Ferrimagnetic Co-Gd-Bilayer-Based Fast and Energy-Efficient Synaptic Devices for Neuromorphic Computing

Abstract

Ferromagnetic devices, where current pulses flowing through the heavy metal layer below the ferromagnetic layer move the ferromagnetic domain wall through spin-orbit torque, have been proposed and experimentally demonstrated as synapses for neuromorphic computing [1–3]. But since ferrimagnets are known to exhibit faster domain wall motion compared to ferromagnets, the potential for ferrimagnetic synapses also needs to be explored [4].Here, we first carry out micromagnetic simulations of current-induced domain wall motion in a ferromagnetic device as well as a ferrimagnetic Co/Gd-bilayer-based device. The working principle of the ferrimagnetic synapse is just the same as the ferromagnetic synapse: current flowing through the underlying heavy metal layer moves the domain wall in the ferrimagnetic bi-layer just like it moves it in the ferromagnetic layer (Fig. 1a) [4]. Motion of the domain wall leads to a change in conductance and hence an update in the weight stored in the synapse [1, 2]. In our simulation, the spin Hall angle of the heavy metal (Pt), current flow through which generates the necessary spin-orbit toque for domain wall motion, is considered to be 0.13 [4]. For the ferrimagnetic system, dynamics of the magnetic moments of both the Co and Gd layers, exchange-coupled with each other (coupling strength = -0.9 mJ/m2), has been modeled in ‘mumax3’ [4]. The temperature-dependent variation of the Co and Gd magnetic moments is also considered.From our simulations (Fig. 1b), we observe that in the ferrimagnetic system, the domain wall velocity is highest at the angular-momentum-compensation temperature, T= 165 K, at which moment in Gd layer (mGd) = 0.9 times moment in Co layer (mCo). This is consistent with the experimental observation and corresponding one-dimensional-domain-wall calculations reported by Blasing et al [4]. Fig. 2a shows that across a wide range of current density through the heavy metal layer, domain wall velocity in the ferrimagnetic system at the angular-momentum-compensation temperature (165 K) is 2X–2.5X higher than that in the ferromagnetic system at room temperature.Next, we carry out system-level simulations with the device characteristic in Fig. 2a to compare the performance of the ferromagnetic and the ferrimagnetic devices as synapses in a crossbar-array-based neuromorphic system that mimics a Fully Connected Neural Network (FCNN) with a hidden layer. Synaptic weights are updated in both the ferromagnet-synapse and ferrimagnet-synapse crossbars using the thresholding algorithm, proposed by Kaushik et al. [5], to achieve on-chip learning in the crossbars on Iris data set of flowers and MNIST data set of handwritten digits.Using this thresholding algorithm, for Iris data set, we obtain train accuracy of 100% and test accuracy of 96%, and for MNIST, we obtain train accuracy of 98% and test accuracy of 92%. We obtain these same accuracy numbers for both ferromagnetic and ferrimagnetic synapse crossbars because we allow the same number of conductance states for both these types of synapses (50).According to this thresholding algorithm, for each synapse in the FCNN, the synaptic weight/ conductance is either increased or decreased by a fixed amount or kept the same at any particular iteration [5]. Thus training can be achieved only by applying current pulses of fixed magnitude and duration to the ferrimagnetic or ferromagnetic synapses — positive polarity of current for weight increase and negative polarity for weight decrease (Fig. 1a). A shorter duration pulse needs the domain wall to move with a higher velocity compared to a longer duration pulse to cause the same weight update. Hence, a shorter pulse needs to be of higher current magnitude and will consume more energy. Fig. 2b shows how energy consumed by a pulse increases with a decrease in duration of the pulse, both in the case of the ferrimagnetic system and the ferromagnetic system. We do observe that for the same duration of current pulse, energy consumed is 4X lower for the ferrimagnetic system than for the ferromagnetic system. Similarly, if the energy consumption per pulse is kept constant, pulses of time duration 4X lower can be used for the ferrimagnet compared to the ferromagnet.As a result, when we compare the energy consumption and time taken for on-chip learning in the two aforementioned crossbar systems, we observe that for the same net energy consumption in the system, the ferrimagnetic crossbar can be trained 4X faster than the ferromagnetic crossbar. Similarly, for the same speed across the two crossbars, the ferrimagnetic crossbar can be trained at 4X lower energy than the ferromagnetic crossbar. Thus, our study shows that ferrimagnetic-bilayer-based systems can pave the way for fast and energy-efficient neuromorphic computing in the future. **