Spin-torque Nano-oscillators Research Articles

Reservoir computing using photon-magnon coupling

The current demand for large-volume data processing has led to the emergence of brain-inspired devices and algorithms, such as reservoir computing (RC), a promising computational framework for temporal-data processing. As inspired by a demonstration of RC using spin-torque nano-oscillators [Marković et al., Appl. Phys. Lett. 114, 012409 (2019)], we experimentally demonstrated RC using the non-linear dynamical responses of photon-magnon coupling (PMC) modes, i.e., the magnitude, phase, and frequency of the transmission spectra in a specially designed hybrid system consisting of an inverted split-ring resonator and an yttrium iron garnet film. Through the outputs decoded from the magnitude and frequency of the PMC transmission spectra, we experimentally achieved a 100% classification rate for recognitions of non-degenerate sine and square waveforms in a wide range of DC magnetic fields (DC currents) center, thanks to the extremely high signal-to-noise ratios and the non-linearity of the dynamical variables. The experimental realization of RC based on PMC can pave an alternative pathway to the development of high-performance RC devices.

Ultrahigh frequency spin-torque nano-oscillator based on bilayer-skyrmions

A skyrmion in a nanodisk with a single free layer (Single-layer Skyrmion) can be excited by the spin-polarized current to a steady state of circular motion for high-frequency applications. However, limited by the threshold of the driving current owning to the skyrmion Hall effect (SkHE), the maximum frequency of the skyrmion oscillation is usually 1 ∼ 3 GHz. In this work, the dynamics of skyrmions in the nanodisk with two antiferromagnetic-coupled free layers (Bilayer-skyrmions) are investigated. Our simulations show that the maximum frequency of Bilayer-skyrmions can be increased up to above 10 GHz, about one order of magnitude larger than that of Single-layer Skyrmion because of the disappearance of the SkHE in the antiferromagnetic-coupled system. In addition, it is found that the oscillation frequency of Bilayer-skyrmions linearly increases with the current density. Finally, spin-torque nano-oscillators based on multiple pairs of Bilayer-skyrmions are further demonstrated to increase the frequency limit up to 36.5 GHz. Our results may be useful for the design and applications of current-induced skyrmion-based oscillators for ultrahigh-frequency applications.

Spintronic RF-Direct on-off Keying Modulation Using a Frequency Division Multiplex

This paper presents the results of spintronic wireless communication using a new modulation method, spin RF-direct on-off keying modulation using a frequency division multiplex (FDM), which modulates amplitude and frequency simultaneously with a spin torque nano-oscillator (STNO) array. For the new modulation technique, each channel can be assigned to every STNO on the STNO array, and each STNO is simultaneously modulated by on-off keying with digital data directly. These modulation technologies have the advantage of increasing the data transmission rate by the number of operating STNOs. In recent years, efforts to increase the speed of transmission are important as the amount of data it sends increase. The receiver demodulates data on every channel through a band pass filter acquiring the frequency assigned to each channel, respectively. To initially confirm the possibility of realizing spin RF-direct on-off keying modulation using an FDM, we demonstrated the proposed modulation technique with two STNOs in an array, setting one STNO at 3.5 GHz frequency and the other at 4.2 GHz, and communicated wirelessly with a two-channel receiver in the near field. A data rate of up to 4 Mbps is obtained with the new modulation technique under 10 mm distance, and the DC power consumption is 0.18 mW per STNO in transmitter, including logic circuit operation.

Analog and Digital Phase Modulation and Signal Transmission with Spin-Torque Nano-Oscillators

Researchers present a method of phase modulation and phase-shift keying for spin-torque nano-oscillators (STNOs), and demonstrate transmission of a voice signal (telephony) with their STNO-based gear. The key elements of the proposed method are the ability of an STNO to be synchronized by an external signal, and to shift its phase relative to the source's phase according to an additional control signal. These properties allow not only control of the phase, but also reduction of phase noise, which is a main issue for all oscillators with nanoscale dimensions. The results comprise a significant advance for wireless data and signal communication with nano-oscillators.

Non-volatile artificial synapse based on a vortex nano-oscillator

In this work, a new mechanism to combine a non-volatile behaviour with the spin diode detection of a vortex-based spin torque nano-oscillator (STVO) is presented. Experimentally, it is observed that the spin diode response of the oscillator depends on the vortex chirality. Consequently, fixing the frequency of the incoming signal and switching the vortex chirality results in a different rectified voltage. In this way, the chirality can be deterministically controlled via the application of electrical signals injected locally in the device, resulting in a non-volatile control of the output voltage for a given input frequency. Micromagnetic simulations corroborate the experimental results and show the main contribution of the Oersted field created by the input RF current density in defining two distinct spin diode detections for different chiralities. By using two non-identical STVOs, we show how these devices can be used as programmable non-volatile synapses in artificial neural networks.

Effect of Oersted field on the localized droplet mode and propagating spin waves mode excited in spin-torque nano-oscillator

Magnetic droplets are self-localized spin wave solitons that can be excited in spin valves with perpendicular magnetic anisotropy by using spin-transfer torque generated by a dc current through a nano-contact. Using micromagnetic simulations, we demonstrate that the droplet soliton mode could be switched to a localized spiral precession mode due to the resistance effect of current-induced Oersted fields whose rotation direction is opposite to the precession direction of droplet. This spiral mode can switch back to the droplet mode by increasing current. With an assistance of electric field, both the localized droplet and spiral modes can develop to the radially propagating spin waves. The frequencies of all these localized spiral and droplet as well as the propagating spin wave modes show linear increase relationship with a magnetic field applied in out-of-plane direction. These results are of fundamental interest in understanding the rich dynamics of magnetic excitation properties, which will be helpful for the droplet-based spintronic devices.

Hysteretic mutual phase-locking of perpendicular-to-plane polarizer spin-torque nano-oscillator pairs analyzed by a generalized pendulum-like model

At present, the Kuramoto model is the standard and widely accepted theoretical approach for analyzing the synchronization of spin-torque nano-oscillators (STNOs) coupled by an interaction. Nevertheless, the oscillatory decaying regime and the initial condition (IC)-dependence (hysteretic) that exist in the synchronization of many types of STNOs cannot be explained by this model. In order to more precisely elucidate the physical mechanisms behind the two phenomena, in this paper we develop a generalized pendulum-like model based on the two common features of non-linear auto-oscillators: one is the stability of the amplitude/energy of dynamic states and the other is the non-linear dynamic state energy of oscillators. In this new model, we find that the Newtonian-like particle with sufficient kinetic energy can overcome the barrier of phase-locking potential to evolve into a stable asynchronization state, leading to the IC-dependent synchronization. Furthermore, due to the presence of kinetic energy, this particle can also oscillate around the minima of the phase-locking potential, leading to the oscillatory decaying regime. Thereby, in this work, we adopt this new model to analyze the IC-dependent mutual synchronization of perpendicular-to-plane-STNO pairs, and then we suggest that the initial conditions can be controlled to avoid such a phenomenon by using magnetic dipolar coupling.

Dancing synchronization in coupled spin-torque nano-oscillators

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 turns out to be universal, and can exist in two nonlinear Van der Pol oscillators coupled both reactively and dissipativly. Our findings open doors for new functional STNO-based devices.

Spin torque nano-oscillators based on isolated edge skyrmions in nano-pillars with perpendicular anisotropy

The magnetic skyrmions have received a lot of attention because they have potential applications in spin torque nano-oscillators. In this paper, we numerically and analytically study the dynamics of edge skyrmions in circular nano-pillar oscillators with perpendicular magnetic anisotropy (PMA) free layer and spin polarizer. Numerical simulations demonstrate that a steady edge skyrmion oscillation mode with GHz frequency can be driven by spin currents and magnetic fields. The oscillation frequencies in circular nano-pillars with different radius are analytically derived, which agrees well with the numerical results. In addition, the steady oscillations of edge skyrmions are also observed in elliptical nano-pillars, in which the oscillation frequencies strongly depend on the eccentricity and perimeter of the elliptical nanopillar. It is found that the oscillation frequency of this edge skyrmion can range from 1 GHz to 6.7 GHz. The line width is about 55 MHz.

Electrical characterisation of higher order spin wave modes in vortex-based magnetic tunnel junctions

NiFe-based vortex spin-torque nano-oscillators (STNO) have been shown to be rich dynamic systems which can operate as efficient frequency generators and detectors, but with a limitation in frequency determined by the gyrotropic frequency, typically sub-GHz. In this report, we present a detailed analysis of the nature of the higher order spin wave modes which exist in the Super High Frequency range (3–30 GHz). This is achieved via micromagnetic simulations and electrical characterisation in magnetic tunnel junctions, both directly via the spin-diode effect and indirectly via the measurement of the coupling with the gyrotropic critical current. The excitation mechanism and spatial profile of the modes are shown to have a complex dependence on the vortex core position. Additionally, the inter-mode coupling between the fundamental gyrotropic mode and the higher order modes is shown to reduce or enhance the effective damping depending upon the sense of propagation of the confined spin wave.

Vortex gyrotropic mode in curved nanodots

In this work, we present the influence of the curvature of magnetic nanodot on the vortex gyrotropic mode frequency. We show that gyrotropic oscillation of the magnetic vortices is highly influenced by the rounding of the nanodot shape due to the formation of the apex and single domain state in the upper part of the dot. The curved shape of nanodot could arise during the fabrication process of the nanodots, i.e., during lithography. We find that strong dependence of the gyrotropic mode frequency on curvature parameter is related to magnetic phase transition: from vortex to out-of-plane state. The found effect can be used, e.g., for the design of the spin torque nano oscillators.

Phase variation in the locked state of mutually synchronized spin torque nano-oscillators

Spin torque nano-oscillators (STNOs) have been shown to efficiently “lock” to electrical signals whether these are from external sources, self-reflected signals, or other STNOs via mutual synchronization. Traditionally, the locked state of an STNO has been considered digital, either “ON” or “OFF.” In this report, we show how the phase in the locked state can vary significantly as a function of the applied dc to the STNO with the phase strongly affecting the emitted power. This phase dependence demonstrates the analogue nature of the locked state, offering an extra degree of freedom when designing STNO-based neural networks.

Ultrafast Ising Machines using spin torque nano-oscillators

Combinatorial optimization problems are known for being particularly hard to solve on traditional von Neumann architectures. This has led to the development of Ising Machines (IMs) based on quantum annealers and optical and electronic oscillators, demonstrating speed-ups compared to central processing unit (CPU) and graphics processing unit (GPU) algorithms. Spin torque nano-oscillators (STNOs) have shown GHz operating frequency, nanoscale size, and nanosecond turn-on time, which would allow their use in ultrafast oscillator-based IMs. Here, we show using numerical simulations based on STNO auto-oscillator theory that STNOs exhibit fundamental characteristics needed to realize IMs, including in-phase/out-of-phase synchronization and second harmonic injection locking phase binarization. Furthermore, we demonstrate numerically that large STNO network IMs can solve Max-Cut problems on nanosecond timescales.

Flicker and random telegraph noise between gyrotropic and dynamic C-state of a vortex based spin torque nano oscillator

Vortex based spin torque nano oscillators (STVOs) can present more complex dynamics than the spin torque induced gyrotropic (G) motion of the vortex core. The respective dynamic modes and the transition between them can be controlled by experimental parameters such as the applied dc current. An interesting behavior is the stochastic transition from the G-to a dynamic C-state occurring for large current densities. Moreover, the C-state oscillations exhibit a constant active magnetic volume. We present noise measurements in the different dynamic states that allow accessing specific properties of the stochastic transition, such as the characteristic state transition frequency. Furthermore, we confirm, as theoretically predicted, an increase of flicker noise with Idc2 when the oscillation volume remains constant with the current. These results bring insight into the potential optimization of noise properties sought for many potential rf applications with spin torque oscillators. Furthermore, the investigated stochastic characteristics open up new potentialities, for instance in the emerging field of neuromorphic computing schemes.

Tuning the dynamics of magnetic droplet solitons using dipolar interactions

Magnetic droplets are dissipative magnetodynamical solitons that can form under current driven nanocontacts in magnetic layers with large perpendicular magnetic anisotropy. Here, we extend the original droplet theory by studying the impact of the dipolar interactions on the dynamics of droplet solitons. By varying the thickness of the free layer of a spin torque nano-oscillator, we systematically tune the internal field of the free layer to investigate the dynamics of droplet solitons. Our numerical results show that increasing the free layer thickness increases the droplet threshold current, decreases the droplet frequency and diameter, enlarges the current hysteresis and also modifies the structure of the droplet. The Oersted field of the current breaks the phase coherency and deteriorates the stability of the droplet in free layers with larger thicknesses. Moreover, our findings show a simple relation to determine the impact of the free layer thickness on the droplet nucleation boundaries. Our study presents the missing brick on the physics behind magnetic droplet solitons, and further illustrates that magnetic droplets in thinner layers possess more promising characteristics for spintronic applications and enable devices with higher speed of operation.

Stability phase diagrams and tuning of magnetic skyrmionium and other states

Topological magnetic states such as skyrmions have widely been investigated as a suitable candidate for memory bits in next generation data storage device applications including random access memory (RAM) or race-track memory as well as spin-torque nano-oscillators etc. Energy efficient multistate switching of these states based on electric control of magnetization involves the electric field tuning of perpendicular magnetic anisotropy (PMA). By using micromagnetic simulation study, we demonstrate the strain-mediated electric manipulation of various topological magnetic states in nanodisc with [Pt/Co/Ta]n trilayer stacks residing on a piezoelectric substrate. A stability phase diagram is derived for the representation of regions of the lowest energy states against the applied strain as a function of disc dimensions. Utilizing this derived phase diagram, various electric field-induced strain-mediated switching scenarios including non-volatile reversible switching of skyrmion into skyrmionium, 3π state and helical stripe domain state, the creation of skyrmionium from uniform single-domain magnetic state and its annihilation and volatile reversible switching between skyrmionium and vortex are achieved. Moreover, an extended phase diagram based on the estimated critical values of the applied strain for different domain structures within the nanodisc is also built and further implemented in designing a multistate sequential switching between various magnetic states triggered by a continuously varying strain pulse. These findings hold a potential for contributing in the development of low-power high-density multistate magneto-electric or magneto-elastic memory and logic device applications involving simple architectural concept applicable to future microelectronic integrated device strategies.

Experiments and SPICE simulations of double MgO-based perpendicular magnetic tunnel junction* *Project supported by State Grid Corporation of China under the 2018 Science and Technology Project of State Grid Corporation: Research on electromagnetic measurement technology based on EIT and TMR (Grant No. JL71-18-007).

We investigate properties of perpendicular anisotropy magnetic tunnel junctions (pMTJs) with a stack structure MgO/CoFeB/Ta/CoFeB/MgO as the free layer (or recording layer), and obtain the necessary device parameters from the tunneling magnetoresistance (TMR) vs. field loops and current-driven magnetization switching experiments. Based on the experimental results and device parameters, we further estimate current-driven switching performance of pMTJ including switching time and power, and their dependence on perpendicular magnetic anisotropy and damping constant of the free layer by SPICE-based circuit simulations. Our results show that the pMTJ cells exhibit a less than 1 ns switching time and write energies < 1.4 pJ; meanwhile the lower perpendicular magnetic anisotropy (PMA) and damping constant can further reduce the switching time at the studied range of damping constant α < 0.1. Additionally, our results demonstrate that the pMTJs with the thermal stability factor ≃ 73 can be easily transformed into spin-torque nano-oscillators from magnetic memory as microwave sources or detectors for telecommunication devices.

Beyond the gyrotropic motion: Dynamic C-state in vortex spin torque oscillators

In the present study, we investigate a dynamical mode beyond the gyrotropic (G) motion of a magnetic vortex core in a confined magnetic disk of a nano-pillar spin torque nano-oscillator (STNO). It is characterized by the in-plane circular precession associated with a C-shaped magnetization distribution. We show a transition between G- and C-state modes, which is found to be stochastic in a current-controllable range. Supporting our experimental findings with micromagnetic simulations, we believe that the results provide further opportunities for the dynamic and stochastic control of STNOs, which could be interesting to be implemented, for example, in neuromorphic networks.

Effect of the Zhang-Li torque on spin-torque nano-oscillators

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 magnetic modes. However, an additional term, known as Zhang-Li term has an effect on magnetization gradients such as domain walls, and could have an effect on localized magnetic modes in STNO. Here we study the effect of Zhang-Li torques in magnetic excitations produced in STNO with a nanocontact geometry. Using micromagnetic simulations we find that Zhang-Li torque modify threshold currents of magnetic modes and their effective sizes. Additionally we show that effects can be controlled by changing the ratio between nanocontact size and layer thickness.

Effects of delayed feedback on the power spectrum of spin-torque nano-oscillators

A theoretical study of delayed feedback in a spin-torque nano-oscillator model is presented. The feedback acts as a modulation of the supercriticality, which results in changes in the oscillator frequency through a strong non-linearity, amplitude modulations, and a rich modulation sideband structure in the power spectrum at long delays. Modulation sidebands persist at finite temperatures but some of the complex structure is lost through the finite coherence time of the oscillations.