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Developing permanent magnets with fewer critical elements requires understanding hysteresis effects and coercivity through visualizing magnetization reversal. Here, we numerically investigate the effect of the geometry of nanoscale ferromagnetic inclusions in a paramagnetic/nonmagnetic matrix to understand the key factors that maximize the magnetic energy product of such nanocomposite systems. Specifically, we have considered a matrix of “3 μm × 3 μm × 40 nm” dimension, which is a sufficiently large volume, two-dimensional representation considering that the ferromagnetic inclusions' thickness is less than 3.33% of the lateral dimensions simulated. Using this approach, which minimizes edge effects to approximate bulk-like magnetic behavior while remaining computationally tractable for simulation, we systematically studied the effect of the thickness of ferromagnetic strips, separation between the ferromagnetic strips due to the nonmagnetic matrix material, different saturation magnetization values, and the length of these ferromagnetic strips on magnetic coercivity and remanence by simulating the hysteresis loop plots for each geometry. Furthermore, we study the underlying micromagnetic mechanism for magnetic reversal to understand the factors that could help attain the maximum magnetic energy densities for ferromagnetic nanocomposite systems in a paramagnetic/nonmagnetic material matrix. In this study, we have used material parameters of an exemplary Alnico alloy system, a rare-earth-free, thermally stable nanocomposite, which could potentially replace high-strength NdFeB magnets in applications that do not require large energy products. However, we project the energy density (BH)max of materials with higher saturation magnetization to have an ideal theoretical limit of (BH)max ∼94 kJ/m3 (∼12 MGOe), which is ∼(35%–40%) of the energy density of Rare-Earth Free Magnets. This energy density could be higher if exchange bias from antiferromagnets, defects, and pinning is included and could stimulate further experimental work on the fabrication and large-scale manufacturing of RE-free PMs with different nanocomposite systems. 

An artificial neural network (ANN) inference involves matrix vector multiplications that require a very large number of multiply and accumulate operations, resulting in high energy cost and large device footprint. Stochastic computing (SC) offers a less resource-intensive ANN implementation with minimal accuracy loss. Random number generators (RNG) are required to implement SC in hardware. These can be realized through stochastic-magnetic tunnel junctions (s-MTJ), where the energy barrier to switch between the ‘up’ and ‘down’ states is designed to be small, enabling thermal noise to generate a random bit stream. While s-MTJs have previously been used to implement SC-ANNs, these studies have been limited to architectures with continuously varying (i.e.,analog) weights. In this work, we study the use of SC for matrix vector multiplication withquantizedsynaptic weights and quantized outputs. We show that a quantized SC-ANN, implemented by using experimentally obtained s-MTJ bitstreams and a limited number of discrete quantized states for both weights and hidden layer nodes in an ANN, can effectively reduce time (latency) and energy consumption in SC compared to an analog implementation, while largely preserving accuracy. We implemented quantization with 5 and 11 quantized states, along with SC configured with stochastic bitstream lengths of 100, 200, 300, 400, and 500 on neural networks with one hidden layer and three hidden layers. Inference was performed on the MNIST dataset for both training with SC and without SC. Training with SC provided better accuracy for all cases. For the shortest bitstream of 100 bits, the highest accuracies were 92% for one hidden layer and over 96% for three hidden layers. The overall system attained its peak accuracy of 96.82% using a 400 bit stochastic bitstream with three hidden layers. Our investigations demonstrate 9× improvement in latency and 2.6× improvement in energy consumption using the quantized SC approach compared to a similar s-MTJ based ANN architecture without quantization. 

Abstract Anomaly detection in real-time using autoencoders implemented on edge devices is exceedingly challenging due to limited hardware, energy, and computational resources. We show that these limitations can be addressed by designing an autoencoder with low-resolution non-volatile memory-based synapses and employing an effective quantized neural network learning algorithm. We further propose nanoscale ferromagnetic racetracks with engineered notches hosting magnetic domain walls (DW) as exemplary non-volatile memory-based autoencoder synapses, where limited state (5-state) synaptic weights are manipulated by spin orbit torque (SOT) current pulses to write different magnetoresistance states. The performance of anomaly detection of the proposed autoencoder model is evaluated on the NSL-KDD dataset. Limited resolution and DW device stochasticity aware training of the autoencoder is performed, which yields comparable anomaly detection performance to the autoencoder having floating-point precision weights. While the limited number of quantized states and the inherent stochastic nature of DW synaptic weights in nanoscale devices are typically known to negatively impact the performance, our hardware-aware training algorithm is shown to leverage these imperfect device characteristics to generate an improvement in anomaly detection accuracy (90.98%) compared to accuracy obtained with floating-point synaptic weights that are extremely memory intensive. Furthermore, our DW-based approach demonstrates a remarkable reduction of at least three orders of magnitude in weight updates during training compared to the floating-point approach, implying significant reduction in operation energy for our method. This work could stimulate the development of extremely energy efficient non-volatile multi-state synapse-based processors that can perform real-time training and inference on the edge with unsupervised data. 

Multistate memory systems have the ability to store and process more data in the same physical space as binary memory systems, making them a potential alternative to existing binary memory systems. In the past, it has been demonstrated that voltage-controlled magnetic anisotropy (VCMA) based writing is highly energy-efficient compared to other writing methods used in non-volatile nano-magnetic binary memory systems. In this study, we introduce a new, VCMA-based and skyrmion-mediated non-volatile ternary memory system using a perpendicular magnetic tunnel junction (p-MTJ) in the presence of room temperature thermal perturbation. We have also shown that ternary states {− 1, 0, + 1} can be implemented with three magnetoresistance values obtained from a p-MTJ corresponding to ferromagnetic up, down, and skyrmion state, with 99% switching probability in the presence of room temperature thermal noise in an energy-efficient way, requiring ~ 2 fJ energy on an average for each switching operation. Additionally, we show that our proposed ternary memory demonstrates an improvement in area and energy by at least 2X and ~ 10e4 X respectively, compared to state-of-the-art spin-transfer torque (STT)-based non-volatile magnetic multistate memories. Furthermore, these three states can be potentially utilized for energy-efficient, high-density in-memory quantized deep neural network implementation.