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This paper addresses the question: Can spintronic circuits based on Magnetic Tunnel Junction (MTJ) transducers outperform their state-of-the-art CMOS counterparts? To this end, we use the EPFL combinational benchmark sets, synthesize them in 7 nm CMOS and in MTJ-based spintronic technologies, and compare the two implementation methods in terms of Energy-Delay-Product (EDP). To fully utilize the technologies potential, CMOS and spintronic implementations are built upon standard Boolean and Majority Gates, respectively. For the spintronic circuits, we assumed that domain conversion (electric/magnetic to magnetic/electric) is performed by means of MTJs and the computation is accomplished by domain wall based majority gates, and considered two EDP estimation scenarios: (i) Uniform Benchmarking, which ignores the circuit's internal structure and only includes domain transducers power and delay contributions into the calculations, and (ii) Majority-Inverter-Graph Benchmarking, which also embeds the circuit structure, the associated critical path delay and energy consumption by DW propagation. Our results indicate that for the uniform case, the spintronic route is better suited for the implementation of complex circuits with few inputs and outputs. On the other hand, when the circuit structure is also considered via majority and inverter synthesis, our analysis clearly indicates that in order to match and eventually outperform CMOS performance, MTJ efficiency has to be improved by 3-4 orders of magnitude. While it is clear that for the time being the MTJ-based-spintronic way cannot compete with CMOS, further transducer developments may tip the balance, which, when combined with information non-volatility, may make spintronic implementation for certain applications that require a large number of calculations and have a rather limited amount of interaction with the environment., Comment: This work was supported by imec Industrial Affiliation Program on Exploratory Logic Devices. It has also received funding from the European Union Horizon Europe research and innovation programme within the project SPIDER under grant agreement No 101070417

Magnonics is a field of science that addresses the physical properties of spin waves and utilizes them for data processing. Scalability down to atomic dimensions, operations in the GHz-to-THz frequency range, utilization of nonlinear and nonreciprocal phenomena, and compatibility with CMOS are just a few of many advantages offered by magnons. Although magnonics is still primarily positioned in the academic domain, the scientific and technological challenges of the field are being extensively investigated, and many proof-of-concept prototypes have already been realized in laboratories. This roadmap is a product of the collective work of many authors that covers versatile spin-wave computing approaches, conceptual building blocks, and underlying physical phenomena. In particular, the roadmap discusses the computation operations with Boolean digital data, unconventional approaches like neuromorphic computing, and the progress towards magnon-based quantum computing. The article is organized as a collection of sub-sections grouped into seven large thematic sections. Each sub-section is prepared by one or a group of authors and concludes with a brief description of the current challenges and the outlook of the further development of the research directions., Comment: 74 pages, 57 figures, 500 references

In this work, we study experimentally by broadband ferromagnetic resonance measurements, the dependence of the spin-wave excitation spectra on the magnetic applied field in CoFeB meander-shaped films. Two different orientations of the external magnetic field were explored, namely parallel or perpendicular to the lattice cores. The interpretation of the field dependence of the frequency and spatial profiles of major spin-wave modes were obtained by micromagnetic simulations. We show that the vertical segments lead to the easy-axis type of magnetic anisotropy and support the in-phase and out-of-phase spin-wave precession amplitude in the vertical segments. The latter could potentially be used for the design of tunable metasurfaces or in magnetic memories based on meandering 3D magnetic films., 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 develop a generic all-inductive procedure to measure the band structure of spin waves in a magnetic thin stripe. In contrast to existing techniques, our method works even if several spin wave branches coexist in the investigated frequency interval, provided that the branches possess sufficiently different group velocities. We first measure the microwave scattering matrix of a network composed of distant antennas inductively coupled to the spin wave bath of the magnetic film. After a mathematical transformation to the time-domain to get the transmission impulse response, the different spin wave branches are viewed as wavepackets that reach successively the receiving antenna after different travel times. In analogy with time-of flight spectroscopy, the wavepackets are then separated by time-gating. The time-gated responses are used to recalculate the contribution of each spin wave branch to the frequency domain scattering matrix. The dispersion relation of each branch stems from the absolute phase of the time-gated transmission parameter. The spin wave wavevector can be determined unambiguously if the results for several propagation distances are combined, so as to get the dispersion relations., Comment: Submitted to the PRB. This work was funded through the FETOPEN-01-2016-2017-FET-Open research and innovation actions (CHIRON project: Grant Agreement No. 801055) and was partly supported by the French RENATECH network. This work is also supported by a public grant overseen by ANR as part of the "Investissements d'avenir" program (Labex NanoSaclay, reference: ANR-10-LABX-0035)

In this work, we investigate the spin-wave propagation in three-dimensional nanoscale CoFeB/Ta/NiFe meander structures fabricated on a structured SiO2/Si substrate. The magnonic band structure has been experimentally determined by wavevector-resolved Brillouin light scattering (BLS) spectroscopy and a set of stationary modes interposed by two dispersive modes of Bloch type have been identified. The results could be understood by micromagnetic and finite element simulations of the mode distributions in both real space and the frequency domain. The dispersive modes periodically oscillate in frequency over the Brillouin zones and correspond to modes, whose spatial distributions extend over the entire sample and are either localized exclusively in the CoFeB layer or the entire CoFeB/Ta/NiFe magnetic bilayer. Stationary modes are mainly concentrated in the vertical segments of the CoFeB and NiFe layers and show negligible amplitudes in the horizon-tal segments. The findings are compared with those of single-layer CoFeB meander structures with the same geometry parameters, which reveals the influence of the dipolar coupling between the two ferromagnetic layers on the magnonic band structure., Comment: 10 pages, 4 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

We compare the characteristics of electrically transduced Damon-Eshbach (DESWs) and backward volume (BVSWs) configurations within the same, 30 nm thick, ferromagnetic, CoFeB waveguide. Sub-micron U-shaped antennas are used to deliver the necessary in-plane and out-of-plane RF fields. We measure the spin-wave transmission with respect to in-plane field orientation, frequency and propagation distance. Unlike DESW, BVSWs are reciprocally transduced and collected for either direction of propagation, but their ability to transport energy is lower than DESWs for two reasons. This arises first because BVSW are inductively transduced less efficiently than DESWs. Also, in the range of wavevectors (~5 rad. um-1) typically excited by our antennas, the group velocity of BVSWs stays lower than that of DESW, which leads to reduced propagation ability that impact transmission signals in an exponential manner. In contrast, the group velocity of DESWs is maximum at low fields and decreases continuously with the applied field. The essential features of the measured SW characteristics are well reciprocated by a simple, 1-D analytical model which can be used to assess the potential of each configuration., Comment: This work was funded through the FETOPEN-01-2016-2017-FET-Open research and innovation actions (CHIRON project: Grant Agreement No. 801055) and was partly supported by the French RENATECH network

The high frequency performance of strong piezoelectric materials like PZT remains relatively less explored due to the assumption of large dielectric/ferroelectric losses at GHz frequencies. Recently, the advent of magnetoelectric technology as an on-chip route to excite magnetization dynamics has provided the impetus to evaluate the electromechanical performance of PZT at microwave frequencies. In this work, we demonstrate that HBARs fabricated using Barium-doped PZT (BPZT) films can efficiently generate acoustic waves up to 15 GHz. The ferroelectricity of BPZT endows added functionality to the resonator in the form of voltage tunability of the electromechanical performance. We extract the piezoelectric coefficient by numerically comparing the performance of BPZT with the Mason model. The extracted piezoelectric coefficient ~60 pm/V agrees well with reported values on thin film PZT measured at low frequencies (<100 MHz). Our results suggest that with further improvement in device design and material processing, BPZT resonators could operate as large amplitude, tunable stress transducers at GHz frequencies., Comment: This work was funded through the FETOPEN-01-2016-2017-FET-Open research and innovation actions (CHIRON project: Grant Agreement No. 801055) and was partly supported by the French RENATECH network

Magnons, the quanta of spin waves, could be used to encode information in beyond-Moore computing applications, and magnonic device components, including logic gates, transistors, and units for non-Boolean computing, have already been developed. Magnonic directional couplers, which can function as circuit building blocks, have also been explored, but have been impractical because of their millimetre dimensions and multi-mode spectra. Here, we report a magnonic directional coupler based on yttrium iron garnet single-mode waveguides of 350 nm width. We use the amplitude of a spin-wave to encode information and to guide it to one of the two outputs of the coupler depending on the signal magnitude, frequency, and the applied magnetic field. Using micromagnetic simulations, we also propose an integrated magnonic half-adder that consists of two directional couplers and processes all information within the magnon domain with aJ energy consumption., Comment: 26 pages, 10 figures. arXiv admin note: text overlap with arXiv:1902.02855

Featuring low heat dissipation, devices based on spin-wave logic gates promise to comply with increasing future requirements in information processing. In this work, we present the experimental realization of a majority gate based on the interference of spin waves in an Yttrium-Iron-Garnet-based waveguiding structure. This logic device features a three-input combiner with the logic information encoded in the phase of the spin waves. We show that the phase of the output signal represents the majority of the phase of the input signals. A switching time of about 10 ns in the prototype device provides evidence for the ability of sub-nanosecond data processing in future down-scaled devices., Comment: 5 pages, 4 figures

The potential to control the number of the spin-wave band gaps of a magnonic crystal (MC) by variation of its geometry is investigated by numerical simulations. The magnonic crystal is represented by a micro-sized planar ferromagnetic waveguide with periodically variable width. By choosing a step-like or sinusoidal variation of the width, the magnonic crystal reveals multiple or single band gaps, respectively. This allows for additional degrees of freedom in the design of MC based microwave filters and phase shifters with desired characteristics. The MCs band gaps have been studied in the space and frequency domains exploring the spin-wave spectrum dependence on the probing position inside the magnonic crystal., Comment: 8 pages, 3 figures

We have investigated the generation of spin waves in the free layer of an extended spin-valve structure with a nano-scaled point contact driven by both microwave and direct electric current using Brillouin light scattering microscopy. Simultaneously with the directly excited spin waves, strong nonlinear effects are observed, namely the generation of eigenmodes with integer multiple frequencies (2 \emph{f}, 3 \emph{f}, 4 \emph{f}) and modes with non-integer factors (0.5 \emph{f}, 1.5 \emph{f}) with respect to the excitation frequency \emph{f}. The origin of these nonlinear modes is traced back to three magnon scattering processes. The direct current influence on the generation of the fundamental mode at frequency \emph{f} can be related to the spin-transfer torque, while the efficiency of three-magnon-scattering processes is controlled by the Oersted field as an additional effect of the direct current.