Spin Torque Oscillator Research Articles

Linewidth Variation of the Higher Harmonics in Spin-Torque Vortex Oscillators

We have studied microwave emission due to vortex gyration in pseudo-spin-valve nanopillar devices. Subgigahertz emission spectra with a large number of higher harmonics are found with linewidth of the fundamental peak as low as ~500 kHz. Several distinct gyration modes exist whose peak frequencies are separated by a few tens of megahertz, likely corresponding to magnetic oscillations with different metastable vortex core trajectories. In a single spectral measurement, however, only one of the distinct modes appears, indicating that the excited mode is stable. The linewidth of higher harmonics, in many cases, increases linearly with the harmonic number n, indicating that the frequency-amplitude coupling is significant. These results show the strong nonisochronous characteristics of spin-torque vortex oscillators.

Recent Advances in Nanocontact Spin-Torque Oscillators

We present a comprehensive review of the most recent advances in nanocontact spin torque oscillators (NC-STOs). NC-STOs are highly tunable, with both applied magnetic field and dc, broadband microwave signal generators. As opposed to the nanopillar geometry, where the lateral cross section of the entire device has been confined to a typically <;100 nm diameter, in NC-STOs, it is only the current injection site that has been laterally confined on top of an extended magnetic film stack. Three distinct material combinations will be discussed: 1) a Co/Cu/NiFe pseudospin valve (PSV) where both the Co and NiFe have a dominant in-plane anisotropy; 2) a Co/Cu/[Co/Ni] <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> orthogonal PSV where the Co/Ni multilayer has a strong perpendicular anisotropy; and 3) a single NiFe layer with asymmetric non-magnetic Cu leads. We explore the rich and diverse magnetodynamic modes that can be generated in these three distinct sample geometries.

Hysteretic Synchronization in Spin-Torque Nanocontact Oscillators: A Micromagnetic Study

Several experiments report the presence of finite jumps in the properties of spin-torque oscillators at room temperature, such as oscillation frequency and power as functions of current or field. On the basis of micromagnetic simulations, this paper links those experimental discontinuities to the changes in the curve slope numerically observed in the absence of thermal effects. Our numerical results show the key ingredient triggering this behavior is the presence of abrupt changes in the oscillation axis of the magnetization precession. We also predict that by fixing the bias point of the oscillator near those critical regions, it is possible to observe hysteretic synchronization. This result should be a key point in the design of nanoscale on-chip phase-locked loop receivers with improved sensitivity.

Investigation of the Tunability of the Spin Configuration Inside Exchange Coupled Springs of Hard/Soft Magnets

Magnetic multilayer (ML) structures comprising a perpendicular magnetic anisotropy (PMA) layer coupled to an in-plane magnetic anisotropy (IMA) layer are promising materials for zero/low field operating spin-torque oscillators and bit patterned recording media. The magnetization tilt angle can be easily tuned by varying the IMA layer thickness due to the competition between PMA and IMA layers. To explore the underlying magnetization reversal mechanism and to further understand the control of tilt angle and uniformity of the magnetization, the IMA (NiFe, Co, and CoFeB)/PMA (Co/Pd MLs) exchange spring systems are systematically studied. Experimental data obtained from magnetometry show good agreement with 1-D micromagnetic simulations, allowing us to design tunable exchange coupled spring as a function of IMA thickness.

Effect of Excitation Fatigue on the Synchronization of Multiple Nanocontact Spin-Torque Oscillators

Nanocontact spin-torque oscillators (NC-STOs) act as intrinsically nanoscale and highly current and magnetic field tunable, ultrawide band microwave signal generators. However, their low output power and high phase noise remain critical obstacles toward actual applications. Mutual synchronization of multiple NCs is one possibility to overcome these shortcomings. This letter presents a detailed study of the mutual synchronization in a NC-STO with two NCs. In particular, the effect of repeated measurements on the synchronization behavior is explored. Repeated measurements at high drive currents are shown to significantly degrade the performance of the devices with the most striking consequence being that the devices can no longer be synchronized. Ferromagnetic resonance measurements reveal a decrease in the saturation magnetization and an increase in the damping coefficient in annealed NiFe films, consistent with Cu diffusion into the NiFe from the adjacent Cu layers. This increase in damping will act to sever the spin wave-mediated communication channel between the NCs necessary for synchronization. These results highlight an important consideration when studying the synchronization behavior of multi-NC devices where Joule heating is expected to scale unfavorably with the number of NCs.

Self-Modulated Soliton Modes Excited in a Nanocontact Spin-Torque Oscillator

Self-modulated bubble-like solitons, namely droplets, recently observed in spin-torque nanooscillators with a perpendicular free layer, are promising for applications in spintronics, magnonics, and magnetic logic devices. This letter presents a micromagnetic analysis on soliton dynamics. Our results identify the role of physical parameters (i.e., external field, saturation magnetization, and exchange constant) in achieving experimental findings such as hysteretic, linear and nonlinear spin-wave excitations. The modes with different excitation frequencies have nonuniform spatial distributions of power, and the power of frequency sidebands is mostly located near the outer border of the nanocontact. At high currents, a wavelet-based analysis highlights that the magnetoresistive signal due to the sideband modes is not stationary, providing a possible origin of the asymmetric sidebands observed in spintronic self-modulators. We also identify the thermal field as the key ingredient for the excitation of linear modes in a subcritical regime.

Advanced Circuit-Level Model of Magnetic Tunnel Junction-based Spin-Torque Oscillator with Perpendicular Anisotropy Field

Interest in spin-torque oscillators (STOs) has been increasing due to their potential use in communication devices. In particular the magnetic tunnel junction-based STO (MTJ-STO) with high perpendicular anisotropy is gaining attention since it can generate high output power. In this paper, a circuit-level model for an in-plane magnetized MTJSTO with partial perpendicular anisotropy is proposed. The model includes the perpendicular torque and the shift field for more accurate modeling. The bias voltage dependence of perpendicular torque is represented as quadratic. The model is written in Verilog-A, and simulated using HSPICE simulator with a current-mirror circuit and a multi-stage wideband amplifier. The simulation results show the proposed model can accurately replicate the experimental data such that the power increases and the frequency decreases as the value of the perpendicular anisotropy gets close to the value of the demagnetizing field.

Zero field high frequency oscillations in dual free layer spin torque oscillators

We observe microwave oscillations in relatively simple spin valve spin torque oscillators consisting of two in-plane free layers without spin polarizing layers. These devices exhibit two distinct modes which can reach frequencies &amp;gt;25 GHz in the absence of an applied magnetic field. Macrospin simulations identify these two modes as optical and acoustic modes excited by the coupling of the two layers through dipole field and spin torque effects. These results demonstrate the potential of this system as a large output power, ultrahigh frequency signal generator that can operate without magnetic field.

Mutually synchronized bottom-up multi-nanocontact spin–torque oscillators

Spin-torque oscillators offer a unique combination of nanosize, ultrafast modulation rates and ultrawide band signal generation from 100 MHz to close to 100 GHz. However, their low output power and large phase noise still limit their applicability to fundamental studies of spin-transfer torque and magnetodynamic phenomena. A possible solution to both problems is the spin-wave-mediated mutual synchronization of multiple spin-torque oscillators through a shared excited ferromagnetic layer. To date, synchronization of high-frequency spin-torque oscillators has only been achieved for two nanocontacts. As fabrication using expensive top-down lithography processes is not readily available to many groups, attempts to synchronize a large number of nanocontacts have been all but abandoned. Here we present an alternative, simple and cost-effective bottom-up method to realize large ensembles of synchronized nanocontact spin-torque oscillators. We demonstrate mutual synchronization of three high-frequency nanocontact spin-torque oscillators and pairwise synchronization in devices with four and five nanocontacts.

Analytical theory of modulated magnetic solitons

Droplet solitons are coherently precessing solitary waves that have been recently realized in thin ferromagnets with perpendicular anisotropy. In the strongly nonlinear regime, droplets can be well approximated by a slowly precessing, circular domain wall with a hyperbolic tangent form. Utilizing this representation, this work develops a general droplet modulation theory and applies it to study the long-range effects of the magnetostatic field and a nanocontact spin torque oscillator (NC-STO) where spin polarized currents act as a gain source to counteract magnetic damping. An analysis of the dynamical equations for the droplet's center, frequency, and phase demonstrates a negative precessional frequency shift due to long-range dipolar interactions, dependent on film thickness. Further analysis also demonstrates the onset of a saddle-node bifurcation at the minimum sustaining current for the NC-STO. The basin of attraction associated with the stable node demonstrates that spin torque enacts a restoring force to excursions of the droplet from the nanocontact center, observed previously in numerical simulations. Large excursions lead to the droplet's eventual decay into spin waves.

Magnetic droplet solitons in orthogonal nano-contact spin torque oscillators

We study microwave signal generation as a function of drive current and applied perpendicular magnetic field in nano-contact spin torque oscillators (NC-STOs) based on orthogonal (pseudo) spin valves where the Co fixed layer has strong easy-plane anisotropy, and the [Co/Ni] free layer has a strong perpendicular magnetic anisotropy. The orthogonal NC-STOs exhibit a dramatic transition from the conventional ferromagnetic resonance-like spin wave mode to a magnetic droplet soliton mode. In particular, the field and current dependence of the droplet soliton near threshold are discussed. Near threshold the droplet soliton undergoes complex dynamics that include mode hopping, as evident in the experimental frequency domain and magnetoresistance response.

Non-stationary excitation of two localized spin-wave modes in a nano-contact spin torque oscillator

We measure and simulate micromagnetically a framework based upon a nano-contact spin torque oscillator where two distinct localized evanescent spin-wave modes can be detected. The resulting frequency spectrum is composed by two peaks, corresponding to the excited modes, which lie below the ferromagnetic resonance frequency, and a low-frequency tail, which we attribute to the non-stationary switching between these modes. By using Fourier, wavelet, and Hilbert-Huang transforms, we investigate the properties of these modes in time and spatial domains, together with their spatial distribution. The existence of an additional localized mode (which was neither predicted by theory nor by previous numerical and experimental findings) has to be attributed to the large influence of the current-induced Oersted field strength which, in the present setup, is of the same order of magnitude as the external field. As a further consequence, the excited spin-waves, contrarily to what usually assumed, do not possess cylindrical symmetry: the Oersted field induces these modes to be excited at the two opposite sides of the region beneath the nano-contact.

Synchronization of propagating spin-wave modes in a double-contact spin-torque oscillator: A micromagnetic study

This work tackles theoretical investigations on the synchronization of spin-wave modes generated by spin-transfer-torque in a double nano-contact geometry. The interaction mechanisms between the resulting oscillators are analyzed in the case of propagating modes which are excited via a normal-to-plane magnetic bias field. To characterize the underlying physical mechanisms, a multi-domain analysis is performed. It makes use of an equivalent electrical circuit, to deduce the output electrical power, and of micromagnetic simulations, through which information on the frequency spectra and on the spatial distribution of the wavefront of the emitted spin-waves is extracted. This study provides further and intriguing insights into the physical mechanisms giving rise to synchronization of spin-torque oscillators.

Micro-TEG Voltage Supplies for Spin Torque Oscillators

Spin torque oscillators (STOs) can be viewed as current-controlled oscillators. Oscillations start if the current exceeds some critical value-threshold current. A low critical current is required to achieve a high output power. Recently, the critical current was reduced to as low as 0.1 mA and STO majority gate was proposed. To operate STO logic, an mV-level voltage source with output current greater than the critical current (0.1 mA), and very low impedance is needed. This paper proposes power supplies that use microthermoelectric generators (μTEGs) to convert heat into electric power. A complete analytical μTEG model was developed that includes all the relevant physical effects. This model is used to predict power and perform geometry optimization to maximize thermal energy conversion. We propose metallic thermocouples to realize the low impedance source and connect them electrically in parallel to deliver sufficient current. The proposed μTEG consists of four thermocouples connected in parallel both thermally and electrically. Thermo-legs are homogeneous and thermally isolated with a thermal isolation cavity to minimize heat leakage. Simulations with a 30-K temperature drop across μTEGs showed that the proposed structure can potentially integrate ~ 50 000 μTEGs/cm2 and efficiently harvest heat to supply new STO logic.

Physics-Based SPICE-Compatible Compact Model for Simulating Hybrid MTJ/CMOS Circuits

A simulation framework that can comprehend the impact of material changes from the device level to the system level design can be of great value, especially to evaluate the impact of emerging devices on various applications. To that effect, we developed a SPICE-based hybrid magnetic tunnel junction (MTJ)/CMOS simulator, which can be used to explore new opportunities in large scale system design. In the proposed simulation framework, MTJ modeling is based on Landau-Lifshitz-Gilbert (LLG) equation incorporating both spin-torque and external magnetic field(s). LLG, along with heat diffusion equation, thermal variations, and electron transport, is implemented using SPICE-in-built voltage-dependent current sources and capacitors. The proposed simulation framework is flexible because the physical device parameters such as MgO thickness, ferromagnet material anisotropy (Ku), and device dimensions are user-defined parameters. Furthermore, we benchmarked this model with experiments in terms of switching current density (JC), switching time (TSWITCH), and tunneling magnetoresistance. Finally, we used the simulation framework to study different MTJ structures, such as in-plane magnet anisotropy and perpendicular magnet anisotropy, the impact of parametric process variations and temperature on the yield of spin transfer torque magnetoresistive random access memories, magnetic flip-flops, and spin-torque oscillators.

A comparison between advanced time–frequency analyses of non-stationary magnetization dynamics in spin-torque oscillators

We report re`sults of different time–frequency analyses (Wavelet and Hilbert–Huang Transform (HHT)) of voltage measurements related to a spin-torque oscillator working in a regime of non-stationary dynamics. Our results indicate that the Wavelet analysis identifies the non-stationary magnetization dynamics revealing the existence of intermittent and independent excited modes while the HHT is able to accurately extract the time domain traces of each independent mode. Overall performance indicates a route for a complete characterization of time–frequency domain data of a STO, pointing out that the combined Wavelet-HHT methodology developed is general and can be also used for a variety of other different scenarios.

Out-of-plane precession of an in-plane magnetized free layer submitted to the spin-transfer torque of a perpendicular polarizer: An analytical perturbative approach

An analytical perturbative approach is presented to calculate the out-of-plane precessional motion of the magnetization of an in-plane free layer submitted to the spin torque of a perpendicular polarizer in the macrospin model. We consider the effects of the uniaxial anisotropy field, of an in-plane applied field, and of the perturbation due to the in-plane reference layer on the otherwise circular and monochromatic oscillations of the free layer. We calculate the frequency change due to these perturbations, the amplitude of the second harmonics, and the critical current for the existence of oscillations. This approach is rather general in the treatment of harmonics in spin torque oscillators

Beyond first-order finite element schemes in micromagnetics

Magnetization dynamics in ferromagnetic materials is ruled by the Landau–Lifshitz–Gilbert equation (LLG). Reliable schemes must conserve the magnetization norm, which is a nonconvex constraint, and be energy-decreasing unless there is pumping. Some of the authors previously devised a convergent finite element scheme that, by choice of an appropriate test space – the tangent plane to the magnetization – reduces to a linear problem at each time step. The scheme was however first-order in time. We claim it is not an intrinsic limitation, and the same approach can lead to efficient micromagnetic simulation. We show how the scheme order can be increased, and the nonlocal (magnetostatic) interactions be tackled in logarithmic time, by the fast multipole method or the non-uniform fast Fourier transform. Our implementation is called feeLLGood. A test-case of the National Institute of Standards and Technology is presented, then another one relevant to spin-transfer effects (the spin-torque oscillator).

Time Domain Mapping of Spin Torque Oscillator Effective Energy

Stochastic dynamics of spin torque oscillators 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 spin torque oscillator. We show that the effective energy approach provides a simple recipe for predicting spectral linewidths and line shapes near the generation threshold. Our time domain technique also accurately measures the fieldlike component of spin torque in a wide range of the voltage bias values.

Resonant and non-resonant microwave absorption as a probe of the magnetic dynamics and switching in spin valves

We use the resonant and non-resonant microwave absorption to probe the dynamic and static magnetic parameters of weakly coupled spin valves. The sample series include spin valve structures with varying thickness of the non-magnetic metallic spacer and reference samples comprised only a free or fixed magnetic layer. Beside the common resonance absorption peaks, the observed microwave spectra present step-like features with hysteretic behavior. The latter effect is a direct manifestation of the interlayer coupling between the ferromagnetic layers and provides two static magnetic parameters, the switching field and coercivity of the fixed layer. The analysis of the microwave absorption spectra under in-plane rotation of the applied magnetic field at different spacer thicknesses permits a deeper insight in the magnetic interactions in this system as compared to the conventional magnetometry. We combine the standard Smit-Beljers formalism for the angular dependence of the resonance fields with a Landau-Lifshitz-Gilbert dynamics extended to describe in detail the intensity of microwave absorption in the spin valves. In this way, we extract a set of parameters for each layer including the effective magnetization and anisotropy, exchange bias and interlayer coupling, as well as Gilbert damping. The model reproduces well the experimental findings, both qualitatively and quantitatively, and the estimated parameters are in a reasonable agreement with the values known from the literature. The proposed theoretical treatment can be adopted for other multilayered dynamic systems as, e.g., spin-torque oscillators.