This letter presents a model system for controllable two-magnon interference in the time domain. This two magnon interference, i.e., a magnonic analog to the photonic Hong-Ou-Mandel effect, is supported by a tunable magnonic beamsplitter operation formed in a hybrid cavity magnonic system comprising a pair of mutually coupled magnon modes. By applying a time-dependent magnetic field, magnons can be excited independently in each mode and subsequently brought into interaction, shifting from independent to collective oscillations, to realize a controllable magnonic beamsplitter. Whenthe beamsplitter operation is applied to an initially unentangled two-magnon state, a maximally entangled magnonic N00N state with tunable phase sensitivity is produced. These findings suggest that two-magnon interference in hybrid cavity magnonic systems may enable novel quantum metrological devices to study fundamental magnon dynamics and contribute to developing hybrid magnonic quantum computing architectures.

We present the design and numerical simulation of a spiking neuron capable of on-chip machine learning. Built within the CMOS+X framework, the spiking neuron consists of an NMOS transistor combined with a magnetic tunnel junction (MTJ). This NMOS+MTJ unit, when simulated in the industry-standard circuit simulation software LTspice, reproduces multiple functions of a biological neuron, including threshold spiking, latency, refractory periods, synaptic integration, inhibition, and adaptation. These behaviors arise from the intrinsic magnetization dynamics of the MTJ and do not require any additional control circuitry. By interconnecting the NMOS+MTJ neurons, we construct a model of an analog multilayer network that learns through spike-timing-dependent weight updates derived from a gradient-descent rule, with both training and inference modeled in the analog domain. The simulated CMOS+X network achieves reliable spike propagation and successful training on a nonlinear task, indicating a feasible path toward compact, low-power, in-memory neuromorphic hardware for edge applications.

Spiking neural networks encode information in spike timing and offer a pathway toward energy efficient artificial intelligence. However, a key challenge in spiking neural networks is realizing nonlinear and expressive computation in compact, energy-efficient hardware without relying on additional circuit complexity. In this work, we examine nonlinear computation in a CMOS+X spiking neuron implemented with a magnetic tunnel junction connected in series with an NMOS transistor. Circuit simulations of a multilayer network solving the XOR classification problem show that three intrinsic neuronal properties enable nonlinear behavior: threshold activation, response latency, and absolute refraction. Threshold activation determines which neurons participate in computation, response latency shifts spike timing, and absolute refraction suppresses subsequent spikes. These results show that magnetization dynamics of MTJ devices can support nonlinear computation in compact neuromorphic hardware.

This letter presents a model system for controllable two-magnon interference in the time domain. This two-magnon interference, i.e., a magnonic analog to the photonic Hong-Ou-Mandel effect, is supported by a tunable magnonic beamsplitter operation formed in a hybrid cavity magnonic system comprising a pair of mutually coupled magnon modes. By applying a time-dependent magnetic field, magnons can be excited independently in each mode and subsequently brought into interaction, shifting from independent to collective oscillations, to realize a controllable magnonic beamsplitter. When the beamsplitter operation is applied to an initially unentangled two-magnon state, a maximally entangled magnonic N00N state with tunable phase sensitivity is produced. These findings suggest that two-magnon interference in hybrid cavity magnonic systems may enable novel quantum metrological devices to study fundamental magnon dynamics and contribute to developing hybrid magnonic quantum computing architectures.

A temporal magnon-qubit Mach-Zehnder (MZ) interferometer is proposed. The interferometer is based on controllable entanglement of a microwave qubit and a magnonic state, achieved by application of a pulsed magnetic field playing the role of a magnon-qubit temporal "beam splitter". Analogous to a typical MZ interferometer, the generated interference pattern of the final qubit population carries information about the magnon dynamics. One important application of the proposed scheme is the study of single magnon decoherence. Interestingly, this scheme allows one to independently determine rates of two possible decoherence channels. This may help enable single magnon state applications and answer fundamental questions of quasi-particle decoherence at single quantum levels.

Dynamics of a ferromagnetic macrospin (e.g., a free layer of a magnetic tunnel junction (MTJ)) can be described in terms of equivalent capacitor charge Q and inductor flux Φ, in a manner similar to a standard electric LC circuit, but with strongly nonlinear and coupled capacitance and inductance. This description allows for the inclusion of Gilbert damping and spin transfer torques and yields a relatively simple equivalent electric circuit, which can be easily modeled in LTspice or other electrical engineering software. It allows one to easily simulate advanced electrical circuits containing MTJs and conventional electronic components in standard simulation software.

This work presents an equivalent circuit model for Magnetic Tunnel Junctions (MTJs) that accurately captures their magnetization dynamics and electrical behavior. Implemented in LTspice, the model is validated against direct numerical solutions of the Landau-Lifshitz-Gilbert-Slonczewski (LLGS) equation. It effectively simulates essential spintronic phenomena, including ferromagnetic resonance, field- and spin-torque-induced switching, and spin-torque-induced oscillations. Simulation results demonstrate strong agreement between LTspice and LLGS solutions, confirming the model accuracy and utility for efficient circuit-level analysis of spintronic devices. The ability to incorporate time-dependent magnetic fields and voltage inputs makes the proposed model suitable for diverse applications such as neuromorphic computing, microwave signal processing, and spintronic memory technologies. By providing a computationally efficient yet physically accurate circuit representation, this work enables seamless integration of MTJs into larger electronic systems, potentially accelerating the development of advanced spintronic circuit architectures.

This paper proposes a novel spiking artificial neuron design based on a combined spin valve/magnetic tunnel junction (SV/MTJ). Traditional hardware used in artificial intelligence and machine learning faces significant challenges related to high power consumption and scalability. To address these challenges, spintronic neurons, which can mimic biologically inspired neural behaviors, offer a promising solution. We present a model of an SV/MTJ-based neuron which uses technologies that have been successfully integrated with CMOS in commercially available applications. The operational dynamics of the neuron are derived analytically through the Landau-Lifshitz-Gilbert-Slonczewski (LLGS) equation, demonstrating its ability to replicate key spiking characteristics of biological neurons, such as response latency and refractive behavior. Simulation results indicate that the proposed neuron design can operate on a timescale of about 1 ns, without any bias current, and with power consumption as low as 50 uW.

Replicating neural responses observed in biological systems using artificial neural networks holds significant promise in the fields of medicine and engineering. In this study, we employ ultra-fast artificial neurons based on antiferromagnetic (AFM) spin Hall oscillators to emulate the biological withdrawal reflex responsible for self-preservation against noxious stimuli, such as pain or temperature. As a result of utilizing the dynamics of AFM neurons, we are able to construct an artificial neural network that can mimic the functionality and organization of the biological neural network responsible for this reflex. The unique features of AFM neurons, such as inhibition that stems from an effective AFM inertia, allow for the creation of biologically realistic neural network components, like the interneurons in the spinal cord and antagonist motor neurons. To showcase the effectiveness of AFM neuron modeling, we conduct simulations of various scenarios that define the withdrawal reflex, including responses to both weak and strong sensory stimuli, as well as voluntary suppression of the reflex.

Spintronic devices offer a promising avenue for the development of nanoscale, energy-efficient artificial neurons for neuromorphic computing. It has previously been shown that with antiferromagnetic (AFM) oscillators, ultra-fast spiking artificial neurons can be made that mimic many unique features of biological neurons. In this work, we train an artificial neural network of AFM neurons to perform pattern recognition. A simple machine learning algorithm called spike pattern association neuron (SPAN), which relies on the temporal position of neuron spikes, is used during training. In under a microsecond of physical time, the AFM neural network is trained to recognize symbols composed from a grid by producing a spike within a specified time window. We further achieve multi-symbol recognition with the addition of an output layer to suppress undesirable spikes. Through the utilization of AFM neurons and the SPAN algorithm, we create a neural network capable of high-accuracy recognition with overall power consumption on the order of picojoules.

Spiking artificial neurons emulate the voltage spikes of biological neurons and constitute the building blocks of a new class of energy efficient, neuromorphic computing systems. Antiferromagnetic materials can, in theory, be used to construct spiking artificial neurons. When configured as a neuron, the magnetization in antiferromagnetic materials has an effective inertia that gives them intrinsic characteristics that closely resemble biological neurons, in contrast with conventional artificial spiking neurons. It is shown here that antiferromagnetic neurons have a spike duration on the order of picoseconds, a power consumption of about 10−3 pJ per synaptic operation, and built-in features that directly resemble biological neurons, including response latency, refraction, and inhibition. It is also demonstrated that antiferromagnetic neurons interconnected into physical neural networks can perform unidirectional data processing even for passive symmetrical interconnects. The flexibility of antiferromagnetic neurons is illustrated by simulations of simple neuromorphic circuits realizing Boolean logic gates and controllable memory loops.

Replicating neural responses observed in biological systems using artificial neural networks has novel applications in medicine and engineering. Here we use ultra-fast artificial neurons based on antiferromagnetic (AFM) spin Hall oscillators to model the biological withdrawal reflex responsible for the preservation of self from a harmful stimulus. We build an artificial neural network with AFM neurons that simulates the biological neural network responsible for this reflex. The unique features of AFM neurons, such as inhibition, allow for the creation of biologically realistic neural network components, like the interneurons in the spinal cord. The effectiveness of AFM neuron modeling is proven by simulating various scenarios that define the withdrawal reflex, such as response to a weak or strong stimulus.

The advent of electric and flying vehicles (EnFVs) has brought significant advancements to the transportation industry, offering improved sustainability, reduced congestion, and enhanced mobility. However, the efficient routing of messages in EnFVs presents unique challenges that demand specialized algorithms to address their specific constraints and objectives. This study analyzes several case studies that investigate the effectiveness of genetic algorithms (GAs) in optimizing routing for EnFVs. The major contributions of this research lie in demonstrating the capability of GAs to handle complex optimization problems with multiple objectives, enabling the simultaneous consideration of factors like energy efficiency, travel time, and vehicle utilization. Moreover, GAs offer a flexible and adaptive approach to finding near-optimal solutions in dynamic transportation systems, making them suitable for real-world EnFV networks. While GAs show promise, there are also limitations, such as computational complexity, difficulty in capturing real-world constraints, and potential sub-optimal solutions. Addressing these challenges, the study highlights several future research directions, including the integration of real-time data and dynamic routing updates, hybrid approaches with other optimization techniques, consideration of uncertainty and risk management, scalability for large-scale routing problems, and enhancing energy efficiency and sustainability in routing. By exploring these avenues, researchers can further improve the efficiency and effectiveness of routing algorithms for EnFVs, paving the way for their seamless integration into modern transportation systems.

Recent research on hybrid magnonics has been restricted by the long magnon wavelengths of the ferromagnetic resonance modes. We present an experiment on the hybridization of 250-nm-wavelength magnons with microwave photons in a multimode magnonic system consisting of a planar cavity and a magnetic bilayer. The coupling between magnon modes in the two magnetic layers, i.e., the uniform mode in Permalloy and the perpendicular standing spin waves (PSSWs) in yttrium iron garnet, serves as an effective means for exciting short-wavelength PSSWs, which is further hybridized with the photon mode of the microwave resonator. The demonstrated magnon-photon coupling approaches the superstrong coupling regime, and can even be achieved near zero bias field.

Hybrid magnonic systems host a variety of characteristic quantum phenomena such as the magnetically-induced transparency (MIT) and Purcell effect, which are considered useful for future coherent quantum information processing. In this work, we experimentally demonstrate a tunable MIT effect in the Y3Fe5O12(YIG)/Permalloy(Py) magnon-magnon coupled system via changing the magnetic field orientations. By probing the magneto-optic effects of Py and YIG, we identify clear features of MIT spectra induced by the mode hybridization between the uniform mode of Py and the perpendicular standing spin-wave modes of YIG. By changing the external magnetic field orientations, we observe a tunable coupling strength between the YIG's spin-wave modes and the Py's uniform mode, upon the application of an out-of-plane magnetic field. This observation is theoretically interpreted by a geometrical consideration of the Py and YIG magnetization under the oblique magnetic field even at a constant interfacial exchange coupling. Our findings show high promise for investigating tunable coherent phenomena with hybrid magnonic platforms.

The advantage of an ultrafast frequency-tunability of spin-torque nano-oscillators (STNOs) that have a large (>100 MHz) relaxation frequency of amplitude fluctuations is exploited to realize ultrafast wide-band time-resolved spectral analysis at nanosecond time scale with a frequency resolution limited only by the "bandwidth" theorem. The demonstration is performed with an STNO generating in the 9 GHz frequency range and comprised of a perpendicular polarizer and a perpendicularly and uniformly magnetized "free" layer. It is shown that such a uniform-state STNO-based spectrum analyzer can efficiently perform spectral analysis of frequency-agile signals with rapidly varying frequency components.

We demonstrate that a spin-torque nano-oscillator (STNO) rapidly sweep-tuned by a bias voltage can be used to perform an ultrafast time-resolved spectral analysis of frequency-manipulated microwave signals. The critical reduction in the time of the spectral analysis comes from the naturally small-time constants of a nanosized STNO (1-100 ns). The demonstration is performed on a vortex-state STNO generating in a frequency range around 300 MHz, when frequency down-conversion and matched filtering is used for signal processing. It is shown that this STNO-based spectrum analyzer can perform analysis of frequency-agile signals, having multiple rapidly changing frequency components with temporal resolution in a μs time scale and frequency resolution limited only by the "bandwidth" theorem. Our calculations show that using uniform magnetization state STNOs it would be possible to increase the operating frequency of a spectrum analyzer to tens of GHz.

A method to perform spectrum analysis on low power signals between 0.1 and 10 THz is proposed. It utilizes a nanoscale antiferromagnetic tunnel junction (ATJ) that produces an oscillating tunneling anisotropic magnetoresistance, whose frequency is dependent on the magnitude of an evanescent spin current. It is first shown that the ATJ oscillation frequency can be tuned linearly with time. Then, it is shown that the ATJ output is highly dependent on matching conditions that are highly dependent on the dimensions of the dielectric tunneling barrier. Spectrum analysis can be performed by using an appropriately designed ATJ, whose frequency is driven to increase linearly with time, a low pass filter, and a matched filter. This method of THz spectrum analysis, if realized in the experiment, will allow miniaturized electronics to rapidly analyze low power signals with a simple algorithm. It is also found by simulation and analytical theories that for an ATJ with a 0.09μm2 footprint, spectrum analysis can be performed over a 0.25THz bandwidth in just 25 ns on signals that are at the Johnson–Nyquist thermal noise floor.