Inverse-design magnonic devices

Goos-Hänchen shift of inelastically scattered spin-wave beams and cascade nonlinear magnon processes

We study, using micromagnetic simulations, the inelastic scattering of spin-wave beams on edge-localized spin-wave modes in a thin ferromagnetic film. In the splitting and confluence processes, the new spin-wave beams are generated with frequencies shifted by the edge-mode frequency. We report that inelastically scattered spin-wave beams in both processes not only change their direction of propagation but also undergo lateral shifts along the interface, analogous to the Goos-Hänchen effect known in optics. These shifts of inelastically scattered beams, for a few special cases described in the paper, can be in the range of several wavelengths, which is larger than the Goos-Hänchen shift of elastically reflected beam. Unexpectedly, at selected frequencies, we found a significant increase in the value of the lateral shifts of the scattered spin-wave beams formed in the confluence process. We show that this effect is associated with the cascading nonlinear processes taking place at the edge of the film and involving the primary edge spin wave. Our results make an important contribution to the understanding of the nonlinear nature of spin waves and provide a way to exploit it in signal processing with magnons.

Optical control of spin waves in hybrid magnonic-plasmonic structures

Magnonics, which harnesses the unique properties of spin waves, offers promising advancements in data processing due to its broad frequency range, nonlinear dynamics, and scalability for on-chip integration. Effective information encoding in magnonic systems requires precise spatial and temporal control of spin waves. Here, we demonstrate the rapid optical control of spin-wave transport in hybrid magnonic-plasmonic structures. By using thermoplasmonic heating in yttrium iron garnet films integrated with gold nanodisk arrays, we achieve a suppression of spin-wave signals by 20 dB using single laser pulses lasting just a few hundred nanoseconds. Our results reveal a strong correlation between plasmonic light absorption and spin-wave manipulation, as supported by micromagnetic simulations that emphasize the crucial role of magnonic refraction. This study establishes thermoplasmonics as a powerful tool for controlling spin-wave propagation, bridging the fields of magnonics and plasmonics, and paving the way for the development of multifunctional hybrid magnonic devices.

Handedness manipulation of propagating antiferromagnetic magnons

Antiferromagnetic magnons possess a distinctive feature absent in their ferromagnetic counterparts: the presence of two distinct handedness modes, the right-handed (RH) and left-handed (LH) precession modes. The magnon handedness determines the sign of spin polarization carried by the propagating magnon, which is indispensable for harnessing the diverse functionalities in magnonic devices, such as data encoding, magnon polarization-based logic systems, and quantum applications involving magnons. However, the control of coherently propagating magnon handedness in antiferromagnets has remained elusive. Here we demonstrate the manipulation and electrical readout of propagating magnon handedness in perpendicularly magnetized synthetic antiferromagnets (SAF). We find that the antiferromagnetic magnon handedness can be directly identified by measuring the inverse spin Hall effect (ISHE) voltage, which arises from the spin pumping effect caused by the propagating antiferromagnetic magnons in the SAF structure. The RH and LH modes of the magnon can be distinguishable when the SAF structure is sandwiched by heavy metals with the same sign of spin Hall angle. This work unveils promising avenues for harnessing the unique properties of antiferromagnetic magnons.

Recent Progress in Two-Dimensional Magnetic Materials

The giant magnetoresistance effect in two-dimensional (2D) magnetic materials has sparked substantial interest in various fields; including sensing; data storage; electronics; and spintronics. Their unique 2D layered structures allow for the manifestation of distinctive physical properties and precise performance regulation under different conditions. In this review, we present an overview of this rapidly developing research area. Firstly, these 2D magnetic materials are catalogued according to magnetic coupling types. Then, several vital effects in 2D magnets are highlighted together with theoretical investigation, such as magnetic circular dichroism, magneto-optical Kerr effect, and anomalous Hall effect. After that, we forecast the potential applications of 2D magnetic materials for spintronic devices. Lastly, research advances in the attracting magnons, skyrmions and other spin textures in 2D magnets are discussed.

Investigation of Mode-Induced Spin Wave Transmission Blockage by In Situ Nanoscale Grooves

In the pursuit of advancing spin-wave optics, the propagation of magnetostatic surface spin-waves is investigated in a uniform permalloy waveguide with in-situ nanopatterned grooves created through Atomic Force Microscopy nanolithography and Focused Ion Beam etching. The study unveils that the introduction of narrow constrictions and grooves leads to a non-monotonic reduction of the transmitted spin-wave signal intensity as the spin-wave pathway is shrinked. The remarkable feature that a stronger signal extinction is obtained for a narrow groove compared to a spin-waveguide interrupted by a full gap, where only inefficient transport through dipolar coupling is allowed, is highlighted. Combining experimental and numerical analyses, the intricate interplay between spin-wave diffraction and reflection at the waveguide edges is unraveled, being at the origin of a transverse-mode variation responsible for the signal extinction when detected using coplanar antennas. The findings offer insights into the controllable manipulation of detected spin-wave intensity, thereby opening promising avenues for the improvement of spin-wave switches and interferometers, and for the nanopatterning of graded index magnonics.

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.

Electric-Field Manipulation of Magnetic Chirality in a Homo-Ferro-Rotational Helimagnet

Ferro-rotational (FR) materials, renowned for their distinctive material functionalities, present challenges in the growth of homo-FR crystals (i.e., single FR domain). This study explores a cost-effective approach to growing homo-FR helimagnetic RbFe(SO4)2 (RFSO) crystals by lowering the crystal growth temperature below the TFR threshold using the high-pressure hydrothermal method. Through polarized neutron diffraction experiments, it is observed that nearly 86% of RFSO crystals consist of a homo-FR domain. Notably, RFSO displays remarkable stability in the FR phase, with an exceptionally high TFR of ≈573 K. Furthermore, RFSO exhibits a chiral helical magnetic structure with switchable ferroelectric polarization below 4 K. Importantly, external electric fields can induce a single magnetic domain state and manipulate its magnetic chirality. The findings suggest that the search for new FR magnets with outstanding material properties should consider magnetic sulfates as promising candidates.

Emergent coherent modes in nonlinear magnonic waveguides detected at ultrahigh frequency resolution

Nonlinearity of dynamic systems plays a key role in neuromorphic computing, which is expected to reduce the ever-increasing power consumption of machine learning and artificial intelligence applications. For spin waves (magnons), nonlinearity combined with phase coherence is the basis of phenomena like Bose-Einstein condensation, frequency combs, and pattern recognition in neuromorphic computing. Yet, the broadband electrical detection of these phenomena with high-frequency resolution remains a challenge. Here, we demonstrate the generation and detection of phase-coherent nonlinear magnons in an all-electrical GHz probe station based on coplanar waveguides connected to a vector network analyzer which we operate in a frequency-offset mode. Making use of an unprecedented frequency resolution, we resolve the nonlocal emergence of a fine structure of propagating nonlinear magnons, which sensitively depends on both power and a magnetic field. These magnons are shown to maintain coherency with the microwave source while propagating over macroscopic distances. We propose a multi-band four-magnon scattering scheme that is in agreement with the field-dependent characteristics of coherent nonlocal signals in the nonlinear excitation regime. Our findings are key to enable the seamless integration of nonlinear magnon processes into high-speed microwave electronics and to advance phase-encoded information processing in magnonic neuronal networks.

Magnetization dynamics in single and trilayer nanowires

We have studied the magnetization dynamics of single Py(t) (t= 20 nm, 50 nm) and trilayer [Py(50)/Pd(tPd)/Py(20)] nanowire arrays fabricated over large areas using deep ultraviolet lithography technique. The dynamic properties are sensitive to the field orientation and magnetic film thicknesses. A single resonant mode corresponding to the excitations at the bulk part of the wire is detected in all the single-layer nanowire arrays. Furthermore, the spacer layer thickness influenced the dynamic properties in trilayer samples due to the different coupling mechanisms. A single resonant mode is observed intPd= 2 nm trilayer nanowires with a sharp frequency jump from 13 GHz to 15 GHz across the reversal regime. This indicates the exchange coupling and the coherence in magnetization precession in the ferromagnetic layers. On the other hand, wires with 10 nm-spacer display two well-resolved modes separated by ∼3 GHz with a gradual change in frequency across the reversal regime from-26mT to-46mT, indicating the presence of long-range dipolar interactions instead of exchange coupling. The spacer layer of the proposed spin-valve-type structure can be tailored for desired microwave splitters or combiners.

Tailoring magnon modes by extending square, kagome, and trigonal spin ice lattices vertically via interlayer coupling of trilayer nanomagnets

In this work high-frequency magnetization dynamics and statics of artificial spin-ice lattices with different geometric nanostructure array configurations are studied where the individual nanostructures are composed of ferromagnetic/non-magnetic/ferromagnetic trilayers with different non-magnetic thicknesses. These thickness variations enable additional control over the magnetic interactions within the spin-ice lattice that directly impacts the resulting magnetization dynamics and the associated magnonic modes. Specifically the geometric arrangements studied are square, kagome and trigonal spin ice configurations, where the individual lithographically patterned nanomagnets (NMs) are trilayers, made up of two magnetic layers ofNi81Fe19of 30 nm and 70 nm thickness respectively, separated by a non-magnetic copper layer of either 2 nm or 40 nm. We show that coupling via the magnetostatic interactions between the ferromagnetic layers of the NMs within square, kagome and trigonal spin-ice lattices offers fine-control over magnetization states and magnetic resonant modes. In particular, the kagome and trigonal lattices allow tuning of an additional mode and the spacing between multiple resonance modes, increasing functionality beyond square lattices. These results demonstrate the ability to move beyond quasi-2D single magnetic layer nanomagnetics via control of the vertical interlayer interactions in spin ice arrays. This additional control enables multi-mode magnonic programmability of the resonance spectra, which has potential for magnetic metamaterials for microwave or information processing applications.

The 2024 magnonics roadmap

Magnonicsis a research field that has gained an increasing interest in both the fundamental and applied sciences in recent years. This field aims to explore and functionalize collective spin excitations in magnetically ordered materials for modern information technologies, sensing applications and advanced computational schemes. Spin waves, also known as magnons, carry spin angular momenta that allow for the transmission, storage and processing of information without moving charges. In integrated circuits, magnons enable on-chip data processing at ultrahigh frequencies without the Joule heating, which currently limits clock frequencies in conventional data processors to a few GHz. Recent developments in the field indicate that functional magnonic building blocks for in-memory computation, neural networks and Ising machines are within reach. At the same time, the miniaturization of magnonic circuits advances continuously as the synergy of materials science, electrical engineering and nanotechnology allows for novel on-chip excitation and detection schemes. Such circuits can already enable magnon wavelengths of 50 nm at microwave frequencies in a 5G frequency band. Research into non-charge-based technologies is urgently needed in view of the rapid growth of machine learning and artificial intelligence applications, which consume substantial energy when implemented on conventional data processing units. In its first part, the 2024 Magnonics Roadmap provides an update on the recent developments and achievements in the field of nano-magnonics while defining its future avenues and challenges. In its second part, the Roadmap addresses the rapidly growing research endeavors on hybrid structures and magnonics-enabled quantum engineering. We anticipate that these directions will continue to attract researchers to the field and, in addition to showcasing intriguing science, will enable unprecedented functionalities that enhance the efficiency of alternative information technologies and computational schemes.

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

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

Inverse design of an ultra-compact dual-band wavelength demultiplexing power splitter with detailed analysis of hyperparameters

Inverse design has been widely studied as an efficient method to reduce footprint and improve performance for integrated silicon photonic (SiP) devices. In this study, we have used inverse design to develop a series of ultra-compact dual-band wavelength demultiplexing power splitters (WDPSs) that can simultaneously perform both wavelength demultiplexing and 1:1 optical power splitting. These WDPSs could facilitate the potential coexistence of dual-band passive optical networks (PONs). The design is performed on a standard silicon-on-insulator (SOI) platform using, what we believe to be, a novel two-step direct binary search (TS-DBS) method and the impact of different hyperparameters related to the physical structure and the optimization algorithm is analyzed in detail. Our inverse-designed WDPS with a minimum feature size of 130 nm achieves a 12.77-times reduction in footprint and a slight increase in performance compared with the forward-designed WDPS. We utilize the optimal combination of hyperparameters to design another WDPS with a minimum feature size reduced to 65 nm, which achieves ultra-low insertion losses of 0.36 dB and 0.37 dB and crosstalk values of -19.91 dB and -17.02 dB at wavelength channels of 1310 nm and 1550 nm, respectively. To the best of our knowledge, the hyperparameters of optimization-based inverse design are systematically discussed for the first time. Our work demonstrates that appropriate setting of hyperparameters greatly improves device performance, throwing light on the manipulation of hyperparameters for future inverse design.

magnum.np: a PyTorch based GPU enhanced finite difference micromagnetic simulation framework for high level development and inverse design

magnum.np is a micromagnetic finite-difference library completely based on the tensor library PyTorch. The use of such a high level library leads to a highly maintainable and extensible code base which is the ideal candidate for the investigation of novel algorithms and modeling approaches. On the other hand magnum.np benefits from the device abstraction and optimizations of PyTorch enabling the efficient execution of micromagnetic simulations on a number of computational platforms including graphics processing units and potentially Tensor processing unit systems. We demonstrate a competitive performance to state-of-the-art micromagnetic codes such as mumax3 and show how our code enables the rapid implementation of new functionality. Furthermore, handling inverse problems becomes possible by using PyTorch's autograd feature.

3D Magnonic Conduits by Direct Write Nanofabrication

Magnonics is a rapidly developing domain of nanomagnetism, with application potential in information processing systems. Realisation of this potential and miniaturisation of magnonic circuits requires their extension into the third dimension. However, so far, magnonic conduits are largely limited to thin films and 2D structures. Here, we introduce 3D magnonic nanoconduits fabricated by the direct write technique of focused-electron-beam induced deposition (FEBID). We use Brillouin light scattering (BLS) spectroscopy to demonstrate significant qualitative differences in spatially resolved spin-wave resonances of 2D and 3D nanostructures, which originates from the geometrically induced non-uniformity of the internal magnetic field. This work demonstrates the capability of FEBID as an additive manufacturing technique to produce magnetic 3D nanoarchitectures and presents the first report of BLS spectroscopy characterisation of FEBID conduits.

Spin-Wave Optics in YIG Realized by Ion-Beam Irradiation

Direct focused-ion-beam writing is presented as an enabling technology for realizing functional spin-wave devices of high complexity, and demonstrate its potential by optically-inspired designs. It is shown that ion-beam irradiation changes the characteristics of yttrium iron garnet films on a submicron scale in a highly controlled way, allowing one to engineer the magnonic index of refraction adapted to desired applications. This technique does not physically remove material, and allows rapid fabrication of high-quality architectures of modified magnetization in magnonic media with minimal edge damage (compared to more common removal techniques such as etching or milling). By experimentally showing magnonic versions of a number of optical devices (lenses, gratings, Fourier-domain processors) this technology is envisioned as the gateway to building magnonic computing devices that rival their optical counterparts in their complexity and computational power.

Experimental Realization of a Skyrmion Circulator

Magnetic skyrmions are mobile topological spin textures that can be manipulated by different means. Their applications have been frequently discussed in the context of information carriers for racetrack memory devices, which on the other hand, exhibit a skyrmion Hall effect as a result of the nontrivial real-space topology. While the skyrmion Hall effect is believed to be detrimental for constructing racetrack devices, we show here that it can be implemented for realizing a three-terminal skyrmion circulator. In analogy to the microwave circulator, nonreciprocal transportation and circulation of skyrmions are studied both numerically and experimentally. In particular, successful control of the circulating direction of being either clockwise or counterclockwise is demonstrated, simply by changing the sign of the topological charge. Our studies suggest that the topological property of skyrmions can be incorporated for enabling novel spintronic functionalities; the skyrmion circulator is just one example.

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

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

A review on quantum computing and deep learning algorithms and their applications

In this paper, we describe a review concerning the Quantum Computing (QC) and Deep Learning (DL) areas and their applications in Computational Intelligence (CI). Quantum algorithms (QAs), engage the rules of quantum mechanics to solve problems using quantum information, where the quantum information is concerning the state of a quantum system, which can be manipulated using quantum information algorithms and other processing techniques. Nowadays, many QAs have been proposed, whose general conclusion is that using the effects of quantum mechanics results in a significant speedup (exponential, polynomial, super polynomial) over the traditional algorithms. This implies that some complex problems currently intractable with traditional algorithms can be solved with QA. On the other hand, DL algorithms offer what is known as machine learning techniques. DL is concerned with teaching a computer to filter inputs through layers to learn how to predict and classify information. Observations can be in the form of plain text, images, or sound. The inspiration for deep learning is the way that the human brain filters information. Therefore, in this research, we analyzed these two areas to observe the most relevant works and applications developed by the researchers in the world.

FORC-Diagram Analysis for a Step-like Magnetization Reversal in Nanopatterned Stripe Array

The fabrication approach of a magnonic crystal with a step-like hysteresis behavior based on a uniform non-monotonous iron layer made by shadow deposition on a preconfigured substrate is reported. The origin of the step-like hysteresis loop behavior is studied with local and integral magnetometry methods, including First-Order Reversal Curves (FORC) diagram analysis, accompanied with magnetic microstructure dynamics measurements. The results are validated with macroscopic magnetic properties and micromagnetic simulations using the intrinsic switching field distribution model. The proposed fabrication method can be used to produce magnonic structures with the controllable hysteresis plateau region's field position and width that can be used to control the magnonic crystal's band structure by changing of an external magnetic field.

Nanoscale neural network using non-linear spin-wave interference

We demonstrate the design of a neural network hardware, where all neuromorphic computing functions, including signal routing and nonlinear activation are performed by spin-wave propagation and interference. Weights and interconnections of the network are realized by a magnetic-field pattern that is applied on the spin-wave propagating substrate and scatters the spin waves. The interference of the scattered waves creates a mapping between the wave sources and detectors. Training the neural network is equivalent to finding the field pattern that realizes the desired input-output mapping. A custom-built micromagnetic solver, based on the Pytorch machine learning framework, is used to inverse-design the scatterer. We show that the behavior of spin waves transitions from linear to nonlinear interference at high intensities and that its computational power greatly increases in the nonlinear regime. We envision small-scale, compact and low-power neural networks that perform their entire function in the spin-wave domain.

Wave based computing has sparked much interest for neuromorphic computing due to the inherent interconnectedness of such wave based approaches. Here, Papp, Porod and Csaba show how neural networks can be implemented using spin-waves, taking advantage of spin-waves intrinsic non-linearity.

Controlling the three dimensional propagation of spin waves in continuous ferromagnetic films with an increasing out of plane undulation

The role of three-dimensionality in a ferromagnetic medium in ruling the propagation properties of spin-waves (SW) has been one of the main focuses of the research activity in recent years. In this context, we investigate the evolution of the SW dispersion (frequency vs wave vector) induced by a progressive vertical undulation of a ferromagnetic film. The geometric undulation is taken along a single direction and is periodic with constant period, while the amplitude (differential maximum height with respect to the film thickness) is gradually increased from 0 to 60 nm. We study the characteristic modification of the internal effective field and link it to the resulting SW dispersions and spatial profile. These systems display at once features both of a planar film and a discretized medium, and the dispersion curves change not only when SWs propagate along the undulation direction, but also perpendicular to it. We discuss the geometric and magnetic conditions for having either the invariance of the SW group velocity with respect to even major changes in the undulation, or a large group velocity for some edge modes. We address a potential dual-band activity, namely the simultaneous propagation of two independent SW-signals, with separated frequency bands and disjoint oscillation regions.

The 2021 Magnonics Roadmap

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