In this study, we numerically evaluate the learning performance of a vortex spin-torque oscillator (VSTO) with a modified free layer, called a modified VSTO (m-VSTO), in which an additional layer (AL) of smaller radius is stacked on the free layer, for physical reservoir computing. The vortex-core dynamics are computed using the Thiele equation incorporating the potential deformation induced by the AL. We identify the edge of chaos from the maximal Lyapunov exponent and quantify the short-term memory capacity (STMC) as well as the information processing capacity (IPC) in a time-multiplexed reservoir scheme. We find that the m-VSTO exhibits finite STMC and IPC in a low-current and low-field regime below the threshold current of the conventional VSTO, and can achieve up to approximately twice the IPC with about one quarter of the power consumption. The pulse-width dependence of the IPC can be further interpreted by combining an analytical estimate of the transient time with Lyapunov-exponent data. Longer pulse widths promote stronger recovery-induced contraction toward the groove-trapped orbit over a wide range of subthreshold currents. In contrast, this difference in contraction rate becomes less pronounced near the threshold current, where the transient time increases rapidly. Consequently, the IPC is enhanced in a stable regime with a negative Lyapunov exponent rather than exactly at the edge of chaos. These results suggest that engineering the potential landscape and pulse-width-dependent recovery dynamics enables low-power spintronic physical reservoirs.
We numerically study reservoir computing on a spin-torque oscillator (STO) array, describing the magnetization dynamics of the STO array by a nonlinear oscillator model. The STOs exhibit synchronized oscillation due to coupling by magnetic dipolar fields. We show that reservoir computing can be performed using the synchronized oscillation state. The performance can be improved by increasing the number of STOs. The performance becomes highest at the boundary between the synchronized and disordered states. Using an STO array, we can achieve higher performance than that of an echo-state network w…
Spin-torque nano-oscillators can emulate neurons at the nanoscale. Recent works show that the non-linearity of their oscillation amplitude can be leveraged to achieve waveform classification for an input signal encoded in the amplitude of the input voltage. Here we show that the frequency and the phase of the oscillator can also be used to recognize waveforms. For this purpose, we phase-lock the oscillator to the input waveform, which carries information in its modulated frequency. In this way we considerably decrease amplitude, phase and frequency noise. We show that this method allows classi…
Vortex-based spin-torque oscillators can be made from extended spin valves connected to an electrical nanocontact. We study the implementation of frequency shift keying modulation in these oscillators. Upon a square modulation of the current in the 10 MHz range, the vortex frequency follows the current command, with easy identification of the two swapping frequencies in the spectral measurements. The frequency distribution of the output power can be accounted for by convolution transformations of the dc current vortex waveform, and the current modulation. Modeling indicates that the frequency …
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…
Equilibrium magnetization distribution of the vortex state magnetic nanoparticle is affected by the influence of the spin-transfer torque: an off-center out--of--plane vortex appears in the case of the disk shape particle and pure planar vortex in the case of asymmetric ring shape particle. The spin current causes extra out-of-plane magnetization structures identical to well known dip structures for the moving vortex. The shape of the dip structure depends on the current strength and value of the off-center displacement and it does not depend on the vortex polarity. The critical current depend…
Low frequency noise close to the carrier remains little explored in spin torque nano oscillators. However, it is crucial to investigate as it limits the oscillator's frequency stability. This work addresses the low offset frequency flicker noise of a TMR-based spin-torque vortex oscillator in the regime of large amplitude steady oscillations. We first phenomenologically expand the nonlinear auto-oscillator theory aiming to reveal the properties of this noise. We then present a thorough experimental study of the oscillator's $1/f$ flicker noise and discuss the results based on the theoretical p…
We study the agility of current-tunable oscillators based on a magnetic vortex orbiting around a point contact in spin-valves. Theory predicts frequency-tuning by currents occurs at constant orbital radius, so an exceptional agility is anticipated. To test this, we have inserted an oscillator in a microwave interferometer to apply abrupt current variations while time resolving its emission. Using frequency shift keying, we show that the oscillator can switch between two stabilized frequencies differing by 25% in less than ten periods. With a wide frequency tunability and a good agility, such o…
A numerical analysis on the computational capability of physical reservoir computing utilizing a spin-torque oscillator with two free layers is reported. Conventional spintronics devices usually consist of two ferromagnets, where the direction of magnetization in one layer, called the free layer, can move while that of the other, the reference layer, is fixed. Recently, however, devices with two free layers, where the reference layer is replaced by another free layer, have been developed for various practical applications. Adding another free layer drastically changes the dynamical response of…
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 investigate the dynamics of a magnetic vortex driven by spin-transfer torque due to spin current in the adiabatic case. The vortex core represented by collective coordinate experiences a transverse force proportional to the product of spin current and gyrovector, which can be interpreted as the geometric force determined by topological charges. We show that this force is just a reaction force of Lorentz-type force from the spin current of conduction electrons. Based on our analyses, we propose analytically and numerically a possible experiment to check the vortex displacement by spin curren…
In a nanopillar with dipolarly coupled vortices, we present an experimental and simulation study to understand how the interplay between the bias field and spin transfer torque impacts reversal of the vortex cores. We find that, depending on the current values, vortex cores might experience different physical mechanisms for their reversal, namely a static or a dynamic switching. We believe that our results might be useful in the context of vortex based non volatile memories, as a current controlled selective core switching is proposed.
We have employed complete micromagnetic simulations to analyze dc current driven self-oscillations of a vortex core in a spin-valve nanopillar in a perpendicular field by including the coupled effect of the spin-torque and the magnetostatic field computed self-consistently for the entire spin-valve. The vortex in the thicker nanomagnet moves along a quasi-elliptical trajectory that expands with applied current, resulting in blue-shifting of the frequency, while the magnetization of the thinner nanomagnet is non-uniform due to the bias current. The simulations explain the experimental magnetore…
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 …
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 …
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…
Spin-polarised radio-frequency currents, whose frequency is equal to that of the gyrotropic mode, will cause an excitation of the core of a magnetic vortex confined in a magnetic tunnel junction. When the excitation radius of the vortex core is greater than that of the junction radius, vortex core expulsion is observed, leading to a large change in resistance, as the layer enters a predominantly uniform magnetisation state. Unlike the conventional spin-torque diode effect, this highly tunable resonant effect will generate a voltage which does not decrease as a function of rf power, and has the…
We study, both experimentally and by numerical modeling, the magnetic dynamics that can be excited in a magnetic thin-film nanopillar device using the spin torque from a spatially localized current injected via a 10s-of-nm-diameter aperture. The current-driven magnetic dynamics can produce large amplitude microwave emission at zero magnetic field, with a frequency well below that of the uniform ferromagnetic resonance mode. Micromagnetic simulations indicate that the physical origin of this efficient microwave nano-oscillator is the nucleation and subsequent steady-state rotational dynamics of…
We show that asymmetrical mesoscopic superconductors bring new insight into vortex physics where we found the remarkable coexistence of long and short vortices. We study an asymmetrical mesoscopic sphere, that lacks one of its quadrants, and obtain its three-dimensional vortex patterns by solving the Ginzburg-Landau theory. We find that the vortex patterns are asymmetric whose effects are clearly visible and detectable in the transverse magnetization and torque.
We investigate analytically and numerically the synchronization dynamics of dipolarly coupled vortex based Spin-Torque Nano Oscillators (STNO) with different pillar diameters. We identify the critical interpillar distances on which synchronization occurs as a function of their diameter mismatch. We obtain numerically a phase diagram showing the transition between unsynchronized and synchronized states and compare it to analytical predictions we make using Thiele approach. Our study demonstrates that for relatively small diameters differences the synchronization dynamics can be described qualit…
We experimentally demonstrate that large magnetic vortex oscillations can be parametrically excited in a magnetic tunnel junction by the injection of radio-frequency (rf) currents at twice the natural frequency of the gyrotropic vortex core motion. The mechanism of excitation is based on the parallel pumping of vortex motion by the rf orthoradial field generated by the injected current. Theoretical analysis shows that experimental results can be interpreted as the manifestation of parametric amplification when rf current is small, and of parametric instability when rf current is above a certai…
Spin-orbit-torque-driven dynamics have recently gained interest in the field of magnetism due to the reduced requirement of current densities and an increase in efficiency, as well as the ease of implementation of different devices and materials. From a practical point of view, the low-frequency dynamics below 1 GHz is particularly interesting since dynamics associated with magnetic domains lie in this frequency range. While spin-torque excitation of high-frequency modes has been extensively studied, the intermediate low-frequency dynamics have received less attention, although spin torques co…
Strongly-interacting artificial spin systems are moving beyond mimicking naturally-occurring materials to emerge as versatile functional platforms, from reconfigurable magnonics to neuromorphic computing. Typically artificial spin systems comprise nanomagnets with a single magnetisation texture: collinear macrospins or chiral vortices. By tuning nanoarray dimensions we achieve macrospin/vortex bistability and demonstrate a four-state metamaterial spin-system 'Artificial Spin-Vortex Ice' (ASVI). ASVI can host Ising-like macrospins with strong ice-like vertex interactions, and weakly-coupled vor…
Time-resolved scanning Kerr microscopy has been used to directly image the magnetization dynamics of nano-contact (NC) spin-torque vortex oscillators (STVOs) when phase-locked to an injected microwave (RF) current. The Kerr images reveal free layer magnetization dynamics that extend outside the NC footprint, where they cannot be detected electrically, but which are crucial to phase-lock STVOs that share common magnetic layers. For a single NC, dynamics were observed not only when the STVO frequency was fully locked to that of the RF current, but also for a partially locked state characterized …
We report on a theoretical study about the magneto-dipolar coupling and synchronization between two vortex-based spin-torque nano-oscillators. In this work we study the dependence of the coupling efficiency on the relative magnetization parameters of the vortices in the system. For that purpose, we combine micromagnetic simulations, Thiele equation approach, and analytical macro-dipole approximation model to identify the optimized configuration for achieving phase-locking between neighboring oscillators. Notably, we compare vortices configurations with parallel (P) polarities and with opposite…
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…
Solitons are very promising for the design of next generation of ultralow power devices for storage and computation. The key ingredient to achieve this goal is the fundamental understanding of their stabilization and manipulation. Here, we show how the interfacial Dzyaloshinskii Moriya Interaction (i DMI) is able to lift the energy degeneracy of a magnetic vortex state by stabilizing a topological soliton with radial chirality, hereafter called radial vortex. It has a non-integer skyrmion number S (0.5<|S|<1) due to both the vortex core polarity and the magnetization tilting induced by the i D…
Performance of magnetoresistive sensors is today mainly limited by their 1/f low-frequency noise. Here, we study this noise component in vortex-based TMR sensors. We compare the noise level in different magnetization configurations of the device, i.e vortex state or uniform parallel or antiparallel states. We find that the vortex state is at least an order of magnitude noisier than the uniform states. Nevertheless, by activating the spin-transfer induced dynamics of the vortex configuration, we observe a reduction of the 1/f noise, close to the values measured in the AP state, as the vortex co…
We report experimental and analytical work on spin-transfer torque induced vortex dynamics in metallic nanopillars with in-plane magnetized layers. We study nanopillars with a diameter of 150 nm, containing two Fe layers with a thickness of 15 nm and 30 nm respectively, separated by a 6 nm Ag spacer. The sample geometry is such that it allows for the formation of magnetic vortices in the Fe disks. As confirmed by micromagnetic simulations, we are able to prepare states where one magnetic layer is homogeneously magnetized while the other contains a vortex. We experimentally show that in this co…
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).
Non-linear magnetization dynamics in ferromagnetic nanoelements excited by the spin-polarized dc-current is one of the most intensively studied phenomena in solid state magnetism. Despite immense efforts, synchronization of oscillations induced in several such nanoelements (spin-torque driven nanooscillators, or STNO) still represents a major challenge both from the fundamental and technological points of view. In this paper we propose a system where synchronization of any number of STNOs, represented by magnetization vortices inside squared nanoelements, can be easily achieved. Using full-sca…
We study the influence of the spin torque, which depends on the space and time derivative of magnetization, on magnetization reversal time in a ferromagnetic fine particle. The spin torque operates to dissipate the angular momentum of the magnetization precession, and the torque increases in a spin vortex structure. We calculate the magnetization reversal time under a DC magnetic field using the Landau-Lifshitz-Gilbert equation containing a spin torque term. We found that the spin torque changes the magnetization switching speed significantly during the reversal process by maintaining a spin v…
The role of the feedback effect on physical reservoir computing is studied theoretically by solving the vortex-core dynamics in a nanostructured ferromagnet. Although the spin-transfer torque due to the feedback current makes the vortex dynamics complex, it is clarified that the feedback effect does not always contribute to the enhancement of the memory function in a physical reservoir. The memory function, characterized by the correlation coefficient between the input data and the dynamical response of the vortex core, becomes large when the delay time of the feedback current is not an integr…
A vortex-antivortex dipole can be generated due to current with in-plane spin-polarization, flowing into a magnetic element, which then behaves as a spin transfer oscillator. Its dynamics is analyzed using the Landau-Lifshitz equation including a Slonczewski spin-torque term. We establish that the vortex dipole is set in steady state rotational motion due to the interaction between the vortices, while an external in-plane magnetic field can tune the frequency of rotation. The rotational motion is linked to the nonzero skyrmion number of the dipole. The spin-torque acts to stabilize the vortex …
Super-harmonic injection locking of single nano-contact (NC) spin-torque vortex oscillators (STVOs) subject to a small microwave current has been explored. Frequency locking was observed up to the fourth harmonic of the STVO fundamental frequency $f_{0}$ in microwave magneto-electronic measurements. The large frequency tunability of the STVO with respect to $f_{0}$ allowed the device to be locked to multiple sub-harmonics of the microwave frequency $f_{RF}$, or to the same sub-harmonic over a wide range of $f_{RF}$ by tuning the DC current. In general, analysis of the locking range, linewidth,…
In this paper, the spin transfer torque (STT) and the exchange coupling of the Josephson junctions containing interesting cases of diffusive/ballistic-triplet/singlet ferromagnetic superconductor materials together with diffusive Josephson junction of the form S$_{1}$/F$_{1}$/I$_1$/N/I$_2$/F$_2$ with I being insulating barrier are investigated. Using the Nazarov quantum circuit theory, it is found that for the diffusive FS$_1$/N/FS$_2$ structure the only emerged torque in normal direction to the plane of the exchange fields of F$_1$ and F$_2$ results in antiparallel/parallel or vice versa para…
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…
Physical reservoir computing is a type of recurrent neural network that applies the dynamical response from physical systems to information processing. However, the relation between computation performance and physical parameters/phenomena still remains unclear. This study reports our progress regarding the role of current-dependent magnetic damping in the computational performance of reservoir computing. The current-dependent relaxation dynamics of a magnetic vortex core results in an asymmetric memory function with respect to binary inputs. A fast relaxation caused by a large input leads to …
A vortex-antivortex (VA) dipole may be generated due to a spin-polarized current flowing through a nano-aperture in a magnetic element. We study the vortex dipole dynamics using the Landau-Lifshitz equation in the presence of an in-plane applied magnetic field and a Slonczewski spin-torque term with in-plane polarization. We establish that the vortex dipole is set in steady state rotational motion. The frequency of rotation is due to two independent forces: the interaction between the two vortices and the external magnetic field. The nonzero skyrmion number of the dipole is responsible for bot…
We analyze a quantum-classical hybrid system of steadily precessing slow classical localized magnetic moments, forming a head-to-head domain wall, embedded into an open quantum system of fast nonequilibrium electrons. The electrons reside within a metallic wire connected to macroscopic reservoirs. The model captures the essence of dynamical noncollinear and noncoplanar magnetic textures in spintronics, while making it possible to obtain the exact time-dependent nonequilibrium density matrix of electronic system and split it into four contributions. The Fermi surface contribution generates diss…
The Einstein-de Haas (EdH) effect and its reciprocal the Barnett effect are fundamental to magnetism and uniquely yield measures of the ratio of magnetic moment to total angular momentum. These effects, small and generally difficult to observe, are enjoying a resurgence of interest as contemporary techniques enable new approaches to their study. The high mechanical resonance frequencies in nanomechanical systems offer a tremendous advantage for the observation of EdH torques in particular. At radio frequencies, the EdH effect can become comparable to or even exceed in magnitude conventional cr…
We fabricated a current-perpendicular-to-plane pseudo-spin-valve nanopillar comprising a thick and a thin Co rings with deep submicron lateral sizes. The dc current can effectively induce the flux-closure vortex states in the rings with desired chiralities. Abrupt transitions between the vortex states are also realized by the dc current and detected with the giant magnetoresistance effect. Both Oersted field and spin-transfer torque are found important to the magnetic transitions, but the former is dominant. They can be designed to cooperate with each other in the vortex-to-vortex transitions …
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 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…
Current-driven vortex wall dynamics is studied by means of a two-dimensional analytical model and micromagnetic simulation. By constructing a trial function for the vortex wall in the magnetic wire, we analytically solve for domain wall velocity and deformation in the presence of the current-induced spin torque. A critical current for the domain wall transformation from the vortex wall to the transverse wall is calculated. A comparison between the field- and current-driven wall dynamics is carried out. Micromagnetic simulations are performed to verify our analytical results.
Spin-polarized radio frequency (RF) currents and RF-Oersted fields resonantly excite a magnetic vortex core confined in a micron-scale soft magnetic disk. In this study, we measured the rectifying voltage spectra caused by the anisotropic magnetoresistance oscillation due to the gyration of the vortex with different polarity and chirality. The measured spectra are presented such that we can determine the vortex properties and strength of the spin torques and Oersted field accurately and directly through analytical calculation.
The induced motion of a magnetic vortex in a micron-sized ferromagnetic disk due to the DC current injection is studied by measuring planar Hall effect. The DC current injection is found to induce the spin torque that sweeps the vortex out of the disk at the critical current while bias magnetic field are applied. The current-induced vortex core displacement deduced from the change in planar Hall resistance is quantitatively consistent with theoretical prediction. Peak structures similar to those originated from spin wave excitations are observed in the differential planar Hall resistance curve…
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.
Spin transfer magnetization dynamics have led to considerable advances in Spintronics, including opportunities for new nanoscale radiofrequency devices. Among the new functionalities is the radiofrequency(rf) detection using the spin diode rectification effect in spin torque nano-oscillators (STNOs). In this study, we focus on a new phenomenon, the resonant expulsion of a magnetic vortex in STNOs. This effect is observed when the excitation vortex radius, due to spin torques associated to rf currents, becomes larger than the actual radius of the STNO. This vortex expulsion is leading to a shar…
Hidden chirality and half-vortex formation in exciton-polariton condensates
School of Physics and Engineering, ITMO University（ITMO大学物理与工程学院）；Hybrid Photonics Laboratory, Skolkovo Institute of Science and Technology（斯科尔科沃科学技术学院混合光子学实验室）
The magnetization dynamics equation predicts that a domain wall that changes structure should undergo a displacement by itself - automotion - due to the relaxation of the linear momentum that is associated with the wall structure. We experimentally demonstrate this effect in soft nanostrips,transforming under spin transfer torque a metastable asymmetric transverse wall into a vortex wall. Displacements more than three times as large as under spin transfer torque only are measured for 1~ns pulses. The results are explained by analytical and numerical micromagnetics. Their relevance to domain wa…
Current-induced spin torque and magnetization dynamics in the presence of spin diffusion in magnetic textures is studied theoretically. We uncover an additional torque on the form \sim{\bm\nabla}^2[{\bf M}x({\bf u}\cdot{\bm \nabla}){\bf M}], where {\bf M} is the local magnetization and {\bf u} is the direction of injected current. This torque is inversely proportional to the square of the domain wall width (\approx\frac{1}{W^2}) and strongly depends on the domain wall structure. Whereas its influence remains moderate for transverse domain walls, it can significantly increase the transverse vel…
We present an experimental study of spin-torque driven vortex self-oscillations in magnetic nanocontacts. We find that above a certain threshold in applied currents, the vortex gyration around the nanocontact is modulated by relaxation oscillations, which involve periodic reversals of the vortex core. This modulation leads to the appearance of commensurate but also more interestingly here, incommensurate states, which are characterized by devil's staircases in the modulation frequency. We use frequency- and time-domain measurements together with advanced time-series analyses to provide experim…
We perform a comparative study of spin transfer induced excitation of the gyrotropic motion of a vortex core with either uniform or vortex spin polarizers. The microwave output voltage associated with the vortex dynamics, detected in both cases, displays a strong reduction of phase fluctuations in the case of the vortex polarizer, with a decrease of the peak linewidth by one order of magnitude down to 200kHz at zero field. A thorough study of rf emission features for the different accessible vortex configurations shows that this improvement is related to the excitation of coupled vortex dynami…
