Stochastic Tunneling Research Articles

Probabilistic computing enabled by continuous random numbers sampled from in-plane magnetized stochastic magnetic tunnel junctions

Hardware acceleration of probabilistic computing has recently attracted significant attention in the slowing down of Moore's law. A randomly fluctuating bit called as p-bit constitutes a fundamental building block for this type of physics-inspired computing scheme, which can be efficiently built out of emerging devices. Here, we report a probabilistic computing set-up, where random numbers are sampled from stochastic magnetic tunnel junctions with in-plane magnetic anisotropy. Although the sampled data have largely bipolar-like probability distributions compared to the ideally uniform ones, the results show a reasonable performance in a standard simulated annealing process on Boolean satisfiability problems up to 100 variables. The systematic simulations suggest the importance of probability distribution where some additional intermediate states help to increase the performance.

Voltage-insensitive stochastic magnetic tunnel junctions with double free layers

Stochastic magnetic tunnel junction (s-MTJ) is a promising component of probabilistic bit (p-bit), which plays a pivotal role in probabilistic computers. For a standard cell structure of the p-bit, s-MTJ is desired to be insensitive to voltage across the junction over several hundred millivolts. In conventional s-MTJs with a reference layer having a fixed magnetization direction, however, the stochastic output significantly varies with the voltage due to spin-transfer torque (STT) acting on the stochastic free layer. In this work, we study a s-MTJ with a “double-free-layer” design theoretically proposed earlier, in which the fixed reference layer of the conventional structure is replaced by another stochastic free layer, effectively mitigating the influence of STT on the stochastic output. We show that the key device property characterized by the ratio of relaxation times between the high- and low-resistance states is one to two orders of magnitude less sensitive to bias voltage variations compared to conventional s-MTJs when the top and bottom free layers are designed to possess the same effective thickness. This work opens a pathway for reliable, nanosecond-operation, high-output, and scalable spintronics-based p-bits.

Neuroscience-inspired information-integration system based on stochastic magnetic tunnel junctions

Neuroscience-inspired information-integration system based on stochastic magnetic tunnel junctions

Experimental demonstration of an on-chip p-bit core based on stochastic magnetic tunnel junctions and 2D MoS2 transistors

Probabilistic computing is a computing scheme that offers a more efficient approach than conventional complementary metal-oxide–semiconductor (CMOS)-based logic in a variety of applications ranging from optimization to Bayesian inference, and invertible Boolean logic. The probabilistic bit (or p-bit, the base unit of probabilistic computing) is a naturally fluctuating entity that requires tunable stochasticity; by coupling low-barrier stochastic magnetic tunnel junctions (MTJs) with a transistor circuit, a compact implementation is achieved. In this work, by combining stochastic MTJs with 2D-MoS2 field-effect transistors (FETs), we demonstrate an on-chip realization of a p-bit building block displaying voltage-controllable stochasticity. Supported by circuit simulations, we analyze the three transistor-one magnetic tunnel junction (3T-1MTJ) p-bit design, evaluating how the characteristics of each component influence the overall p-bit output. While the current approach has not reached the level of maturity required to compete with CMOS-compatible MTJ technology, the design rules presented in this work are valuable for future experimental implementations of scaled on-chip p-bit networks with reduced footprint.

Temperature dependence of the properties of stochastic magnetic tunnel junction with perpendicular magnetization

Stochastic magnetic tunnel junctions (s-MTJs) are attracting attention as key elements for spintronics-based probabilistic (p-) computers. The performance of p-computers is governed by the time-domain and the time-averaged response of single s-MTJs varying with temperature. Here we present results of the time-domain (rf) voltage and time-averaged (dc) resistance R of s-MTJs with perpendicular magnetization as functions of perpendicular magnetic fields H z and temperatures T = 20 °C–130 °C. We observe that both relaxation time (time-domain response) and the slope of the R – Hz curve (time-averaged response) decrease with increasing temperature. We discuss the physics underlying these results including the thermally induced spatially non-uniform collective spin dynamics.

Double-free-layer stochastic magnetic tunnel junctions with synthetic antiferromagnets

Double-free-layer stochastic magnetic tunnel junctions with synthetic antiferromagnets

Tunneling current-controlled spin states in few-layer van der Waals magnets.

Effective control of magnetic phases in two-dimensional magnets would constitute crucial progress in spintronics, holding great potential for future computing technologies. Here, we report a new approach of leveraging tunneling current as a tool for controlling spin states in CrI3. We reveal that a tunneling current can deterministically switch between spin-parallel and spin-antiparallel states in few-layer CrI3, depending on the polarity and amplitude of the current. We propose a mechanism involving nonequilibrium spin accumulation in the graphene electrodes in contact with the CrI3 layers. We further demonstrate tunneling current-tunable stochastic switching between multiple spin states of the CrI3 tunnel devices, which goes beyond conventional bi-stable stochastic magnetic tunnel junctions and has not been documented in two-dimensional magnets. Our findings not only address the existing knowledge gap concerning the influence of tunneling currents in controlling the magnetism in two-dimensional magnets, but also unlock possibilities for energy-efficient probabilistic and neuromorphic computing.

Programmable electrical coupling between stochastic magnetic tunnel junctions

Programmable electrical coupling between stochastic magnetic tunnel junctions

CMOS plus stochastic nanomagnets enabling heterogeneous computers for probabilistic inference and learning

Extending Moore’s law by augmenting complementary-metal-oxide semiconductor (CMOS) transistors with emerging nanotechnologies (X) has become increasingly important. One important class of problems involve sampling-based Monte Carlo algorithms used in probabilistic machine learning, optimization, and quantum simulation. Here, we combine stochastic magnetic tunnel junction (sMTJ)-based probabilistic bits (p-bits) with Field Programmable Gate Arrays (FPGA) to create an energy-efficient CMOS + X (X = sMTJ) prototype. This setup shows how asynchronously driven CMOS circuits controlled by sMTJs can perform probabilistic inference and learning by leveraging the algorithmic update-order-invariance of Gibbs sampling. We show how the stochasticity of sMTJs can augment low-quality random number generators (RNG). Detailed transistor-level comparisons reveal that sMTJ-based p-bits can replace up to 10,000 CMOS transistors while dissipating two orders of magnitude less energy. Integrated versions of our approach can advance probabilistic computing involving deep Boltzmann machines and other energy-based learning algorithms with extremely high throughput and energy efficiency.

Effect of stochastic activation function on reconstruction performance of restricted Boltzmann machines with stochastic magnetic tunnel junctions

Stochastic Magnetic Tunnel Junctions (SMTJs) emerge as a promising candidate for neuromorphic computing. The inherent stochasticity of SMTJs makes them ideal for implementing stochastic synapses or neurons in neuromorphic computing. However, the stochasticity of SMTJs may impair the performance of neuromorphic systems. In this study, we conduct a systematic examination of the influence of three stochastic effects (shift, change of slope, and broadening) on the sigmoid activation function. We further explore the implications of these effects on the reconstruction performance of Restricted Boltzmann Machines (RBMs). We find that the trainability of RBMs is robust against the three stochastic effects. However, reconstruction error is strongly related to the three stochastic effects in SMTJs-based RBMs. Significant reconstruction error is found when the stochastic effect is strong. Last, we identify the correlation of the reconstruction error with each stochastic factor. Our results might help develop more robust neuromorphic systems based on SMTJs.

Probabilistic computing with voltage-controlled dynamics in magnetic tunnel junctions

Probabilistic (p-) computing is a physics-based approach to addressing computational problems which are difficult to solve by conventional von Neumann computers. A key requirement for p-computing is the realization of fast, compact, and energy-efficient probabilistic bits. Stochastic magnetic tunnel junctions (MTJs) with low energy barriers, where the relative dwell time in each state is controlled by current, have been proposed as a candidate to implement p-bits. This approach presents challenges due to the need for precise control of a small energy barrier across large numbers of MTJs, and due to the need for an analog control signal. Here we demonstrate an alternative p-bit design based on perpendicular MTJs that uses the voltage-controlled magnetic anisotropy (VCMA) effect to create the random state of a p-bit on demand. The MTJs are stable (i.e. have large energy barriers) in the absence of voltage, and VCMA-induced dynamics are used to generate random numbers in less than 10 ns/bit. We then show a compact method of implementing p-bits by using VC-MTJs without a bias current. As a demonstration of the feasibility of the proposed p-bits and high quality of the generated random numbers, we solve up to 40 bit integer factorization problems using experimental bit-streams generated by VC-MTJs. Our proposal can impact the development of p-computers, both by supporting a fully spintronic implementation of a p-bit, and alternatively, by enabling true random number generation at low cost for ultralow-power and compact p-computers implemented in complementary metal-oxide semiconductor chips.

Micromagnetic realization of energy-based models using stochastic magnetic tunnel junctions

Micromagnetic realization of energy-based models using stochastic magnetic tunnel junctions

Easy-plane dominant stochastic magnetic tunnel junction with synthetic antiferromagnetic layers

Easy-plane dominant stochastic magnetic tunnel junction with synthetic antiferromagnetic layers

Stochastic domain wall-magnetic tunnel junction artificial neurons for noise-resilient spiking neural networks

The spatiotemporal nature of neuronal behavior in spiking neural networks (SNNs) makes SNNs promising for edge applications that require high energy efficiency. To realize SNNs in hardware, spintronic neuron implementations can bring advantages of scalability and energy efficiency. Domain wall (DW)-based magnetic tunnel junction (MTJ) devices are well suited for probabilistic neural networks given their intrinsic integrate-and-fire behavior with tunable stochasticity. Here, we present a scaled DW-MTJ neuron with voltage-dependent firing probability. The measured behavior was used to simulate a SNN that attains accuracy during learning compared to an equivalent, but more complicated, multi-weight DW-MTJ device. The validation accuracy during training was also shown to be comparable to an ideal leaky integrate and fire device. However, during inference, the binary DW-MTJ neuron outperformed the other devices after Gaussian noise was introduced to the Fashion-MNIST classification task. This work shows that DW-MTJ devices can be used to construct noise-resilient networks suitable for neuromorphic computing on the edge.

Stochastic magnetic tunnel junction with easy-plane dominant anisotropy

Super-paramagnetic fluctuation of a nanomagnet, when confined by a strong easy-plane anisotropy, can yield GHz speed random signal. A magnetic tunnel junction converts such moment movement into conductance fluctuation, and is useful as an entropy source for modern computing circuits. Here, the authors experimentally explore the base-line behavior of easy-plane magnetic tunnel junctions in the super-paramagnetic limit, using a CMOS back-end integrated fabrication process, and introduce some measurement methodologies to identify factors in device materials and fabrication in need of future optimization.

Effects of response spectrum of pulse-like ground motion on stochastic seismic response of tunnel

It is widely accepted that near-fault pulse-like ground motions potentially cause more severe damage to structures than ordinary ground motions. However, the effects of stochastic pulse-like ground motions on underground structures are not effectively considered. The impacts of response spectra of pulse-like ground motions on seismic response are also unclear. Hence, this study utilizes an underground tunnel to investigate the effects of response spectra of pulse-like ground motions on the stochastic seismic response by combining a pulse-like ground motion simulation method and a finite element method. The combination procedure enables stochastic seismic response analysis under spectrum-compatible pulse-like/ordinary ground motions. The finite element model considers the nonlinear dynamic properties of soil and soil–structure interaction. Monte Carlo simulations are carried out to quantify uncertainties of stochastic tunnel response. Results show that pulse-like ground motions cause larger bending moments for tunnel lining even when they match the same target spectrum of ordinary ground motions. Furthermore, the bending moment of tunnel lining is significantly amplified when the spectral acceleration of pulse-like ground motion contains bulges or multiple peaks in the ranges of 1 s–6 s. Therefore, the seismic risk of tunnels may be significantly underestimated in the near-fault regions without considering pulse-like ground motions and their spectral acceleration characteristics.

Spintronic Heterostructures for Artificial Intelligence: A Materials Perspective

With the advent of the Big Data era, neuromorphic computing (NC) (also known as brain‐inspired computing) has gained a lot of research interest. Spintronic devices are the emerging candidates for implementing the NC due to their intrinsic nonvolatility, extremely high endurance, low‐power consumption, and complementary metal‐oxide compatibility. Many research groups have proposed various NC architectures based on spintronic devices. Herein, a collective survey of different spintronic‐based approaches is given for NC. The reviewed approaches include the progress of stochastic magnetic tunnel junction (MTJ) devices, spin‐torque nano‐oscillator, spin‐Hall nano‐oscillator, domain walls, and skyrmion devices. In all of these approaches, spin–orbit torque (SOT)‐based magnetization control, which is achieved via spintronics heterostructures, plays a significant role. Various heterostructures of heavy metal and ferromagnetic layers that have been proposed are reviewed for generating SOT. In addition, the phenomena and materials involved in the generation of orbital torque are summarized due to the orbital Hall effect (OHE), which has recently gained researchers’ attention. Finally, an outlook on the opportunities and challenges for spintronic‐based NC hardware is provided, shedding light on its great potential for artificial intelligence (AI) applications.

Primordial black holes from stochastic tunnelling

If the inflaton gets trapped in a local minimum of its potential shortly before the end of inflation, it escapes by building up quantum fluctuations in a process known as stochastic tunnelling. In this work we study cosmological fluctuations produced in such a scenario, and how likely they are to form Primordial Black Holes (PBHs). This is done by using the stochastic-δ N formalism, which allows us to reconstruct the highly non-Gaussian tails of the distribution function of the number of e-folds spent in the false-vacuum state. We explore two different toy models, both analytically and numerically, in order to identify which properties do or do not depend on the details of the false-vacuum profile. We find that when the potential barrier is small enough compared to its width, ΔV/V < Δϕ 2/M Pl 2, the potential can be approximated as being flat between its two local extrema, so results previously obtained in a “flat quantum well” apply.Otherwise, when Δ V/V < V/M Pl 4, the PBH abundance depends exponentially on the height of the potential barrier, and when Δ V/V > V/M Pl it depends super-exponentially (i.e. as the exponential of an exponential) on the barrier height. In that later case PBHs are massively produced.This allows us to quantify how much flat inflection points need to be fine-tuned.In a deep false vacuum, we also find that slow-roll violations are typically encountered unless the potential is close to linear. This motivates further investigations to generalise our approach to non–slow-roll setups.

External-Field-Robust Stochastic Magnetic Tunnel Junctions Using a Free Layer with Synthetic Antiferromagnetic Coupling

The stochastic magnetic tunnel junction (MTJ), the resistance of which fluctuates in time between low and high states under thermal fluctuation, is expected to serve as a key element in probabilistic computers. For reliable operation and versatile application, one needs to address the challenge that the relaxation time in each state should be virtually independent of external magnetic fields in the range of, for example, several mT. In this research, we fabricate in-plane easy-axis elliptical stochastic MTJs with a synthetic antiferromagnetic (SAF) free layer and examine the robustness of their properties against external fields while comparing them with stochastic MTJs with a conventional single ferromagnetic structure. We show that the MTJ with a SAF free layer shows more robust relaxation times against fields applied along the easy- and hard-axis directions. The results are reproduced with a macrospin simulation, from which design guidelines for robust stochastic MTJs targeting probabilistic computers are discussed.

Bayesian neural networks using magnetic tunnel junction-based probabilistic in-memory computing

Bayesian neural networks (BNNs) combine the generalizability of deep neural networks (DNNs) with a rigorous quantification of predictive uncertainty, which mitigates overfitting and makes them valuable for high-reliability or safety-critical applications. However, the probabilistic nature of BNNs makes them more computationally intensive on digital hardware and so far, less directly amenable to acceleration by analog in-memory computing as compared to DNNs. This work exploits a novel spintronic bit cell that efficiently and compactly implements Gaussian-distributed BNN values. Specifically, the bit cell combines a tunable stochastic magnetic tunnel junction (MTJ) encoding the trained standard deviation and a multi-bit domain-wall MTJ device independently encoding the trained mean. The two devices can be integrated within the same array, enabling highly efficient, fully analog, probabilistic matrix-vector multiplications. We use micromagnetics simulations as the basis of a system-level model of the spintronic BNN accelerator, demonstrating that our design yields accurate, well-calibrated uncertainty estimates for both classification and regression problems and matches software BNN performance. This result paves the way to spintronic in-memory computing systems implementing trusted neural networks at a modest energy budget.