This chapter reviews the state of the art in mutually synchronized spin-torque and spin Hall nano-oscillator (STNO and SHNO) arrays. After briefly introducing the underlying physics, we discuss different nano-oscillator implementations and their functional properties with respect to frequency range, output power, phase noise, and modulation rates. We then introduce the concepts and the theory of mutual synchronization and discuss the possible coupling mechanisms in spintronic nano-oscillators, such as dipolar, electrical, and spin-wave coupling. We review the experimental literature on mutually synchronized STNOs and SHNOs in one- and two-dimensional arrays and discuss ways to increase the number of mutually synchronized nano-oscillators. Finally, the potential for applications ranging from microwave signal sources/detectors and ultrafast spectrum analyzers to neuromorphic computing elements and Ising machines is discussed together with the specific electronic circuitry that has been designed so far to harness this potential.
Spin torque oscillators placed onto a nonmagnetic heavy metal show synchronized auto-oscillations due to the coupling originating from spin Hall magnetoresistance effect. Here, we study a system having two spin torque oscillators under the effect of the spin Hall torque, and show that switching the external current direction enables us to control the phase difference of the synchronization between in-phase and antiphase.
We are reporting a new type of synchronization, termed dancing synchronization, between two spin-torque nano-oscillators (STNOs) coupled through spin waves. Different from the known synchronizations in which two STNOs are locked with various fixed relative phases, in this new synchronized state two STNOs have the same frequency, but their relative phase varies periodically within the common period, resulting in a dynamic waving pattern. The amplitude of the oscillating relative phase depends on the coupling strength of two STNOs, as well as the driven currents. The dancing synchronization turn…
We report on a time-domain study of parametric synchronization in a magnetic tunnel junction based spin torque nano-oscillator (STNO). Time-domain measurements of the instantaneous frequency ($f_{i}$) of a parametrically synchronized STNO show random short-term unlocking of the STNO signal for low injected radio-frequency (RF) power, which cannot be revealed in time-averaged frequency domain measurements. Macrospin simulations reproduce the experimental results and reveal that the random unlocking during synchronization is driven by thermal fluctuations. We show that by using a high injected R…
A theoretical study on how synchronization and resonance-like phenomena in superparamagnetic tunnel junctions can be driven by spin-transfer torques is presented. We examine the magnetization of a superparamagnetic free layer that reverses randomly between two well-defined orientations due to thermal fluctuations, acting as a stochastic oscillator. When subject to an external ac forcing this system can present stochastic resonance and noise-enhanced synchronization. We focus on the roles of the mutually perpendicular damping-like and field-like torques, showing that the response of the system …
The concept of spin torque driven high frequency magnetization dynamics has opened up the field of spintronics to non-linear physics, potentially in complex networks of dynamical systems. In the scarce demonstrations of synchronized spin-torque oscillators, the local nature of the magnetic coupling that is used have largely hampered a good understanding and thus the control of the synchronization process. Here we take advantage of the non-local nature of an electrical coupling to mutually synchronize spin-torque oscillators through their self-emitted microwave currents. The control of the sync…
We have proposed a method to synchronize multiple spin-transfer torque oscillators based on spin pumping, inverse spin Hall, and spin Hall effects. The proposed oscillator system consists of a series of nano-magnets in junction with a normal metal with high spin-orbit coupling, and an accumulative feedback loop. We conduct simulations to demonstrate the effect of modulated charge currents in the normal metal due to spin pumping from each nano-magnet. We show that the interplay between the spin Hall effect and inverse spin Hall effect results in synchronization of the nano-magnets.
In this paper, we propose to control the strength of phase-locking between two dipolarly coupled vortex based spin-torque nano-oscillators by placing an intermediate oscillator between them. We show through micromagnetic simulations that the strength of phase-locking can be largely tuned by a slight variation of current in the intermediate oscillator. We develop simplified numerical simulations based on analytical expressions of the vortex core trajectories that will be useful for investigating large arrays of densely packed spin-torque oscillators interacting through their stray fields.
We demonstrate that the synchronization of an array of electrically coupled spin torque nano-oscillators (STNO) modelled by Landau-Lifshitz-Gilbert-Slonczewski (LLGS) equation can be enhanced appreciably in the presence of a common external microwave magnetic field. The applied microwave magnetic field stabilizes and enhances the regions of synchronization in the parameter space of our analysis, where the oscillators are exhibiting synchronized oscillations thereby emitting improved microwave power. To characterize the synchronized oscillations we have calculated the locking range in the domai…
A mutual synchronization of spin-torque oscillators coupled through current injection is studied theoretically. Models of electrical coupling in parallel and series circuits are proposed. Solving the Landau-Lifshitz-Gilbert equation, excitation of in-phase or antiphase synchronization, depending on the ways the oscillators are connected, is found. It is also found from both analytical and numerical calculations that the current-frequency relations for both parallel and series circuits are the same as that for a single spin-torque oscillator.
Synchronization and chaos caused by alternating current and microwave field in a spin torque oscillator consisting of a perpendicularly magnetized free layer and an in-plane magnetized reference layer is comprehensively studied theoretically. A forced synchronization by the alternating current is observed in numerical simulation over wide ranges of its amplitude and frequency. An analytical theory clarifies that the nonlinear frequency shift, as well as the spin-transfer torque asymmetry, plays a key role in determining locking range and phase difference between the oscillator and current. Cha…
The collective dynamics in populations of magnetic spin torque oscillators (STO) is an intensely studied topic in modern magnetism. Here, we show that arrays of STO coupled via dipolar fields can be modeled using a variant of the Kuramoto model, a well-known mathematical model in non-linear dynamics. By investigating the collective dynamics in arrays of STO we find that the synchronization in such systems is a finite size effect and show that the critical coupling-for a complete synchronized state-scales with the number of oscillators. Using realistic values of the dipolar coupling strength be…
Recent studies have revealed that domain walls in magnetic nanostructures can serve as compact, energy-efficient spin-wave waveguides for building magnonic devices that are considered promising candidates for overcoming the challenges and bottlenecks of today's CMOS technologies. However, imprinting long strip-domain walls into magnetic nanowires remains a challenge, especially in curved geometries. Here, through micromagnetic simulations, we present a method for writing strip-domain walls into curved magnetic nanowires using spin-orbit torque. We employ Y-shaped magnetic nanostructures as wel…
Nanomechanical Detection of Itinerant Electron Spin Flip
自旋是一种固有的量子性质，其特征在于角动量。自旋状态的变化相当于角动量或机械扭矩的变化。这种自旋感应力矩在从测量光子的角动量、金属的g因子和磁共振到磁性多层膜中的磁化反转的实验中被称为内在机制。引入到纳米线中的自旋极化电流产生与巡游电子自旋翻转相关的力矩。在这里，我们报告的直接测量这种机械扭矩和巡回电子自旋极化在一个集成的纳米扭转振荡器，这可能会产生新的信息巡回的d-带电子。10^{-22} N m/ \sqrt{Hz}的前所未有的扭矩灵敏度可以使自旋电子学、CP破坏力的精确测量、DNA的解扭和扭矩产生分子的应用成为可能。
Magnetic droplet solitons are non-linear dynamical modes that can be excited in a thin film with perpendicular magnetic anisotropy with a spin-transfer-torque. Although droplet solitons have been proved to be stable with a hysteretic response to applied currents and magnetic fields at low temperature, measurements at room temperature indicate less stability and reduced hysteresis width. Here, we report evidence of droplet soliton drift instabilities, leading to drift resonances, at room temperature that explains their lower stability. Micromagnetic simulations show that the drift instability i…
We show that the spin-orbit torque induced magnetization switching in nanomagnets presenting Dzyaloshinskii-Moriya (DMI) interaction is governed by a chiral domain nucleation at the edges. The nucleation is induced by the DMI and the applied in-plane magnetic field followed by domain wall propagation. Our micromagnetic simulations show that the DC switching current can be defined as the edge nucleation current, which decreases strongly with increasing amplitude of the DMI. This description allows us to build a simple analytical model to quantitatively predict the switching current. We find tha…
Manipulating operation states of coupled spin-torque nano-oscillators (STNOs), including their synchronization, is essential for applications such as complex oscillator networks. In this work we experimentally demonstrate selective control of two coupled vortex STNOs through microwave-assisted switching of their vortex core polarities. First, the two oscillators are shown to synchronize due to dipolar interaction in a broad frequency range tuned by external biasing field. Coherent output is demonstrated along with strong linewidth reduction. Then, we show individual vortex polarity control of …
We report the possibility of achieving an order of magnitude reduction in the energy dissipation needed to write bits in perpendicular magnetic tunnel junctions (p-MTJs) by simulating the magnetization dynamics under a combination of resonant surface acoustic waves (r-SAW) and spin-transfer-torque (STT). The magnetization dynamics were simulated using the Landau-Lifshitz-Gilbert equation under macrospin assumption with the inclusion of thermal noise. The resonant magnetization dynamics in the magnetostrictive nanomagnet build over few 10s of cycles of SAW application that drives the magnetizat…
Spin torque from spin current applied to a nanoscale region of a ferromagnet can act as negative magnetic damping and thereby excite self-oscillations of its magnetization. In contrast, spin torque uniformly applied to the magnetization of an extended ferromagnetic film does not generate self-oscillatory magnetic dynamics but leads to reduction of the saturation magnetization. Here we report studies of the effect of spin torque on a system of intermediate dimensionality - a ferromagnetic nanowire. We observe coherent self-oscillations of magnetization in a ferromagnetic nanowire serving as the…
Spin orbit torque (SOT) provides an efficient way of generating spin current that promises to significantly reduce the current required for switching nanomagnets. However, an in-plane current generated SOT cannot deterministically switch a perpendicularly polarized magnet due to symmetry reasons. On the other hand, perpendicularly polarized magnets are preferred over in-plane magnets for high-density data storage applications due to their significantly larger thermal stability in ultra-scaled dimensions. Here we show that it is possible switch a perpendicularly polarized magnet by SOT without …
Arrays of spin-torque nano-oscillators are promising for broadband microwave signal detection and processing, as well as for neuromorphic computing. In many of these applications, the oscillators should be engineered to have equally-spaced frequencies and equal sensitivity to microwave inputs. Here we design spin-torque nano-oscillator arrays with these rules and estimate their optimum size for a given sensitivity, as well as the frequency range that they cover. For this purpose, we explore analytically and numerically conditions to obtain vortex spin-torque nano-oscillators with equally-space…
The self-synchronization of spin torque oscillators is investigated experimentally by re-injecting its radiofrequency (rf) current after a certain delay time. We demonstrate that the emission power and the spectral linewidth are improved for optimal delay times. Moreover by varying the phase difference between the emitted power and the re-injected one, we find a clear oscillatory dependence with a 2π periodicity of the frequency of the oscillator as well as its power and linewidth. Such periodical behavior within the self-injection regime is well described by the general model of nonlinear aut…
Spin currents can exert spin-transfer torques on magnetic systems even in the limit of vanishingly small net magnetization, as is the case for antiferromagnets. Here, we experimentally show that a spin-transfer torque is operative in a material with weak, short-range magnetic order -- namely, a macroscopic ensemble of superparamagnetic-like Co nanomagnets. We employ element- and time-resolved X-ray ferromagnetic resonance (XFMR) spectroscopy to directly detect sub-ns dynamics of the Co nanomagnets, excited into precession with cone angle $\geq$0.003$^{\circ}$ by an oscillating spin current. XF…
Skyrmion-based spin torque nano-oscillators are potential next-generation microwave signal generators. However, ferromagnetic skyrmion-based spin torque nano-oscillators cannot reach high oscillation frequencies. In this work, we propose to use the circular motion of an antiferromagnetic skyrmion to create the oscillation signal in order to overcome this obstacle. Micromagnetic simulations demonstrate that the antiferromagnetic skyrmion-based spin torque nano-oscillators can produce high frequencies (tens of GHz). Furthermore, the speed of the circular motion for an antiferromagnetic skyrmion …
Spin-torque nano-oscillators (STNO) are microwave auto-oscillators based on magnetic resonances having a nonlinear response with the oscillating amplitude, which provides them with a large frequency tunability including the possibility of mutual synchronization. The magnetization dynamics in STNO are induced by spin transfer torque (STT) from spin currents and can be detected by changes in electrical resistance due to giant magnetoresistance or tunneling magnetoresistance. The STT effect is usually treated as a damping-like term that reduces magnetic dissipation and promotes excitation of magn…
Spin torque and spin Hall effect nanooscillators 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 nanoconstrictions in single 15 and 20 nm thick permalloy layers. Using a combination of spin torque ferromagnetic resonance measurements,…
Based on theoretical models, the dynamics of spin-torque nano-oscillators can be substantially modified by re-injecting the emitted signal to the input of the oscillator after some delay. Numerical simulations for vortex magnetic tunnel junctions show that with reasonable parameters this approach can decrease critical currents as much as 25 % and linewidths by a factor of 4. Analytical calculations, which agree well with simulations, demonstrate that these results can be generalized to any kind of spin-torque oscillator.
A phase diagram of the magnetization dynamics is studied by numerically solving the Landau-Lifshitz-Gilbert (LLG) equation in a spin torque oscillator consisting of asymmetric two free layers that are magnetized in in-plane direction. We calculated the dynamics for a wide range of current density for both low and high field cases, and found many dynamical phases such as synchronization, auto-oscillation with different frequencies, and chaotic dynamics. The observation of the synchronization indicates the presence of a dynamical phase which has not been found experimentally by using the convent…
A model for a spin-torque nano-oscillator based on the self-sustained oscillation of a magnetic skyrmion is presented. The system involves a circular nanopillar geometry comprising an ultrathin film free magnetic layer with a strong Dzyaloshinkii-Moriya interaction and a polariser layer with a vortex-like spin configuration. It is shown that spin-transfer torques due to current flow perpendicular to the film plane leads to skyrmion gyration that arises from a competition between geometric confinement due to boundary edges and the vortex-like polarisation of the spin torques. A phenomenology fo…
