Hardware emulation of stochastic p-bits for invertible logic

Pervaiz, Ahmed Zeeshan; Ghantasala, Lakshmi Anirudh; Çamsarı, Kerem Y.; Datta, Supriyo

doi:10.1038/s41598-017-11011-8

Cited by 70 publications

(34 citation statements)

References 31 publications

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“…For interconnected networks of p-bits, a distribution of correlation times for each p-bit needs to be considered as shown in Ref. [33]. Note that IMA-based designs can achieve sub-nanosecond correlation times even with fairly large volumes, provided that monodomain behavior can be preserved with a small enough diameter, while PMA-based designs tend to be much slower making IMA magnets more suitable for BSN applications.…”

Section: Low Barrier Magnetsmentioning

confidence: 99%

Low-Barrier Magnet Design for Efficient Hardware Binary Stochastic Neurons

et al. 2019

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Binary stochastic neurons (BSN's) form an integral part of many machine learning algorithms, motivating the development of hardware accelerators for this complex function. It has been recognized that hardware BSN's can be implemented using low barrier magnets (LBM's) by minimally modifying presentday magnetoresistive random access memory (MRAM) devices. A crucial parameter that determines the response of these LBM based BSN designs is the correlation time of magnetization, τc. In this letter, we show that for magnets with low energy barriers (∆ ≈ kBT and below), circular disk magnets with inplane magnetic anisotropy (IMA) lead to τc values that are two orders of magnitude smaller compared to τc for magnets having perpendicular magnetic anisotropy (PMA) and provide analytical descriptions. We show that this striking difference in τc is due to a precession-like fluctuation mechanism that is enabled by the large demagnetization field in IMA magnets. We provide a detailed energy-delay performance evaluation of previously proposed BSN designs based on Spin-Orbit-Torque (SOT) MRAM and Spin-Transfer-Torque (STT) MRAM employing low barrier circular IMA magnets by SPICE simulations. The designs exhibit sub-ns response times leading to energy requirements of ∼a few fJ to evaluate the BSN function, orders of magnitude lower than digital CMOS implementations with a much larger footprint. While modern MRAM technology is based on PMA magnets, results in this paper suggest that low barrier circular IMA magnets may be more suitable for this application.Index Terms-Binary stochastic neuron, hardware implementation, low barrier magnet, embedded MTJ, probabilistic computing

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Section: Low Barrier Magnetsmentioning

confidence: 99%

Low-Barrier Magnet Design for Efficient Hardware Binary Stochastic Neurons

et al. 2019

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“…If the magnet is fabricated as a circular magnet without any uniaxial anisotropy, the magnetization would fluctuate randomly in the plane due to the presence of thermal noise. Due to the back-voltage that would be induced by the fluctuations of magnetization, this 2-terminal device can operate as a voltage controllable tunable random number generator [32][33][34][35][36][37] that operates without any external magnetic fields 4 .…”

Section: Resultsmentioning

confidence: 99%

Demonstration of a pseudo-magnetization based simultaneous write and read operation in a Co60Fe20B20/Pb(Mg1/3Nb2/3)0.7Ti0.3O3 heterostructure

Shen¹,

Ostwal²,

Appenzeller³

2020

Sci Rep

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Taking advantage of the magnetoelectric and its inverse effect, this article demonstrates strainmediated magnetoelectric write and read operations simultaneously in co 60 fe 20 B 20 /pb(Mg 1/3 nb 2/3) 0.7 ti 0.3 o 3 heterostructures based on a pseudo-magnetization µ ≡ m x 2 − m y 2. By applying an external DC-voltage across a (011)-cut PMN-PT substrate, the ferroelectric polarization is reoriented , which results in an anisotropic in-plane strain that transfers to the CoFeB thin film and changes its magnetic anisotropy H k. The change in H k in-turn results in a 90° rotation of the magnetic easy axis for sufficiently high voltages. Simultaneously, the inverse effect is employed to read changes of the magnetic properties. The change of magnetization in ferromagnetic (FM) layer induces an elastic stress in the piezoelectric (PE) layer, which generates a PE potential that can be used to readout the magnetic state of the FM layer. The experimental results are in excellent qualitative agreement with an equivalent circuit model that considers how magnetic properties are electrically controlled in such a PE/FM heterostructure and how a back-voltage is generated due to changing magnetic properties in a self-consistent model. We demonstrated that a change of easy axis of magnetization due to an applied voltage can be directly used for information processing, which is essential for future ME based devices. Recently, so-called Magnetoelectric (ME) effects 1-4 in piezoelectric (PE)/FerroMagnetic (FM) structures have attracted substantial research interest, since these may open a path towards controlling magnetic properties by means of an electric field-rather than currents-to achieve low energy dissipation in the writing process of magnetic memory cells 5-22. As to the reading process, the Giant Magneto-Resistance (GMR) 18 or Tunneling Magneto-Resistance (TMR) 1 is usually utilized to readout the stored magnetic information. However, the readout energy based on magneto-resistive methods is not negligible compared with the extremely low writing energies. In addition, the integration of GMR or Magnetic Tunnel Junction (MTJ) stacks with piezoelectric substrates remains a challenge. This raises the question whether voltages that are used in case of the write operation could also be used in a reverse configuration to read the magnetic information in a more power efficient way. To demonstrate this idea, in this article, we have measured the reciprocal ME effect simultaneously and achieved a strain-mediated magnetoelectric write and read unit in a Co 60 Fe 20 B 20 /Pb(Mg 1/3 Nb 2/3) 0.7 Ti 0.3 O 3 heterostructure based on a pseudo-magnetization µ ≡ m x 2-m y 2 rather than a net magnetization m x , m y or m z. Single crystal PMN-PT with (011) orientation was employed in this work as the piezoelectric substrate for achieving large ME effects due to its large piezoelectric coefficients with d 31 ~ −3,100 pC/N along the [100] direction and d 32 ~ 1,400 pC/N along the [01-1] direction 23-29. The write operation in the magnetic subsystem...

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“…A serious research effort is currently underway to implement non-Boolean computing machinery with nanomagnets [38][39][40][41][42][43][44][45][46][47][48][49][50][51]. Their requirements are very different from those of Boolean logic and fortunately are well suited to the features of nanomagnetic switches, especially their attribute of non-volatility.…”

Section: Discussionmentioning

confidence: 99%

Nanomagnetic Boolean Logic—The Tempered (and Realistic) Vision

Bandyopadhyay

2021

IEEE Access

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The idea of nanomagnetic Boolean logic was advanced more than two decades ago. It envisaged the use of nanomagnets with two stable magnetization orientations as the primitive binary switch for implementing logic gates and ultimately combinational/sequential circuits. Enthusiastic proclamations of how nanomagnetic logic will eclipse traditional (transistor-based) logic circuits proliferated the applied physics literature. Two decades later there is not a single viable nanomagnetic logic chip in sight, let alone one that is a commercial success. In this perspective article, I offer my reasons on why this has come to pass. I present a realistic and tempered vision of nanomagnetic logic, pointing out many misconceptions about this paradigm, flaws in some proposals that appeared in the literature, shortcomings, and likely pitfalls that might stymie progress in this field.

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Hardware emulation of stochastic p-bits for invertible logic

Cited by 70 publications

References 31 publications

Low-Barrier Magnet Design for Efficient Hardware Binary Stochastic Neurons

Low-Barrier Magnet Design for Efficient Hardware Binary Stochastic Neurons

Demonstration of a pseudo-magnetization based simultaneous write and read operation in a Co60Fe20B20/Pb(Mg1/3Nb2/3)0.7Ti0.3O3 heterostructure

Nanomagnetic Boolean Logic—The Tempered (and Realistic) Vision

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