modes of Microstates and Microwave-Induced Avalanche in Kagome Artificial Spin Ice with Topological Defects

We investigate spin dynamics of microstates in artificial spin ice (ASI) in Ni_{81}Fe_{19} nanomagnets arranged in an interconnected kagome lattice using microfocus Brillouin light scattering, broadband ferromagnetic resonance, magnetic force microscopy, x-ray photoemission electron microscopy, and simulations. We experimentally reconfigure microstates in ASI using a 2D vector field protocol and apply microwave-assisted switching to intentionally trigger reversal. Our work is key for the creation of avalanches inside the kagome ASI and reprogrammable magnonics based on ASIs.

Writing 3D Nanomagnets Using Focused Electron Beams

Focused electron beam induced deposition (FEBID) is a direct-write nanofabrication technique able to pattern three-dimensional magnetic nanostructures at resolutions comparable to the characteristic magnetic length scales. FEBID is thus a powerful tool for 3D nanomagnetism which enables unique fundamental studies involving complex 3D geometries, as well as nano-prototyping and specialized applications compatible with low throughputs. In this focused review, we discuss recent developments of this technique for applications in 3D nanomagnetism, namely the substantial progress on FEBID computational methods, and new routes followed to tune the magnetic properties of ferromagnetic FEBID materials. We also review a selection of recent works involving FEBID 3D nanostructures in areas such as scanning probe microscopy sensing, magnetic frustration phenomena, curvilinear magnetism, magnonics and fluxonics, offering a wide perspective of the important role FEBID is likely to have in the coming years in the study of new phenomena involving 3D magnetic nanostructures.

Magnonic crystals: towards terahertz frequencies

This topical review presents an overview of the recent experimental and theoretical attempts on designing magnonic crystals for operation at different frequencies. The focus is put on the microscopic physical mechanisms involved in the formation of the magnonic band structure, allowed as well as forbidden magnon states in various systems, including ultrathin films, multilayers and artificial magnetic structures. The essential criteria for the formation of magnonic bandgaps in different frequency regimes are explained in connection with the magnon dynamics in such structures. The possibility of designing small-size magnonic crystals for operation at ultrahigh frequencies (terahertz and sub-terahertz regime) is discussed. Recently discovered magnonic crystals based on topological defects and using periodic Dzyaloshinskii-Moriya interaction, are outlined. Different types of magnonic crystals, capable of operation at different frequency regimes, are put within a rather unified picture.

Magnetization dynamics in artificial spin ice

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

Stray-Field Imaging of a Chiral Artificial Spin Ice during Magnetization Reversal

Artificial spin ices are a class of metamaterials consisting of magnetostatically coupled nanomagnets. Their interactions give rise to emergent behavior, which has the potential to be harnessed for the creation of functional materials. Consequently, the ability to map the stray field of such systems can be decisive for gaining an understanding of their properties. Here, we use a scanning nanometer-scale superconducting quantum interference device (SQUID) to image the magnetic stray field distribution of an artificial spin ice system exhibiting structural chirality as a function of applied magnetic fields at 4.2 K. The images reveal that the magnetostatic interaction gives rise to a measurable bending of the magnetization at the edges of the nanomagnets. Micromagnetic simulations predict that, owing to the structural chirality of the system, this edge bending is asymmetric in the presence of an external field and gives rise to a preferred direction for the reversal of the magnetization. This effect is not captured by models assuming a uniform magnetization. Our technique thus provides a promising means for understanding the collective response of artificial spin ices and their interactions.

Generation of DC, AC, and Second-Harmonic Spin Currents by Electromagnetic Fields in an Inversion-Asymmetric Antiferromagnet

Manipulating spin currents in magnetic insulators is a key technology in spintronics. We theoretically study a simple inversion-asymmetric model of quantum antiferromagnets, where both the exchange interaction and the magnetic field are staggered. We calculate spin currents generated by external electric and magnetic fields by using a quantum master equation. We show that an ac electric field with amplitude E 0 leads, through exchange-interaction modulation, to the dc and second-order harmonic spin currents proportional to E 0 2 . We also show that dc and ac staggered magnetic fields B 0 generate the dc and ac spin currents proportional to B 0 , respectively. We elucidate the mechanism by an exactly solvable model, and thereby propose the ways of spin current manipulation by electromagnetic fields.

Three port logic gate using forward volume spin wave interference in a thin yttrium iron garnet film

We demonstrate a logic gate based on interference of forward volume spin waves (FVSWs) propagating in a 54 nm thick, 100 μm wide yttrium iron garnet waveguide grown epitaxially on a garnet substrate. Two FVSWs injected by coplanar waveguides were made to interfere constructively and destructively by varying their phase difference, showing an XNOR logic function. The reflected and resonant waves generated at the edges of the waveguide were suppressed using spin wave absorbers. The observed isolation ratio was 19 dB for a magnetic field of ~2.80 kOe ( = 223 kA m^-1) applied perpendicular to the film. The wavelength and device length were ~8.9 μm and ~53 μm, respectively. Further, the interference state of the SWs was analyzed using three-dimensional radio frequency simulations.

Magnetic reversal in perpendicularly magnetized antidot arrays with intrinsic and extrinsic defects

Defects can significantly affect performance of nanopatterned magnetic devices, therefore their influence on the material properties has to be understood well before the material is used in technological applications. However, this is experimentally challenging due to the inability of the control of defect characteristics in a reproducible manner. Here, we construct a micromagnetic model, which accounts for intrinsic and extrinsic defects associated with the polycrystalline nature of the material and with corrugated edges of nanostructures. The predictions of the model are corroborated by the measurements obtained for highly ordered arrays of circular Co/Pd antidots with perpendicular magnetic anisotropy. We found that magnetic properties, magnetic reversal and the evolution of the domain pattern are strongly determined by density of defects, heterogeneity of nanostructures, and edge corrugations. In particular, an increase in the Néel domain walls, as compared to Bloch walls, was observed with a increase of the antidot diameters, suggesting that a neck between two antidots can behave like a nanowire with a width determined by the array period and antidot size. Furthermore, the presence of edge corrugations can lead to the formation of a network of magnetic bubbles, which are unstable in non-patterned flat films.

Ferromagnet/Superconductor Hybrid Magnonic Metamaterials

In this work, a class of metamaterials is proposed on the basis of ferromagnet/superconductor hybridization for applications in magnonics. These metamaterials comprise of a ferromagnetic magnon medium that is coupled inductively to a superconducting periodic microstructure. Spectroscopy of magnetization dynamics in such hybrid evidences formation of areas in the medium with alternating dispersions for spin wave propagation, which is the basic requirement for the development of metamaterials known as magnonic crystals. The spectrum allows for derivation of the impact of the superconducting structure on the dispersion: it takes place due to a diamagnetic response of superconductors on the external and stray magnetic fields. In addition, the spectrum displays a dependence on the superconducting critical state of the structure: the Meissner and the mixed states of a type II superconductor are distinguished. This dependence hints toward nonlinear response of hybrid metamaterials on the magnetic field. Investigation of the spin wave dispersion in hybrid metamaterials shows formation of allowed and forbidden bands for spin wave propagation. The band structures are governed by the geometry of spin wave propagation: in the backward volume geometry the band structure is conventional, while in the surface geometry the band structure is nonreciprocal and is formed by indirect band gaps.

Spin Pinning and Spin-Wave Dispersion in Nanoscopic Ferromagnetic Waveguides

Spin waves are investigated in yttrium iron garnet waveguides with a thickness of 39 nm and widths ranging down to 50 nm, i.e., with an aspect ratio thickness over width approaching unity, using Brillouin light scattering spectroscopy. The experimental results are verified by a semianalytical theory and micromagnetic simulations. A critical width is found, below which the exchange interaction suppresses the dipolar pinning phenomenon. This changes the quantization criterion for the spin-wave eigenmodes and results in a pronounced modification of the spin-wave characteristics. The presented semianalytical theory allows for the calculation of spin-wave mode profiles and dispersion relations in nanostructures.

Strongly coupled magnon-phonon dynamics in a single nanomagnet

Polaritons are widely investigated quasiparticles with fundamental and technological significance due to their unique properties. They have been studied most extensively in semiconductors when photons interact with various elementary excitations. However, other strongly coupled excitations demonstrate similar dynamics. Specifically, when magnon and phonon modes are coupled, a hybridized magnon–phonon quasiparticle can form. Here, we report on the direct observation of coupled magnon–phonon dynamics within a single thin nickel nanomagnet. We develop an analytic description to model the dynamics in two dimensions, enabling us to isolate the parameters influencing the frequency splitting. Furthermore, we demonstrate tuning of the magnon–phonon interaction into the strong coupling regime via the orientation of the applied magnetic field.

Exploring the magnon and phonon coupling may enable high efficiency magnonic applications. Here the authors show the observation, understanding and control of the magnon–phonon interaction by studying the magneto-acoustic resonance modes of a single thin-film Ni nanomagnet.

Backscattering Immunity of Dipole-Exchange Magnetostatic Surface Spin Waves

The existence of backscattering-immune spin-wave modes is demonstrated in magnetic thin films of nanoscale thickness. Our results reveal that chiral magnetostatic surface waves (CMSSWs), which propagate perpendicular to the magnetization direction in an in-plane magnetized thin film, are robust against backscattering from surface defects. CMSSWs are protected against various types of surface inhomogeneities and defects as long as their frequency lies inside the gap of the volume modes. Our explanation is independent of the topology of the modes and predicts that this robustness is a consequence of symmetry breaking of the dynamic magnetic fields of CMSSWs due to the off-diagonal part of the dipolar interaction tensor, which is present both for long- (dipole-dominated) and short-wavelength (exchange-dominated) spin waves. Micromagnetic simulations confirm the robust character of the CMSSWs. Our results open a new direction in designing highly efficient magnonic logic elements and devices employing CMSSWs in nanoscale thin films.

Spin-Wave Phase Inverter upon a Single Nanodefect

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 shifters upon a single nanogroove milled by a 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 inversion. The microscopic mechanism of the phase shift is based on the combined action of the nanogroove as a geometrical defect and the lower spin-wave group velocity in the waveguide under the groove where the magnetization is reduced due to the incorporation of Ga ions during the ion-beam milling. The proposed phase shifter can easily be on-chip integrated with spin-wave logic gates and other magnonic devices. Our findings are crucial for designing nanomagnonic circuits and for the development of spin-wave nano-optics.