Nanowire spin torque oscillator driven by spin orbit torques

Electrical Detection of Spin-Hall-Induced Auto-oscillations in Lithium Aluminate Ferrite Thin Films

Ferrimagnetic insulators with ultralow damping are of great interest for their potential applications in energy-efficient computing devices. Here, we report the direct electrical detection of magnetic auto-oscillations in unpatterned ultralow damping ferrimagnetic insulator epitaxial Li0.5Al0.5Fe2O4 thin films, driven by a current in a proximal Pt nanowire. Auto-oscillations occur for only one current polarity, consistent with the spin-Hall effect inducing the oscillation state. Micromagnetic modeling shows good agreement with the experimental frequency and field dispersions, showing only one dominant oscillation mode, in contrast to the multiple modes typically observed in transition-metal nanowire-type spin-Hall nanooscillators. This study illustrates a new material system for neuromorphic computing and magnonics, a simple material platform with the direct-current generation of high-frequency (∼10 GHz) signals and their electrical detection.

Nano-wire spin Hall nano-oscillator fabricated by novel sidewall transfer lithography

Spin Hall nano-oscillators (SHNOs) have garnered significant attention in the field of spintronics in recent years, particularly for their potential in neuromorphic computing. However, their sensitive regions, often below 200 nm, present considerable challenges for fabrication. The current mainstream approach relies on electron beam lithography (EBL) to define the shapes of SHNOs. While EBL is both costly and time-consuming, it is less ideal for the large-scale development and application of SHNOs. In this paper, we proposed a novel fabrication method for nano-wire SHNOs using sidewall transfer lithography. This approach offers a practical solution to enhance fabrication efficiency while simultaneously reducing production costs, making it more suitable for mass production. Through experimental demonstrations, we validated the feasibility of this method and provided detailed insights into the sidewall transfer lithography process. Our findings suggest that this technique achieves higher theoretical accuracy than current fabrication methods, offering a cost-effective pathway for realizing large-scale arrays of SHNOs and promoting their application in advanced computing technologies.

Anomalous Hall spin current drives self-generated spin-orbit torque in a ferromagnet

Spin-orbit torques enable energy-efficient manipulation of magnetization by electric current and hold promise for applications ranging from non-volatile memory to neuromorphic computing. Here we report the discovery of a giant spin-orbit torque induced by anomalous Hall current in ferromagnetic conductors. This anomalous Hall torque is self-generated as it acts on the magnetization of the ferromagnet that engenders the torque. The magnitude of the anomalous Hall torque is sufficiently large to fully negate magnetic damping of the ferromagnet, which allows us to implement a microwave spin torque nano-oscillator driven by this torque. The peculiar angular symmetry of the anomalous Hall torque favours its use over the conventional spin Hall torque in coupled nano-oscillator arrays. The universal character of the anomalous Hall torque makes it an integral part of the description of coupled spin transport and magnetization dynamics in magnetic nanostructures.

Field-free spin hall oscillator based on giant magnetoresistance effect and its potential for electrical synchronization

Spin Hall nano oscillators (SHNOs) have attracted much attention in recent years due to their great potential for applications in neuromorphic computation. However, the output power of SHNOs is very low and an external magnetic field is required to generate microwave signal continuously, which hinders the further development of SHNOs. In order to solve the two problems, we propose a new-type SHNO based on the giant magnetoresistance (GMR) effect, while retaining the advantage of the simple fabrication process of the conventional oscillator. The huge magnetoresistance ratio provided by the GMR effect can increase the power of this novel oscillator by several orders of magnitude. In addition, by designing the magnetization easy axis of the free and reference layers in the GMR film layers, this novel oscillator can operate effectively without the need of and external magnetic field. Furthermore, we have preliminarily investigated the feasibility of electrical synchronization in the field of SHNOs from the perspective of microspin simulation and found that parallel connection can provide stronger coupling strength compared with series connection. Our research solves the core problems that currently hinder the further development of SHNOs, facilitating the realization and application of large-scale synchronized array of SHNOs.

Nanoscale Mapping of Magnetic Auto-Oscillations with a Single Spin Sensor

Spin Hall nano-oscillators convert DC to magnetic auto-oscillations in the microwave regime. Current research on these devices is dedicated to creating next-generation energy-efficient hardware for communication technologies. Despite intensive research on magnetic auto-oscillations within the past decade, the nanoscale mapping of those dynamics remained a challenge. We image the distribution of free-running magnetic auto-oscillations by driving the electron spin resonance transition of a single spin quantum sensor, enabling fast acquisition (100 ms/pixel). With quantitative magnetometry, we experimentally demonstrate for the first time that the auto-oscillation spots are localized at magnetic field minima acting as local potential wells for confining spin-waves. By comparing the magnitudes of the magnetic stray field at these spots, we decipher the different frequencies of the auto-oscillation modes. The insights gained regarding the interaction between auto-oscillation modes and spin-wave potential wells enable advanced engineering of real devices.

High data rate spin-wave transmitter

Spin-wave devices have recently become a strong competitor in computing and information processing owing to their excellent energy efficiency. Researchers have explored magnons, the quanta of spin-waves, as an information carrier and significant progress has occurred in both excitation and computation. However, most transmission designs remain immature in terms of data rate and information complexity as they only utilize simple spin-wave pulses and suffer from signal distortion. In this work, using micromagnetic simulations, we demonstrate a spin-wave transmitter that operates reliably at a data rate of 4 Gbps over significant (multi-micron) distances with error rates as low as 10-14. Spin-wave amplitude is used to encode information. Carrier frequency and data rate are carefully chosen to restrict dispersion spreading, which is the main reason for signal distortion. We show that this device can be integrated into either pure-magnonic circuits or modern electronic networks. Our study reveals the potential for achieving an even higher data rate of 10 Gbps and also offers a comprehensive and logical methodology for performance tuning.

Spin Inertia and Auto-Oscillations in Ferromagnets

Recent experimental confirmation of spin inertia in ferromagnets positions this well-developed material class as a prime candidate for THz frequency applications. Spin-torque driven critical spin dynamics, such as auto-oscillations, play the central role in many spin-based technologies. Yet, the pressing question on spin inertia's effect on spin-torque driven dynamics in ferromagnets has remained unexplored. Here, we develop the theoretical framework of precessional auto-oscillations for ferromagnets with spin inertia. We discover and introduce the concept of nutational auto-oscillations and demonstrate that they can become pivotal for future ultrahigh frequency technologies. We conclude by revealing parallels between spin dynamics in ferrimagnets and inertial ferromagnets and derive an isomorphism that establishes a foundation for synergistic knowledge transfer between these research fields.

Ultra-Low Current 10 nm Spin Hall Nano-Oscillators

Nano-constriction based spin Hall nano-oscillators (SHNOs) are at the forefront of spintronics research for emerging technological applications, such as oscillator-based neuromorphic computing and Ising Machines. However, their miniaturization to the sub-50 nm width regime results in poor scaling of the threshold current. Here, it shows that current shunting through the Si substrate is the origin of this problem and studies how different seed layers can mitigate it. It finds that an ultra-thin Al2 O3 seed layer and SiN (200 nm) coated p-Si substrates provide the best improvement, enabling us to scale down the SHNO width to a truly nanoscopic dimension of 10 nm, operating at threshold currents below 30 μ $\umu$ A. In addition, the combination of electrical insulation and high thermal conductivity of the Al2 O3 seed will offer the best conditions for large SHNO arrays, avoiding any significant temperature gradients within the array. The state-of-the-art ultra-low operational current SHNOs hence pave an energy-efficient route to scale oscillator-based computing to large dynamical neural networks of linear chains or 2D arrays.

Coherent magnon-induced domain-wall motion in a magnetic insulator channel

Advancing the development of spin-wave devices requires high-quality low-damping magnetic materials where magnon spin currents can efficiently propagate and effectively interact with local magnetic textures. Here we show that magnetic domain walls can modulate spin-wave transport in perpendicularly magnetized channels of Bi-doped yttrium iron garnet. Conversely, we demonstrate that the magnon spin current can drive domain-wall motion in the Bi-doped yttrium iron garnet channel device by means of magnon spin-transfer torque. The domain wall can be reliably moved over 15-20 µm distances at zero applied magnetic field by a magnon spin current excited by a radio-frequency pulse as short as 1 ns. The required energy for driving the domain-wall motion is orders of magnitude smaller than those reported for metallic systems. These results facilitate low-switching-energy magnonic devices and circuits where magnetic domains can be efficiently reconfigured by magnon spin currents flowing within magnetic channels.

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.

Classification tasks using input driven nonlinear magnetization dynamics in spin Hall oscillator

The inherent nonlinear magnetization dynamics in spintronic devices make them suitable candidates for neuromorphic hardware. Among spintronic devices, spin torque oscillators such as spin transfer torque oscillators and spin Hall oscillators have shown the capability to perform recognition tasks. In this paper, with the help of micromagnetic simulations, we model and demonstrate that the magnetization dynamics of a single spin Hall oscillator can be nonlinearly transformed by harnessing input pulse streams and can be utilized for classification tasks. The spin Hall oscillator utilizes the microwave spectral characteristics of its magnetization dynamics for processing a binary data input. The spectral change due to the nonlinear magnetization dynamics assists in real-time feature extraction and classification of 4-binary digit input patterns. The performance was tested for the classification of the standard MNIST handwritten digit data set and achieved an accuracy of 83.1% in a simple linear regression model. Our results suggest that modulating time-driven input data can generate diverse magnetization dynamics in the spin Hall oscillator that can be suitable for temporal or sequential information processing.

Hybrid spin Hall nano-oscillators based on ferromagnetic metal/ferrimagnetic insulator heterostructures

Spin-Hall nano-oscillators (SHNOs) are promising spintronic devices to realize current controlled GHz frequency signals in nanoscale devices for neuromorphic computing and creating Ising systems. However, traditional SHNOs devices based on transition metals have high auto-oscillation threshold currents as well as low quality factors and output powers. Here we demonstrate a new type of hybrid SHNO based on a permalloy (Py) ferromagnetic-metal nanowire and low-damping ferrimagnetic insulator, in the form of epitaxial lithium aluminum ferrite (LAFO) thin films. The superior characteristics of such SHNOs are associated with the excitation of larger spin-precession angles and volumes. We further find that the presence of the ferrimagnetic insulator enhances the auto-oscillation amplitude of spin-wave edge modes, consistent with our micromagnetic modeling. This hybrid SHNO expands spintronic applications, including providing new means of coupling multiple SHNOs for neuromorphic computing and advancing magnonics.

Nanostructure-induced L10-ordering of twinned single-crystals in CoPt ferromagnetic nanowires

L10-ordered ferromagnetic nanowires with large coercivity are essential for realizing next-generation spintronic devices. Ferromagnetic nanowires have been commonly fabricated by first L10-ordering of initially disordered ferromagnetic films by annealing and then etching them into nanowire structures using lithography. If the L10-ordered nanowires can be fabricated using only lithography and subsequent annealing, the etching process can be omitted, which leads to an improvement in the fabrication process for spintronic devices. However, when nanowires are subjected to annealing, they easily transform into droplets, which is well-known as Plateau-Rayleigh instability. Here, we propose a concept of "nanostructure-induced L10-ordering" of twinned single-crystals in CoPt ferromagnetic nanowires with a 30 nm scale ultrafine linewidth on Si/SiO2 substrates. The driving forces for nanostructure-induced L10-ordering during annealing are atomic surface diffusion and extremely large internal stress at ultrasmall 10 nm scale curvature radii of the nanowires. (Co/Pt)6 multilayer nanowires are fabricated by a lift-off process combining electron-beam lithography and electron-beam evaporation, followed by annealing. Cross-sectional scanning transmission electron microscope images and nano-beam electron diffraction patterns clearly indicate nanostructure-induced L10-ordering of twinned single-crystals in the CoPt ferromagnetic nanowires, which exhibit a large coercivity of 10 kOe for perpendicular, longitudinal, and transversal directions of the nanowires. Two-dimensional grazing incidence X-ray diffraction shows superlattice peaks with Debye-Scherrer ring shapes, which also supports the nanostructure-induced L10-ordering. The fabrication method for nanostructure-induced L10-ordered CoPt ferromagnetic nanowires with twinned single-crystals on Si/SiO2 substrates would be significant for future silicon-technology-compatible spintronic applications.

Voltage-driven gigahertz frequency tuning of spin Hall nano-oscillators

Spin Hall nano-oscillators (SHNOs) exploiting current-driven magnetization auto-oscillation have recently received much attention because of their potential for neuromorphic computing. Widespread applications of neuromorphic devices with SHNOs require an energy-efficient method of tuning oscillation frequency over broad ranges and storing trained frequencies in SHNOs without the need for additional memory circuitry. While the voltage-driven frequency tuning of SHNOs has been demonstrated, it was volatile and limited to megahertz ranges. Here, we show that the frequency of SHNOs is controlled up to 2.1 GHz by an electric field of 1.25 MV/cm. The large frequency tuning is attributed to the voltage-controlled magnetic anisotropy (VCMA) in a perpendicularly magnetized Ta/Pt/[Co/Ni]_n/Co/AlO_x structure. Moreover, the non-volatile VCMA effect enables cumulative control of the frequency using repetitive voltage pulses which mimic the potentiation and depression functions of biological synapses. Our results suggest that the voltage-driven frequency tuning of SHNOs facilitates the development of energy-efficient neuromorphic devices.

Spin-Orbit Torque Nano-oscillators by Dipole-Field-Localized Spin Wave Modes

We demonstrate a high-quality spin-orbit torque nano-oscillator comprised of spin wave modes confined by the magnetic field by the strongly inhomogeneous dipole field of a nearby micromagnet. This approach enables variable spatial confinement and systematic tuning of magnon spectrum and spectral separations for studying the impact of multimode interactions on auto-oscillations. We find these dipole-field-localized spin wave modes exhibit good characteristic properties as auto-oscillators─narrow line width and large amplitude─while persisting up to room temperature. We find that the line width of the lowest-lying localized mode is approximately proportional to temperature in good agreement with theoretical analysis of the impact of thermal fluctuations. This demonstration of a clean oscillator with tunable properties provides a powerful tool for understanding the fundamental limitations and line width contributions to improve future spin-Hall oscillators.

Observation of Pure-Spin-Current Diodelike Effect at the Au/Pt Interface

Asymmetric charge transport at the interface of two materials with dissimilar electrical properties, such as metal-semiconductor and p-n junctions, is the fundamental feature behind modern diode and transistor technology. Spin pumping from a ferromagnet into an adjacent nonmagnetic material is a powerful technique to generate pure-spin currents, wherein spin transport is unaccompanied by net charge transport. It is therefore interesting to study pure-spin transport at the interface of two materials with different spin transport properties. Here we demonstrate asymmetric transport of pure-spin currents across an interface of dissimilar nonmagnetic materials Au/Pt. We exploit Py/Au/Pt/Co structures where spin pumping can generate pure-spin current from either Py or Co independently. We find that the transmission of pure-spin current from Au into Pt is twice as efficient as transmission from Pt into Au. Experimental results are interpreted by extending conventional spin-pumping, spin-diffusion theory to include boundary conditions of reflected and transmitted spin current at the Au/Pt interface that are proportional to the established spin chemical potentials on either side of the interface.

Switching of a Magnet by Spin-Orbit Torque from a Topological Dirac Semimetal

Recent experiments show that topological surface states (TSS) in topological insulators (TI) can be exploited to manipulate magnetic ordering in ferromagnets. In principle, TSS should also exist for other topological materials, but it remains unexplored as to whether such states can also be utilized to manipulate ferromagnets. Herein, current-induced magnetization switching enabled by TSS in a non-TI topological material, namely, a topological Dirac semimetal α-Sn, is reported. The experiments use an α-Sn/Ag/CoFeB trilayer structure. The magnetization in the CoFeB layer can be switched by a charge current at room temperature, without an external magnetic field. The data show that the switching is driven by the TSS of the α-Sn layer, rather than spin-orbit coupling in the bulk of the α-Sn layer or current-produced heating. The switching efficiency is as high as in TI systems. This shows that the topological Dirac semimetal α-Sn is as promising as TI materials in terms of spintronic applications.

Current-Induced Spin-Orbit Torques for Spintronic Applications

Control of magnetization in magnetic nanostructures is essential for development of spintronic devices because it governs fundamental device characteristics such as energy consumption, areal density, and operation speed. In this respect, spin-orbit torque (SOT), which originates from the spin-orbit interaction, has been widely investigated due to its efficient manipulation of the magnetization using in-plane current. SOT spearheads novel spintronic applications including high-speed magnetic memories, reconfigurable logics, and neuromorphic computing. Herein, recent advances in SOT research, highlighting the considerable benefits and challenges of SOT-based spintronic devices, are reviewed. First, the materials and structural engineering that enhances SOT efficiency are discussed. Then major experimental results for field-free SOT switching of perpendicular magnetization are summarized, which includes the introduction of an internal effective magnetic field and the generation of a distinct spin current with out-of-plane spin polarization. Finally, advanced SOT functionalities are presented, focusing on the demonstration of reconfigurable and complementary operation in spin logic devices.

Giant voltage-controlled modulation of spin Hall nano-oscillator damping

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.

Planar Hall Driven Torque in a Ferromagnet/Nonmagnet/Ferromagnet System

An important goal of spintronics is to covert a charge current into a spin current with a controlled spin polarization that can exert torques on an adjacent magnetic layer. Here we demonstrate such torques in a two ferromagnet system. A CoNi multilayer is used as a spin current source in a sample with structure CoNi/Au/CoFeB. Spin torque ferromagnetic resonance is used to measure the torque on the CoFeB layer. The response as a function of the applied field angle and current is consistent with the symmetry expected for a torque produced by the planar Hall effect originating in CoNi. We find the strength of this effect to be comparable to that of the spin Hall effect in platinum, indicating that the planar Hall effect holds potential as a spin current source with a controllable polarization direction.

Perspectives of Electrically generated spin currents in ferromagnetic materials

Spin-orbit coupling enables charge currents to give rise to spin currents and vice versa, which has applications in non-volatile magnetic memories, miniature microwave oscillators, thermoelectric converters and Terahertz devices. In the past two decades, a considerable amount of research has focused on electrical spin current generation in different types of nonmagnetic materials. However, electrical spin current generation in ferromagnetic materials has only recently been actively investigated. Due to the additional symmetry breaking by the magnetization, ferromagnetic materials generate spin currents with different orientations of spin direction from those observed in nonmagnetic materials. Studies centered on ferromagnets where spin-orbit coupling plays an important role in transport open new possibilities to generate and detect spin currents. We summarize recent developments on this subject and discuss unanswered questions in this emerging field.

Mutual control of coherent spin waves and magnetic domain walls in a magnonic device

The successful implementation of spin-wave devices requires efficient modulation of spin-wave propagation. Using cobalt/nickel multilayer films, we experimentally demonstrate that nanometer-wide magnetic domain walls can be applied to manipulate the phase and magnitude of coherent spin waves in a nonvolatile manner. We further show that a spin wave can, in turn, be used to change the position of magnetic domain walls by means of the spin-transfer torque effect generated from magnon spin current. This mutual interaction between spin waves and magnetic domain walls opens up the possibility of realizing all-magnon spintronic devices, in which one spin-wave signal can be used to control others by reconfiguring magnetic domain structures.

Controlled nonlinear magnetic damping in spin-Hall nano-devices

Large-amplitude magnetization dynamics is substantially more complex compared to the low-amplitude linear regime, due to the inevitable emergence of nonlinearities. One of the fundamental nonlinear phenomena is the nonlinear damping enhancement, which imposes strict limitations on the operation and efficiency of magnetic nanodevices. In particular, nonlinear damping prevents excitation of coherent magnetization auto-oscillations driven by the injection of spin current into spatially extended magnetic regions. Here, we propose and experimentally demonstrate that nonlinear damping can be controlled by the ellipticity of magnetization precession. By balancing different contributions to anisotropy, we minimize the ellipticity and achieve coherent magnetization oscillations driven by spatially extended spin current injection into a microscopic magnetic disk. Our results provide a route for the implementation of efficient active spintronic and magnonic devices driven by spin current.

Strong Coupling between Microwave Photons and Nanomagnet Magnons

Coupled microwave photon-magnon hybrid systems offer promising applications by harnessing various magnon physics. At present, in order to realize high coupling strength between the two subsystems, bulky ferromagnets with large spin numbers are utilized, which limits their potential applications for scalable quantum information processing. By enhancing single spin coupling strength using lithographically defined superconducting resonators, we report high cooperativities between a resonator mode and a Kittel mode in nanometer thick Permalloy wires. The on-chip, lithographically scalable, and superconducting quantum circuit compatible design provides a direct route towards realizing hybrid quantum systems with nanomagnets, whose coupling strength can be precisely engineered and dynamic properties can be controlled by various mechanisms derived from spintronic studies.

Domain Wall Based Spin-Hall Nano-Oscillators

In the last decade, two revolutionary concepts in nanomagnetism emerged from research for storage technologies and advanced information processing. The first suggests the use of magnetic domain walls in ferromagnetic nanowires to permanently store information in domain-wall racetrack memories. The second proposes a hardware realization of neuromorphic computing in nanomagnets using nonlinear magnetic oscillations in the gigahertz range. Both ideas originate from the transfer of angular momentum from conduction electrons to localized spins in ferromagnets, either to push data encoded in domain walls along nanowires or to sustain magnetic oscillations in artificial neurones. Even though both concepts share a common ground, they live on very different timescales which rendered them incompatible so far. Here, we bridge both ideas by demonstrating the excitation of magnetic auto-oscillations inside nanoscale domain walls using pure spin currents. This Letter will shed light on the current characteristic and spatial distribution of the excited auto-oscillations.

Magnetization switching using topological surface states

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.

Spin-orbit torque driven by a planar Hall current

Spin-orbit torques (SOTs) in multilayers of ferromagnetic (FM) and non-magnetic (NM) metals can manipulate the magnetization of the FM layer efficiently. This is employed, for example, in non-volatile magnetic memories for energy-efficient mobile electronics^1,2 and spin torque nano-oscillators^3-7 for neuromorphic computing⁸. Recently, spin torque nano-oscillators also found use in microwave-assisted magnetic recording, which enables ultrahigh-capacity hard disk drives⁹. Most SOT devices employ spin Hall^10,11 and Rashba¹² effects, which originate from spin-orbit coupling within the NM layer and at the FM/NM interfaces, respectively. Recently, SOTs generated by the anomalous Hall effect in FM/NM/FM multilayers were predicted¹³ and experimentally realized¹⁴. The control of SOTs through crystal symmetry was demonstrated as well¹⁵. Understanding all the types of SOTs that can arise in magnetic multilayers is needed for a formulation of a comprehensive SOT theory and for engineering practical SOT devices. Here we show that a spin-polarized electric current known to give rise to anisotropic magnetoresistance (AMR) and the planar Hall effect (PHE) in a FM¹⁶ can additionally generate large antidamping SOTs with an unusual angular symmetry in NM₁/FM/NM₂ multilayers. This effect can be described by a recently proposed magnonic mechanism¹⁷. Our measurements reveal that this torque can be large in multilayers in which both spin Hall and Rashba torques are negligible. Furthermore, we demonstrate the operation of a spin torque nano-oscillator driven by this SOT. These findings significantly expand the class of materials that exhibit giant SOTs.

Antiferromagnetism Emerging in a Ferromagnet with Gain

We present a theoretical mapping to show that a ferromagnet with gain (loss) is equivalent to an antiferromagnet with an equal amount of loss (gain). Our findings indicate a novel first-order ferromagnet-antiferromagnet phase transition by tuning the gain-loss parameter. As an appealing application, we demonstrate the realization as well as the manipulation of the antiferromagnetic Skyrmion, a stable topological quasiparticle not yet observed experimentally, in a chiral ferromagnetic thin film with gain. We also consider ferromagnetic bilayers with balanced gain and loss and show that the antiferromagnetic Skyrmion can be found only in cases with a broken parity-time symmetry phase. Our results pave the way for investigating the emerging antiferromagnetic spintronics and parity-time symmetric magnonics in ferromagnets.

Discussing the high frequency intrinsic permeability of nanostructures using first order reversal curves

First order reversal curves (FORC) and intrinsic high frequency permeability spectra have been simulated and analyzed for '1 × 3' iron nanowire (NW) arrays with different interwire distances (D). Discrete interaction constants are found and gradually disappeared with increasing D value. The number of weak resonance peaks decreases with increasing D value. Two strong resonance peaks are found for each array with different D values: the lower one is ascribed to the 'edge mode'. The higher one is ascribed to the 'bulk mode'. The magnetic loss due to the edge mode cannot be neglected. The difference in bulk mode resonance in the simulated and the calculated are believed to arise from the interaction between NWs. It is believed that the local effective magnetic fields determine the orientation of magnetic moments in the equilibrium states, and consequently determine the high frequency intrinsic permeability spectra. FORC diagrams are helpful to reveal the distribution of local coercive fields.

Injection locking of multiple auto-oscillation modes in a tapered nanowire spin Hall oscillator

Spin Hall oscillators (SHO) are promising candidates for the generation, detection and amplification of high frequency signals, that are tunable through a wide range of operating frequencies. They offer to be read out electrically, magnetically and optically in combination with a simple bilayer design. Here, we experimentally study the spatial dependence and spectral properties of auto-oscillations in SHO devices based on Pt(7 nm)/Ni₈₀Fe₂₀(5 nm) tapered nanowires. Using Brillouin light scattering microscopy, we observe two individual self-localized spin-wave bullets that oscillate at two distinct frequencies (5.2 GHz and 5.45 GHz) and are localized at different positions separated by about 750 nm within the SHO. This state of a tapered SHO has been predicted by a Ginzburg-Landau auto-oscillator model, but not yet been directly confirmed experimentally. We demonstrate that the observed bullets can be individually synchronized to external microwave signals, leading to a frequency entrainment, linewidth reduction and increase in oscillation amplitude for the bullet that is selected by the microwave frequency. At the same time, the amplitude of other parasitic modes decreases, which promotes the single-mode operation of the SHO. Finally, the synchronization of the spin-wave bullets is studied as a function of the microwave power. We believe that our findings promote the realization of extended spin Hall oscillators accomodating several distinct spin-wave bullets, that jointly cover an extended range of tunability.

Phase difference dependence of output power in synchronized stacked spin Hall nano-oscillators

Synchronization between stacked spin Hall nano-oscillators (SHNO), attributed to the spin Hall effect and anisotropic magnetoresistance effect, was studied by numerical calculations. In order to obtain the synchronized state of the SHNOs, we considered the magneto-dipolar field, which was calculated in the rectangular prism. We revealed that the output power depended on the distance between the SHNOs, as the phase difference between the SHNOs depended on the coupling strength. For N  =  3 (number of SHNOs), we investigated the phase difference by considering the influence of the coupling strength of all magnetic layers. Furthermore, we observed that the output power increased with the number of SHNOs in the synchronization system.

Relativistic torques induced by currents in magnetic materials: physics and experiments

In this review article, an insight of the physics that explains the phenomenon of torques induced by currents in systems comprising ferromagnetic (FM)-non-magnetic (NM) materials has been provided with particular emphasis on experiments that concern the observation of such torques. An important requirement of systems that enables observation of such relativistic torques is that the material needs to possess large spin-orbit coupling (SOC). In addition, the FM/NM interface should be of high quality so that spin angular momentum can be transferred across the interface. Under such conditions, the magnetization of a magnetic material experiences a torque, and can be reversed, thanks to the phenomenon of the spin Hall effect in the NM layer with large SOC. A reciprocal process also occurs, in which a changing magnetization orientation can produce spin current, i.e. current that supports spin angular momentum. It is important to know how these processes occur which often tells us about the close connection between magnetization and spin transport. This paves the way to transform technologies that process information via magnetization direction, namely in magnetic recording industry. This field of physics being relatively young much remains to be understood and explored. Through this review we have attempted to provide a glimpse of existing understanding of current induced torques in ferromagnetic thin film heterostructures along with some future challenges and opportunities of this evolving area of spintronics. Specifically, we have discussed the state-of-the art demonstrations of current-induced torque devices that show great promise for enhancing the functionality of magnetic memory devices.

Excitation and Amplification of Spin Waves by Spin-Orbit Torque

The emerging field of nanomagnonics utilizes high-frequency waves of magnetization-spin waves-for the transmission and processing of information on the nanoscale. The advent of spin-transfer torque has spurred significant advances in nanomagnonics, by enabling highly efficient local spin wave generation in magnonic nanodevices. Furthermore, the recent emergence of spin-orbitronics, which utilizes spin-orbit interaction as the source of spin torque, has provided a unique ability to exert spin torque over spatially extended areas of magnonic structures, enabling enhanced spin wave transmission. Here, it is experimentally demonstrated that these advances can be efficiently combined. The same spin-orbit torque mechanism is utilized for the generation of propagating spin waves, and for the long-range enhancement of their propagation, in a single integrated nanomagnonic device. The demonstrated system exhibits a controllable directional asymmetry of spin wave emission, which is highly beneficial for applications in nonreciprocal magnonic logic and neuromorphic computing.

Oscillatory interlayer coupling in spin Hall systems

Many spintronics applications consist of ultrathin magnetic and nonmagnetic multilayers and require an in-depth understanding of interfacial magnetism and spin transport. Here, we study permalloy/copper/platinum multilayer systems. We find that magnetic damping, perpendicular anisotropy, and proximity magnetization exhibit correlated oscillations as a function of the copper thickness. We ascribe these observations to an oscillatory interlayer coupling between permalloy and platinum. Such interlayer coupling may have a significant impact on the performance of spintronics applications.

Spin Hall-induced auto-oscillations in ultrathin YIG grown on Pt

We experimentally study nanowire-shaped spin-Hall nano-oscillators based on nanometer-thick epitaxial films of Yttrium Iron Garnet grown on top of a layer of Pt. We show that, although these films are characterized by significantly larger magnetic damping in comparison with the films grown directly on Gadolinium Gallium Garnet, they allow one to achieve spin current-driven auto-oscillations at comparable current densities, which can be an indication of the better transparency of the interface to the spin current. These observations suggest a route for improvement of the flexibility of insulator-based spintronic devices and their compatibility with semiconductor technology.

Chemical potential of quasi-equilibrium magnon gas driven by pure spin current

Pure spin currents provide the possibility to control the magnetization state of conducting and insulating magnetic materials. They allow one to increase or reduce the density of magnons, and achieve coherent dynamic states of magnetization reminiscent of the Bose-Einstein condensation. However, until now there was no direct evidence that the state of the magnon gas subjected to spin current can be treated thermodynamically. Here, we show experimentally that the spin current generated by the spin-Hall effect drives the magnon gas into a quasi-equilibrium state that can be described by the Bose-Einstein statistics. The magnon population function is characterized either by an increased effective chemical potential or by a reduced effective temperature, depending on the spin current polarization. In the former case, the chemical potential can closely approach, at large driving currents, the lowest-energy magnon state, indicating the possibility of spin current-driven Bose-Einstein condensation.

Spin caloritronic nano-oscillator

Energy loss due to ohmic heating is a major bottleneck limiting down-scaling and speed of nano-electronic devices, and harvesting ohmic heat for signal processing is a major challenge in modern electronics. Here, we demonstrate that thermal gradients arising from ohmic heating can be utilized for excitation of coherent auto-oscillations of magnetization and for generation of tunable microwave signals. The heat-driven dynamics is observed in Y₃Fe₅O₁₂/Pt bilayer nanowires where ohmic heating of the Pt layer results in injection of pure spin current into the Y₃Fe₅O₁₂ layer. This leads to excitation of auto-oscillations of the Y₃Fe₅O₁₂ magnetization and generation of coherent microwave radiation. Our work paves the way towards spin caloritronic devices for microwave and magnonic applications.

Harvesting ohmic heat for signal processing is one of major challenges in modern electronics and spin caloritronics, but not yet well accomplished. Here the authors demonstrate a spin torque oscillator device driven by pure spin current arising from thermal gradient across an Y₃Fe₅O₁₂/Pt interface.

Interface-Induced Phenomena in Magnetism

This article reviews static and dynamic interfacial effects in magnetism, focusing on interfacially-driven magnetic effects and phenomena associated with spin-orbit coupling and intrinsic symmetry breaking at interfaces. It provides a historical background and literature survey, but focuses on recent progress, identifying the most exciting new scientific results and pointing to promising future research directions. It starts with an introduction and overview of how basic magnetic properties are affected by interfaces, then turns to a discussion of charge and spin transport through and near interfaces and how these can be used to control the properties of the magnetic layer. Important concepts include spin accumulation, spin currents, spin transfer torque, and spin pumping. An overview is provided to the current state of knowledge and existing review literature on interfacial effects such as exchange bias, exchange spring magnets, spin Hall effect, oxide heterostructures, and topological insulators. The article highlights recent discoveries of interface-induced magnetism and non-collinear spin textures, non-linear dynamics including spin torque transfer and magnetization reversal induced by interfaces, and interfacial effects in ultrafast magnetization processes.

Antiferromagnetic THz-frequency Josephson-like Oscillator Driven by Spin Current

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 10⁸ A/cm² to 10⁹ A/cm². 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.

A 20 nm spin Hall nano-oscillator

Spin Hall nano-oscillators (SHNOs) are an emerging class of pure spin current driven microwave signal generators. Through the fabrication of 20 nm nano-constrictions in Pt/NiFe bilayers, we demonstrate that SHNOs can be scaled down to truly nanoscopic dimensions, with the added benefit of ultra-low operating currents and improved power conversion efficiency. The lateral confinement leads to a strong shape anisotropy field as well as an additional demagnetizing field whose reduction with increasing auto-oscillation amplitude can yield a positive current tunability contrary to the negative tunability commonly observed for localized excitations in extended magnetic layers. Micromagnetic simulations corroborate the experimental findings and suggest that the active magnetodynamic area resides up to 100 nm outside of the nano-constriction.

Spin-Hall nano-oscillator with oblique magnetization and Dzyaloshinskii-Moriya interaction as generator of skyrmions and nonreciprocal spin-waves

Spin-Hall oscillators (SHO) are promising sources of spin-wave signals for magnonics applications, and can serve as building blocks for magnonic logic in ultralow power computation devices. Thin magnetic layers used as “free” layers in SHO are in contact with heavy metals having large spin-orbital interaction, and, therefore, could be subject to the spin-Hall effect (SHE) and the interfacial Dzyaloshinskii-Moriya interaction (i-DMI), which may lead to the nonreciprocity of the excited spin waves and other unusual effects. Here, we analytically and micromagnetically study magnetization dynamics excited in an SHO with oblique magnetization when the SHE and i-DMI act simultaneously. Our key results are: (i) excitation of nonreciprocal spin-waves propagating perpendicularly to the in-plane projection of the static magnetization; (ii) skyrmions generation by pure spin-current; (iii) excitation of a new spin-wave mode with a spiral spatial profile originating from a gyrotropic rotation of a dynamical skyrmion. These results demonstrate that SHOs can be used as generators of magnetic skyrmions and different types of propagating spin-waves for magnetic data storage and signal processing applications.

Current driven spin-orbit torque oscillator: ferromagnetic and antiferromagnetic coupling

We consider theoretically the impact of Rashba spin-orbit coupling on spin torque oscillators (STOs) in synthetic ferromagnets and antiferromagnets that have either a bulk multilayer or a thin film structure. The synthetic magnets consist of a fixed polarizing layer and two free magnetic layers that interact through the Ruderman-Kittel-Kasuya-Yosida interaction. We determine analytically which collinear states along the easy axis that are stable, and establish numerically the phase diagram for when the system is in the STO mode and when collinear configurations are stable, respectively. It is found that the Rashba spin-orbit coupling can induce anti-damping in the vicinity of the collinear states, which assists the spin transfer torque in generating self-sustained oscillations, and that it can substantially increase the STO part of the phase diagram. Moreover, we find that the STO phase can extend deep into the antiferromagnetic regime in the presence of spin-orbit torques.

Direct observation of dynamic modes excited in a magnetic insulator by pure spin current

Excitation of magnetization dynamics by pure spin currents has been recently recognized as an enabling mechanism for spintronics and magnonics, which allows implementation of spin-torque devices based on low-damping insulating magnetic materials. Here we report the first spatially-resolved study of the dynamic modes excited by pure spin current in nanometer-thick microscopic insulating Yttrium Iron Garnet disks. We show that these modes exhibit nonlinear self-broadening preventing the formation of the self-localized magnetic bullet, which plays a crucial role in the stabilization of the single-mode magnetization oscillations in all-metallic systems. This peculiarity associated with the efficient nonlinear mode coupling in low-damping materials can be among the main factors governing the interaction of pure spin currents with the dynamic magnetization in high-quality magnetic insulators.

Spin-orbit torque-assisted switching in magnetic insulator thin films with perpendicular magnetic anisotropy

As an in-plane charge current flows in a heavy metal film with spin–orbit coupling, it produces a torque on and thereby switches the magnetization in a neighbouring ferromagnetic metal film. Such spin–orbit torque (SOT)-induced switching has been studied extensively in recent years and has shown higher efficiency than switching using conventional spin-transfer torque. Here we report the SOT-assisted switching in heavy metal/magnetic insulator systems. The experiments used a Pt/BaFe₁₂O₁₉ bilayer where the BaFe₁₂O₁₉ layer exhibits perpendicular magnetic anisotropy. As a charge current is passed through the Pt film, it produces a SOT that can control the up and down states of the remnant magnetization in the BaFe₁₂O₁₉ film when the film is magnetized by an in-plane magnetic field. It can reduce or increase the switching field of the BaFe₁₂O₁₉ film by as much as about 500 Oe when the film is switched with an out-of-plane field.

By virtue of strong spin-orbit coupling, a current-carrying heavy metal may generate a torque on the magnetization of an interfaced ferromagnetic metal. Here, the authors demonstrate how this effect assists the magnetic reversal of ferromagnetic insulators with perpendicular magnetic anisotropy.

Excitation of coherent propagating spin waves by pure spin currents

Utilization of pure spin currents not accompanied by the flow of electrical charge provides unprecedented opportunities for the emerging technologies based on the electron's spin degree of freedom, such as spintronics and magnonics. It was recently shown that pure spin currents can be used to excite coherent magnetization dynamics in magnetic nanostructures. However, because of the intrinsic nonlinear self-localization effects, magnetic auto-oscillations in the demonstrated devices were spatially confined, preventing their applications as sources of propagating spin waves in magnonic circuits using these waves as signal carriers. Here, we experimentally demonstrate efficient excitation and directional propagation of coherent spin waves generated by pure spin current. We show that this can be achieved by using the nonlocal spin injection mechanism, which enables flexible design of magnetic nanosystems and allows one to efficiently control their dynamic characteristics.

Generation of coherent spin-wave modes in yttrium iron garnet microdiscs by spin-orbit torque

In recent years, spin–orbit effects have been widely used to produce and detect spin currents in spintronic devices. The peculiar symmetry of the spin Hall effect allows creation of a spin accumulation at the interface between a metal with strong spin–orbit interaction and a magnetic insulator, which can lead to a net pure spin current flowing from the metal into the insulator. This spin current applies a torque on the magnetization, which can eventually be driven into steady motion. Tailoring this experiment on extended films has proven to be elusive, probably due to mode competition. This requires the reduction of both the thickness and lateral size to reach full damping compensation. Here we show clear evidence of coherent spin–orbit torque-induced auto-oscillation in micron-sized yttrium iron garnet discs of thickness 20 nm. Our results emphasize the key role of quasi-degenerate spin-wave modes, which increase the threshold current.

Spin-orbit interactions allow for pure spin current to be injected into a ferromagnetic insulator from a current-carrying heavy metal, generating torque on the magnetization. Here, the authors evidence magnetic auto-oscillations driven by spin-orbit torque in thin film microdiscs of yttrium iron garnet.

Reduction of phase noise in nanowire spin orbit torque oscillators

Spin torque oscillators (STOs) are compact, tunable sources of microwave radiation that serve as a test bed for studies of nonlinear magnetization dynamics at the nanometer length scale. The spin torque in an STO can be created by spin-orbit interaction, but low spectral purity of the microwave signals generated by spin orbit torque oscillators hinders practical applications of these magnetic nanodevices. Here we demonstrate a method for decreasing the phase noise of spin orbit torque oscillators based on Pt/Ni80Fe20 nanowires. We experimentally demonstrate that tapering of the nanowire, which serves as the STO active region, significantly decreases the spectral linewidth of the generated signal. We explain the observed linewidth narrowing in the framework of the Ginzburg-Landau auto-oscillator model. The model reveals that spatial non-uniformity of the spin current density in the tapered nanowire geometry hinders the excitation of higher order spin-wave modes, thus stabilizing the single-mode generation regime. This non-uniformity also generates a restoring force acting on the excited self-oscillatory mode, which reduces thermal fluctuations of the mode spatial position along the wire. Both these effects improve the STO spectral purity.

Deterministic Domain Wall Motion Orthogonal To Current Flow Due To Spin Orbit Torque

Spin-polarized electrons can move a ferromagnetic domain wall through the transfer of spin angular momentum when current flows in a magnetic nanowire. Such current induced control of a domain wall is of significant interest due to its potential application for low power ultra high-density data storage. In previous reports, it has been observed that the motion of the domain wall always happens parallel to the current flow – either in the same or opposite direction depending on the specific nature of the interaction. In contrast, here we demonstrate deterministic control of a ferromagnetic domain wall orthogonal to current flow by exploiting the spin orbit torque in a perpendicularly polarized Ta/CoFeB/MgO heterostructure in presence of an in-plane magnetic field. Reversing the polarity of either the current flow or the in-plane field is found to reverse the direction of the domain wall motion. Notably, such orthogonal motion with respect to current flow is not possible from traditional spin transfer torque driven domain wall propagation even in presence of an external magnetic field. Therefore the domain wall motion happens purely due to spin orbit torque. These results represent a completely new degree of freedom in current induced control of a ferromagnetic domain wall.

Spin-current nano-oscillator based on nonlocal spin injection

Nonlocal spin injection has been recognized as an efficient mechanism for creation of pure spin currents not tied to the electrical charge transfer. Here we demonstrate experimentally that it can induce coherent magnetization dynamics, which can be utilized for the implementation of novel microwave nano-sources for spintronic and magnonic applications. We show that such sources exhibit a small oscillation linewidth and are tunable over a wide frequency range by the static magnetic field. Spatially resolved measurements of the dynamical magnetization indicate a relatively large oscillation area, resulting in a high stability of the oscillation with respect to thermal fluctuations. We propose a simple quasilinear dynamical model that reproduces well the oscillation characteristics.