There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Physical Review B

The computational brain: Patricia S. Churchland and Terrence J. Sejnowski (MIT Press, Cambridge, MA, 1992); xi, 544 pages, $39.95

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Electronic Transport In Mesoscopic Systems

Journal of Physics Condensed Matter: Preface

A two-terminal stochastic switch is disclosed. The switch includes a magnetic tunnel junction (MTJ) stack, an access switch controlled by a first terminal and coupled to the MTJ stack, such that when the access switch is on, electrical current flows from a first source coupled to the MTJ stack, through the MTJ stack, and through the access switch to a second source, and a digital buffer coupled to the MTJ stack and the access switch which is configured to transform an analog signal associated with a voltage division across the MTJ stack and the access switch to a digital signal, output of the digital buffer forming a second terminal.

Stochastic switching device with adjustable randomness

Extending Moore's law by augmenting complementary-metal-oxide semiconductor (CMOS) transistors with emerging nanotechnologies (X) has become increasingly important. Accelerating Monte Carlo algorithms that rely on random sampling with such CMOS+X technologies could have significant impact on a large number of fields from probabilistic machine learning, optimization to quantum simulation. In this paper, we show the combination of stochastic magnetic tunnel junction (sMTJ)-based probabilistic bits (p-bits) with versatile Field Programmable Gate Arrays (FPGA) to design a CMOS + X (X = sMTJ) prototype. Our approach enables high-quality true randomness that is essential for Monte Carlo based probabilistic sampling and learning. Our heterogeneous computer successfully performs probabilistic inference and asynchronous Boltzmann learning, despite device-to-device variations in sMTJs. A comprehensive comparison using a CMOS predictive process design kit (PDK) reveals that compact sMTJ-based p-bits replace 10,000 transistors while dissipating two orders of magnitude of less energy (2 fJ per random bit), compared to digital CMOS p-bits. Scaled and integrated versions of our CMOS + stochastic nanomagnet approach can significantly advance probabilistic computing and its applications in various domains by providing massively parallel and truly random numbers with extremely high throughput and energy-efficiency.

CMOS + stochastic nanomagnets: heterogeneous computers for probabilistic inference and learning

One of the big challenges of current electronics is the design and implementation of hardware neural networks that perform fast and energy-efficient machine learning Spintronics is a promising catalyst for this field with the capabilities of nanosecond operation and compatibility with existing microelectronics Considering large-scale, viable neuromorphic systems however, variability of device properties is a serious concern In this paper, we show an autonomously operating circuit that performs hardware-aware machine learning utilizing probabilistic neurons built with stochastic magnetic tunnel junctions We show that in-situ learning of weights and biases in a Boltzmann machine can counter device-to-device variations and learn the probability distribution of meaningful operations such as a full adder This scalable autonomously operating learning circuit using spintronics-based neurons could be especially of interest for standalone artificial-intelligence devices capable of fast and efficient learning at the edge

Hardware-aware in-situ Boltzmann machine learning using stochastic magnetic tunnel junctions.

This paper introduces a novel oscillator that combines the tunability of spin Hall-driven nano oscillators with the high quality factor (Q) of high overtone bulk acoustic wave resonators (HBAR), integrating both reference and tunable oscillators on the same chip with CMOS. In such magneto acoustic spin Hall (MASH) oscillators, voltage oscillations across the magnetic tunnel junction (MTJ) that arise from a spin-orbit torque (SOT) are shaped by the transmission response of the HBAR that acts as a multiple peak-bandpass filter and a delay element due to its large time constant, providing delayed feedback. The filtered voltage oscillations can be fed back to the MTJ via a) strain, b) current, or c) magnetic field. We develop a SPICE-based circuit model by combining experimentally benchmarked models including the stochastic Landau-Lifshitz-Gilbert (sLLG) equation for magnetization dynamics and the Butterworth Van Dyke (BVD) circuit for the HBAR. Using the self-consistent model, we project up to $\sim$ 50X enhancement in the oscillator linewidth with Q reaching up to 52825 at 3 GHz, while preserving the tunability by locking the STNO to the nearest high Q peak of the HBAR. We expect that our results will inspire MEMS-based solutions to spintronic devices by combining attractive features of both fields for a variety of applications.

Magneto Acoustic Spin Hall Oscillators

We propose a new type of magnetoelectric memory device that stores magnetic easy-axis information or pseudo-magnetization, rather than a definite magnetization direction, in magnetoelectrically coupled heterostructures. Theoretically, we show how a piezoelectric/ferromagnetic (PE/FM) combination can lead to non-volatility in pseudo-magnetization exhibiting overall ferroelectric-like behavior. The pseudo-magnetization can be manipulated by extremely low voltages especially when the FM is a low-barrier nano-magnet. Using a circuit model benchmarked against experiments, we determine the switching energy, delay, switching probability and retention time of the envisioned 1T/1C memory device in terms of magnetic and circuit parameters and discuss its thermal stability in terms of a key parameter called back-voltage vm which is an electrical measure of the strain-induced magnetic field. Taking advantage of ferromagnetic resonance measurements, we experimentally extract values for vm in CoFeB films and circular nano-magnets deposited on Pb(Mg1/3Nb2/3)0.7Ti0.3O3 which agree well with the theoretical values. Our experimental findings indeed indicate the feasibility of the proposed novel device and confirm the assumed parameters in our modeling effort.

Kerem Y. Camsari

Papers

Stochastic switching device with adjustable randomness

CMOS + stochastic nanomagnets: heterogeneous computers for probabilistic inference and learning

Hardware-aware in-situ Boltzmann machine learning using stochastic magnetic tunnel junctions.

Magneto Acoustic Spin Hall Oscillators

A magnetoelectric memory device based on pseudo-magnetization