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We observed strong tripartite magnon-phonon-magnon coupling in a two-dimensional periodic array of magnetostrictive nanomagnets deposited on a piezoelectric substrate, forming a 2D magnetoelastic “crystal”; the coupling occurred between two Kittel-type spin wave (magnon) modes and a (non-Kittel) magnetoelastic spin wave mode caused by a surface acoustic wave (SAW) (phonons). The strongest coupling occurred when the frequencies and wavevectors of the three modes matched, leading to perfect phase matching. We achieved this condition by carefully engineering the frequency of the SAW, the nanomagnet dimensions and the bias magnetic field that determined the frequencies of the two Kittel-type modes. The strong coupling (cooperativity factor exceeding unity) led to the formation of a new quasi-particle, called a binary magnon-polaron, accompanied by nearly complete (~100%) transfer of energy from the magnetoelastic mode to the two Kittel-type modes. This coupling phenomenon exhibited significant anisotropy since the array did not have rotational symmetry in space. The experimental observations were in good agreement with the theoretical simulations.

 

In the ‘Beyond Moore’s Law’ era, with increasing edge intelligence, domain-specific computing embracing unconventional approaches will become increasingly prevalent. At the same time, adopting a variety of nanotechnologies will offer benefits in energy cost, computational speed, reduced footprint, cyber resilience, and processing power. The time is ripe for a roadmap for unconventional computing with nanotechnologies to guide future research, and this collection aims to fill that need. The authors provide a comprehensive roadmap for neuromorphic computing using electron spins, memristive devices, two-dimensional nanomaterials, nanomagnets, and various dynamical systems. They also address other paradigms such as Ising machines, Bayesian inference engines, probabilistic computing with p-bits, processing in memory, quantum memories and algorithms, computing with skyrmions and spin waves, and brain-inspired computing for incremental learning and problem-solving in severely resource-constrained environments. These approaches have advantages over traditional Boolean computing based on von Neumann architecture. As the computational requirements for artificial intelligence grow 50 times faster than Moore’s Law for electronics, more unconventional approaches to computing and signal processing will appear on the horizon, and this roadmap will help identify future needs and challenges. In a very fertile field, experts in the field aim to present some of the dominant and most promising technologies for unconventional computing that will be around for some time to come. Within a holistic approach, the goal is to provide pathways for solidifying the field and guiding future impactful discoveries.

 

Abstract In Part I of this topical review, we discussed dynamical phenomena in nanomagnets, focusing primarily on magnetization reversal with an eye to digital applications. In this part, we address mostly wave-like phenomena in nanomagnets, with emphasis on spin waves in myriad nanomagnetic systems and methods of controlling magnetization dynamics in nanomagnet arrays which may have analog applications. We conclude with a discussion of some interesting spintronic phenomena that undergird the rich physics exhibited by nanomagnet assemblies. 

Abstract When magnets are fashioned into nanoscale elements, they exhibit a wide variety of phenomena replete with rich physics and the lure of tantalizing applications. In this topical review, we discuss some of these phenomena, especially those that have come to light recently, and highlight their potential applications. We emphasize what drives a phenomenon, what undergirds the dynamics of the system that exhibits the phenomenon, how the dynamics can be manipulated, and what specific features can be harnessed for technological advances. For the sake of balance, we point out both advantages and shortcomings of nanomagnet based devices and systems predicated on the phenomena we discuss. Where possible, we chart out paths for future investigations that can shed new light on an intriguing phenomenon and/or facilitate both traditional and non-traditional applications. 

The Landau-Lifshitz-Gilbert (LLG) equation, used to model magneto-dynamics in ferromagnets, tacitly assumes that the angular momentum associated with spin precession can relax instantaneously when the real or effective magnetic field causing the precession is turned off. This neglect of “spin inertia” is unphysical and would violate energy conservation. Recently, the LLG equation was modified to account for inertia effects. The consensus, however, seems to be that such effects would be unimportant in slow magneto-dynamics that take place over time scales much longer that the relaxation time of the angular momentum, which is typically few fs to perhaps ~100 ps in ferromagnets. Here, we show that there is at least one very serious and observable effect of spin inertia even in slow magneto-dynamics. It involves the switching error probability associated with flipping the magnetization of a nanoscale ferromagnet with an external agent, such as a magnetic field. The switching may take ~ns to complete when the field strength is close to the threshold value for switching, which is much longer than the angular momentum relaxation time, and yet the effect of spin inertia is felt in the switching error probability. This is because the ultimate fate of a switching trajectory, i.e. whether it results in success or failure, is influenced by what happens in the first few ps of the switching action when nutational dynamics due to spin inertia holds sway. Spin inertia increases the error probability, which makes the switching more error-prone. This has vital technological significance because it relates to the reliability of magnetic logic and memory. 

Binary switches, which are the primitive units of all digital computing and information processing hardware, are usually benchmarked on the basis of their ‘energy–delay product’, which is the product of the energy dissipated in completing the switching action and the time it takes to complete that action. The lower the energy–delay product, the better the switch (supposedly). This approach ignores the fact that lower energy dissipation and faster switching usually come at the cost of poorer reliability (i.e., a higher switching error rate) and hence the energy–delay product alone cannot be a good metric for benchmarking switches. Here, we show the trade-off between energy dissipation, energy–delay product and error–probability for an electronic switch (a metal oxide semiconductor field effect transistor), a magnetic switch (a magnetic tunnel junction switched with spin transfer torque) and an optical switch (bistable non-linear mirror). As expected, reducing energy dissipation and/or energy–delay product generally results in increased switching error probability and reduced reliability.