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Neuromorphic architectures with low energy barrier nanomagnetic devices have been attracting increasing interest over the past few years. More recently, a low barrier nanomagnet (LBNM)-based probabilistic device (p-bit) has been shown to be the basis of neuronal nodes in deep belief networks (DBNs). The LBNMs with perpendicular magnetic anisotropy (PMA) are analyzed and optimized in the interest of achieving stochasticity present in the learning system. In p-bit-based DBNs, several defects, such as variation of the nanomagnet diameter ( $\sigma d$ ), thickness ( $\sigma t_{f}$ ), and anisotropy field ( $\sigma H_{K}$ ), which results in alteration of the fluctuation speed of the p-bit’s nanomagnet can impair functionality. In this article, the accuracy of p-bit-based DBNs is examined under variation of nanomagnet diameter, thickness, and anisotropy field for various tilt angles and temperatures. As evaluated for the MNIST data set for temperature and tilt angle of 300 K and 25°, accordingly, it is shown that the process variation (PV) of $\sigma d$ , $\sigma t_{f}$ , and $\sigma H_{K}$ can be tolerated up to 8%, 23%, and 25%, respectively. A new method is developed to control the fluctuation frequency of the output of a p-bit device by employing a feedback mechanism. The feedback can alleviate this PV sensitivity of p-bit-based DBNs. The compact and low complexity method, which is presented by introducing the self-compensating circuit, can alleviate the influences of PV in fabrication and practical implementation.

Bayesian networks are powerful statistical models to understand causal relationships in real-world probabilistic problems such as diagnosis, forecasting, computer vision, etc. For systems that involve complex causal dependencies among many variables, the complexity of the associated Bayesian networks become computationally intractable. As a result, direct hardware implementation of these networks is one promising approach to reducing power consumption and execution time. However, the few hardware implementations of Bayesian networks presented in literature rely on deterministic CMOS devices that are not efficient in representing the inherently stochastic variables in a Bayesian network. This work presents an experimental demonstration of a Bayesian network building block implemented with naturally stochastic spintronic devices. These devices are based on nanomagnets with perpendicular magnetic anisotropy, initialized to their hard axes by the spin orbit torque from a heavy metal under-layer utilizing the giant spin Hall effect, enabling stochastic behavior. We construct an electrically interconnected network of two stochastic devices and manipulate the correlations between their states by changing connection weights and biases. By mapping given conditional probability tables to the circuit hardware, we demonstrate that any two node Bayesian networks can be implemented by our stochastic network. We then present the stochastic simulation of an example case of a four node Bayesian network using our proposed device, with parameters taken from the experiment. We view this work as a first step towards the large scale hardware implementation of Bayesian networks., 9 pages, 4 figures

Energy-efficient methods are addressed for lever-aging low energy barrier nanomagnetic devices within neuro-morphic architectures. Using a Magnetoresistive Random Access Memory (MRAM) probabilistic device (p-bit) as the basis of neuronal structures in Deep Belief Networks (DBNs), the impact of increasing the Magnetic Tunnel Junction's (MTJ's) energy barrier is assessed and optimized for the resulting stochasticity present in the learning system. A self-compensating circuit is developed herein providing a compact, and low complexity approach to mitigating process variation impacts towards practical implementation and fabrication. As evaluated for the MNIST dataset for energy barriers (E B ) at near-zero kT to 2.0 kT, it is shown that the proposed variation-tolerant circuit can effectively increase the reduced probabilistic fluctuation speed of the nanomagnet in p-bits with E B > OkT achieving approximately 5x improvement in the total energy consumption of a 784 × 200 × 10 DBN.

Spin Orbit Torque Magnetic RAM (SOT-MRAM) is emerging as a promising memory technology owing to its high endurance, reliability and speed. A critical factor for its success is the development of materials that exhibit efficient conversion of charge current to spin current, characterized by their spin Hall efficiency. In this work, it is experimentally demonstrated that the spin Hall efficiency of the industrially relevant ultra-thin Ta can be enhanced by more than 25× when a monolayer (ML) WSe2 is inserted as an underlayer. The enhancement is attributed to spin absorption at the Ta/WSe2 interface, suggested by harmonic Hall measurements. The presented hybrid spin Hall stack with a 2D WSe2 underlayer has a total body thickness of less than 2 nm and exhibits greatly enhanced spin Hall efficiency, which makes this hybrid a promising candidate for energy efficient SOT-MRAM.

Employing the probabilistic nature of unstable nano-magnet switching has recently emerged as a path towards unconventional computational systems such as neuromorphic or Bayesian networks. In this letter, we demonstrate proof-of-concept stochastic binary operation using hard axis initialization of nano-magnets and control of their output state probability (activation function) by means of input currents. Our method provides a natural path towards addition of weighted inputs from various sources, mimicking the integration function of neurons. In our experiment, spin orbit torque (SOT) is employed to “drive” nano-magnets with perpendicular magnetic anisotropy (PMA) -to their metastable state, i.e. in-plane hard axis. Next, the probability of relaxing into one magnetization state (+mi) or the other (−mi) is controlled using an Oersted field generated by an electrically isolated current loop, which acts as a “charge” input to the device. The final state of the magnet is read out by the anomalous Hall effect (AHE), demonstrating that the magnetization can be probabilistically manipulated and output through charge currents, closing the loop from charge-to-spin and spin-to-charge conversion. Based on these building blocks, a two-node directed network is successfully demonstrated where the status of the second node is determined by the probabilistic output of the previous node and a weighted connection between them. We have also studied the effects of various magnetic properties, such as magnet size and anisotropic field on the stochastic operation of individual devices through Monte Carlo simulations of Landau Lifshitz Gilbert (LLG) equation. The three-terminal stochastic devices demonstrated here are a critical step towards building energy efficient spin based neural networks and show the potential for a new application space.

Probabilistic spin logic (PSL) is a new paradigm of computing that relies on probabilistic bits (p-bits) that fluctuate randomly between metastable states. PSL may be more efficient than conventional CMOS-based logic in terms of intrinsic optimization, Bayesian inference, invertible Boolean logic, and hardware machine learning. Effectively tunable random number generators, p-bits, can be realized as stochastic nanomagnets that can be made to prefer one state over others by an external input, such as voltage or current. This letter looks at the design of stochastic nanomagnets that is most suitable as p-bits for PSL. Experimental evidence, supported by theory and numerical simulation, shows that the scaling of magnetic anisotropy is more effective than the scaling of the net magnetic moment for voltage-driven PSL applications. A novel system that can be used as a tunable random number generator is demonstrated experimentally and analyzed theoretically: a magnet with perpendicular magnetic anisotropy that is initialized to its hard axis by giant spin Hall effect torque. With zero external input, this system provides a potentially better alternative to other nanomagnet-based random number generators. By tuning the randomness through an external input, this system is suitable for probabilistic networks for Bayesian inference.

Low barrier nanomagnets have attracted a lot of research interest for their use as sources of high quality true random number generation. More recently, low barrier nanomagnets with tunable output have been shown to be a natural hardware platform for unconventional computing paradigms such as probabilistic spin logic. Efficient generation and tunability of high quality random bits is critical for these novel applications. However, current spintronic random number generators are based on superparamagnetic tunnel junctions (SMTJs) with tunability obtained through spin transfer torque (STT), which unavoidably leads to challenges in designing concatenated networks using these two terminal devices. The more recent development of utilizing spin orbit torque (SOT) allows for a three terminal device design, but can only tune in-plane magnetization freely, which is not very energy efficient due to the needs of overcoming a large demagnetization field. In this work, we experimentally demonstrate for the first time, a stochastic device with perpendicular magnetic anisotropy (PMA) that is completely tunable by SOT without the aid of any external magnetic field. Our measurements lead us to hypothesize that a tilted anisotropy might be responsible for the observed tunability. We carry out stochastic Landau-Lifshitz-Gilbert (sLLG) simulations to confirm our experimental observation. Finally, we build an electrically coupled network of two such stochastic nanomagnet based devices and demonstrate that finite correlation or anti-correlation can be established between their output fluctuations by a weak interconnection, despite having a large difference in their natural fluctuation time scale. Simulations based on a newly developed dynamical model for autonomous circuits composed of low barrier nanomagnets show close agreement with the experimental results.

Spin based logic devices have attracted a lot of research interest due to their potential low-power operation, non-volatility and possibility to enable new computing applications. Here we present an experimental demonstration of a novel spin logic device working at room temperature without the requirement of an external magnetic field. Our device is based on a pair of coupled in-plane magnetic anisotropy (IMA) magnet and a perpendicular magnetic anisotropy (PMA) magnet. The information written in the state of the IMA magnet is transferred to the state of the PMA magnet by means of a symmetry breaking dipolar field, while the two layers are electrically isolated. In addition to having the basic tenets of a logic device, our device has inbuilt memory, taking advantage of the non-volatility of nanomagnets. In another mode of operation, the same device is shown to have the functionality of a true random number generator (TRNG). The combination of logic functionality, nonvolatility and capability to generate true random numbers all in the same spin logic device, makes it uniquely suitable as a hardware for many new computing ideas.