Low-Barrier Magnet Design for Efficient Hardware Binary Stochastic Neurons

Binary stochastic neurons (BSNs) 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 BSNs can be implemented using low-barrier magnets (LBMs) by minimally modifying present-day magnetoresistive random-access memory (MRAM) devices. A crucial parameter that determines the response of these LBM-based BSN designs is the <italic>correlation time</italic> of magnetization <inline-formula><tex-math notation="LaTeX">$\tau _c$</tex-math></inline-formula>. In this letter, we show that, for magnets with low-energy barriers (<inline-formula><tex-math notation="LaTeX">$\Delta \approx k_BT$</tex-math></inline-formula> and below), circular disk magnets with in-plane magnetic anisotropy (IMA) lead to <inline-formula><tex-math notation="LaTeX">$\tau _c$</tex-math></inline-formula> values that are two orders of magnitude smaller than <inline-formula><tex-math notation="LaTeX">$\tau _c$</tex-math></inline-formula> of magnets with perpendicular magnetic anisotropy (PMA). Analytical descriptions demonstrate that this striking difference in <inline-formula><tex-math notation="LaTeX">$\tau _c$</tex-math></inline-formula> is due to a precessionlike 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 MRAM and spin-transfer torque MRAM employing low-barrier circular IMA magnets by SPICE simulations. The designs exhibit subnanosecond response times leading to energy requirements of approximately a few femtojoules to evaluate the BSN function, orders of magnitude lower than digital CMOS implementations with a much larger surface area. While modern MRAM technology is based on PMA magnets, results in this letter suggest that low-barrier circular IMA magnets may be more suitable for this application.

[1]  Kaushik Roy,et al.  Stochastic Spiking Neural Networks Enabled by Magnetic Tunnel Junctions: From Nontelegraphic to Telegraphic Switching Regimes , 2017 .

[2]  Ugur Cilingiroglu,et al.  A purely capacitive synaptic matrix for fixed-weight neural networks , 1991 .

[3]  Bo Yuan,et al.  VLSI Architectures for the Restricted Boltzmann Machine , 2017, ACM J. Emerg. Technol. Comput. Syst..

[4]  Joseph S. Friedman,et al.  Circuit-Level Evaluation of the Generation of Truly Random Bits with Superparamagnetic Tunnel Junctions , 2018, 2018 IEEE International Symposium on Circuits and Systems (ISCAS).

[5]  S. Datta,et al.  Low-Barrier Nanomagnets as p-Bits for Spin Logic , 2016, IEEE Magnetics Letters.

[6]  Supriyo Datta,et al.  Zero-Threshold Rectification Using Low Energy Barrier Nano-Magnets , 2018 .

[7]  Supriyo Datta,et al.  Modular Approach to Spintronics , 2015, Scientific Reports.

[8]  Wei Yang Lu,et al.  Nanoscale memristor device as synapse in neuromorphic systems. , 2010, Nano letters.

[9]  Seung H. Kang,et al.  Systematic optimization of 1 Gbit perpendicular magnetic tunnel junction arrays for 28 nm embedded STT-MRAM and beyond , 2015, 2015 IEEE International Electron Devices Meeting (IEDM).

[10]  Supriyo Datta,et al.  Voltage-Driven Building Block for Hardware Belief Networks , 2018, IEEE Design & Test.

[11]  Supriyo Datta,et al.  Implementing p-bits With Embedded MTJ , 2017, IEEE Electron Device Letters.

[12]  H. Ohno,et al.  Spintronics based random access memory: a review , 2017 .

[13]  Hitoshi Kubota,et al.  Neural-like computing with populations of superparamagnetic basis functions , 2016, Nature Communications.

[14]  J. W. Brown.  Thermal Fluctuations of a Single-Domain Particle , 1963 .

[15]  John P. Hayes,et al.  Survey of Stochastic Computing , 2013, TECS.

[16]  S. Datta,et al.  Rectification in Spin-Orbit Materials Using Low-Energy-Barrier Magnets , 2018, Physical Review Applied.

[17]  Supriyo Datta,et al.  Hardware emulation of stochastic p-bits for invertible logic , 2017, Scientific Reports.

[18]  Punyashloka Debashis,et al.  Design of Stochastic Nanomagnets for Probabilistic Spin Logic , 2018, IEEE Magnetics Letters.

[19]  Naoya Onizawa,et al.  VLSI Implementation of Deep Neural Network Using Integral Stochastic Computing , 2015, IEEE Transactions on Very Large Scale Integration (VLSI) Systems.

[20]  Daniel J. Amit,et al.  Modeling brain function: the world of attractor neural networks, 1st Edition , 1989 .

[21]  Supriyo Datta,et al.  Experimental demonstration of nanomagnet networks as hardware for Ising computing , 2016, 2016 IEEE International Electron Devices Meeting (IEDM).

[22]  Supriyo Datta,et al.  Intrinsic optimization using stochastic nanomagnets , 2016, Scientific Reports.

[23]  S. Majetich,et al.  Superparamagnetic perpendicular magnetic tunnel junctions for true random number generators , 2018 .

[24]  Andrew S. Cassidy,et al.  Cognitive computing systems: Algorithms and applications for networks of neurosynaptic cores , 2013, The 2013 International Joint Conference on Neural Networks (IJCNN).

[25]  Supriyo Datta,et al.  Composable Probabilistic Inference Networks Using MRAM-based Stochastic Neurons , 2018, ACM J. Emerg. Technol. Comput. Syst..

[26]  Jonathan Z. Sun.  Spin-current interaction with a monodomain magnetic body: A model study , 2000 .

[27]  W. Coffey,et al.  Thermal fluctuations of magnetic nanoparticles: Fifty years after Brown , 2012, 1209.0298.

[28]  Jian-Ping Wang,et al.  Telegraphic switching signals by magnet tunnel junctions for neural spiking signals with high information capacity , 2018, Journal of Applied Physics.

[29]  Geoffrey E. Hinton,et al.  A Learning Algorithm for Boltzmann Machines , 1985, Cogn. Sci..

[30]  R. Cowburn,et al.  Single-Domain Circular Nanomagnets , 1999 .

[31]  Andrew S. Cassidy,et al.  A million spiking-neuron integrated circuit with a scalable communication network and interface , 2014, Science.

[32]  Dmitri E. Nikonov,et al.  Benchmarking of Beyond-CMOS Exploratory Devices for Logic Integrated Circuits , 2015, IEEE Journal on Exploratory Solid-State Computational Devices and Circuits.

[33]  E. Moro,et al.  Transition from ferromagnetism to superparamagnetism on the nanosecond time scale , 2002 .

[34]  Supriyo Datta,et al.  Ultrafast Fluctuations in Low-Barrier Magnets , 2019 .

[35]  Brian M. Sutton,et al.  Stochastic p-bits for Invertible Logic , 2016, 1610.00377.

[36]  Joseph S. Friedman,et al.  Low-Energy Truly Random Number Generation with Superparamagnetic Tunnel Junctions for Unconventional Computing , 2017, 1706.05262.