Coupled oscillators are highly complex dynamical systems, and it is an intriguing concept to use this oscillator dynamics for computation. The idea is not new, but is currently the subject to intense research as part of the quest for “beyond Moore” electronic devices. To a large extent, these efforts are motivated by biological observations: neural systems and mammalian brains, which seem to operate on oscillatory signals. In this paper, we give a survey of oscillator-based computing, with the goal of understanding its promise and limitation for next-generation computing. Our focus will be on the physics of (mostly nanoscale) oscillatory systems and on their characteristics that may enable effective computing.

We demonstrate the design of a neural network hardware, where all neuromorphic computing functions, including signal routing and nonlinear activation are performed by spin-wave propagation and interference. Weights and interconnections of the network are realized by a magnetic-field pattern that is applied on the spin-wave propagating substrate and scatters the spin waves. The interference of the scattered waves creates a mapping between the wave sources and detectors. Training the neural network is equivalent to finding the field pattern that realizes the desired input-output mapping. A custom-built micromagnetic solver, based on the Pytorch machine learning framework, is used to inverse-design the scatterer. We show that the behavior of spin waves transitions from linear to nonlinear interference at high intensities and that its computational power greatly increases in the nonlinear regime. We envision small-scale, compact and low-power neural networks that perform their entire function in the spin-wave domain.

With the rapid development of artificial intelligence in recent years, mankind is facing an unprecedented demand for data processing. Today, almost all data processing is performed using electrons in conventional CMOS circuits. Over the past few decades, scientists have been searching for faster and more efficient ways to process data. Now, magnons, the quanta of spin waves, show the potential for higher efficiency and lower energy consumption in solving some specific problems. While magnonics remains predominantly in the realm of academia, significant efforts are being made to explore the scientific and technological challenges of the field. Numerous proof-of-concept prototypes have already been successfully developed and tested in laboratories. In this Perspective, we review the developed magnonic devices and discuss the current challenges in realizing magnonic circuits based on these building blocks. We look at the application of spin waves in neuromorphic networks, stochastic, reservoir, and quantum computing and discuss the advantages over conventional electronics in these areas. We then discuss a powerful tool, inverse design magnonics, which has the potential to revolutionize the field by enabling the precise design and optimization of magnonic devices in a short time. Finally, we provide a theoretical prediction of energy consumption and propose benchmarks for universal magnonic circuits.

As we approach the end of the silicon road map, alternative computing models that can solve at-scale problems in the data-centric world are becoming important. This is accompanied by the realization that binary abstraction and Boolean logic, which have been the foundations of modern computing revolution, fall short of the desired performance and power efficiency. In particular, hard computing problems relevant to pattern matching, image and signal processing, optimizations, and neuromorphic applications require alternative approaches. In this paper, we review recent advances in oscillatory dynamical system-based models of computing and their implementations. We show that simple configurations of oscillators connected using simple electrical circuits can result in interesting phase and frequency dynamics of such coupled oscillatory systems. Such networks can be controlled, programmed, and observed to solve computationally hard problems. Although our discussion in this paper is limited to insulator-to-metal transition devices and spin-torque oscillators, the general philosophy of such a computing paradigm of ``let physics do the computing'' can be translated to other mediums as well, including micromechanical and optical systems. We present an overview of the mathematical treatments necessary to understand the time evolution of these systems and highlight the recent experimental results in this area that suggest the potential of such computational models.

Topological surface states (TSSs) in a topological insulator are expected to be able to produce a spin-orbit torque that can switch a neighboring ferromagnet. This effect may be absent if the ferromagnet is conductive because it can completely suppress the TSSs, but it should be present if the ferromagnet is insulating. This study reports TSS-induced switching in a bilayer consisting of a topological insulator Bi₂Se₃ and an insulating ferromagnet BaFe₁₂O₁₉. A charge current in Bi₂Se₃ can switch the magnetization in BaFe₁₂O₁₉ up and down. When the magnetization is switched by a field, a current in Bi₂Se₃ can reduce the switching field by ~4000 Oe. The switching efficiency at 3 K is 300 times higher than at room temperature; it is ~30 times higher than in Pt/BaFe₁₂O₁₉. These strong effects originate from the presence of more pronounced TSSs at low temperatures due to enhanced surface conductivity and reduced bulk conductivity.

We present the design of a spin-wave-based microwave signal processing device. The microwave signal is first converted into spin-wave excitations, which propagate in a patterned magnetic thin-film. An interference pattern is formed in the film and its intensity distribution at appropriate read-out locations gives the spectral decomposition of the signal. We use analytic calculations and micromagnetic simulations to verify and to analyze the operation of the device. The results suggest that all performance figures of this magnetoelectric device at room temperature (speed, area, power consumption) may be significantly better than what is achievable in a purely electrical system. We envision that a new class of low-power, high-speed, special-purpose signal processors can be realized by spin-waves.