Spin Hall Nano-oscillator Research Articles

Antiferromagnetic–ferromagnetic heterostructure-based spin Hall nano-oscillator

Spin oscillators relying on ferromagnetic (FM) materials have been limited to frequency generation in the range of only a few gigahertz. In contrast, antiferromagnetic (AFM) material-based oscillators have a potential for beyond gigahertz range oscillations. However, the use of AFM oscillators is limited due to challenges in detecting and controlling magnetic orientation. This arises from the inherent lack of significant net magnetization in AFMs. This work focuses on exploring the dynamic characteristics of a spin Hall nano-oscillator (SHNO) that addresses these challenges by leveraging the inter-layer exchange interaction between AFM and FM layers. The proposed design demonstrates stable and power-efficient oscillation in the FM layer, relying on the dynamics of the AFM layer. The proposed AFM–FM-based SHNO design achieves a maximum frequency of 16.4 GHz at ISOT = 180 μA. Furthermore, considering the thermal effects at 300 K, the stable oscillation frequency is achieved at 15.94 GHz. The proposed device exhibits robust and tunable oscillations over a wide frequency range with a power consumption of 4 μW. Moreover, this oscillator achieves 3.35× and 2.44× higher oscillation frequency compared to spin torque nano-oscillators and conventional SHNO-based oscillators, respectively.

Field-Free Spin Hall Nano-Oscillator Using the Exchange Bias in Ferro/Anti-Ferromagnetic Structures

Field-Free Spin Hall Nano-Oscillator Using the Exchange Bias in Ferro/Anti-Ferromagnetic Structures

Phase and frequency-resolved microscopy of operating spin Hall nano-oscillator arrays.

Coherent optical detection is a powerful technique for characterizing a wide range of physical excitations. Here, we use two optical approaches (fundamental and parametric pumping) to microscopically characterize the high-frequency auto-oscillations of single and multiple nano-constriction spin Hall nano-oscillators (SHNOs). To validate the technique and demonstrate its robustness, we study SHNOs made from two different material stacks, NiFe/Pt and W/CoFeB/MgO, and investigate the influence of both the RF injection power and the laser power on the measurements, comparing the optical results to conventional electrical measurements. To demonstrate the key features of direct, non-invasive, submicron, spatial, and phase-resolved characterization of the SHNO magnetodynamics, we map out the auto-oscillation magnitude and phase of two phase-binarized SHNOs used in Ising machines. This proof-of-concept platform establishes a strong foundation for further extensions, contributing to the ongoing development of crucial characterization techniques for emerging computing technologies based on spintronics devices.

Reconfigurable neural spiking in bias field free spin Hall nano-oscillator

Reconfigurable neural spiking in bias field free spin Hall nano-oscillator

Nonlinear dynamics of a spin-Hall nano-oscillator based on the canted antiferromagnet.

The theory of the nonlinear dynamics of a canted antiferromagnet-based (AFM) spin-Hall oscillator with weak ferromagnetism caused by the strong Dzyaloshinskii-Moriya interaction between magnetic sublattices is rigorously studied. The AFM oscillator's frequency tuning is carried out both due to a DC spin-polarized current flowing through the normal metal layer and an external permanent magnetic field. A feature of the operation of this oscillator is the presence of a hysteresis region between the subcritical (damping) and overcritical (self-oscillating) regimes. We show that it is necessary to reduce an effective easy-plane anisotropy field of the AFM or choose antiferromagnetic material with a smaller exchange field between magnetic sublattices to get a smaller hysteresis region. The action of an external permanent magnetic field on an antiferromagnet leads to the presence of two stable equilibrium states, and the self-oscillating regime is characterized by two-mode generation. We find the conditions for the absence of two-mode generation on the "current density-magnetic field strength" plane. We believe that our results can be helpful for the practical development of a sub-THz frequency tunable oscillator based on the AFM with weak ferromagnetism.

Excitation and voltage-gated modulation of single-mode dynamics in a planar nanogap spin Hall nano-oscillator

Excitation and voltage-gated modulation of single-mode dynamics in a planar nanogap spin Hall nano-oscillator

Robust Mutual Synchronization in Long Spin Hall Nano-oscillator Chains.

Mutual synchronization of N serially connected spintronic nano-oscillators boosts their coherence by N and peak power by N2. Increasing the number of synchronized nano-oscillators in chains holds significance for improved signal quality and emerging applications such as oscillator based unconventional computing. We successfully fabricate spin Hall nano-oscillator chains with up to 50 serially connected nanoconstrictions using W/NiFe, W/CoFeB/MgO, and NiFe/Pt stacks. Our experiments demonstrate robust and complete mutual synchronization of 21 nanoconstrictions at an operating frequency of 10 GHz, achieving line widths <134 kHz and quality factors >79,000. As the number of mutually synchronized oscillators increases, we observe a quadratic increase in peak power, resulting in 400-fold higher peak power in long chains compared to individual nanoconstrictions. While chains longer than 21 nanoconstrictions also achieve complete mutual synchronization, it is less robust, and their signal quality does not improve significantly, as they tend to break into partially synchronized states.

Dynamical modes in a vertical nanocontact-based spin Hall nano-oscillator

Spin-torque nano-oscillators (STNOs) with high nonlinear tunability can serve as nanoscale spin-wave emitters for high-speed magnon-based logic circuits and neural networks for promising new energy-efficiency computing. Although various STNOs have been modeled theoretically and characterized experimentally, there is a sustained effort to improve their coherence and nonlinear tunability. By using numerical simulation, here we explore the evolution rule of spectral characteristics and nonlinearities of the emitted coherent spin waves in a type of spin Hall nano-oscillator (SHNO) with a perpendicular magnetic anisotropy (PMA) coefficient ${K}_{u}$, which is based on a vertical nanocontact fabricated on an extended heavy metal/ferromagnet bilayer. There exist three distinct dynamic regimes with varying ${K}_{u}$. At the easy-plane anisotropy-dominated in-plane magnetized regime, the SHNO exhibits coexistence of the nonlinear self-localized spin-wave bullet mode with a significantly negative nonlinearity coefficient $\ensuremath{\aleph}$ and a secondary high-frequency quasilinear edge mode at higher current density. The latter excitation is supported by the energy transfer from the former via nonlinear coupling rather than the injected spin currents located in the center nanogap of the device. When the easy-plane shape anisotropy is effectively compensated by PMA, only a single quasipropagating spin-wave mode with a near-zero $\ensuremath{\aleph}$ is excited at lower current density, consistent with minimization of nonlinear damping due to the suppression of nonlinear mode coupling. For the out-of-plane magnetized SHNOs with ${K}_{u}$ above the demagnetization energy, a well-defined propagating spin-wave mode with a positive $\ensuremath{\aleph}$, characterized by a significant frequency blueshift and a rightward elongated spatial profile perpendicular to the in-plane component of the applied magnetic field, is observed. This detailed evolution diagram of auto-oscillating dynamics on the PMA coefficient ${K}_{u}$ provides a practical approach to selectively excite dynamical modes and optimize the spectral characteristics of the SHNO for applications in microwave technology and spin-wave logic.

Compensation of Anisotropy in Spin Hall Devices for Neuromorphic Applications

Spintronic nano-oscillators and diodes with reduced nonlinearity benefit from low phase noise and improved device properties. Moreover, they could offer key advantages for realizing neuromorphic applications, such as spike-based neurons and frequency multiplexing in neural networks. Here, we experimentally demonstrate the reduction in nonlinearity of a spin Hall nano-oscillator (SHNO) by compensation of its effective magnetic anisotropy. The study involves optimization of $\mathrm{Co}/\mathrm{Ni}$ multilayer growth to achieve the compensation, followed by spin-diode measurements on patterned microstrips to quantify their anisotropy. The relationship between the second- $({H}_{{k}_{2}}=0.47\phantom{\rule{0.25em}{0ex}}\mathrm{mT})$ and first-order $({H}_{{k}_{1}}^{\mathrm{eff}}=\ensuremath{-}0.8\phantom{\rule{0.25em}{0ex}}\mathrm{mT})$ anisotropy fields reveals the existence of an easy cone, thereby validating the presence of compensation. Furthermore, we demonstrate a compensated spin diode that has a fixed frequency when the input power is varied. We then study the current-induced auto-oscillation properties of SHNOs on compensated films by patterning nanoconstrictions of 200 and 100 nm wide. The invariance of the resonance frequency and linewidth of the compensated SHNO with applied dc current indicates the absence of nonlinearity. This independence is maintained irrespective of the applied external fields and their orientations. The compensated SHNO obtained has a linewidth of 1.1 MHz and a peak output power of up to 1 pW/MHz.

Self-Oscillations in a Nanogap Spin Hall Nano-Oscillator with a Perpendicularly Magnetized External Film

We study spin-current-induced magnetodynamics in a planar nanogap spin Hall nano-oscillator (SHNO) based on $\mathrm{Pt}/[\mathrm{Co}/\mathrm{Ni}{]}_{4}$ with a large perpendicular magnetic anisotropy (PMA) at in-plane field geometry. Two distinct dynamic modes are observed in the spin-torque ferromagnetic resonance (FMR) and the generated microwave spectra. The primary mode has a frequency above the FMR frequency and a significant blueshift of the frequency with the increasing current $I$, consistent with the propagating spin-wave mode. The secondary higher-frequency mode with a much weaker power intensity, discrete frequency jump, and a slight redshift of frequency is only observed at low fields below the saturation field of 2 kOe, suggesting that it is likely related to the emerged domain region with in-plane magnetization due to grain-boundary defects, which is further supported by the frequency enhancement with reducing temperature. The primary propagating mode decreases its frequency and broadens its minimum linewidth by reducing the temperature, indicating that the frequency-drift instability dominates its dynamical decoherence due to the boundary-pinning effect. Furthermore, the micromagnetic simulation reproduces the experimentally observed propagating spin-wave and in-plane domain modes, and provides their spatial characteristics. Our demonstrated propagating spin waves in a SHNO with an out-of-plane magnetization extended bilayer can facilitate long-distance mutual synchronization in the SHNO network arrays for enhancing coherence and power as spin-wave sources in magnon-based devices or spin-based neuromorphic computing.

Injection Locking of Linearlike and Soliton Spin-Wave Modes in Nanoconstriction Spin Hall Nano-oscillators

We study injection locking of two different spin wave (SW) modes (a field-localized linearlike interior mode and a self-localized SW bullet soliton) in a single nanoconstriction-based spin Hall nano-oscillator. Mode selection is achieved by varying the oblique magnetic field angle and magnitude. The two modes show dramatically different responses to injection locking, in terms of locking bandwidth and linewidth and output power in the locked state. Extracting the locking range graphically from the experimental data yields apparent thresholds for the required injected power, with the bullet mode showing a larger threshold than the linearlike mode. By instead fitting the full detuning behavior using a model including thermal noise, the apparent threshold vanishes, while the very different locking behavior of the two modes can instead be ascribed to the order of magnitude difference in their mode volumes.

Interlayer-Exchange-Dominant Spin Hall Nano-Oscillator

The spin Hall nano-oscillator (SHNO) is a promising spintronic device to produce high-frequency and low-linewidth microwave signals. We study a type of SHNO based on the $L{1}_{0}\text{\ensuremath{-}}\mathrm{Fe}\mathrm{Pt}/\mathrm{Ni}\mathrm{Fe}/\mathrm{Pt}$ exchange-spring system with an ultrahigh perpendicular magnetic anisotropy by micromagnetic simulation. The hard-soft magnetic exchange-spring system has a very high interlayer-exchange-interaction field, resulting in a more than 30-GHz emission frequency and 38.6-GHz/T field tunability. Apart from conventional localized and nonlocalized auto-oscillation modes, localized or nonlocalized modes with central antisymmetry also appear in this SHNO. Two oscillation centers possess nonequal amplitudes and opposite phases in these antisymmetrical modes. Different modes are determined by the competition between three factors: the exchange-interaction field, the perpendicular anisotropic field, and spin-orbit torque. The spin dynamics in the SHNO exhibit complex field and current dependence. Our results provide a possible direction for the design of SHNOs, which may be beneficial for the research and development of spintronic nano-oscillators.

Spin Hall Nano-Oscillator Based on an Antiferromagnetic Domain Wall

We propose here a high-frequency spin-Hall nano-oscillator based on a simple magnetic texture, such as a domain wall, located in an antiferromagnet with an easy-axis anisotropy type. We show that the spin current, polarized along the anisotropy axis, excites a conical precession of the N\'eel vector in such a domain wall, which allows obtaining a robust ac output signal---contrary to the planar precession in a uniform uniaxial antiferromagnet, where ac output is hard to achieve. The frequency of the auto-oscillations is easily tunable by the applied current up to the terahertz range, and the threshold current vanishes for a pure uniaxial antiferromagnet. By micromagnetic simulations, we demonstrate that the pinning of the domain wall is crucial for the oscillator design, which can be achieved in the nanoconstriction layout of the free layer.

Magnetic force microscopy of an operational spin nano-oscillator

Magnetic force microscopy (MFM) is a powerful technique for studying magnetic microstructures and nanostructures that relies on force detection by a cantilever with a magnetic tip. The detected magnetic tip interactions are used to reconstruct the magnetic structure of the sample surface. Here, we demonstrate a new method using MFM for probing the spatial profile of an operational nanoscale spintronic device, the spin Hall nano-oscillator (SHNO), which generates high-intensity spin wave auto-oscillations enabling novel microwave applications in magnonics and neuromorphic computing. We developed an MFM system by adding a microwave probe station to allow electrical and microwave characterization up to 40 GHz during the MFM process. SHNOs—based on NiFe/Pt bilayers with a specific design compatible with the developed system—were fabricated and scanned using a Co magnetic force microscopy tip with 10 nm spatial MFM resolution, while a DC current sufficient to induce auto-oscillation flowed. Our results show that this developed method provides a promising path for the characterization and nanoscale magnetic field imaging of operational nano-oscillators.

Spatial coexistence of multiple modes in a nanogap spin Hall nano-oscillator with extended Pt/Ni/Fe trilayers

We experimentally study the microwave generation characteristics of a spin Hall nano-oscillator driven by a local spin current injected into a nanoscale region of extended Pt/Ni/Fe trilayers due to the spin Hall effect in the Pt layer and the interfacial Rashba effect at the Pt/Ni interface. The dependence of the generated microwave spectra on the exciting current and on the magnitude and angle of the magnetic field indicates that multiple spin-wave modes with either higher frequencies than the ferromagnetic resonance frequency ${f}_{\mathrm{FMR}}$ at low out-of-plane tilting angles and small fields or lower frequencies than ${f}_{\mathrm{FMR}}$ at high tilting angles and large fields are excited by local spin currents. Furthermore, the temperature dependence of the generated spectra in the extended Pt/Ni/Fe trilayers demonstrates that the thermally activated mode transition between these distinct dynamical modes is significantly suppressed. These results suggest that the observed multiple modes are physically separated in different local potential wells created by the spatial inhomogeneity of the internal field in the asymmetric ferromagnetic bilayer with strong interfacial exchange coupling and anisotropy fields. Finally, the very weak dependence of the minimum linewidth on temperature further confirms the lack of thermal-fluctuation-induced mode coupling and mode transition between these individual dynamical modes.

Synchronization of nanowire-based spin Hall nano-oscillators

The synchronization of the spin Hall nano-oscillator (SHNO) device driven by the pure spin current has been investigated with micromagnetic simulations. It was found that the power spectra of nanowire-based SHNO devices can be synchronized by varying the current flowing in the heavy metal (HM) layer. The synchronized signals have relatively high power and narrow linewidth, favoring the potential applications. We also found that the synchronized spectra are strongly dependent on both the number and length of nanowires. Moreover, a periodic modulation of power spectra can be obtained by introducing interfacial Dzyaloshinskii–Moriya interaction (iDMI). Our findings could enrich the current understanding of spin dynamics driven by the pure spin current. Further, it could help to design novel spintronic devices.

Phase-Binarized Spin Hall Nano-Oscillator Arrays: Towards Spin Hall Ising Machines

Ising machines (IMs) are physical systems designed to find solutions to combinatorial optimization (CO) problems mapped onto the IM via the coupling strengths between its binary spins. Using its intrinsic dynamics and different annealing schemes, the IM relaxes over time to its lowest-energy state, which is the solution to the CO problem. IMs have been implemented on different platforms, and interacting nonlinear oscillators are particularly promising candidates. Here we demonstrate a pathway towards an oscillator-based IM using arrays of nanoconstriction spin Hall nano-oscillators (SHNOs). We show how SHNOs can be readily phase binarized and how their resulting microwave power corresponds to well-defined global phase states. To distinguish between degenerate states, we use phase-resolved Brillouin-light-scattering microscopy and directly observe the individual phase of each nanoconstriction. Micromagnetic simulations corroborate our experiments and confirm that our proposed IM platform can solve CO problems, showcased by how the phase states of a $2\ifmmode\times\else\texttimes\fi{}2$ SHNO array are solutions to a modified max-cut problem. Compared with the commercially available D-Wave ${\mathrm{Advantage}}^{\mathrm{TM}}$, our architecture holds significant promise for faster sampling, substantially reduced power consumption, and a dramatically smaller footprint.

Fabrication of voltage-gated spin Hall nano-oscillators.

We demonstrate an optimized fabrication process for electric field (voltage gate) controlled nano-constriction spin Hall nano-oscillators (SHNOs), achieving feature sizes of <30 nm with easy to handle ma-N 2401 e-beam lithography negative tone resist. For the nanoscopic voltage gates, we utilize a two-step tilted ion beam etching approach and through-hole encapsulation using 30 nm HfOx. The optimized tilted etching process reduces sidewalls by 75% compared to no tilting. Moreover, the HfOx encapsulation avoids any sidewall shunting and improves gate breakdown. Our experimental results on W/CoFeB/MgO/SiO2 SHNOs show significant frequency tunability (6 MHz V-1) even for moderate perpendicular magnetic anisotropy. Circular patterns with diameter of 45 nm are achieved with an aspect ratio better than 0.85 for 80% of the population. The optimized fabrication process allows incorporating a large number of individual gates to interface to SHNO arrays for unconventional computing and densely packed spintronic neural networks.

Memristive control of mutual spin Hall nano-oscillator synchronization for neuromorphic computing.

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/AlOx-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.

Controllable excitation of multiple spin wave bullet modes in a spin Hall nano-oscillator based on [Ni/Co]/Pt multilayers.

Spin-torque nano-oscillators are promising candidates for many radio frequency and magnon-based nanodevices due to their broad frequency tunability, easy fabrication and high durability. To explore the tunability, we chose a [Ni/Co]/Pt-based spin Hall nano-oscillator with a moderate uniaxial anisotropy to systematically study the corresponding magnetodynamics excited by locally injecting a dc current into a nanoscale region of the extended multilayers [Ni/Co]/Pt under certain conditions. We find that the excitation current, the magnitude and orientation of magnetic field, and temperature can be used as a tool to selectively excite certain frequency bullet modes. The transition between nonlinear self-localized bullet modes with different frequencies is caused by the experimental parameter-induced change of energy landscape because, in the [Ni/Co]/Pt system, the strong spatial fluctuation of interfacial magnetic anisotropy leads to the variations of the internal magnetic field of the actual device. Our results demonstrate that the fluctuations of magnetic properties can promote experimental control of spin-torque driven magnetization dynamics in spin Hall nano-oscillators, and the application of expediting nonlinear magnetization oscillators in magnon-based devices and neuromorphic computing.