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In spin Hall nano-oscillators (SHNOs), pure spin currents drive local regions of magnetic films and nanostructures into auto-oscillating precession. If such regions are placed in close proximity to each other they can interact and may mutually synchronize. Here, we demonstrate robust mutual synchronization of two-dimensional SHNO arrays ranging from 2 × 2 to 8 × 8 nano-constrictions, observed both electrically and using micro-Brillouin light scattering microscopy. On short time scales, where the auto-oscillation linewidth Δf is governed by white noise, the signal quality factor, Q=f∕Δf, increases linearly with the number of mutually synchronized nano-constrictions (N), reaching 170,000 in the largest arrays. We also show that SHNO arrays exposed to two independently tuned microwave frequencies exhibit the same synchronization maps as can be used for neuromorphic vowel recognition. Our demonstrations may hence enable the use of SHNO arrays in two-dimensional oscillator networks for high-quality microwave signal generation and ultra-fast neuromorphic computing.Synchronization of oscillators can be used to carry out cognitive tasks. Large two-dimensional arrays of synchronized spin Hall nano-oscillators have now been demonstrated, and may in future enable neuromorphic computing on the nanoscale.

Synchronization of large spin Hall nano-oscillator (SHNO) arrays is an appealing approach toward ultrafast non-conventional computing. However, interfacing to the array, tuning its individual oscillators and providing built-in memory units remain substantial challenges. Here, we address these challenges using memristive gating of W/CoFeB/MgO/AlO x -based SHNOs. In its high resistance state, the memristor modulates the perpendicular magnetic anisotropy at the CoFeB/MgO interface by the applied electric field. In its low resistance state the memristor adds or subtracts current to the SHNO drive. Both electric field and current control affect the SHNO auto-oscillation mode and frequency, allowing us to reversibly turn on/off mutual synchronization in chains of four SHNOs. We also demonstrate that two individually controlled memristors can be used to tune a four-SHNO chain into differently synchronized states. Memristor gating is therefore an efficient approach to input, tune and store the state of SHNO arrays for non-conventional computing models. This allows versatile non-volatile tuning of the mutual synchronization of chains of up to four oscillators and provides a path toward individual oscillator control in large oscillatory arrays.

Spin torque and spin Hall effect nano-oscillators generate high intensity spin wave auto-oscillations on the nanoscale enabling novel microwave applications in spintronics, magnonics, and neuromorphic computing. For their operation, these devices require externally generated spin currents either from an additional ferromagnetic layer or a material with a high spin Hall angle. Here we demonstrate highly coherent field and current tunable microwave signals from nano-constrictions in single 15–20 nm thick permalloy layers with oxide interfaces. Using a combination of spin torque ferromagnetic resonance measurements, scanning micro-Brillouin light scattering microscopy, and micromagnetic simulations, we identify the auto-oscillations as emanating from a localized edge mode of the nano-constriction driven by spin-orbit torques. Our results pave the way for greatly simplified designs of auto-oscillating nano-magnetic systems only requiring single ferromagnetic layers with oxide interfaces. Spin torque nano-oscillatiors promise novel microwave applications but the functioning relies on the spin current from additional ferromagnetic or metal layers. The authors here achieved in a single ferromagnetic layer sandwiched by nonmagnetic insulators the spin wave auto-oscillations due to a localized edge mode of the nano-constriction.

The development of compact and tunable room temperature sources of coherent THz-frequency signals would open a way for numerous new applications. The existing approaches to THz-frequency generation based on superconductor Josephson junctions (JJ), free electron lasers, and quantum cascades require cryogenic temperatures or/and complex setups, preventing the miniaturization and wide use of these devices. We demonstrate theoretically that a bi-layer of a heavy metal (Pt) and a bi-axial antiferromagnetic (AFM) dielectric (NiO) can be a source of a coherent THz signal. A spin-current flowing from a DC-current-driven Pt layer and polarized along the hard AFM anisotropy axis excites a non-uniform in time precession of magnetizations sublattices in the AFM, due to the presence of a weak easy-plane AFM anisotropy. The frequency of the AFM oscillations varies in the range of 0.1–2.0 THz with the driving current in the Pt layer from 10 8  A/cm 2 to 10 9  A/cm 2 . The THz-frequency signal from the AFM with the amplitude exceeding 1 V/cm is picked up by the inverse spin-Hall effect in Pt. The operation of a room-temperature AFM THz-frequency oscillator is similar to that of a cryogenic JJ oscillator, with the energy of the easy-plane magnetic anisotropy playing the role of the Josephson energy.

Spin Hall nano-oscillators (SHNOs) are emerging spintronic devices for microwave signal generation and oscillator-based neuromorphic computing combining nano-scale footprint, fast and ultra-wide microwave frequency tunability, CMOS compatibility, and strong non-linear properties providing robust large-scale mutual synchronization in chains and two-dimensional arrays. While SHNOs can be tuned via magnetic fields and the drive current, neither approach is conducive to individual SHNO control in large arrays. Here, we demonstrate electrically gated W/CoFeB/MgO nano-constrictions in which the voltage-dependent perpendicular magnetic anisotropy tunes the frequency and, thanks to nano-constriction geometry, drastically modifies the spin-wave localization in the constriction region resulting in a giant 42% variation of the effective damping over four volts. As a consequence, the SHNO threshold current can be strongly tuned. Our demonstration adds key functionality to nano-constriction SHNOs and paves the way for energy-efficient control of individual oscillators in SHNO chains and arrays for neuromorphic computing. Spin Hall nano-oscillators can be tuned via magnetic fields and the drive current, but individual oscillator control in large arrays remains a challenge. Here, the authors provide individual control of the threshold current and the auto-oscillation frequency by voltage-controlled magnetic anisotropy.

Spin–orbit torque can drive auto-oscillations of propagating spin-wave modes in nano-constriction spin Hall nano-oscillators. These modes facilitate both long-range coupling and the possibility of controlling their phase, which is a crucial aspect for device application. Here, we demonstrate variable-phase coupling between two nano-constriction spin Hall nano-oscillators and their mutual synchronization driven by propagating spin waves. Using electrical measurements and phase-resolved micro-focused Brillouin light scattering microscopy, we show that the phase of the mutual synchronization can be tuned by modulating the drive current or the applied field. Our micromagnetic simulations explore the phase tunability using voltage gating. Our results advance the capabilities of mutually synchronized spin Hall nano-oscillators and open the possibilities for applications in spin-wave logic-based devices. Phase tuning of propagating spin waves is a crucial step in the development of devices based on magnons, which are the quanta of spin waves. Now, this has been demonstrated in a device comprising two spin Hall nano-oscillators.

We demonstrate analytically and numerically, that a thin film of an antiferromagnetic (AFM) material, having biaxial magnetic anisotropy and being driven by an external spin-transfer torque signal, can be used for the generation of ultra-short “Dirac-delta-like” spikes. The duration of the generated spikes is several picoseconds for typical AFM materials and is determined by the inplane magnetic anisotropy and the effective damping of the AFM material. The generated output signal can consist of a single spike or a discrete group of spikes (“bursting”), which depends on the repetition (clock) rate, amplitude, and shape of the external control signal. The spike generation occurs only when the amplitude of the control signal exceeds a certain threshold, similar to the action of a biological neuron in response to an external stimulus. The “threshold” behavior of the proposed AFM spike generator makes possible its application not only in the traditional microwave signal processing but also in the future neuromorphic signal processing circuits working at clock frequencies of tens of gigahertz.

Magnetic droplets are non-topological magnetodynamical solitons displaying a wide range of complex dynamic phenomena with potential for microwave signal generation. Bubbles, on the other hand, are internally static cylindrical magnetic domains, stabilized by external fields and magnetostatic interactions. In its original theory, the droplet was described as an imminently collapsing bubble stabilized by spin transfer torque and, in its zero-frequency limit, as equivalent to a bubble. Without nanoscale lateral confinement, pinning, or an external applied field, such a nanobubble is unstable, and should collapse. Here, we show that we can freeze dynamic droplets into static nanobubbles by decreasing the magnetic field. While the bubble has virtually the same resistance as the droplet, all signs of low-frequency microwave noise disappear. The transition is fully reversible and the bubble can be thawed back into a droplet if the magnetic field is increased under current. Whereas the droplet collapses without a sustaining current, the bubble is highly stable and remains intact for days without external drive. Electrical measurements are complemented by direct observation using scanning transmission x-ray microscopy, which corroborates the analysis and confirms that the bubble is stabilized by pinning. Magnetic droplets are a type of non-topological magnetic soliton, which are stabilised and sustained by spin-transfer torques for instance. Without this, they would collapse. Here Ahlberg et al show that by decreasing the applied magnetic field, droplets can be frozen, forming a static nanobubble

Time-multiplexed spinwave Ising Machines have unveiled a route towards miniaturized and low-cost combinatorial optimization solvers but are constrained in the number of spins by nonlinear spinwave dispersion. In contrast, surface acoustic waves offer an intrinsically linear dispersion and high thermal stability. Here, we demonstrate an all-to-all, fully programmable, 50-spin Ising machine using a surface acoustic wave delay line and off-the-shelf microwave components. Our device solves random 50-spin MAX-CUT problems with a single run compute time of 10 ms and a figure of merit of 55 solutions s −1  W − 1 reaching success probability of 84% for 99%-accurate solutions on 0.5-density matrices. Moreover, it demonstrates 4–5 orders of magnitude better thermal stability than optical Coherent Ising Machines while having similar scalability potential. Our results illustrate the general merits of wave-based time-multiplexed Ising machines operating in the microwave domain as compact, energy-efficient, and high-performance platforms for commercially feasible combinatorial optimization solvers. Combinatorial optimization problems are challenging to solve due to their NP-hardness and the limitations of classical computing. This study introduces a surface acoustic wave-based Ising machine demonstrating similar scalability, improved thermal stability, and reduced power consumption compared to coherent Ising machines, offering a promising solution for large-scale optimization tasks.

Time-multiplexed Coherent Ising Machines (CIMs) have demonstrated promising results in rapidly solving large-scale combinatorial problems. However, CIMs remain relatively large and power-demanding. Here, we demonstrate a spinwave-based Ising machine (SWIM) that due to the low spinwave group velocity allows for sufficient miniaturization and reduced power consumption. The SWIM is implemented using a 10-mm-long 5- μ m-thick Yttrium Iron Garnet film with off-the-shelf microwave components and can support an 8-spin MAX-CUT problem and solve it in less than 4 μ s consuming only 7 μ J. As the SWIM minimizes its energy, we observe that the spin states can demonstrate both uniform and domain-propagation-like switching. The developed SWIM has the potential for substantial further miniaturization with reduction of power consumption, scalability in the number of supported spins, increase of operational speed, and may become a versatile platform for commercially feasible high-performance solvers of combinatorial optimization problems. The authors propose and experimentally demonstrate a magnonic version of a coherent Ising machine that implements a thin film Yttrium Iron Garnet spin-wave delay-line combined with microwave components. The work emphasizes the relative advantages that a slower more compact spin-wave system has over optical machines using similar principles.