A theoretical analysis is developed on spin-torque diode effect in nonlinear region. An analytical solution of the diode voltage generated from spin-torque oscillator by the rectification of an alternating current is derived. The diode voltage is revealed to depend nonlinearly on the phase difference between the oscillator and the alternating current. The validity of the analytical prediction is confirmed by numerical simulation of the Landau-Lifshitz-Gilbert equation. The results indicate that the spin-torque diode effect is useful to evaluate the phase of a spin-torque oscillator in forced synchronization state.
The optimum condition of the magnetization alignment to maximize the spin torque diode voltage is derived by solving the Landau-Lifshitz-Gilbert equation. We show that the optimized diode voltage can be one order of magnitude larger than that of the conventional alignment where the easy axes of the free and the pinned layers are parallel. These analytical predictions are confirmed by numerical simulations.
This paper predicts the effect of the Dzyaloshinskii-Moriya interaction (DMI) and spin Hall effect in the spin-torque diode response of a Magnetic Tunnel Junction built over a Tantalum strip. Our results indicate that, for a microwave current large enough, the DMI can change qualitatively the resonant response by splitting the ferromagnetic resonance peak. We also find out that the two modes have a non-uniform spatial distribution.
The optimum condition of an applied field direction to maximize spin torque diode voltage was theoretically derived for a magnetic tunnel junction with a perpendicularly magnetized free layer and an in-plane magnetized pinned layer. We found that the diode voltage for a relatively small applied field is maximized when the projection of the applied field to the film-plane is parallel or anti-parallel to the magnetization of the pinned layer. However, by increasing the applied field magnitude, the optimum applied field direction shifts from the parallel or anti-parallel direction. These analytic…
We report on a voltage tunable radio-frequency (RF) detector based on a magnetic tunnel junction (MTJ). The spin-torque diode effect is used to excite and/or detect RF oscillations in the magnetic free layer of the MTJ. In order to reduce the overall in-plane magnetic anisotropy of the free layer, we take advantage of the perpendicular magnetic anisotropy at the interface between ferromagnetic and insulating layers. The applied bias voltage is shown to have a significant influence on the magnetic anisotropy, and thus on the resonance frequency of the device. This influence also depends on the …
We report the rectifying effect of a constant-wave radio frequency (RF) current by a magnetic domain wall (DW) on a single-layered ferromagnetic wire. A direct-current (DC) voltage is generated by the spin torque diode effect, which is a consequence of magnetoresistance oscillation due to the resonant spin wave excitation induced by the spin-polarized RF current. The DC voltage spectrum strongly depends on the internal spin structure in the DW, which corresponds to the magnetic fingerprint of the spin structure in the ferromagnetic wire.
We calculate the efficiency with which magnetic tunnel junctions can be used as resonant detectors of incident microwave radiation via the spin-torque diode effect. The expression we derive is in good agreement with the sensitivities we measure for MgO-based magnetic tunnel junctions with an extended (unpatterned) magnetic pinned layer. However, the measured sensitivities are reduced below our estimate for a second set of devices in which the pinned layer is a patterned synthetic antiferromagnet (SAF). We suggest that this reduction may be due to an undesirable coupling between the magnetic fr…
The relaxation phenomena of spin-torque oscillators consisting of nanostructured ferromagnets are interesting research targets in magnetism. A theoretical study on the relaxation time of a spin-torque oscillator from one self-oscillation state to another is investigated. By solving the Landau-Lifshitz-Gilbert equation both analytically and numerically, it is shown that the oscillator relaxes to the self-oscillation state exponentially within a few nanoseconds, except when magnetization is close to a critical point. The relaxation rate, which is an inverse of relaxation time, is proportional to…
Microwave detectors based on the spin-transfer torque diode effect are among the key emerging spintronic devices. By utilizing the spin of electrons in addition to charge, they have the potential to overcome the theoretical performance limits of their semiconductor (Schottky) counterparts, which cannot operate at low input power. Here, we demonstrate nanoscale microwave detectors exhibiting record-high detection sensitivity of 75400 mV mW$^{-1}$ at room temperature, without any external bias fields, for input microwave power down to 10 nW. This sensitivity is 20x and 6x larger than state-of-th…
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.
Magnetic tunnel junctions are nanoscale spintronic devices with microwave generation and detection capabilities. Here we use the rectification effect called "spin-diode" in a magnetic tunnel junction to wirelessly detect the microwave emission of another junction in the auto-oscillatory regime. We show that the rectified spin-diode voltage measured at the receiving junction end can be reconstructed from the independently measured auto-oscillation and spin diode spectra in each junction. Finally we adapt the auto-oscillator model to the case of spin-torque oscillator and spin-torque diode and w…
We assess the potential of two-terminal graphene-hBN-graphene resonant tunneling diodes as high-frequency oscillators, using self-consistent quantum transport and electrostatic simulations to determine the time-dependent response of the diodes in a resonant circuit. We quantify how the frequency and power of the current oscillations depend on the diode and circuit parameters including the doping of the graphene electrodes, device geometry, alignment of the graphene lattices, and the circuit impedances. Our results indicate that current oscillations with frequencies of up to several hundred GHz…
We study dynamics of a serial array of spin-torque-oscillators with a parallel inductor-capacitor-resistor (LCR) load. In a large range of parameters the fully synchronous regime, where all the oscillators have the same state and the output field is maximal, is shown to be stable. However, not always such a robust complete synchronization develops from the random initial state, in many cases nontrivial clustering is observed, with a partial synchronization resulting in a quasiperiodic or chaotic mean field dynamics.
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.
Spin-orbit torque nano-oscillators based on bilayers of ferromagnetic (FM) and nonmagnetic (NM) metals are ultra-compact current-controlled microwave signal sources. They serve as a convenient testbed for studies of spin-orbit torque physics and are attractive for practical applications such as microwave assisted magnetic recording, neuromorphic computing, and chip-to-chip wireless communications. However, a major drawback of these devices is low output microwave power arising from the relatively small anisotropic magnetoresistance (AMR) of the FM layer. Here we experimentally show that the ou…
This Habilitation Thesis written in 2013 reviews my research work on spin torque nano-oscillators (from zero-field oscillations, to synchronization and vortex oscillators) and memristive devices (spin Torque and ferroelectric memristors).
Oscillation frequency of spin torque oscillator with a perpendicularly magnetized free layer and an in-plane magnetized pinned layer is theoretically investigated by taking into account the field-like torque. It is shown that the field-like torque plays an important role in finding the balance between the energy supplied by the spin torque and the dissipation due to the damping, which results in a steady precession. The validity of the developed theory is confirmed by performing numerical simulations based on the Landau-Lifshitz-Gilbert equation.
Characterization of Tunnel Diode Oscillator for Qubit Readout Applications
RIKEN Center for Quantum Computing, RIKEN（RIKEN量子计算中心）；Department of Applied Sciences, Delft University of Technology（代尔夫特理工大学应用科学系）；Physics of Quantum Fluids and Crystals, B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine（乌克兰国家科学院B.维尔金低温物理与工程研究所量子流体与晶体物理部）；Institute of Physics, Kazan Federal University（喀山联邦大学物理研究所）；Cluster for Pioneering Research, RIKEN（RIKEN前沿研究集群）
The self-oscillation of the magnetization in a spin torque oscillator (STO) with a perpendicularly magnetized free layer and an in-plane magnetized pinned layer in the absence of an applied magnetic field was studied by numerically solving the Landau-Lifshitz-Gilbert equation. It was pointed out that field-like torque was necessary to realize stable self-oscillation in this type of STO at zero field. The numerical simulation at finite temperature showed that the presence of the field-like torque led to a high power with a relatively high oscillation frequency.
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…
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.
We discuss the coherence of magnetic oscillations in a magnetic tunnel junction-based spin-torque oscillator as a function of external field angle. Time-frequency analysis shows mode-hopping between distinct oscillator modes, which arises from linear and nonlinear couplings in the Landau-Lifshitz-Gilbert equation, analogous to mode-hopping observed in semiconductor ring lasers. These couplings and therefore mode-hopping are minimized near the current threshold for antiparallel (AP) alignment of free layer with reference layer magnetization. Away from the AP alignment, mode-hopping limits oscil…
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 …
We study the current controlled modulation of a nano-contact spin torque oscillator. Three principally different cases of frequency non-linearity ($d^{2}f/dI^{2}_{dc}$ being zero, positive, and negative) are investigated. Standard non-linear frequency modulation theory is able to accurately describe the frequency shifts during modulation. However, the power of the modulated sidebands only agrees with calculations based on a recent theory of combined non-linear frequency and amplitude modulation.
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.
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…
We show that the phase of a spin-torque oscillator generically acquires a geometric contribution upon slow and cyclic variation of the parameters that govern its dynamics. As an example, we compute the geometric phase that results from a cyclic excursion of the magnitude of the external field and the current. We consider thermal phase fluctuations and conclude that the geometric phase should be experimentally observable at room temperature with current setups. We briefly comment on arrays of spin-torque oscillators and possible applications.
We consider a synthetic antiferromagnetic spin-torque oscillator with anisotropic interlayer exchange coupling. This system exhibits exceptional points in its linearized dynamics. We find the non-linear dynamics and the dynamical phase diagram of the system both analytically and numerically. Moreover, we show that, near one of the exceptional points, the power of the oscillator depends extremely sensitively on the injected spin current. Our findings may be useful for designing sensitive magnetometers and for other applications of spin-torque oscillators.
A theory of magnetization dynamics in ferrimagnetic materials with antiparallel aligned spin sub-lattices under action of spin-transfer torques (STT) is developed. We consider magnetization dynamics in GdFeCo layers in two cases of magnetic anisotropy: easy plane and easy axis. We demonstrate that, (i) for the easy plane anisotropy the precession of the Néel vector is conical and the cone angle depends on the STT strength and the value of spin non-compensation, while the frequency of precession can reach sub-THz frequencies; (ii) for the easy axis anisotropy two regimes are possible: determini…
We present a combined analytical and numerical study on double-vortex spin-torque nano-oscillators and describe a mechanism that suppresses the windmill modes. The magnetization dynamics is dominated by the gyrotropic precession of the vortex in one of the ferromagnetic layers. In the other layer the vortex gyration is strongly damped. The dominating layer for the magnetization dynamics is determined by the current polarity. Measurements on Fe/Ag/Fe nano-pillars support these findings. The results open up a new perspective for building high quality-factor spin-torque oscillators operating at s…
The oscillation properties of a spin torque oscillator consisting of a perpendicularly magnetized free layer and an in-plane magnetized pinned layer are studied based on an analysis of the energy balance between spin torque and damping. The critical value of an external magnetic field applied normal to the film plane is found, below which the controllable range of the oscillation frequency by the current is suppressed. The value of the critical field depends on the magnetic anisotropy, the saturation magnetization, and the spin torque parameter.
A number of recent experimental works have shown that the dynamics of a single spin torque oscillator can exhibit complex behavior that stems from interactions between two or more modes of the oscillator. Examples are observed mode-hopping or mode coexistence. There has been some intial work indicating how the theory for a single-mode (macro-spin) spin torque oscillator should be generalized to include several modes and the interactions between them. In the present work, we derive such a theory starting with the Landau-Lifshitz-Gilbert equation for magnetization dynamics. We compare our result…
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…
The magnetization dynamics of spin torque oscillator (STO) consisting of a perpendicularly magnetized free layer and an in-plane magnetized pinned layer was studied by solving the Landau-Lifshitz-Gilbert equation. We derived the analytical formula of the relation between the current and the oscillation frequency of the STO by analyzing the energy balance between the work done by the spin torque and the energy dissipation due to the damping. We also found that the field-like torque breaks the energy balance, and change the oscillation frequency.
A numerical investigation is conducted for a single spin-torque oscillator under the non-linear region. A large angle precession triggers the generation of multiple modes without any feedbacked circuits and/or magnetic couplings with neighboring oscillators. Our simulations show that a single eigenmode of a given spin-torque oscillator can trigger up to six discrete modes as the sideband modes. These findings will offer the new functionality to the STO for developing the spintronic logic circuits.
Phase coupling between auto-oscillators is central for achieving coherent responses such as synchronization. Here we present an experimental approach to probe it in the case of two dipolarly coupled spin-torque vortex nano-oscillators using an external microwave field. By phase-locking one oscillator to the microwave field, we observe frequency pulling on the second oscillator. From coupled Thiele equations we show analytically that this frequency pulling results from concerted actions of dipolar and microwave couplings. The analysis allows us to determine the amplitude of dipolar coupling and…
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 investigate how the ability of the vortex oscillation mode of a spin-torque nano-oscillator to lock to an external microwave signal is modified when it is coupled to another oscillator. We show experimentally that mutual electrical coupling can lead to locking range enhancements of a factor 1.64. Furthermore, we analyze the evolution of the locking range as a function of the coupling strength through experiments and numerical simulations. By uncovering the mechanisms at stake in the locking range enhancement, our results will be useful for designing spin-torque nano-oscillators arrays with …
The mutual interaction between the different eigenmodes of a spin-torque oscillator can lead to a large variety of physical mechanisms from mode hopping to multi-mode generation, that usually reduce their performances as radio-frequency devices. To tackle this issue for the future applications, we investigate the properties of a model spin-torque oscillator that is composed of two coupled vortices with one vortex in each of the two magnetic layers of the oscillator. In such double-vortex system, the remarkable properties of energy transfer between the coupled modes, one being excited by spin t…
Deterministic magnetization switching using spin-orbit torque (SOT) has recently emerged as an efficient means to electrically control the magnetic state of ultrathin magnets. The SOT switching still lacks in oscillatory switching characteristics over time, therefore, it is limited to bipolar operation where a change in polarity of the applied current or field is required for bistable switching. The coherent rotation based oscillatory switching schemes cannot be applied to SOT because the SOT switching occurs through expansion of magnetic domains. Here, we experimentally achieve oscillatory sw…
The correlation of phase fluctuations in any type of oscillator fundamentally defines its spectral shape. However, in nonlinear oscillators, such as spin torque nano oscillators, the frequency spectrum can become particularly complex. This is specifically true when not only considering thermal but also colored $1/f$ flicker noise processes, which are crucial in the context of the oscillator's long term stability. In this study, we address the frequency spectrum of spin torque oscillators in the regime of large-amplitude steady oscillations experimentally and as well theoretically. We particula…
A theoretical study of delayed feedback in spin-torque nano-oscillators is presented. A macrospin geometry is considered, where self-sustained oscillations are made possible by spin transfer torques associated with spin currents flowing perpendicular to the film plane. By tuning the delay and amplification of the self-injected signal, we identify dynamical regimes in this system such as chaos, switching between precession modes with complex transients, and oscillator death. Such delayed feedback schemes open up a new field of exploration for such oscillators, where the complex transient states…
This paper reviews the state of the art in spin-torque and spin Hall effect driven nano-oscillators. After a brief introduction to the underlying physics, the authors discuss different implementations of these oscillators, their functional properties in terms of frequency range, output power, phase noise, and modulation rates, and their inherent propensity for mutual synchronization. Finally, the potential for these oscillators in a wide range of applications, from microwave signal sources and detectors to neuromorphic computation elements, is discussed together with the specific electronic ci…
We show how a charge current through a single antiferromagnetic layer can excite and control self-oscillations. Sustained oscillations with tunable amplitudes and frequencies are possible in a variety of geometries using certain classes of non-centrosymmetric materials that exhibit finite dissipative spin-orbit torque. We compute the steady-state phase diagram as a function of the current and spin-orbit torque magnitude. The anisotropic magnetoresistance causes the conversion of the resulting AF oscillations to a terahertz AC output voltage. These findings provide an attractive and novel route…
We report an approach to improving the performance of spin torque nano-oscillators (STNOs) that utilizes power-dependent negative feedback to achieve a significantly enhanced dynamic damping. In combination with a sufficiently slow variation of frequency with power this can result in a quasi-linear STNO, with very weak non-linear coupling of power and phase fluctuations over a range of bias current and field. An implementation of this approach that utilizes a non-uniform spin-torque demonstrates that highly coherent room temperature STNOs can be achieved while retaining a significant tunabilit…
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. It is characterized by the in-plane circular precession associated to a C-shaped magnetization distribution. We show a transition between G and C-state mode which is found to be purely stochastic in a current-controllable range. Supporting our experimental findings with micromagnetic simulations, we believe that the results provide novel opportunities for the dynamic and stochastic control of STOs, which could…
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 o…
An analytical model of the spin-diode effect induced by resonant spin-transfer torque in a ferromagnetic bilayer with strong dipolar coupling provides the resonance frequencies and the lineshapes of the magnetic field spectra obtained under field or laser-light modulation. The effect of laser irradiation is accounted for by introducing the temperature dependence of the saturation magnetization and anisotropy, as well as thermal spin-transfer torques. The predictions of the model are compared with experimental data obtained with single Co/Cu/Co spin valves, embedded in nanowires and produced by…
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…
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.
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…
Stochastic dynamics of spin torque oscillators (STOs) can be described in terms of magnetization drift and diffusion over a current-dependent effective energy surface given by the Fokker-Planck equation. Here we present a method that directly probes this effective energy surface via time-resolved measurements of the microwave voltage generated by a STO. We show that the effective energy approach provides a simple recipe for predicting spectral line widths and line shapes near the generation threshold. Our time domain technique also accurately measures the field-like component of spin torque in…
The dynamics of vortex based spin-torque nano-oscillators is investigated theoretically. Starting from a fully analytical model based on the Thiele equation approach, fine-tuned data-driven corrections are carried out to the gyrotropic and damping terms. These adjustments, based on micromagnetic simulation results, allow to quantitatively model the response of such oscillators to any dc current within the range of the vortex stability. Both, the transient and the steady-state regimes are accurately predicted under the proposed data-driven Thiele equation approach. Furthermore, the computation …
