Spintronic Hodgkin-Huxley-Analogue Neuron Implemented with a Single Magnetic Tunnel Junction

Davi R. Rodrigues, Rayan Moukhader, Yanxiang Luo, Bin Fang, Adrien Pontlevy, Abbas Hamadeh, Zhongming Zeng, Mario Carpentieri, and Giovanni Finocchio

Phys. Rev. Applied 19, 064010 – Published 2 June 2023

Abstract

Spiking neural networks aim to emulate the brain’s properties to achieve similar parallelism and high processing power. A caveat of these neural networks is the high computational cost for emulation, while current proposals for analogue implementations are energy inefficient and not scalable. We propose a device based on a single magnetic tunnel junction to perform neuron firing for spiking neural networks without the need for any resetting procedure. We leverage two areas of physics, magnetism and thermal effects, to obtain biorealistic spiking behavior analogous to the Hodgkin-Huxley model of the neuron. The device is also able to emulate the simpler leaky-integrate-and-fire model. Numerical simulations using experimental-based parameters demonstrate firing frequency in the megahertz to gigahertz range under constant input at room temperature. The compactness, scalability, low cost, CMOS compatibility, and power efficiency of magnetic tunnel junctions advocates for their broad use in hardware implementations of spiking neural networks.

Received 22 February 2023
Revised 13 April 2023
Accepted 26 April 2023

DOI:https://doi.org/10.1103/PhysRevApplied.19.064010

Physics Subject Headings (PhySH)

Physics of computation Spiking neurons Spintronics

Artificial neural networks Magnetic tunnel junctions

Hodgkin-Huxley model

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Davi R. Rodrigues^1,*, Rayan Moukhader ^2,3, Yanxiang Luo ⁴, Bin Fang⁴, Adrien Pontlevy², Abbas Hamadeh ⁵, Zhongming Zeng ⁴, Mario Carpentieri^1,†, and Giovanni Finocchio ^2,‡

¹Department of Electrical and Information Engineering, Politecnico di Bari, Bari 70125, Italy
²Department of Mathematical and Computer Sciences, Physical Sciences and Earth Sciences, University of Messina, Messina I-98166, Italy
³Multi-Disciplinary Physics Laboratory, Faculty of Sciences, Lebanese University, Beirut 1500, Lebanon
⁴Key Laboratory of Multifunctional Nanomaterials and Smart Systems, Suzhou Institute of Nano-Tech and Nano-Bionics, CAS, Suzhou, Jiangsu 215123, People’s Republic of China
⁵Fachbereich Physik and Landesforschungszentrum OPTIMAS, Technische Universität Kaiserslautern, Kaiserslautern 67663, Germany

^*davi.rodrigues@poliba.it
^†mario.carpentieri@poliba.it
^‡gfinocchio@unime.it

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Vol. 19, Iss. 6 — June 2023

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Images

Figure 1
MTJ implementation of biorealistic firing behavior. (a) Left, a sketch of the device concept of the proposed MTJ spiking device; right, a sketch of a biological neuron. Both receive the input in terms of currents and produce an output in terms of a voltage variation. In the spintronic device, the potential variation is due to changes in resistance produced by the input current and thermal effects. In the neuron, the potential variation is due to sodium ( ${Na}^{+}$ ), potassium ( $K^{+}$ ), and leakage currents. (b),(c) Comparison of resistance variation of the proposed MTJ device with the potential spiking in a biological neuron, according to the Hodgkin-Huxley model. In (b), from top to bottom, spikes in the resistance through the device, dynamics of the magnetization components, and temperature variation of the device. (c) Example of a numerical simulation of the dynamics of a H-H neuron. It can be observed that the behavior of a sharp firing signal followed by a refractory period is a common feature in both models. For a comparison between the two neurons, see Table 1.
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Figure 2
Dependence of (a) the average normalized resistance and (b) temperature as a function of the applied current density. In (a), we identify three regions where (i) the magnetization is strongly biased towards the easy axis in the free layer (n_PMA), (ii) there is an auto-oscillation around the easy axis of the free layer (n_PMA), and (iii) the magnetization is strongly biased towards the direction of magnetization in the polarizer (p). Firing behavior corresponds to a thermally induced alternation between auto-oscillation and the strongly biased state, as shown in the inset corresponding to the magnetization dynamics of the free layer, as shown in the right panel of (a). Notably, the resistance in this case is given by the m_x component, which is represented in blue.
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Figure 3
(a) Frequency of neuron firing as a function of applied current density. (b),(c) Time-domain behavior of the resistance (top), magnetization components (middle; green, m_z; orange, m_y; blue, m_x), and temperature (bottom) for low (2 × 10¹⁰ A/m²) and high (2.4 × 10¹⁰ A/m²) current density, respectively.
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Figure 4
(a) Difference between the H-H model and the LIF model. In the LIF model, we consider pulses of amplitude Δι and period Δτ. (b) Evolution of the device properties in the presence of current pulses. From top to bottom panels, we show the normalized resistance, the evolution of the magnetization components, the profile of the applied current, and the temperature of the device. (c) Time between the first pulse and the first synapse. Different colors represent different pulse sizes, while the x axis represents the lowest-current value in the pulse. To include thermal-induced stochasticity, we simulate each pulse amplitude and size 5 times. (d) Time of the first synapse for a constant current.
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Figure 5
Example of a SNN built with the proposed MTJ device. (a) Behavior of a SNN with four neurons. Currents of the two input neurons are set as constants. For each MTJ, we show the behavior of the resistance (upper panel) and input current (lower panel). Input currents of the output neurons are generated according to Eq. (11), with the respective weights, $W_{m n}$ , shown. (b) Two sets considered for verifying the learning process. (c) Sketch of the feed-forward all-connected SNN. Each pixel is associated with a single input neuron. (d) Evolution of the weight matrix. Starting from a random distribution of weights, after the training process, each figure can be represented by a single output neuron, which has the highest frequency.
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Figure 6
Behavior of magnetization dynamics for different currents and including the fieldlike torque. Material parameters are those give in Table 2.
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Physical Review Applied