A Neuromorphic Computational Model for Spintronics-Based Hopfield Oscillatory Neural Network

The human brain is competent in information processing and learning, largely due to the coordinated activity of neuronal populations. These populations exhibit rhythmic fluctuations in activity known as oscillatory dynamics, observed across different brain regions. These oscillations are crucial in various cognitive functions, such as memory consolidation, sensory processing, and motor control. This work proposes a novel neuromorphic computational (NC) model comprising analytical derivation for a spintronics-based Hopfield oscillatory neural network (HONN) employing frequency synchronization inspired by the brain’s oscillatory mechanism of pattern recognition and associative memory. Kuramoto model, which represents the phase-based coupling of two oscillators, this work presents an extended mathematical analysis (modeling) of frequency and phase-based dual coupling mechanism. Further, this model is translated to the Theile equation which governs the dynamics of magnetic vortex core (such as core position and oscillation frequency) applicable to spintronic-based HONN. This approach uses spin-torque vortex nanooscillators (SVNOs) as neurons connected via resistive synapses representing synaptic coupling strength. The model describes the analytical relation between the SVNOs and the synaptic element, and how it influences the synchronized frequency (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$f_{\mathrm {sync}}$ </tex-math></inline-formula>). Stronger coupling aligns <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$f_{\mathrm {sync}}$ </tex-math></inline-formula> closer to the higher gyrotropic frequency of the magnetic vortex core within the network, while weaker coupling promotes <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$f_{\mathrm {sync}}$ </tex-math></inline-formula> closer to the lower one. The synaptic connections transition between low resistance state (LRS) and high resistance state (HRS) mimicking biological brain plasticity. This NC model is then utilized to design a spintronic-based HONN circuit to illustrate oscillatory properties, frequency-based synchronization, and resistive coupling to create an energy-efficient and scalable architecture. The proposed NC model represents a promising approach to advancing large-scale HONN hardware architecture, particularly by enabling the integration of SVNOs as neurons, resistive memories as synapses, and conventional electronics as peripherals. This model serves as a foundational framework for exploring the feasibility, functionality, and reliability of advanced neural network architectures, crucial for evaluating the potential of these hybrid systems in practical, large-scale applications.