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Back propagation (BP) is the default solution for gradient computation in neural network training. However, implementing BP-based training on various edge devices such as FPGA, microcontrollers (MCUs), and analog computing platforms face multiple major challenges, such as the lack of hardware resources, long time-to-market, and dramatic errors in a low-precision setting. This paper presents a simple BP-free training scheme on an MCU, which makes edge training hardware design as easy as inference hardware design. We adopt a quantized zeroth-order method to estimate the gradients of quantized model parameters, which can overcome the error of a straight-through estimator in a low-precision BP scheme. We further employ a few dimension reduction methods (e.g., node perturbation, sparse training) to improve the convergence of zeroth-order training. Experiment results show that our BP-free training achieves comparable performance as BP-based training on adapting a pre-trained image classifier to various corrupted data on resource-constrained edge devices (e.g., an MCU with 1024-KB SRAM for dense full-model training, or an MCU with 256-KB SRAM for sparse training). This method is most suitable for application scenarios where memory cost and time-to-market are the major concerns, but longer latency can be tolerated.

Ferroelectricity is characterized by the presence of spontaneous and switchable macroscopic polarization. Scaling limits of ferroelectricity have been of both fundamental and technological importance, but the probes of ferroelectricity have often been indirect due to confounding factors such as leakage in the direct electrical measurements. Recent interest in low-voltage switching electronic devices squarely puts the focus on ultrathin limits of ferroelectricity in an electronic device form, specifically on the robustness of ferroelectric characteristics such as retention and endurance for practical applications. Here, we illustrate how manipulating the kinetic energy of the plasma plume during pulsed laser deposition can yield ultrathin ferroelectric capacitor heterostructures with high bulk and interface quality, significantly low leakage currents and a broad "growth window". These heterostructures venture into previously unexplored aspects of ferroelectric properties, showcasing ultralow switching voltages ($<$0.3 V), long retention times ($>$10$^{4}$s), and high endurance ($>$10$^{11}$cycles) in 20 nm films of the prototypical perovskite ferroelectric, BaTiO$_{3}$. Our work demonstrates that materials engineering can push the envelope of performance for ferroelectric materials and devices at the ultrathin limit and opens a direct, reliable and scalable pathway to practical applications of ferroelectrics in ultralow voltage switches for logic and memory technologies.

The development of spin-orbitronic devices, such as magneto-electric spin-orbit logic devices, calls for materials with a high resistivity and a high spin-charge interconversion efficiency. One of the most promising candidates in this regard is sputtered Bi$_x$Se$_{1-x}$. Although there are several techniques to quantify spin-charge interconversion, to date reported values for sputtered Bi$_x$Se$_{1-x}$ have often been overestimated due to spurious effects related to local currents combined with a lack of understanding of the effect of the interfaces and the use of approximations for unknown parameters, such as the spin diffusion length. In the present study, non-local spin valves are used to inject pure spin currents into Bi$_x$Se$_{1-x}$, allowing us to directly obtain its spin diffusion length as well as its spin Hall angle, from 10 K up to 300 K. These values, which are more accurate than those previously reported in sputtered Bi$_x$Se$_{1-x}$, evidence that the efficiency of this material is not exceptional. Indeed, the figure of merit for spin-charge interconversion, given by the product of these two parameters, is slightly under 1 nm. Our work demonstrates the importance of considering all material parameters and interfaces when quantifying the spin transport properties of materials with strong spin-orbit coupling., Comment: 12 pages, 4 figures, 1 table, and Supplemental Material

The Magnetoelectric Spin-Orbit (MESO) technology aims to bring logic into memory by combining a ferromagnet with a magnetoelectric (ME) element for information writing, and a spin-orbit (SO) element for information read-out through spin-charge conversion. Among candidate SO materials to achieve a large MESO output signal, oxide Rashba two-dimensional electron gases (2DEGs) have shown very large spin-charge conversion efficiencies, albeit mostly in spin-pumping experiments. Here, we report all-electrical spin-injection and spin-charge conversion experiments in nanoscale devices harnessing the inverse Edelstein effect of SrTiO3 2DEGs. We have designed, patterned and fabricated nanodevices in which a spin current injected from a cobalt layer into the 2DEG is converted into a charge current. We optimized the spin-charge conversion signal by applying back-gate voltages, and studied its temperature evolution. We further disentangled the inverse Edelstein contribution from spurious effects such as the planar Hall effect, the anomalous Hall effect or the anisotropic magnetoresistance. The combination of non-volatility and high energy efficiency of these devices could potentially lead to new technology paradigms for beyond-CMOS computing architectures.

In this work we use a phenomenological theory of ferroelectric switching in BiFeO$_3$ thin films to uncover the mechanism of the two-step process that leads to the reversal of the weak magnetization of these materials. First, we introduce a realistic model of a BiFeO$_3$ film, including the Landau energy of isolated domains as well as the constraints that account for the presence of the substrate and the multidomain configuration found experimentally. We use this model to obtain statistical information about the switching behavior - by running dynamical simulations based on the Landau-Khalatnikov time-evolution equation, including thermal fluctuations - and we thus identify the factors that drive the two-step polarization reversal observed in the experiments. Additionally, we apply our model to test potential strategies for optimizing the switching characteristics., Comment: 16 pages, 9 figures

As CMOS technologies face challenges in dimensional and voltage scaling, the demand for novel logic devices has never been greater, with spin-based devices offering scaling potential, at the cost of significantly high switching energies. Alternatively, magnetoelectric materials are predicted to enable low-power magnetization control, a solution with limited device-level results. Here, we demonstrate voltage-based magnetization switching and reading in nanodevices at room temperature, enabled by exchange coupling between multiferroic BiFeO$_3$ and ferromagnetic CoFe, for writing, and spin-to-charge current conversion between CoFe and Pt, for reading. We show that upon the electrical switching of the BiFeO$_3$, the magnetization of the CoFe can be reversed, giving rise to different voltage outputs. Through additional microscopy techniques, magnetization reversal is linked with the polarization state and antiferromagnetic cycloid propagation direction in the BiFeO$_3$. This study constitutes the building block for magnetoelectric spin-orbit logic, opening a new avenue for low-power beyond-CMOS technologies., Comment: 16 pages, 5 figures and Supplementary Information

One of the major obstacles to realizing spintronic devices such as MESO logic devices is the small signal magnitude used for magnetization readout, making it important to find materials with high spin-to-charge conversion efficiency. Although intermixing at the junction of two materials is a widely occurring phenomenon, its influence on material characterization and the estimation of spin-to-charge conversion efficiencies is easily neglected or underestimated. Here, we demonstrate all electrical spin-to-charge conversion in Bi$_x$Se$_{1-x}$ nanodevices and show how the conversion efficiency can be overestimated by tens of times depending on the adjacent metal used as a contact. We attribute this to the intermixing-induced compositional change and the properties of a polycrystal that lead to drastic changes in resistivity and spin Hall angle. Strategies to improve the spin-to-charge conversion signal in similar structures for functional devices are discussed., Comment: Main text (18 pages, 3 figures, 2 tables) and supporting information (18 pages)

Monolayer transition metal dichalcogenides are promising materials for spintronics due to their robust spin-valley locked valence states, enabling efficient charge-to-spin conversion via valley Hall effect with non-equilibrium spins possessing long spin diffusion lengths of hundreds of nanometers. In this work, we show that the injection of a pure valley current, induced by valley Hall effect in a WSe2 monolayer, imparts a spin torque on the magnetization of an overlaid Fe or CoFe in a tunneling structure. The torque efficiency is found to be comparable to that in conventional perpendicular magnetic tunnel junctions and can be further optimized with valley Hall angle in WSe2. The valley nature of the spin torque gives rise to out-of-plane damping-like torques in a current-in-plane configuration, vanishing charge transport perpendicular-to-the-plane as well as torque efficiency tunable through gating.

In this work we introduce the simplest, lowest-order Landau-like potential for BiFeO$_3$ and La-doped BiFeO$_3$ as an expansion around the paraelectric cubic phase in powers of polarization, FeO$_6$ octahedral rotations and strains. We present an analytical approach for computing the model parameters from density functional theory. We illustrate our approach by computing the potentials for BiFeO$_3$ and La$_{0.25}$Bi$_{0.75}$FeO$_3$ and show that, overall, we are able to capture the first-principles results accurately. The computed models allow us to identify and explain the main interactions controlling the relative stability of the competing low-energy phases of these compounds., Comment: 12 pages, 6 figures

Spin transport through magnetic insulators has been demonstrated in a variety of materials and is an emerging pathway for next-generation spin-based computing. To modulate spin transport in these systems, one typically applies a sufficiently strong magnetic field to allow for deterministic control of magnetic order. Here, we make use of the well-known multiferroic magnetoelectric, BiFeO3, to demonstrate non-volatile, hysteretic, electric-field control of thermally excited magnon current in the absence of an applied magnetic field. These findings are an important step toward magnon-based devices, where electric-field-only control is highly desirable., Comment: 34 pages, 4 figures, 9 supplemental figures

The joint extremal spatial dependence of wind speed and significant wave height in the North East Atlantic is quantified using Metop satellite scatterometer and hindcast observations for the period 2007-2018, and a multivariate spatial conditional extremes (MSCE) model, ultimately motivated by the work of Heffernan and Tawn (2004). The analysis involves (a) registering individual satellite swaths and corresponding hindcast data onto a template transect (running approximately north-east to south-west, between the British Isles and Iceland), (b) non-stationary directional-seasonal marginal extreme value analysis at a set of registration locations on the transect, (c) transformation from physical to standard Laplace scale using the fitted marginal model, (d) estimation of the MSCE model on the set of registration locations, and assessment of quality of model fit. A joint model is estimated for three spatial quantities: Metop wind speed, hindcast wind speed and hindcast significant wave height. Results suggest that, when conditioning on extreme Metop wind speed, extremal spatial dependence for all three quantities decays over approximately 600-800 km.

Generating high-quality random numbers with a Gaussian probability distribution function is an important and resource consuming computational task for many applications in the fields of machine learning and Monte Carlo algorithms. Recently, CMOS-based digital hardware architectures have been explored as specialized Gaussian random number generators (GRNGs). These CMOS-based GRNGs have a large area and require entropy sources at their input which increase the computing cost. Here, we propose a GRNG that works on the principle of the Boltzmann law in a physical system made from an interconnected network of thermally unstable magnetic tunnel junctions. The proposed hardware can produce multi-bit Gaussian random numbers at a gigahertz speed and can be configured to generate distributions with a desired mean and variance. An analytical derivation of the required interconnection and bias strengths is provided followed by numerical simulations to demonstrate the functionalities of the GRNG., Comment: 14 pages, 5 figures

Spintronic devices are a promising beyond-CMOS device option thanks to their energy efficiency and compatibility with CMOS. To accurately capture their multi-physics dynamics, a rigorous treatment of both spin and charge and their inter-conversion is required. Here we present physics-based device models based on 4x4 matrices for the spin-orbit coupling part of the magneto-electric spin-orbit (MESO) device. Also, a more rigorous physics model of ferroelectric and magnetoelectric switching of ferromagnets, based on Landau-Lifshitz-Gilbert (LLG) and Landau-Khalatnikov (LK) equations, is presented. With the combined model implemented in a SPICE circuit simulator environment, simulation results were obtained which show feasibility of MESO implementation and functional operation of buffers, oscillators, and majority gates., Comment: 11 pages, 21 figures

Oxide interfaces exhibit a broad range of physical effects stemming from broken inversion symmetry. In particular, they can display non-reciprocal phenomena when time reversal symmetry is also broken, e.g., by the application of a magnetic field. Examples include the direct and inverse Edelstein effects (DEE, IEE) that allow the interconversion between spin currents and charge currents. The DEE and IEE have been investigated in interfaces based on the perovskite SrTiO$_3$ (STO), albeit in separate studies focusing on one or the other. The demonstration of these effects remains mostly elusive in other oxide interface systems despite their blossoming in the last decade. Here, we report the observation of both the DEE and IEE in a new interfacial two-dimensional electron gas (2DEG) based on the perovskite oxide KTaO$_3$. We generate 2DEGs by the simple deposition of Al metal onto KTaO$_3$ single crystals, characterize them by angle-resolved photoemission spectroscopy and magnetotransport, and demonstrate the DEE through unidirectional magnetoresistance and the IEE by spin-pumping experiments. We compare the spin-charge interconversion efficiency with that of STO-based interfaces, relate it to the 2DEG electronic structure, and give perspectives for the implementation of KTaO$_3$ 2DEGs into spin-orbitronic devices.

SrTiO$_3$-based two-dimensional electron gases (2DEGs) can be formed through the deposition of epitaxial oxides like LaAlO$_3$ or of reactive metals such as Al. Such 2DEGs possess a finite Rashba spin-orbit coupling that has recently been harnessed to interconvert charge and spin currents through the direct and inverse Edelstein and spin Hall effects. Here we compare the formation and properties of 2DEGs generated in SrTiO$_3$ by the growth of Al, Ta and Y ultrathin films by magnetron sputtering. By combining in situ and ex situ X-ray photoelectron spectroscopy (XPS) we gain insight into the reduction of the SrTiO$_3$ and the appearance of Ti$^{3+}$ states associated with 2DEG formation, its reoxidation by exposure to the air, and the transformation of the metal into its binary oxides. We extract the carrier densities through magnetotransport and compare them with the XPS data. Finally, working with samples covered by an extra layer of NiFe, we perform spin-pumping ferromagnetic resonance experiments and investigate spin-charge conversion as a function of gate voltage. We identify trends in the data across the different sample systems and discuss them as a function of the carrier density and the transparency of the metal oxide tunnel barrier.

The negative capacitance (NC) stabilization of a ferroelectric (FE) material can potentially provide an alternative way to further reduce the power consumption in ultra-scaled devices and thus has been of great interest in technology and science in the past decade. In this article, we present a physical picture for a better understanding of the hysteresis-free charge boost effect observed experimentally in metal-ferroelectric-insulator-metal (MFIM) capacitors. By introducing the dielectric (DE) leakage and interfacial trapped charges, our simulations of the hysteresis loops are in a strong agreement with the experimental measurements, suggesting the existence of an interfacial oxide layer at the FE-metal interface in metal-ferroelectric-metal (MFM) capacitors. Based on the pulse switching measurements, we find that the charge enhancement and hysteresis are dominated by the FE domain viscosity and DE leakage, respectively. Our simulation results show that the underlying mechanisms for the observed hysteresis-free charge enhancement in MFIM may be physically different from the alleged NC stabilization and capacitance matching. Moreover, the link between Merz's law and the phenomenological kinetic coefficient is discussed, and the possible cause of the residual charges observed after pulse switching is explained by the trapped charge dynamics at the FE-DE interface. The physical interpretation presented in this work can provide important insights into the NC effect in MFIM capacitors and future studies of low-power logic devices., Comment: 9 pages, 7 captioned figures, 1 table

Over recent decades, the Arctic Ocean has experienced dramatic changes due to climate change. Retreating sea ice has opened up large areas of ocean, resulting in an enhanced wave climate. Taking into account the intense seasonality and the rapid changes to the Arctic climate, a non-stationary approach is applied to time-varying statistical properties to investigate historical trends of extreme values. The analysis is based on a 28-year wave hindcast (from 1991 to 2018) carried out with the WAVEWATCH III wave model forced by ERA5 wind speed. The results show notable seasonal differences and robust positive trends in extreme wave height and wind speed, especially in the Beaufort and East Siberian seas, with increasing rates in areal-average of the 100-year return period of wind speed of approximately 4\% and significant wave height up to 60%. It is concluded that the significant increases in extreme significant wave height are largely associated with sea-ice retreat and the enhanced fetches available for wave generation.

The switching dynamics of a single-domain BiFeO3/CoFe heterojunction is modeled and key parameters such as interface exchange coupling coefficient are extracted from experimental results. The lower limit of the magnetic order response time of CoFe in the BiFeO3/CoFe heterojunction is theoretically quantified to be on to the order of 100 ps. Our results indicate that the switching behavior of CoFe in the BiFeO3/CoFe heterojunction is dominated by the rotation of the Neel vector in BiFeO3 rather than the unidirectional exchange bias at the interface. We also quantify the magnitude of the interface exchange coupling coefficient J_int to be 0.32 pJ/m by comparing our simulation results with the giant magnetoresistance (GMR) curves and the magnetic hysteresis loop in the experiments. To the best of our knowledge, this is the first time that J_int is extracted quantitatively from experiments. Furthermore, we demonstrate that the switching success rate and the thermal stability of the BiFeO3/CoFe heterojunction can be improved by reducing the thickness of CoFe and increasing the length to width aspect ratio of the BiFeO3/CoFe heterojunction. Our theoretical model provides a comprehensive framework to study the magnetoelectric properties and the manipulation of the magnetic order of CoFe in the BiFeO3/CoFe heterojunction.

Efficient detection of the magnetic state at nanoscale dimensions is an important step to utilize spin logic devices for computing. Magnetoresistance effects have been hitherto used in magnetic state detection, but they suffer from energetically unfavorable scaling and do not generate an electromotive force that can be used to drive a circuit element for logic device applications. Here, we experimentally show that a favorable miniaturization law is possible via the use of spin-Hall detection of the in-plane magnetic state of a magnet. This scaling law allows us to obtain a giant signal by spin Hall effect in CoFe/Pt nanostructures and quantify an effective spin-to-charge conversion rate for the CoFe/Pt system. The spin-to-charge conversion can be described as a current source with an internal resistance, i.e., it generates an electromotive force that can be used to drive computing circuits. We predict that the spin-orbit detection of magnetic states can reach high efficiency at reduced dimensions, paving the way for scalable spin-orbit logic devices and memories., Comment: 13 pages, 3 figures, Extended Data, Supplementary Information

In this paper, the multi-domain nature of ferroelectric (FE) polarization switching dynamics in a metal-ferroelectric-metal (MFM) capacitor is explored through a physics-based phase field approach, where the three-dimensional time-dependent Ginzburg-Landau (TDGL) equation and Poisson's equation are self-consistently solved with the SPICE simulator. Systematically calibrated based on the experimental measurements, the model well captures transient negative capacitance in pulse switching dynamics, with domain interaction and viscosity being the key parameters. It is found that the influence of pulse amplitudes on voltage transient behaviors can be attributed to the fact that the FE free energy profile strongly depends on how the domains are interacted. This finding has an important implication on the charge-boost induced by stabilization of negative capacitance in an FE + dielectric (DE) stack since the so-called capacitance matching needs to be designed at a specific operation voltage or frequency. In addition, we extract the domain viscosity dynamics during polarization switching according to the experimental measurements. For the first time, a physics-based circuit-compatible SPICE model for multi-domain phase field simulations is established to reveal the effect of domain interaction on the FE energy profile and microscopic domain evolution., Comment: 17 pages, 6 figures

Numerous neural network circuits and architectures are presently under active research for application to artificial intelligence and machine learning. Their physical performance metrics (area, time, energy) are estimated. Various types of neural networks (artificial, cellular, spiking, and oscillator) are implemented with multiple CMOS and beyond-CMOS (spintronic, ferroelectric, resistive memory) devices. A consistent and transparent methodology is proposed and used to benchmark this comprehensive set of options across several application cases. Promising architecture/device combinations are identified., Comment: 59 pages, 37 figures, 7 tables

The switching dynamics of a single-domain BiFeO$_3$ thin films is investigated through combining the dynamics of polarization and Neel vector. The evolution of the ferroelectric polarization is described by the Landau-Khalatnikov (LK) equation, and the Landau-Lifshitz-Gilbert (LLG) equations for spins in two sublattices to model the time evolution of the antiferromagnetic order (Neel vector) in a G-type antiferromagnet. This work theoretically demonstrates that due to the rotation of the magnetic hard axis following the polarization reversal, the Neel vector can be switched by 180 degrees, while the weak magnetization can remain unchanged. The simulation results are consistent with the ab initio calculation, where the Neel vector rotates during polarization rotation, and also match our calculation of the dynamics of order parameter using Landau-Ginzburg theory. We also find that the switching time of the Neel vector is determined by the speed polarization switching and is predicted to be as short as 30 ps.