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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

The precise control of spins in semiconductor spintronic devices requires electrical means for generating spin packets with a well-defined initial phase. We demonstrate a pulsed electrical scheme that triggers the spin ensemble phase in a similar way as circularly-polarized optical pulses are generating phase coherent spin packets. Here, we use fast current pulses to initialize phase coherent spin packets, which are injected across an Fe/GaAs Schottky barrier into $n$-GaAs. By means of time-resolved Faraday rotation, we demonstrate phase coherence by the observation of multiple Larmor precession cycles for current pulse widths down to 500 ps at 17 K. We show that the current pulses are broadened by the charging and discharging time of the Schottky barrier. At high frequencies, the observable spin coherence is limited only by the finite band width of the current pulses, which is on the order of 2 GHz. These results therefore demonstrate that all-electrical injection and phase control of electron spin packets at microwave frequencies is possible in metallic-ferromagnet/semiconductor heterostructures., Comment: 14 pages, 9 figures

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

Time-resolved electrical spin transport is used to generate and probe spin currents in GaAs electrically. We use high bandwidth current pulses to inject phase-coherent spin packets from Fe into n-GaAs. By means of time-resolved Faraday rotation we demonstrate that spins are injected with a clearly defined phase by the observation of multiple Larmor precession cycles. We furthermore show that spin precession of optically created spin packets in n-GaAs can be probed electrically by spin-polarized photo-current pulses. The injection and detection experiments are not direct reciprocals of each other. In particular, we find that interfacial spin accumulation generated by the photocurrent pulse plays a critical role in time-resolved electrical spin detection., Comment: 11 pages, 4 figures

A longstanding goal of research in semiconductor spintronics is the ability to inject, modulate, and detect electron spin in a single device. A simple prototype consists of a lateral semiconductor channel with two ferromagnetic contacts, one of which serves as a source of spin-polarized electrons and the other as a detector. Based on work in analogous metallic systems, two important criteria have emerged for demonstrating electrical detection of spin transport. The first is the measurement of a non-equilibrium spin population using a non-local ferromagnetic detector through which no charge current flows. The potential at the detection electrode should be sensitive to the relative magnetizations of the detector and the source electrodes, a property referred to as the spin-valve effect. A second and more rigorous test is the existence of a Hanle effect, which is the modulation and suppression of the spin valve signal due to precession and dephasing in a transverse magnetic field. Here we report on the observation of both the spin valve and Hanle effects in lateral devices consisting of epitaxial Fe Schottky tunnel barrier contacts on an n-doped GaAs channel. The dependence on transverse magnetic field, temperature, and contact separation are in good agreement with a model incorporating spin drift and diffusion. Spin transport is detected for both directions of current flow through the source electrode. The sign of the electrical detection signal is found to vary with the injection current and is correlated with the spin polarization in the GaAs channel determined by optical measurements. These results therefore demonstrate a fully electrical scheme for spin injection, transport, and detection in a lateral semiconductor device., Comment: Single PDF file with 4 Figures + supplementary information; submitted to Nature Physics 11/06

We discuss methods for imaging the nonequilibrium spin polarization of electrons in Fe/GaAs spin transport devices. Both optically- and electrically-injected spin distributions are studied by scanning magneto-optical Kerr rotation microscopy. Related methods are used to demonstrate electrical spin detection of optically-injected spin polarized currents. Dynamical properties of spin transport are inferred from studies based on the Hanle effect, and the influence of strain on spin transport data in these devices is discussed., Comment: 5 pages, 6 figs. ICPS-28 proceedings (July'06, Vienna) for J. Appl. Phys

Electrical spin injection from ferromagnetic $\delta$-MnGa into an (Al,Ga)As p-i-n light emitting diode (LED) is demonstrated. The $\delta$-MnGa layers show strong perpendicular magnetocrystalline anisotropy, enabling detection of spin injection at remanence without an applied magnetic field. The bias and temperature dependence of the spin injection are found to be qualitatively similar to Fe-based spin LED devices. A Hanle effect is observed and demonstrates complete depolarization of spins in the semiconductor in a transverse magnetic field., Comment: 4 pages, 3 figures

We show that the accumulation of spin-polarized electrons at a forward-biased Schottky tunnel barrier between Fe and n-GaAs can be detected electrically. The spin accumulation leads to an additional voltage drop across the barrier that is suppressed by a small transverse magnetic field, which depolarizes the spins in the semiconductor. The dependence of the electrical accumulation signal on magnetic field, bias current, and temperature is in good agreement with the predictions of a drift-diffusion model for spin-polarized transport., Comment: Submitted to Phys. Rev. Lett

We have studied hyperfine interactions between spin-polarized electrons and lattice nuclei in Al_0.1Ga_0.9As/GaAs quantum well (QW) heterostructures. The spin-polarized electrons are electrically injected into the semiconductor heterostructure from a metallic ferromagnet across a Schottky tunnel barrier. The spin-polarized electron current dynamically polarizes the nuclei in the QW, and the polarized nuclei in turn alter the electron spin dynamics. The steady-state electron spin is detected via the circular polarization of the emitted electroluminescence. The nuclear polarization and electron spin dynamics are accurately modeled using the formalism of optical orientation in GaAs. The nuclear spin polarization in the QW is found to depend strongly on the electron spin polarization in the QW, but only weakly on the electron density in the QW. We are able to observe nuclear magnetic resonance (NMR) at low applied magnetic fields on the order of a few hundred Oe by electrically modulating the spin injected into the QW. The electrically driven NMR demonstrates explicitly the existence of a Knight field felt by the nuclei due to the electron spin., Comment: 19 Figures - submitted to PRB

Electrical spin injection from the Heusler alloy Co_2MnGe into a p-i-n Al_0.1Ga_0.9As/GaAs light emitting diode is demonstrated. A maximum steady-state spin polarization of approximately 13% at 2 K is measured in two types of heterostructures. The injected spin polarization at 2 K is calculated to be 27% based on a calibration of the spin detector using Hanle effect measurements. Although the dependence on electrical bias conditions is qualitatively similar to Fe-based spin injection devices of the same design, the spin polarization injected from Co_2MnGe decays more rapidly with increasing temperature., Comment: 8 pages, 4 figures

We present a complete description of spin injection and detection in Fe/Al_xGa_{1-x}As/GaAs heterostructures for temperatures from 2 to 295 K. Measurements of the steady-state spin polarization in the semiconductor indicate three temperature regimes for spin transport and relaxation. At temperatures below 70 K, spin-polarized electrons injected into quantum well structures form excitons, and the spin polarization in the quantum well depends strongly on the electrical bias conditions. At intermediate temperatures, the spin polarization is determined primarily by the spin relaxation rate for free electrons in the quantum well. This process is slow relative to the excitonic spin relaxation rate at lower temperatures and is responsible for a broad maximum in the spin polarization between 100 and 200 K. The spin injection efficiency of the Fe/Al_xGa_{1-x}As Schottky barrier decreases at higher temperatures, although a steady-state spin polarization of at least 6 % is observed at 295 K., Comment: 3 Figures Submitted to Phys. Rev. Lett

We study the nucleation of GaN islands grown by plasma-assisted molecular-beam epitaxy on AlN(0001) in a Stranski-Krastanov mode. In particular, we assess the variation of their height and density as a function of GaN coverage. We show that the GaN growth passes four stages: initially, the growth is layer-by-layer; subsequently, two-dimensional precursor islands form, which transform into genuine three-dimensional islands. During the latter stage, island height and density increase with GaN coverage until the density saturates. During further GaN growth, the density remains constant and a bimodal height distribution appears. The variation of island height and density as a function of substrate temperature is discussed in the framework of an equilibrium model for Stranski-Krastanov growth., Comment: Submitted to PRB, 10 pages, 15 figures

We study the adsorption behavior of Ga on (0001) GaN surfaces combining experimental specular reflection high-energy electron diffraction with theoretical investigations in the framework of a kinetic model for adsorption and ab initio calculations of energy parameters. The measurement of a Ga/GaN adsorption isotherm allows the quantification of the equilibrium Ga surface coverage as a function of the impinging Ga flux. The temperature dependence is discussed within an {\em ab initio} based growth model for adsorption taking into account the nucleation of Ga clusters., Comment: 9 pages, 10 figures

We demonstrate the growth of GaN/AlN quantum well structures by plasma-assisted molecular-beam epitaxy by taking advantage of the surfactant effect of Ga. The GaN/AlN quantum wells show photoluminescence emission with photon energies in the range between 4.2 and 2.3 eV for well widths between 0.7 and 2.6 nm, respectively. An internal electric field strength of $9.2\pm 1.0$ MV/cm is deduced from the dependence of the emission energy on the well width., Comment: Submitted to APL