Orthogonal Spin Current Injected Magnetic Tunnel Junction for Convolutional Neural Networks

Abstract

We propose that a spin Hall effect (SHE) driven magnetic tunnel junction (MTJ) device can be engineered to provide a continuous change in the resistance across it when injected with orthogonal spin currents. Using this concept, we develop a hybrid device-circuit simulation platform to design a network that realizes multiple functionalities of a convolutional neural network (CNN). At the atomistic level, we use the Keldysh nonequilibrium Green’s function (NEGF) technique that is coupled self-consistently with the stochastic Landau-Lifshitz-Gilbert–Slonczewski (LLGS) equations, which in turn is coupled with the HSPICE circuit simulator. We demonstrate the simultaneous functionality of the proposed network to evaluate the rectified linear unit (ReLU) and max-pooling functionalities. We present a detailed power and error analysis of the designed network against the thermal stability factor of the free ferromagnets (FMs). Our results show that there exists a nontrivial power-error trade-off in the proposed network, which enables an energy-efficient network design based on unstable free FMs with reliable outputs. The static power for the proposed ReLU circuit is 0.56 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu $</tex-math> </inline-formula> W and whereas the energy cost of a nine-input ReLU -max-pooling network with an unstable free FM ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\sf\Delta$</tex-math> </inline-formula> <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$=$</tex-math> </inline-formula> 15) is 3.4 pJ in the worst case scenario. We also rationalize the magnetization stability of the proposed device by analyzing the vanishing torque gradient points.