Mutual Synchronization in Spin-Torque and Spin Hall Nano-oscillators

This chapter reviews the state of the art in mutually synchronized spin-torque and spin Hall nano-oscillator (STNO and SHNOSpin-Hall nano-oscillator (SHNO)) arrays. After briefly introducing the underlying physics, we discuss different nano-oscillator implementations and their functional properties concerning frequency range, output power, phase noisePhase noise, and modulation rates. We then introduce the concepts and the theory of mutual synchronizationMutual synchronization and discuss the possible coupling mechanisms in spintronic nano-oscillators, such as dipolar, electrical, and spin-wave coupling. We review the experimental literature on mutually synchronized STNOs and SHNOs in one- and two-dimensional arrays and discuss ways to increase the number of mutually synchronized nano-oscillators. Finally, the potential for applications ranging from microwave signal sources/detectors and ultra-fast spectrum analyzers to neuromorphic computingNeuromorphic computing elements and Ising machinesIsing machines is discussed together with the specific electronic circuitry that has been designed so far to harness this potential.