Neural networks are increasing in scale and sophistication, catalyzing the need for efficient hardware. An inevitability when transferring neural networks to hardware is that non-idealities impact performance. Hardware-aware training, where non-idealities are accounted for during training is one way to recover performance, but at the cost of generality. In this work, we demonstrate a binary neural network consisting of an array of 20,000 magnetic tunnel junctions (MTJ) integrated on complementary metal-oxide-semiconductor (CMOS) chips. With 36 dies, we show that even a few defects can degrade the performance of neural networks. We demonstrate hardware-aware training and show that performance recovers close to ideal networks. We then introduce a robust method – statistics-aware training – that compensates for defects regardless of their specific configuration. When evaluated on the MNIST dataset, statistics-aware solutions differ from software-baselines by only 2 %. We quantify the sensitivity of networks trained with statistics-aware and conventional methods and demonstrate that the statistics-aware solution shows less sensitivity to defects when sampling the network loss function.
Many probabilistic computing frameworks have been developed in recent years due to their potential as faster, energy-efficient alternatives to von Neumann computers for combinatorial optimization problems. In this work, we study the dynamics of a two-spin analog Ising computer implemented with superparamagnetic tunnel junctions (SMTJs). The operational-amplifier-based circuit features a polarity selection and a programmable gain parameter, allowing us to achieve both positive and negative coupling and perform simulated annealing if the gain is treated as inverse temperature. Experiments show that correlation between coupled SMTJs approaches 1 in the high-gain limit. Scaling of this design requires only trivial modifications to the circuit; however, scaling up to large networks of spins requires the development of SMTJs with enhanced properties, suggesting that a co-design approach between devices, architectures and algorithms is necessary.
Superparamagnetic tunnel junctions (SMTJs) and spin-torque nano-oscillators (STNOs) show promise for use in energy-efficient unconventional computing schemes based on stochastic information encodings, operating from nanosecond to microsecond time scales. We demonstrate electrical coupling of SMTJs for emulating neuro-synaptic connections and leverage the phase dynamics of STNOs for innovative approaches to unbiased random number generation, with the potential to mimic fast stochastic binary neurons, paving the way for low-energy, hardware-based stochastic neural networks.
We will discuss first-principles calculations of spin transport and spin-orbit torques in disordered films and multilayers within the nonequilibrium Green's function technique. For a nonmagnetic Pt film, the behavior of the spin accumulation and the transverse spin current deviate significantly from the conventional spin-diffusion model. The effective transverse spin-diffusion length is much shorter than the longitudinal spin-diffusion length. For ferromagnetic trilayers, we find dampinglike and fieldlike torques with unconventional spin polarizations. The large rotated fieldlike component in Co/Cu/Co trilayers is inconsistent with diffusive transport in the spacer layer but can be explained by nonlocal interactions between the ferromagnetic layers when the mean-free path is not small compared to the spacer thickness.
Due to their interesting physical properties, myriad operational regimes, small size, and industrial fabrication maturity, magnetic tunnel junctions are uniquely suited for unlocking novel computing schemes for in-hardware neuromorphic computing. In this paper, we focus on the stochastic response of magnetic tunnel junctions, illustrating three different ways in which the probabilistic response of a device can be used to achieve useful neuromorphic computing power.
Magnetic tunnel junctions (MTJs) provide an attractive platform for implementing neural networks because of their simplicity, nonvolatility and scalability. In a hardware realization, however, device variations, write errors, and parasitic resistance will generally degrade performance. To quantify such effects, we perform experiments on a 2-layer perceptron constructed from a 15 × 15 passive array of MTJs, examining classification accuracy and write fidelity. Despite imperfections, we achieve accuracy of up to 95.3 % with proper tuning of network parameters. The success of this tuning process shows that new metrics are needed to characterize and optimize networks reproduced in mixed signal hardware.
In this talk, we explore the variety of ways in which ferromagnets electrically generate spin currents. We present first principles transport calculations giving the strength and magnetization dependence of these various mechanisms in transition metal ferromagnets. We compute full spin current tensors to probe all spin directions and show how each mechanism contributes to the spin currents allowed by symmetry. To help guide the interpretation of experiments, we also present calculations of spin current generation in magnetic heterostructures to quantify their transmission through interfaces and the spin torques they exert. Finally, we discuss experiments that have probed these novel mechanisms of spin current generation. Unlocking the full potential of ferromagnets as spin current sources will help create a powerful tool for spintronic devices such as magnetic memories.
In magnetic heterostructures, an in-plane electrical current can manipulate the magnetization direction of the free ferromagnetic layers through spin-orbit torques. Spin-orbit torques are transfers of angular momentum from the crystal lattice to the magnetization using conduction electrons as the medium for transfer. Traditionally, spin-orbit torques have been attributed to two causes: the spin Hall effect and the Rashba-Edelstein effect. However, this framework is incomplete because 1) experiments cannot reproducibly distinguish these mechanisms and 2) theory predicts other torques of comparable strength. Using the Boltzmann equation and first principles calculations, we have investigated the allowed interfacial contributions to spin-orbit torque. These investigations led to the discovery of a novel effect, interface-generated spin currents, which first principles calculations reveal are strong in relevant heavy metal/ferromagnet bilayers (such as Pt/Co). This work has also resulted in simple drift-diffusion models that can capture interfacial spin-orbit effects through the appropriate boundary conditions. Following this work, our group has performed first principles calculations showing that ferromagnets generate spin currents via the intrinsic mechanism that could exert spin-orbit torques at interfaces. In this talk, we discuss how both novel interfacial spin-orbit effects and spin current generation in ferromagnets could play an important role in spin-orbit torque. Recent experiments done in heterostructures, including those with a single ferromagnetic layer, provide evidence that ferromagnetic layers and interfaces cause the spin-orbit torques discussed here. Shedding light on these mechanisms will help clarify the nature of spin-orbit torque, which is crucial for realizing its potential for magnetic memories.
The brain displays many features typical of non-linear dynamical networks, such as synchronization or chaotic behaviour. These observations have inspired a whole class of models that harness the power of complex non-linear dynamical networks for computing. In this framework, neurons are modeled as non-linear oscillators, and synapses as the coupling between oscillators. These abstract models are very good at processing waveforms for pattern recognition or at generating precise time sequences useful for robotic motion. However there are very few hardware implementations of these systems, because large numbers of interacting non-linear oscillators are indeed. In this talk, I will show that coupled spin-torque nano-oscillators are very promising for realizing cognitive computing at the nanometer and nanosecond scale, and will present our first results in this direction.
We propose an experimental scheme to determine the spin-transfer torque efficiency excited by the spin-orbit interaction in ferromagnetic bilayers from the measurement of the longitudinal magnetoresistace. Solving a diffusive spin-transport theory with appropriate boundary conditions gives an analytical formula of the longitudinal charge current density. The longitudinal charge current has a term that is proportional to the square of the spin-transfer torque efficiency and that also depends on the ratio of the film thickness to the spin diffusion length of the ferromagnet. Extracting this contribution from measurements of the longitudinal resistivity as a function of the thickness can give the spin-transfer torque efficiency.
Spintronics aims to utilize the coupling between charge transport and magnetic dynamics to develop improved and novel memory and logic devices. Future progress in spintronics may be enabled by exploiting the spin-orbit coupling present at the interface between thin film ferromagnets and heavy metals. In these systems, applying an in-plane electrical current can induce magnetic dynamics in single domain ferromagnets, or can induce rapid motion of domain wall magnetic textures. There are multiple effects responsible for these dynamics. They include spin-orbit torques and a chiral exchange interaction (the Dzyaloshinskii-Moriya interaction) in the ferromagnet. Both effects arise from the combination of ferromagnetism and spin-orbit coupling present at the interface. There is additionally a torque from the spin current flux impinging on the ferromagnet, arising from the spin hall effect in the heavy metal. Using first principles calculations, we identify spin-orbit hybridization at the ferromagnet-heavy metal interface as central to the spin-orbit torques present in Co-Pt bilayers. We additionally propose that the transverse spin current (from the spin hall effect) is locally enhanced over its bulk value due to scattering at an interface which is oriented normal to the charge current direction.
Spin-transfer torques (STT) provides a new mechanism to alter the magnetic configurations in magnetic heterostructures, a
feat previously only achieved by an external magnetic field. A current flowing perpendicular through a magnetic
noncollinear spin structure can induce torques on the magnetization, depending on the polarity of the current. This is
because an electron carries angular momentum, or spin, part of which can be transferred to the magnetic layer as a torque.
A spin-polarized current of a substantial current density (e.g., 108 A/cm2) is required to observe the effect of the spin
transfer torques. Consequently, switching by spin-polarized currents is often realized in small structures with sub-micron
cross sections made by nanolithography. Here we demonstrate spin transfer torque effects using point-contact spin
injection involving no lithography. In a continuous Co/Cu/Co trilayer, we have observed hysteretic reversal of sub-100 nm
magnetic elements by spin injection through a metal tip both at low temperature and at room temperature. A small
magnetic domain underneath the tip in the top Co layer can be manipulated to align parallel or anti-parallel to the bottom
Co layer with a unique bias voltage. In an exchange-biased single ferromagnetic layer, we have observed a new form of
STT effect which is the inverse effect of domain wall magnetoresistance effect rather than giant magnetoresistance effect.
We further show that in granular solids, the STT effect that can be exploited to induce a large spin disorder when combined
with a large magnetic field. As a result, we have obtained a spectacular MR effect in excess of 400%, the largest ever
reported in any metallic systems.
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