Spin-transfer Nano-oscillators Research Articles

Response to noise of a vortex based spin transfer nano-oscillator

We investigate experimentally and analytically the impact of thermal noise on the sustained gyrotropic mode of vortex magnetization in spin transfer nano-oscillators and its consequence on the linewidth broadening due to the different nonlinear contributions. Performing time domain measurements, we are able to extract separately the phase noise and the amplitude noise at room temperature for several values of dc current and perpendicular field. For a theoretical description, we extend the general model of nonlinear auto-oscillators to the case of vortex core dynamics and provide analytical expressions of the parameters describing the response to noise of the system. From the analysis of our experimental results, we demonstrate the major role of the amplitude-to-phase noise conversion on the linewidth broadening, and propose several solutions to increase even more the spectral coherence of vortex-based spin transfer nano-oscillators.

Dissipative structures induced by spin-transfer torques in nanopillars.

Macroscopic magnetic systems subjected to external forcing exhibit complex spatiotemporal behaviors as result of dissipative self-organization. Pattern formation from a uniform magnetization state, induced by the combination of a spin-polarized current and an external magnetic field, is studied for spin-transfer nano-oscillator devices. The system is described in the continuous limit by the Landau-Lifshitz-Gilbert equation. The bifurcation diagram of the quintessence parallel state, as a function of the external field and current, is elucidated. We have shown analytically that this state exhibits a spatial supercritical quintic bifurcation, which generates in two spatial dimensions a family of stationary stripes, squares, and superlattice states. Analytically, we have characterized their respective stabilities and bifurcations, which are controlled by a single dimensionless parameter. This scenario is confirmed numerically.

Spin-torque nano-oscillator based on a synthetic antiferromagnet free layer and perpendicular to plane polarizer

Coupled free layers systems used as active elements in spin-transfer nano-oscillators (STNOs) can have improved microwave performances in terms of linewidth or tunability. Here, we report a numerical study on the magnetization dynamics of a synthetic antiferromagnet (SAF) driven by a perpendicularly spin-polarized current and an in-plane applied magnetic field. Compared to the single free layer STNO, the current-field state diagrams, derived for strong and weak RKKY exchange coupling strength inside the SAF, show a more complex structure, with new static or dynamic states (chaotic dynamics), and also a larger zone of out-of-plane precession state (OPP) oscillations. The OPP frequency behaviour is generally similar to that of the single free layer STNO except for the zone near the chaotic dynamics and for fields larger than the spin-flop field of the SAF, where several frequency jumps have been observed.

Ultralow-current-density and bias-field-free spin-transfer nano-oscillator

The spin-transfer nano-oscillator (STNO) offers the possibility of using the transfer of spin angular momentum via spin-polarized currents to generate microwave signals. However, at present STNO microwave emission mainly relies on both large drive currents and external magnetic fields. These issues hinder the implementation of STNOs for practical applications in terms of power dissipation and size. Here, we report microwave measurements on STNOs built with MgO-based magnetic tunnel junctions having a planar polarizer and a perpendicular free layer, where microwave emission with large output power, excited at ultralow current densities, and in the absence of any bias magnetic fields is observed. The measured critical current density is over one order of magnitude smaller than previously reported. These results suggest the possibility of improved integration of STNOs with complementary metal-oxide-semiconductor technology, and could represent a new route for the development of the next-generation of on-chip oscillators.

Spin transfer nano-oscillators

The use of spin transfer nano-oscillators (STNOs) to generate microwave signals in nanoscale devices has aroused tremendous and continuous research interest in recent years. Their key features are frequency tunability, nanoscale size, broad working temperature, and easy integration with standard silicon technology. In this feature article, we give an overview of recent developments and breakthroughs in the materials, geometry design and properties of STNOs. We focus in more depth on our latest advances in STNOs with perpendicular anisotropy, showing a way to improve the output power of STNO towards the μW range. Challenges and perspectives of the STNOs that might be productive topics for future research are also briefly discussed.

PROGRESS ON MAXIMIZING OUTPUT POWER IN SPIN TRANSFER NANO-OSCILLATORS

This paper reviews the current status of maximizing output power in spin transfer nano-oscillators (STNOs). The key factors affecting output power and the methods to maximize output power in STNOs are briefly introduced. The recent development trends for STNOs are also reviewed in this paper. This article is one of a series devoted to the subject of Latest Progress on Spintronics Devices.

High-Power Coherent Microwave Emission from Magnetic Tunnel Junction Nano-oscillators with Perpendicular Anisotropy

The excitation of the steady-state precessions of magnetization opens a new way for nanoscale microwave oscillators by exploiting the transfer of spin angular momentum from a spin-polarized current to a ferromagnet, referred to as spin-transfer nano-oscillators (STNOs). For STNOs to be practical, however, their relatively low output power and their relatively large line width must be improved. Here we demonstrate that microwave signals with maximum measured power of 0.28 μW and simultaneously narrow line width of 25 MHz can be generated from CoFeB-MgO-based magnetic tunnel junctions having an in-plane magnetized reference layer and a free layer with strong perpendicular anisotropy. Moreover, the generation efficiency is substantially higher than previously reported STNOs. The results will be of importance for the design of nanoscale alternatives to traditional silicon oscillators used in radio frequency integrated circuits.

Autonomous and forced dynamics in a spin-transfer nano-oscillator: Quantitative magnetic-resonance force microscopy

Using a magnetic-resonance force microscope (MRFM), the power emitted by a spin-transfer nano-oscillator consisting of a normally magnetized Py$|$Cu$|$Py circular nanopillar is measured both in the autonomous and forced regimes. From the power behavior in the subcritical region of the autonomous dynamics, one obtains a quantitative measurement of the threshold current and of the noise level. Their field dependence directly yields both the spin torque efficiency acting on the thin layer and the nature of the mode which first auto-oscillates: the lowest energy, spatially most uniform spin-wave mode. From the MRFM behavior in the forced dynamics, it is then demonstrated that in order to phase lock this auto-oscillating mode, the external source must have the same spatial symmetry as the mode profile, i.e., a uniform microwave field must be used rather than a microwave current flowing through the nanopillar.

Thermally induced synchronization and stochastic resonance between magnetization regimes in spin-transfer nano-oscillators

The thermally induced synchronization of transitions between different magnetization regimes with weak ac-injected spin-polarized current is considered for a spin-valve-like magnetic nano-system, where magnetization dynamics is described by the Landau-Lifshitz-Slonczewski equation. We apply suitable averaging techniques and derive a non-autonomous stochastic differential equation for the free energy. By using this equation, we demonstrate that synchronization of thermal transitions with weak ac excitation is ascribed to a general form of stochastic resonance. Numerical computations confirm the accuracy of the theory.

Analysis of magnetization instability patterns in spin-transfer nano-oscillators

The stability of large precessional magnetization motions induced by spin-polarized currents in spin-transfer nano-oscillators is discussed. Quantitative analytical predictions are obtained for the critical values of spin-polarized injected current and external magnetic field at which the oscillator magnetization precession becomes unstable. It is shown that the mechanism leading to instability is parametric resonance of well-defined pairs of magnetostatically coupled perturbation modes. The amplitude of these modes grows to large non-thermal values when the oscillator frequency matches the mean of the natural frequencies of the two coupled modes. Analytical predictions are obtained for the space-time structure and symmetry of the magnetization patterns that are formed at the instability. Analytical results are compared with numerical simulations of spin-transfer-driven magnetization dynamics.

Stochastic resonance in noise-induced transitions between self-oscillations and equilibria in spin-valve nanomagnets

The thermally induced synchronization between magnetization transitions and ``weak'' ac excitations is studied for spin-transfer oscillators. A theoretical approach, based on the separation of time scales, is developed to investigate this physical phenomenon. By applying the appropriate averaging technique to the Fokker-Planck equation associated with the stochastic magnetization dynamics, a stochastic differential equation for the ``slow'' (energy) variable is derived. This equation is used to analyze intrawell thermal transitions between magnetization equilibria and self-oscillations. It is demonstrated that the thermally induced synchronization between magnetization transitions and ac excitation can be viewed as a stochastic resonance effect. It is shown that this effect occurs in spin-transfer nano-oscillators both in the classical case of subthreshold ac excitation as well as in the suprathreshold case. The theoretical predictions are in very good agreement with simulations of the Landau-Lifshitz-Slonczewski dynamics.

Analysis of synchronized regimes for injection-locked spin-transfer nano-oscillators

The large-angle magnetization dynamics of an injection-locked spin-transfer nano-oscillator (STNO) is studied. The magnetic system is subject to the action of time-varying spin-polarized currents and external magnetic fields. The uniform mode theory is developed and describes the hysteretic synchronization mechanism in terms of bifurcations of equilibria and limit cycles of appropriate dynamical systems. Analytical predictions of control parameters for the synchronization between the magnetization self-oscillation and the external microwave excitations (current, field) are provided. The effect of temperature on the locking band and the hysteretic character of the oscillation response is analyzed. An analytical approach is developed to determine the thermally induced sidebands in the power spectral density of phase-locked oscillations as a function of control parameters. The analytical predictions are in good agreement with the results of numerical simulations.

Properties of magnetic nanodots with perpendicular anisotropy

Nanodots with magnetic vortices have many potential applications, such as magnetic memories and spin-transfer nano-oscillators. Adding a perpendicular anisotropy term to the magnetic energy of the nanodot, it becomes possible to tune the vortex core properties. This can be obtained, e.g., in Co nanodots by varying the thickness of the Co layer in a Co/Pt stack. Here we discuss the spin configuration of circular and elliptical nanodots for different perpendicular anisotropies; we show for nanodisks that micromagnetic simulations and analytical results agree. Increasing the perpendicular anisotropy, the vortex core radii increase, the phase diagrams are modified, and other configurations appear; the knowledge of these phase diagrams is relevant for the choice of optimum nanodot dimensions for applications. MFM measurements on Co/Pt multilayers confirm the trend of the vortex core diameters with varying Co layer thicknesses.

Analysis of thermally induced magnetization dynamics in spin-transfer nano-oscillators

The thermally induced magnetization dynamics in the presence of spin-polarized currents injected into a spin-valve-like structure used as microwave spin-transfer nano-oscillator (STNO) is considered. Magnetization dynamics is described by the stochastic Landau-Lifshitz-Slonczewski (LLS) equation. First, it is shown that, in the presence of thermal fluctuations, the spectrum of the output signal of the STNO exhibits multiple peaks at low and high frequencies. This circumstance is associated with the occurrence of thermally induced transitions between stationary states and magnetization self-oscillations. Then, a theoretical approach based on the separation of time-scales is developed to obtain a stochastic dynamics only in the slow state variable, namely the energy. The stationary distribution of the energy and the aforementioned transition rates are analytically computed and compared with the results of direct integration of the LLS dynamics, showing very good agreement.

Injection locking of tunnel junction oscillators to a microwave current

Injection locking of a spin transfer nano-oscillator, based on an in-plane magnetized magnetic tunnel junction and generating the frequency f0, to an external signal of varying frequency fe is studied experimentally and with macrospin simulations. It is shown, that if the driving signal has the form of a microwave current, the locking effect is well-pronounced near fe≅2f0, but is almost completely absent near fe≅f0, confirming predictions of analytical theory. It is also shown that noise plays an important role in the locking process, causing the linewidth of the locked oscillation to substantially exceed that of the driving signal.

Micromagnetic study of phase-locking in spin-transfer nano-oscillators driven by currents and ac fields

The magnetization dynamics of a spin-transfer nano-oscillator is studied for a system subject to the combined action of dc spin-polarized electric current and microwave circularly polarized applied field. The uniform mode theory is developed for a spin-valve with an arbitrary orientation of the polarizer. The theory enables one to predict the control parameters for the synchronization between the magnetization self-oscillation and the external microwave field. Full micromagnetic simulations are performed with the predicted control parameters, and they demonstrate the hysteretic nature of the synchronization in very good agreement with the theory.

Bottom-up approach for the fabrication of spin torque nano-oscillators

We report on a bottom-up approach for the fabrication of spin-transfer nano-oscillators (STNOs). Porous alumina is used as a template for the growth by electrodeposition of metallic spin valves in series. Under specific magnetic field and injected current conditions, emission of microwave current is detected with frequency in the 1.5 GHz range and linewidth as low as 8 MHz. We find strong indications that the microwave emission is due to spin-transfer-driven vortex oscillations. This technique is promising for the fabrication of dense arrays of STNOs in view of device synchronization.

Synchronization of spin-transfer nanooscillator using phase-locking loop

It is suggested to use the phase locking (PL) principle for solving problems of synchronization and coherent power addition for spin-transfer microwave nanooscillators employing the phenomenon of magnetization oscillations in the microwave range excited by a spin-polarized current. The dynamics of a model spin-transfer oscillator with an inertial PL loop is considered. The regions of parameters corresponding to various dynamic regimes (synchronous, quasi- synchronous, beats) have been determined using bifurcation analysis. It is shown that the band of existence of synchronous regimes for a spin-transfer nanooscillator with a PL loop increases as compared to the analogous system synchronized by an external field.

Frequency shift of spin waves in tunnel-junction spin-transfer nano-oscillators

The excitations of microwave spin waves in magnetic tunnel junctions are theoretically investigated. An analytical approach which describes the dependence of the microwave precession frequency on the applied voltage is developed. It is shown that the spin-wave frequency is directly related to both the in-plane and perpendicular spin-transfer torques. In the low field regime the perpendicular torque can induce changes in the slope of the oscillation frequency versus applied voltage (df/dv) from negative (redshift) to positive (blueshift) values.

Micromagnetic analysis of injection locking in spin-transfer nano-oscillators

The injection-locking mechanism of a spin-transfer nano-oscillator is studied for a system which is traversed by a spin-polarized electric current with both dc and ac components. The uniform mode theory is used to predict the control parameters for the synchronization between the magnetization self-oscillation and the external microwave current. It is found that micromagnetic simulations at zero temperature are in very good agreement with the theory, showing that magnetization dynamics is practically uniform in space. Then, the effect of temperature on synchronized regimes is analyzed. The locking band as well as the hysteretic character of the oscillation response are determined as function of the control parameters. Computations of the power spectral densities (PSD) of injection-locked and unlocked oscillations reveal that synchronized oscillations are quite stable with respect to thermal fluctuations. Secondary peaks in the PSD of injection-locked oscillations are reported and theoretically explained.