Search

While Spin Waves (SW) interaction provides natural support for low power Majority (MAJ) gate implementations many hurdles still exists on the road towards the realization of practically relevant SW circuits. In this paper we leave the SW interaction avenue and propose Threshold Logic (TL) inspired SW computing, which relies on successive phase rotations applied to one single SW instead of on the interference of an odd number of SWs. After providing a short TL inside we introduce the SW TL gate concept and discuss the way to mirror TL gate weight and threshold values into physical phase-shifter parameters. Subsequently, we design and demonstrate proper operation of a SW TL based Full Adder (FA) by means of micro-magnetic simulations. We conclude the paper by providing inside on the potential advantages of our proposal by means of a conceptual comparison of MAJ and TL based FA implementations., Comment: This work has received funding from the Horizon Europe research and innovation program within the project "Spider" (grant agreement no. 101070417)

This study introduces a method for the characterization of the magnetoelectric coupling in nanoscale Pb(Zr,Ti)O3/CoFeB thin film composites based on propagating spin-wave spectroscopy. Finite element simulations of the strain distribution in the devices indicated that the magnetoelastic effective field in the CoFeB waveguides was maximized in the Damon - Eshbach configuration. All-electrical broadband propagating spin-wave transmission measurements were conducted on Pb(Zr,Ti)O3/CoFeB magnetoelectric waveguides with lateral dimensions down to 700 nm. The results demonstrated that the spin-wave resonance frequency can be modulated by applying a bias voltage to Pb(Zr,Ti)O3. The modulation is hysteretic due to the ferroelastic behavior of Pb(Zr,Ti)O3. An analytical model was then used to correlate the change in resonance frequency to the induced magnetoelastic field in the magnetostrictive CoFeB waveguide. We observe a hysteresis magnetoelastic field strength with values as large as 5.61 mT, and a non-linear magnetoelectric coupling coefficient with a maximum value of 1.69 mT/V., Comment: This project has received funding from the European Union's Horizon Europe research and innovation programme under grant agreement No 101070536 - project MandMEMS

We have studied the effect of chemical-mechanical polishing (CMP) on the ferroelectric, piezoelectric, and microwave dielectric properties of Ba-substituted PZT (BPZT), deposited by pulsed laser deposition. CMP allowed for the reduction of the root mean square surface roughness of 600 nm thick BPZT films from 12.1nm to 0.79 nm. Ammonium peroxide (SC-1) cleaning was effective to remove Si CMP residuals. Measurements of the ferroelectric hysteresis after CMP indicated that the ferroelectric properties of BPZT were only weakly affected by CMP, while the piezoelectric d33 coefficient and the microwave permittivity were reduced slightly by 10%. This can be attributed to the formation of a thin dead layer at the BPZT surface. Moreover, the intrinsic dielectric permittivity at microwave frequencies between 1 and 25 GHz was not influenced by CMP, whereas the dead layer series capacitance decreased by 10%. The results indicate that the CMP process can be used to smoothen the BPZT surface without affecting the film properties strongly., Comment: 13 pages of text, 4 tables and 7 figures. This project has received funding from the European Union's Horizon 2020 research and innovation program under grant agreement No. 801055 "Spin Wave Computing for Ultimately-Scaled Hybrid Low-Power Electronics" - CHIRON

In the "Beyond Moore's Law" era, with increasing edge intelligence, domain-specific computing embracing unconventional approaches will become increasingly prevalent. At the same time, adopting a variety of nanotechnologies will offer benefits in energy cost, computational speed, reduced footprint, cyber resilience, and processing power. The time is ripe for a roadmap for unconventional computing with nanotechnologies to guide future research, and this collection aims to fill that need. The authors provide a comprehensive roadmap for neuromorphic computing using electron spins, memristive devices, two-dimensional nanomaterials, nanomagnets, and various dynamical systems. They also address other paradigms such as Ising machines, Bayesian inference engines, probabilistic computing with p-bits, processing in memory, quantum memories and algorithms, computing with skyrmions and spin waves, and brain-inspired computing for incremental learning and problem-solving in severely resource-constrained environments. These approaches have advantages over traditional Boolean computing based on von Neumann architecture. As the computational requirements for artificial intelligence grow 50 times faster than Moore's Law for electronics, more unconventional approaches to computing and signal processing will appear on the horizon, and this roadmap will help identify future needs and challenges. In a very fertile field, experts in the field aim to present some of the dominant and most promising technologies for unconventional computing that will be around for some time to come. Within a holistic approach, the goal is to provide pathways for solidifying the field and guiding future impactful discoveries., Comment: 80 pages accepted in Nano Futures

In the early stages of a novel technology development, it is difficult to provide a comprehensive assessment of its potential capabilities and impact. Nevertheless, some preliminary estimates can be drawn and are certainly of great interest and in this paper we follow this line of reasoning within the framework of the Spin Wave (SW) computing paradigm. In particular, we are interested in assessing the technological development horizon that needs to be reached in order to unleash the full SW paradigm potential such that SW circuits can outperform CMOS counterparts in terms of energy consumption. In view of the zero power SWs propagation through ferromagnetic waveguides, the overall SW circuit power consumption is determined by the one associated to SWs generation and sensing by means of transducers. While current antenna based transducers are clearly power hungry recent developments indicate that magneto-electric (ME) cells have a great potential for ultra-low power SW generation and sensing. Given that MEs have been only proposed at the conceptual level and no actual experimental demonstration has been reported we cannot evaluate the impact of their utilization on the SW circuit energy consumption. However, we can perform a reverse engineering alike analysis to determine ME delay and power consumption upper bounds that can place SW circuits in the leading position. To this end, we utilize a 32-bit Brent-Kung Adder (BKA) as discussion vehicle and compute the maximum ME delay and power consumption that could potentially enable a SW implementation able to outperform its 7nm CMOS counterpart. We evaluate different BKA SW implementations that rely on conversion or normalization gate cascading and consider continuous or pulsed SW generation scenarios. 31nW is the maximum transducer power consumption for which a 32-bit BKA SW implementation can outperform its 7nm CMOS counterpart., Comment: This work has received funding from the European Union's Horizon 2020 research and innovation program within the FET-OPEN project CHIRON under grant agreement No. 801055

We derive an analytical model for the power transfer in a magnetoelectric film bulk acoustic resonator consisting of a piezoelectric--magnetostrictive bilayer. The model describes the dynamic magnetostrictive influence on the elastodynamics via an effective frequency-dependent stiffness constant. This allows for the calculation of both the magnetic and elastic power absorption in the resonator as well as of its energy efficiency when such a resonator is considered as a magnetic transducer. The model is then applied to example systems consisting of piezoelectric ScAlN and magnetostrictive CoFeB, Ni, or Terfenol-D layers., Comment: 39 pages, 9 figures. This project has received funding from the European Union's Horizon 2020 research and innovation program under grant agreement No. 801055 "Spin Wave Computing for Ultimately-Scaled Hybrid Low-Power Electronics" - CHIRON

The parametric excitation of spin waves by coherent surface acoustic waves is demonstrated experimentally in metallic magnetic thin film structures. The involved magnon modes are analyzed with micro-focused Brillouin light scattering spectroscopy and complementary micromagnetic simulations combined with analytical modelling are used to determine the origin of the spin-wave instabilities. Depending on the experimental conditions, we observe spin-wave instabilities originating from different phonon-magnon and magnon-magnon scattering processes. Our results demonstrate that an efficient excitation of high amplitude, strongly nonlinear magnons in metallic ferromagnets is possible by surface acoustic waves, which opens novel ways to create micro-scaled nonlinear magnonic systems for logic and data processing that can profit from the high excitation efficiency of phonons using piezoelectricity., Comment: This project has received funding from the European Union's Horizon 2020 research and innovation program under grant agreement No. 801055 "Spin Wave Computing for Ultimately-Scaled Hybrid Low-Power Electronics" - CHIRON

We derive a lumped circuit model for inductive antenna spin-wave transducers in the vicinity of a ferromagnetic medium. The model considers the antenna's Ohmic resistance, its inductance, as well as the additional inductance due to the excitation of ferromagnetic resonance or spin waves in the ferromagnetic medium. As an example, the additional inductance is discussed for a wire antenna on top of a ferromagnetic waveguide, a structure that is characteristic for many magnonic devices and experiments. The model is used to assess the scaling properties and the energy efficiency of inductive antennas. Issues related to scaling antenna transducers to the nanoscale and possible solutions are also addressed., Comment: This project has received funding from the European Union's Horizon 2020 research and innovation program under grant agreement No. 801055 "Spin Wave Computing for Ultimately-Scaled Hybrid Low-Power Electronics" CHIRON

In this paper, we propose an energy efficient SW based approximate 4:2 compressor comprising a 3-input and a 5-input Majority gate. We validate our proposal by means of micromagnetic simulations, and assess and compare its performance with one of the state-of-the-art SW, 45nm CMOS, and Spin-CMOS counterparts. The evaluation results indicate that the proposed compressor consumes 31.5\% less energy in comparison with its accurate SW design version. Furthermore, it has the same energy consumption and error rate as the approximate compressor with Directional Coupler (DC), but it exhibits 3x lower delay. In addition, it consumes 14% less energy, while having 17% lower average error rate than the approximate 45nm CMOS counterpart. When compared with the other emerging technologies, the proposed compressor outperforms approximate Spin-CMOS based compressor by 3 orders of magnitude in term of energy consumption while providing the same error rate. Finally, the proposed compressor requires the smallest chip real-estate measured in terms of devices., Comment: This work has received funding from the European Union's Horizon 2020 research and innovation program within the FET-OPEN project CHIRON under grant agreement No. 801055. It has also been partially supported by imec's industrial affiliate program on beyond-CMOS logic. F.V. acknowledges financial support from Flanders Research Foundation (FWO) through grant No.~1S05719N

By their very nature, Spin Waves (SWs) consume ultra-low amounts of energy, which makes them suitable for ultra-low energy consumption applications. In addition, a compressor can be utilized to further reduce the energy consumption and enhance the speed of a multiplier. Therefore, we propose a novel energy efficient SW based 4-2 compressor consisting of 4 XOR gates and 2 Majority gates. The proposed compressor is validated by means of micromagnetic simulations and compared with the state-of-the-art SW, 22nm CMOS, Magnetic Tunnel Junction (MTJ), Domain Wall Motion (DWM), and Spin-CMOS technologies. The performance evaluation shows that the proposed compressor consumes 2.5x less and 1.25x less energy than the 22nm CMOS and the conventional SW compressor, respectively, whereas it consumes at least 3 orders of magnitude less energy than the MTJ, DWM, and Spin-CMOS designs. Furthermore, the compressor achieves the smallest chip real-estate. In summary, the performance evaluation of our proposed compressor shows that the SW technology has the potential to progress the state-of-the-art circuit design in terms of energy consumption and scalability., Comment: This work has received funding from the European Union's Horizon 2020 research and innovation program within the FET-OPEN project CHIRON under grant agreement No. 801055

Due to their very nature, Spin Waves (SWs) created in the same waveguide, but with different frequencies, can coexist while selectively interacting with their own species only. The absence of inter-frequency interferences isolates input data sets encoded in SWs with different frequencies and creates the premises for simultaneous data parallel SW based processing without hardware replication or delay overhead. In this paper we leverage this SW property by introducing a novel computation paradigm, which allows for the parallel processing of n-bit input data vectors on the same basic SW based logic gate. Subsequently, to demonstrate the proposed concept, we present 8-bit parallel 3-input Majority gate implementation and validate it by means of Object Oriented MicroMagnetic Framework (OOMMF) simulations. To evaluate the potential benefit of our proposal we compare the 8-bit data parallel gate with equivalent scalar SW gate based implementation. Our evaluation indicates that 8-bit data 3-input Majority gate implementation requires 4.16x less area than the scalar SW gate based equivalent counterpart while preserving the same delay and energy consumption figures., Comment: This work has received funding from the European Union's Horizon 2020 research and innovation program within the FET-OPEN project CHIRON under grant agreement No. 801055

This paper presents a 2-output Spin-Wave Programmable Logic Gate structure able to simultaneously evaluate any pair of AND, NAND, OR, NOR, XOR, and XNOR Boolean functions. Our proposal provides the means for fanout achievement within the Spin Wave computation domain and energy and area savings as two different functions can be simultaneously evaluated on the same input data. We validate our proposal by means of Object Oriented Micromagnetic Framework (OOMMF) simulations and demonstrate that by phase and magnetization threshold output sensing AND, OR, NAND, NOR and XOR and XNOR functionalities can be achieved, respectively. To get inside into the potential practical implications of our approach we use the proposed gate to implement a 3-input Majority gate, which we evaluate and compare with state of the art equivalent implementations in terms of area, delay, and energy consumptions. Our estimations indicate that the proposed gate provides 33% and 16% energy and area reduction, respectively, when compared with spin-wave counterpart and 42% energy reduction while consuming 12x less area when compared to a 15 nm CMOS implementation., Comment: This work has received funding from the European Union's Horizon 2020 research and innovation program within the FET-OPEN project CHIRON under grant agreement No. 801055

By its very nature, Spin Wave (SW) interference provides intrinsic support for Majority logic function evaluation. Due to this and the fact that the $3$-input Majority (MAJ3) gate and the Inverter constitute a universal Boolean logic gate set, different MAJ3 gate implementations have been proposed. However, they cannot be directly utilized for the construction of larger SW logic circuits as they lack a key cascading mechanism, i.e., fan-out capability. In this paper, we introduce a novel ladder-shaped SW MAJ3 gate design able to provide a maximum fan-out of 2 (FO2). The proper gate functionality is validated by means of micromagnetic simulations, which also demonstrate that the amplitude mismatch between the two outputs is negligible proving that an FO2 is properly achieved. Additionally, we evaluate the gate area and compare it with SW state-of-the-art and 15nm CMOS counterparts working under the same conditions. Our results indicate that the proposed structure requires 12x less area than the 15 nm CMOS MAJ3 gate and that at the gate level the fan-out capability results in 16% area savings, when compared with the state-of-the-art SW majority gate counterparts., Comment: This work has received funding from the European Union's Horizon 2020 research and innovation program within the FET-OPEN project CHIRON under the grant agreement No. 801055

We report on the resonant excitation of spin waves in micro-structured magnetic thin films by surface acoustic waves (SAWs). The spin waves as well as the acoustic waves are studied by micro-focused Brillouin light scattering spectroscopy. Besides the excitation of the ferromagnetic resonance, a process which does not fulfill momentum conservation, also the excitation of finite-wavelength spin waves can be observed at low magnetic fields. Using micromagnetic simulations, we verify that during this excitation both energy and linear momentum are conserved and fully transferred from the SAW to the spin wave., Comment: This project has received funding from the European Union's Horizon 2020 research and innovation program under grant agreement No. 801055 "Spin Wave Computing for Ultimately-Scaled Hybrid Low-Power Electronics" - CHIRON

This work analyzes resonance frequency shift vs. the applied magnetic field strength for GHz operating GaN/Si SAW single resonators. Magnetostrictive elements (Ni and CoFeB) were deposited in the proximity of the interdigitated transducers (IDTs) of the resonators (A-type structures) and also over the IDTs, after covering them with a BCB layer to avoid short circuits with IDTs metal (B-type structures). This work targets emerging applications of SAW resonators in driving spin wave pumping and in coupling of surface acoustic waves (SAW) with superconducting Q-bits. Magnetic sensitivity of the SAWs was analyzed at room temperature (RT) and at cryogenic temperatures, obtaining high magnetic sensitivities at 16 K. According to our knowledge, GaN based SAWs are first time used in magnetic applications; also, cryogenic behavior of magnetic SAW sensors is first time analyzed., Comment: This project has received funding from the European Union's Horizon 2020 research and innovation program under grant agreement No. 801055 "Spin Wave Computing for Ultimately-Scaled Hybrid Low-Power Electronics" - CHIRON

We report on the first experimental demonstration of majority logic operation using spin waves in a scaled device with an in-line input and output layout. The device operation is based on the interference of spin waves generated and detected by inductive antennas in an all-electrical microwave circuit. We demonstrate the full truth table of a majority logic function with the ability to distinguish between strong and weak majority, as well as an inverted majority function by adjusting the operation frequency. Circuit performance projections predict low energy consumption of spin wave based compared to CMOS for large arithmetic circuits., Comment: This project has received funding from the European Union's Horizon 2020 research and innovation program under grant agreement No. 801055 "Spin Wave Computing for Ultimately-Scaled Hybrid Low-Power Electronics" - CHIRON

Spin Waves(SWs) enable the realization of energy efficient circuits as they propagate and interfere within waveguides without consuming noticeable energy. However, SW computing can be even more energy efficient by taking advantage of the approximate computing paradigm as many applications are error-tolerant like multimedia and social media. In this paper we propose an ultra-low energy novel Approximate Full Adder(AFA) and a 2-bit inputs Multiplier(AMUL). We validate the correct functionality of our proposal by means of micromagnetic simulations and evaluate the approximate FA figure of merit against state-of-the-art accurate SW, 7nmCMOS, Spin Hall Effect(SHE), Domain Wall Motion(DWM), accurate and approximate 45nmCMOS, Magnetic Tunnel Junction(MTJ), and Spin-CMOS FA implementations. Our results indicate that AFA consumes 43% and 33% less energy than state-of-the-art accurate SW and 7nmCMOS FA, respectively, and saves 69% and 44% when compared with accurate and approximate 45nm CMOS, respectively, and provides a 2 orders of magnitude energy reduction when compared with accurate SHE, accurate and approximate DWM, MTJ, and Spin-CMOS, counterparts. In addition, it achieves the same error rate as approximate 45nmCMOS and Spin-CMOS FA whereas it exhibits 50% less error rate than the approximate DWM FA. Furthermore, it outperforms its contenders in terms of area by saving at least 29% chip real-estate. AMUL is evaluated and compared with state-of-the-art accurate SW and 16nm CMOS accurate and approximate state-of-the-art designs. The evaluation results indicate that it saves at least 2x and 5x energy in comparison with the state-of-the-art SW designs and 16nm CMOS accurate and approximate designs, respectively, and has an average error rate of 10%, while the approximate CMOS MUL has an average error rate of 13%, and requires at least 64% less chip real-estate., Comment: This project has received funding from the European Union's Horizon 2020 research and innovation program under grant agreement No. 801055 "Spin Wave Computing for Ultimately-Scaled Hybrid Low-Power Electronics" CHIRON

By their very nature, voltage/current excited Spin Waves (SWs) propagate through waveguides without consuming noticeable power. If SW excitation is performed by the continuous application of voltages/currents to the input, which is usually the case, the overall energy consumption is determined by the transducer power and the circuit critical path delay, which leads to high energy consumption because of SWs slowness. However, if transducers are operated in pulses the energy becomes circuit delay independent and it is mainly determined by the transducer power and delay, thus pulse operation should be targeted. In this paper, we utilize a 3-input Majority gate (MAJ) to investigate the Continuous Mode Operation (CMO), and Pulse Mode Operation (PMO). Moreover, we validate CMO and PMO 3-input Majority gate by means of micromagnetic simulations. Furthermore, we evaluate and compare the CMO and PMO Majority gate implementations in term of energy. The results indicate that PMO diminishes MAJ gate energy consumption by a factor of 18. In addition, we describe how PMO can open the road towards the utilization of the Wave Pipelining (WP) concept in SW circuits. We validate the WP concept by means of micromagnetic simulations and we evaluate its implications in term of throughput. Our evaluation indicates that for a circuit formed by four cascaded MAJ gates WP increases the throughput by 3.6x., Comment: This project has received funding from the European Union's Horizon 2020 research and innovation program under grant agreement No. 801055 "Spin Wave Computing for Ultimately-Scaled Hybrid Low-Power Electronics" CHIRON

Spin Waves (SWs) propagate through magnetic waveguides and interfere with each other without consuming noticeable energy, which opens the road to new ultra-low energy circuit designs. In this paper we build upon SW features and propose a novel energy efficient Full Adder (FA) design consisting of The FA 1 Majority and 2 XOR gates, which outputs Sum and Carry-out are generated by means of threshold and phase detection, respectively. We validate our proposal by means of MuMax3 micromagnetic simulations and we evaluate and compare its performance with state-of-the-art SW, 22nm CMOS, Magnetic Tunnel Junction (MTJ), Spin Hall Effect (SHE), Domain Wall Motion (DWM), and Spin-CMOS implementations. Our evaluation indicates that the proposed SW FA consumes 22.5% and 43% less energy than the direct SW gate based and 22nm CMOS counterparts, respectively. Moreover it exhibits a more than 3 orders of magnitude smaller energy consumption when compared with state-of-the-art MTJ, SHE, DWM, and Spin-CMOS based FAs, and outperforms its contenders in terms of area by requiring at least 22% less chip real-estate., Comment: This project has received funding from the European Union's Horizon 2020 research and innovation program under grant agreement No. 801055 "Spin Wave Computing for Ultimately-Scaled Hybrid Low-Power Electronics" CHIRON

Spin waves modes in magnetic waveguides with width down to 320 nm have been studied by electrical propagating spin-wave spectroscopy and micromagnetic simulations for both longitudinal and transverse magnetic bias fields. For longitudinal bias fields, a 1.3 GHz wide spin-wave band was observed in agreement with analytical dispersion relations for uniform magnetization. However, transverse bias field led to several distinct bands, corresponding to different quantized width modes, with both negative and positive slopes. Micromagnetic simulations showed that, in this geometry, the magnetization was nonuniform and tilted due to the strong shape anisotropy of the waveguides. Simulations of the quantized spin-wave modes in such nonuniformly magnetized waveguides resulted in spin wave dispersion relations in good agreement with the experiments., Comment: 11 pages, 5 figures. This work has received funding from the European Union's Horizon 2020 research and innovation program under grant agreement No 801055 "Spin Wave Computing for Ultimately-Scaled Hybrid Low-Power Electronics" - CHIRON

We report on the design, fabrication, and characterization of compact tunable yttrium iron garnet (YIG) based RF resonators based on $\mu$m-sized spin-wave cavities. Inductive antennas with both ladder and meander configurations were used as transducers between spin waves and RF signals. The excitation of ferromagnetic resonance and standing spin waves in the YIG cavities led to sharp resonances with quality factors up to 350. The observed spectra were in excellent agreement with a model based on the spin-wave dispersion relations in YIG, showing a high magnetic field tunability of about 29 MHz/mT., Comment: 13 pages, 5 figures. This project has received funding from the European Union's Horizon 2020 research and innovation program under grant agreement No. 801055 "Spin Wave Computing for Ultimately-Scaled Hybrid Low-Power Electronics" - CHIRON

To bring Spin Wave (SW) based computing paradigm into practice and develop ultra low power Magnonic circuits and computation platforms, one needs basic logic gates that operate and can be cascaded within the SW domain without requiring back and forth conversion between the SW and voltage domains. To achieve this, SW gates have to possess intrinsic fanout capabilities, be input-output data representation coherent, and reconfigurable. In this paper, we address the first and the last requirements and propose a novel 4-output programmable SW logic. First, we introduce the gate structure and demonstrate that, by adjusting the gate output detection method, it can parallelly evaluate any 4-element subset of the 2-input Boolean function set AND, NAND, OR, NOR, XOR, and XNOR. Furthermore, we adjust the structure such that all its 4 outputs produce SWs with the same energy and demonstrate that it can evaluate Boolean function sets while providing fanout capabilities ranging from 1 to 4. We validate our approach by instantiating and simulating different gate configurations such as 4-output AND/OR, 4-output XOR/XNOR, output energy balanced 4-output AND/OR, and output energy balanced 4-output XOR/XNOR by means of Object Oriented Micromagnetic Framework (OOMMF) simulations. Finally, we evaluate the performance of our proposal in terms of delay and energy consumption and compare it against existing state-of-the-art SW and 16nm CMOS counterparts. The results indicate that for the same functionality, our approach provides 3x and 16x energy reduction, when compared with conventional SW and 16nm CMOS implementations, respectively., Comment: This project has received funding from the European Union's Horizon 2020 research and innovation program under grant agreement No. 801055 "Spin Wave Computing for Ultimately-Scaled Hybrid Low-Power Electronics" CHIRON

Having multi-output logic gates saves much energy because the same structure can be used to feed multiple inputs of next stage gates simultaneously. This paper proposes novel triangle shape fanout of 2 spin wave Majority and XOR gates; the Majority gate is achieved by phase detection, whereas the XOR gate is achieved by threshold detection. The proposed logic gates are validated by means of micromagnetic simulations. Furthermore, the energy and delay are estimated for the proposed structures and compared with the state-of-the-art spin wave logic gates, and 16nm and 7nm CMOS. The results demonstrate that the proposed structures provide energy reduction of 25%-50% in comparison to the other 2-output spin-wave devices while having the same delay, and energy reduction between 43x and 0.8x when compared to the 16nm and 7nm CMOS while having delay overhead between 11x and 40x., Comment: This project has received funding from the European Union's Horizon 2020 research and innovation program under grant agreement No. 801055 "Spin Wave Computing for Ultimately-Scaled Hybrid Low-Power Electronics" CHIRON

The characteristics of confined magnetoelastic waves in nanoscale ferromagnetic magnetostrictive waveguides have been investigated by a combination of analytical and numerical calculations. The presence of both magnetostriction and inverse magnetostriction leads to the coupling between confined spin waves and elastic Lamb waves. Numerical simulations of the coupled system have been used to extract the dispersion relations of the magnetoelastic waves as well as their mode profiles., Comment: 30 pages, 9 figures

By their very nature, Spin Waves (SWs) with different frequencies can propagate through the same waveguide without affecting each other, while only interfering with their own species. Therefore, more SW encoded data sets can coexist, propagate, and interact in parallel, which opens the road towards hardware replication free parallel data processing. In this paper, we take advantage of these features and propose a novel data parallel spin wave based computing approach. To explain and validate the proposed concept, byte-wide 2-input XOR and 3-input Majority gates are implemented and validated by means of Object Oriented MicroMagnetic Framework (OOMMF) simulations. Furthermore, we introduce an optimization algorithm meant to minimize the area overhead associated with multifrequency operation and demonstrate that it diminishes the byte-wide gate area by 30% and 41% for XOR and Majority implementations, respectively. To get inside on the practical implications of our proposal we compare the byte-wide gates with conventional functionally equivalent scalar SW gate based implementations in terms of area, delay, and power consumption. Our results indicate that the area optimized 8-bit 2-input XOR and 3-input Majority gates require 4.47x and 4.16x less area, respectively, at the expense of 5% and 7% delay increase, respectively, without inducing any power consumption overhead. Finally, we discuss factors that are limiting the currently achievable parallelism to 8 for phase based gate output detection and demonstrate by means of OOMMF simulations that this can be increased 16 for threshold based detection based gates., Comment: This project has received funding from the European Union's Horizon 2020 research and innovation program under grant agreement No. 801055 "Spin Wave Computing for Ultimately-Scaled Hybrid Low-Power Electronics" CHIRON

The dispersion of spin waves in vertical meander-shaped CoFeB thin films consisting of segments located at 90{\deg} angles with respect to each other is investigated by Brillouin light scattering spectroscopy. We reveal the periodic character of several dispersive branches as well as alternating frequency ranges where spin waves are allowed or forbidden to propagate. Noteworthy is the presence of the frequency band gaps between each couple of successive modes only for wave numbers k=n$\pi$/a, where n is an even integer number and a is the size of the meander unit cell, whereas the spectra show propagating modes in the orthogonal film segments for the other wavenumbers. The micromagnetic simulations and analytical calculations allow us to understand and explain the results in terms of the mode spatial localization and symmetry. The obtained results demonstrate the wave propagation in three dimensions opening the path for multi-level magnonic architectures for signal processing., Comment: 19 pages, 6 figures. This work has received funding from the European Union's Horizon 2020 research and innovation program under grant agreement No 801055 "Spin Wave Computing for Ultimately-Scaled Hybrid Low-Power Electronics" - "CHIRON"

This paper provides a tutorial overview over recent vigorous efforts to develop computing systems based on spin waves instead of charges and voltages. Spin-wave computing can be considered as a subfield of spintronics, which uses magnetic excitations for computation and memory applications. The tutorial combines backgrounds in spin-wave and device physics as well as circuit engineering to create synergies between the physics and electrical engineering communities to advance the field towards practical spin-wave circuits. After an introduction to magnetic interactions and spin-wave physics, all relevant basic aspects of spin-wave computing and individual spin-wave devices are reviewed. The focus is on spin-wave majority gates as they are the most prominently pursued device concept. Subsequently, we discuss the current status and the challenges to combine spin-wave gates and obtain circuits and ultimately computing systems, considering essential aspects such as gate interconnection, logic level restoration, input-output consistency, and fan-out achievement. We argue that spin-wave circuits need to be embedded in conventional CMOS circuits to obtain complete functional hybrid computing systems. The state of the art of benchmarking such hybrid spin-wave--CMOS systems is reviewed and the current challenges to realize such systems are discussed. The benchmark indicates that hybrid spin-wave--CMOS systems promise ultralow-power operation and may ultimately outperform conventional CMOS circuits in terms of the power-delay-area product. Current challenges to achieve this goal include low-power signal restoration in spin-wave circuits as well as efficient spin-wave transducers., Comment: This project has received funding from the European Union's Horizon 2020 research and innovation program under grant agreement No. 801055 "Spin Wave Computing for Ultimately-Scaled Hybrid Low-Power Electronics" - CHIRON

The key enabling factor for Spin Wave (SW) technology utilization for building ultra low power circuits is the ability to energy efficiently cascade SW basic computation blocks. SW Majority gates, which constitute a universal gate set for this paradigm, operating on phase encoded data are not input output coherent in terms of SW amplitude, and as such, their cascading requires information representation conversion from SW to voltage and back, which is by no means energy effective. In this paper, a novel conversion free SW gate cascading scheme is proposed that achieves SW amplitude normalization by means of a directional coupler. After introducing the normalization concept, we utilize it in the implementation of three simple circuits and, to demonstrate its bigger scale potential, of a 2-bit inputs SW multiplier. The proposed structures are validated by means of the Object Oriented Micromagnetic Framework (OOMMF) and GPU-accelerated Micromagnetics (MuMax3). Furthermore, we assess the normalization induced energy overhead and demonstrate that the proposed approach consumes 20% to 33% less energy when compared with the transducers based conventional counterpart. Finally, we introduce a normalization based SW 2-bit inputs multiplier design and compare it with functionally equivalent SW transducer based and 16nm CMOS designs. Our evaluation indicate that the proposed approach provided 26% and 6.25x energy reductions when compared with the conventional approach and 16nm CMOS counterpart, respectively, which demonstrates that our proposal is energy effective and opens the road towards the full utilization of the SW paradigm potential and the development of SW only circuits., Comment: This project has received funding from the European Union's Horizon 2020 research and innovation program under grant agreement No. 801055 "Spin Wave Computing for Ultimately-Scaled Hybrid Low-Power Electronics" CHIRON

This paper discusses the physics of magnetoelasticity and magnetoelastic waves as well as their mathematical description. Magnetoelastic waves occur as a result of strong coupling between spin waves and elastic waves in magnetostrictive ferromagnetic media. In a first part, the basic behavior of spin waves is reviewed in both bulk ferromagnets as well as in thin films. Next, elastic waves are discussed with a focus on thin films. Finally, the interactions between the elastic and magnetic domains are described and it is shown how this results in the formation of magnetoelastic waves. Based on the description of bulk magnetoelastic waves, a theory for magnetoelastic waves in thin films is developed and their dispersion relations are derived. It is shown that the behavior strongly depends on the geometry of the system, especially on the polarization of spin and elastic waves and the direction of the magnetization of the magnetostrictive ferromagnet., Comment: 40 pages, 7 figures

Spin waves are excitations in ferromagnetic media that have been proposed as information carriers in hybrid spintronic devices with much lower operation power than conventional charge-based electronics. Their wave nature can be exploited in majority gates by using interference for computation. However, a scalable spin-wave majority gate that can be co-integrated alongside conventional electronics is still lacking. Here, we demonstrate a sub-micron inline spin-wave majority gate with fan-out. Time-resolved imaging of the magnetization dynamics by scanning transmission x-ray microscopy illustrates the device operation. All-electrical spin-wave spectroscopy further demonstrates majority gates with sub-micron dimensions, reconfigurable input and output ports, and frequency-division multiplexing. Challenges for hybrid spintronic computing systems based on spin-wave majority gates are discussed., Comment: This project has received funding from the European Union's Horizon 2020 research and innovation program under grant agreement No. 801055 "Spin Wave Computing for Ultimately-Scaled Hybrid Low-Power Electronics" - CHIRON

The characteristics of spin waves in ferromagnetic waveguides with nonuniform magnetization have been investigated for situations where the shape anisotropy field of the waveguide is comparable to the external bias field. Spin-wave generation was realized by the magnetoelastic effect by applying normal and shear strain components, as well as by the Oersted field emitted by an inductive antenna. The magnetoelastic excitation field has a nonuniform profile over the width of the waveguide because of the nonuniform magnetization orientation, whereas the Oersted field remains uniform. Using micromagnetic simulations, we indicate that both types of excitation fields generate quantised width modes with both odd and even mode numbers as well as tilted phase fronts. We demonstrate that these effects originate from the average magnetization orientation with respect to the main axes of the magnetic waveguide. Furthermore, it is indicated that the excitation efficiency of the second-order mode generally surpasses that of the first-order mode due to their symmetry. The relative intensity of the excited modes can be controlled by the strain state as well as by tuning the dimensions of the excitation area. Finally, we demonstrate that the nonreciprocity of spin-wave radiation due to the chirality of an Oersted field generated by an inductive antenna is absent for magnetoelastic spin-wave excitation., Comment: This work was funded through the FETOPEN-01-2016-2017-FET-Open research and innovation actions (CHIRON project: Grant Agreement No. 801055). F.V. acknowledges financial support from the Research Foundation-Flanders (FWO) through grant No. 1S05719N

The emerging field of magnonics employs spin waves and their quanta, magnons, to implement wave-based computing on the micro- and nanoscale. Multi-frequency magnon networks would allow for parallel data processing within single logic elements whereas this is not the case with conventional transistor-based electronic logic. However, a lack of experimentally proven solutions to efficiently combine and separate magnons of different frequencies has impeded the intensive use of this concept. In this Letter, the experimental realization of a spin-wave demultiplexer enabling frequency-dependent separation of magnonic signals in the GHz range is demonstrated. The device is based on two-dimensional magnon transport in the form of spin-wave beams in unpatterned magnetic films. The intrinsic frequency-dependence of the beam direction is exploited to realize a passive functioning obviating an external control and additional power consumption. This approach paves the way to magnonic multiplexing circuits enabling simultaneous information transport and processing., Comment: 16 pages, 3 figures

Spin waves and their quanta magnons open up a promising branch of high-speed and low-power information processing. Several important milestones were achieved recently in the realization of separate magnonic data processing units including logic gates, a magnon transistor and units for non-Boolean computing. Nevertheless, the realization of an integrated magnonic circuit consisting of at least two logic gates and suitable for further integration is still an unresolved challenge. Here we demonstrate such an integrated circuit numerically on the example of a magnonic half-adder. Its key element is a nonlinear directional coupler serving as combined XOR and AND logic gate that utilizes the dependence of the spin wave dispersion on its amplitude. The circuit constitutes of only three planar nano-waveguides and processes all information within the magnon domain. Benchmarking of the proposed device is performed showing the potential for sub-aJ energy consumption per operation., Comment: 21 pages, 6 figures, 2 tables

We study the generation of propagating spin waves in Ta/CoFeB waveguides by spin-orbit torque antennas and compare them to conventional inductive antennas. The spin-orbit torque was generated by a transverse microwave current across the magnetic waveguide. The detected spin wave signals for an in-plane magnetization across the waveguide (Damon-Eshbach configuration) exhibited the expected phase rotation and amplitude decay upon propagation when the current spreading was taken into account. Wavevectors up to about 6 rad/$\mu$m could be excited by the spin-orbit torque antennas despite the current spreading, presumably due to the non-uniformity of the microwave current. The relative magnitude of generated anti-damping spin-Hall and Oersted fields was calculated within an analytic model and it was found that they contribute approximately equally to the total effective field generated by the spin-orbit torque antenna. Due to the ellipticity of the precession in the ultrathin waveguide and the different orientation of the anti-damping spin-Hall and Oersted fields, the torque was however still dominated by the Oersted field. The prospects for obtaining a pure spin-orbit torque response are discussed, as are the energy efficiency and the scaling properties of spin-orbit torque antennas., Comment: 20 pages, 5 figures

The mechanical behavior of magnetoelectric transducers consisting of piezoelectric-magnetostrictive bilayers has been modeled. The effect of the aspect ratio of the transducer as well as the influence of non-active surrounding layers has been modeled, including a passivation layer surrounding the active device, a clamping layer above the active device, and an interfacial layer that might be inserted between the magnetostrictive and the piezoelectric layers. Strategies to control and maximize the strain magnitude and orientation based on material selection and device design are proposed., Comment: MNE2017, 6 pages, 4 figures

We study the excitation of spin waves in scaled magnetic waveguides using the magnetoelastic effect. In uniformly magnetized systems, normal strains parallel or perpendicular to the magnetization direction do not lead to spin wave excitation since the magnetoelastic torque is zero. Using micromagnetic simulations, we show that the nonuniformity of the magnetization in submicron waveguides due to the effect of the demagnetizing field leads to the excitation of spin waves for oscillating normal strains both parallel and perpendicular to the magnetization. The excitation by biaxial normal in-plane strain was found to be much more efficient than by uniaxial normal out-of-plane strain. For narrow waveguides with widths of 200\,nm, the excitation efficiency of biaxial normal in-plane strain was comparable to that of shear strain., Comment: 11 pages, 3 figures

We develop an all electrical experiment to perform the broadband phase-resolved spectroscopy of propagating spin waves in micrometer sized thin magnetic stripes. The magnetostatic surface spin waves are excited and detected by scaled down to 125 nm wide inductive antennas, which award ultra broadband wavevector capability. The wavevector selection can be done by applying an excitation frequency above the ferromagnetic resonance. Wavevector demultiplexing is done at the spin wave detector thanks to the rotation of the spin wave phase upon propagation. A simple model accounts for the main features of the apparatus transfer functions. Our approach opens an avenue for the all electrical study of wavevector-dependent spin wave properties including dispersion spectra or non-reciprocal propagation., Comment: 5 pages, 3 figures

We present a micromagnetic analysis of spin-wave propagation in a magnonic crystal realized as a permalloy spin-wave waveguide with a spatial periodical variation of its saturation magnetization. Frequency band gaps were clearly observed in the spin-wave transmission spectra and their origin is traced back to an overlap of individual band gaps of the fundamental and the higher order spin-wave width modes. The control of the depth, width and the position in frequency and space of the rejection band gaps by the width areas with a reduced magnetization and by the modulation level, are discussed in this study., Comment: 5 pages, 4 figures

We investigate spin-wave propagation in a microstructured magnonic-crystal waveguide fabricated by localized ion implantation. The irradiation caused a periodic variation in the saturation magnetization along the waveguide. As a consequence, the spin-wave transmission spectrum exhibits a set of frequency bands, where spin-wave propagation is suppressed. A weak modification of the saturation magnetization by 7% is sufficient to decrease the spin-wave transmission in the band gaps by a factor of 10. These results evidence the applicability of localized ion implantation for the fabrication of efficient micron- and nano-sized magnonic crystals for magnon spintronic applications., Comment: 4 pages, 3 figures, submitted to Applied Physics Letters

We present a micromagnetic study of linear and nonlinear spin-wave modes excited in an extended permalloy thin film by a microwave driven nanocontact. We show that the linear mode having the frequency equal to the excitation frequency (f) is driven by the ac Oersted field component perpendicular to the static external field (applied in-plane of the sample). The nonlinear mode with the frequency f /2 is excited as an independent eigenmode within a parametric longitudinal pumping process (due ac Oersted field component parallel to the bias field). Spectral positions of those modes are determined both in the space and phase domain. The results are important for the transfer of information coded into spin-waves between nanocontacts, and for synchronization of spin transfer torque nano-oscillators., Comment: 5 pages, 4 figures