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Tunable Mode Coupling in Nanocontact Spin-Torque Oscillators

Recent experiments on spin-torque oscillators have revealed interactions between multiple magneto-dynamic modes, including mode coexistence, mode hopping, and temperature-driven crossover between modes. The initial multimode theory indicates that a linear coupling between several dominant modes, arising from the interaction of the subdynamic system with a magnon bath, plays an essential role in the generation of various multimode behaviors, such as mode hopping and mode coexistence. In this work, we derive a set of rate equations to describe the dynamics of coupled magneto-dynamic modes in a nanocontact spin-torque oscillator. Here, expressions for both linear and nonlinear coupling terms are obtained, which allow us to analyze the dependence of the coupled dynamic behaviors of modes on external experimental conditions as well as intrinsic magnetic properties. For a minimal two-mode system, we further map the energy and phase difference of the two modes onto a two-dimensional phase space and demonstrate in the phase portraits how the manifolds of periodic orbits and fixed points vary with an external magnetic field as well as with the temperature.

36 MATERIALS SCIENCE↗

Associative memories using complex-valued Hopfield networks based on spin-torque oscillator arrays

Abstract Simulations of complex-valued Hopfield networks based on spin-torque oscillators can recover phase-encoded images. Sequences of memristor-augmented inverters provide tunable delay elements that implement complex weights by phase shifting the oscillatory output of the oscillators. Pseudo-inverse training suffices to store at least 12 images in a set of 192 oscillators, representing 16 × 12 pixel images. The energy required to recover an image depends on the desired error level. For the oscillators and circuitry considered here, 5% root mean square deviations from the ideal image require approximately 5 μ s and consume roughly 130 nJ. Simulations show that the network functions well when the resonant frequency of the oscillators can be tuned to have a fractional spread less than 10 −3 , depending on the strength of the feedback.

Prasad, Nitin (ORCID:0000000180880164)↗

Diameter dependence of emission power in MgO-based nano-pillar spin-torque oscillators

The dependence on diameter of the emission power in MgO-based nano-pillar spin torque oscillators (STOs) was systematically investigated. A maximum emission power of over 2.5 μW was obtained around 300 nm in diameter, which is the largest reported to date among the out-of-plane precession STOs. By analyzing physical quantities, precession cone angle of the free-layer magnetization was evaluated. In the diameter range below 300 nm, the increase in power was mainly due to the increase of the injected current. The power decrease above 300 nm is possibly attributed to the decrease in the averaged precession cone angle, suggesting spatial phase difference of magnetization precession. This study provides the method for estimating the optimum STO diameter, which is of great importance in practical use.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Temporal Pattern Recognition with Delayed-Feedback Spin-Torque Nano-Oscillators

The recent demonstration of neuromorphic computing with spin-torque nano-oscillators has opened a path to energy efficient data processing. The success of this demonstration hinged on the intrinsic short-term memory of the oscillators. We extend the memory of the spin-torque nano-oscillators through time-delayed feedback. We leverage this extrinsic memory to increase the efficiency of solving pattern recognition tasks that require memory to discriminate different inputs. Here, the large tunability of these nonlinear oscillators allows us to control and optimize the delayed-feedback memory using different operating conditions of applied current and magnetic field.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Simultaneous Optical and Electrical Spin-Torque Magnetometry with Phase-sensitive Detection of Spin Precession

Spin-based coherent information processing and encoding utilize the precession phase of spins in magnetic materials. However, the detection and manipulation of spin precession phases remain a major challenge for advanced spintronic functionalities. By using simultaneous electrical and optical detection, we demonstrate the direct measurement of the spin precession phase of a permalloy device driven by the spin-orbit torques from adjacent heavy metals. The spin Hall angle of the heavy metals can be independently determined from concurrent electrical and optical signals. The phase-sensitive optical detection also allows spatially-resolved measurements of local spin-torque parameters and ferromagnetic resonance with comprehensive amplitude and phase information. Here, our study offers a route toward future advanced characterizations of spin-torque oscillators, magnonic circuits, and tunneling junctions, where measuring the current-induced spin dynamics of individual nanomagnets is required.

36 MATERIALS SCIENCE↗

Mode coupling in spin torque oscillators

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, such as observed mode-hopping or mode coexistence. There has been some initial 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 rigorously derive such a theory starting with the Landau–Lifshitz–Gilbert equation for magnetization dynamics by expanding up to third-order terms in deviation from equilibrium. Here, our results show how a linear mode coupling, which is necessary for observed mode-hopping to occur, arises through coupling to a magnon bath. In conclusion, the acquired temperature dependence of this coupling implies that the manifold of orbits and fixed points may shift with temperature.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Engineering the Spectrum of Dipole Field-Localized Spin-Wave Modes to Enable Spin-Torque Antidamping

Auto-oscillation of a ferromagnet due to spin-orbit torques in response to a dc current is of wide interest as a flexible mechanism for generating controllable high-frequency magnetic dynamics. However, degeneracies of the spin-wave modes and nonlinear magnon-magnon scattering impede coherent precession. Discretization of the spin-wave modes can reduce this scattering. Furthermore, spatial localization of the spin-wave modes by the strongly inhomogeneous dipole magnetic field of a nearby spherical micromagnet provides variable spatial confinement, thus offering the option of systematic tunability of magnon spectrum for studying multimode interactions. Here we demonstrate that field localization generates a discrete spin-wave spectrum observable as a series of well-resolved localized modes in the presence of imposed spin currents arising from the spin Hall effect in a permalloy-platinum (Py/Pt) microstrip. The observation of linewidth reduction through damping control in this micromagnetically engineered spectrum demonstrates that localized modes can be controlled efficiently, an important step toward continuously tunable spin Hall effect–driven auto-oscillators.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Magnetic droplet soliton pairs

We demonstrate magnetic droplet soliton pairs in all-perpendicular spin-torque nano-oscillators (STNOs), where one droplet resides in the STNO free layer (FL) and the other in the reference layer (RL). Typically, theoretical, numerical, and experimental droplet studies have focused on the FL, with any additional dynamics in the RL entirely ignored. Here we show that there is not only significant magnetodynamics in the RL, but the RL itself can host a droplet driven by, and coexisting with, the FL droplet. Both single droplets and pairs are observed experimentally as stepwise changes and sharp peaks in the dc and differential resistance, respectively. While the single FL droplet is highly stable, the coexistence state exhibits high-power broadband microwave noise. Furthermore, micromagnetic simulations reveal that the pair dynamics display periodic, quasi-periodic, and chaotic signatures controlled by applied field and current. The strongly interacting and closely spaced droplet pair offers a unique platform for fundamental studies of highly non-linear soliton pair dynamics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

The zero-moment half metal: How could it change spin electronics?

The Heusler compound Mn{sub 2}Ru{sub x}Ga (MRG) may well be the first compensated half metal. Here, the structural, magnetic and transport properties of thin films of MRG are discussed. There is evidence of half-metallicity up to x = 0.7, and compensation of the two Mn sublattice moments is observed at specific compositions and temperatures, leading to a zero-moment half metal. There are potential benefits for using such films with perpendicular anisotropy for spin-torque magnetic tunnel junctions and oscillators, such as low critical current, high tunnel magnetoresistance ratio, insensitivity to external fields and resonance frequency in the THz range.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Resolving Discrepancies in Spin-Torque Ferromagnetic Resonance Measurements: Lineshape versus Linewidth Analyses

When spin-orbit torques are measured using spin-torque ferromagnetic resonance, two alternative ways of analyzing the results to extract the torque efficiencies—lineshape analysis and analysis of the change in linewidth versus direct current—often give inconsistent results. We identify a source for these inconsistencies. We show that fits of spin-torque ferromagnetic resonance data to the standard analysis framework leave significant residuals that we identify as due to (i) current-induced excitations of a small volume of magnetic material with magnetic damping much larger than that of the bulk of the magnetic layer, which we speculate is associated with the heavy-metal–magnet interface and (ii) oscillations of the sample magnetization at the modulation frequency due to heating. Here, the dependence of the residual signals on direct current can interfere with an accurate extraction of spin-torque efficiencies by the linewidth method. We show that the discrepancies between the two types of analysis can be largely eliminated by extrapolation of the window of magnetic fields used in the linewidth fits to small values so as to minimize the influence of the residual signals.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Field Characteristics of Spin-Torque Diode Sensitivity in the Presence of a Bias Current

The use of the spin-torque diode effect, which is generated upon the current-induced transfer of spin angular momentum in magnetic tunnel junctions, opens the prospect of considerably improving microwave sensitivity in the gigahertz frequency band over that of semiconductor Schottky diodes. In this work, the spin-diode effect of microwave signal rectification in a magnetic tunnel junction upon the resonant excitation of spin waves in the free magnetic layer as a result of the current-induced spin-transfer torque effect is analyzed theoretically. Frequency characteristics of the resonant response of a spin-torque diode to a microwave signal are calculated in the linear macrospin approximation as functions of the direction and value of the applied magnetic field and bias current. It is shown that with zero bias current, the maximum rectified voltage across a junction is obtained in the geometry of mutually perpendicular magnetizations of magnetic layers; as the resonant frequency of oscillations in a magnetic field increases, this voltage drops at the retained equilibrium orientation of spins in the layers. After the bias current is switched on, the resonance amplitude of forced oscillations of the free layer spins upon microwave excitation grows sharply at the critical point of the spin-torque diode’s loss of equilibrium state stability. The linewidth at this point is limited only by nonlinear effects. Improving spin-torque diode sensitivity is important for its use in microwave holographic vision systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Interface-driven spin-torque ferromagnetic resonance by Rashba coupling at the interface between nonmagnetic materials

The Rashba-Edelstein effect stems from the interaction between the electron's spin and its momentum induced by spin-orbit interaction at an interface or a surface. It was shown that the inverse Rashba-Edelstein effect can be used to convert a spin current into a charge current. Here, we demonstrate the reverse process of a charge-to spin-current conversion at a Bi/Ag Rashba interface. We show that this interface-driven spin current can drive an adjacent ferromagnet to resonance. We employ a spin-torque ferromagnetic resonance excitation/detection scheme which was developed originally for a bulk spin-orbital effect, the spin Hall effect. In our experiment, the direct Rashba-Edelstein effect generates an oscillating spin current from an alternating charge current driving the magnetization precession in a neighboring permalloy (Py, Ni 80 Fe 20 ) layer. As a result, electrical detection of the magnetization dynamics is achieved by a rectificationmechanism of the time dependent multilayer resistance arising from the anisotropic magnetoresistance.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Spin-torque driven magnetization switching in ferromagnetic nanopillar with pinned layer biasing configuration

Magnetization switching driven by spin transfer torque in a ferromagnetic nanopillar by biasing the angular polarizer with different orientation has been studied. The free layer dynamics includes the spin torque from the oscillating free layer with magneto crystalline anisotropy and shape anisotropy, which is governed by the Landau-Lifshitsz-Gilbert-Slonczweski (LLGS) equation and solving it numerically by using embedded Runge Kutta fourth order method. Results of numerical simulation shows that there is a drastic reduction of switching time in the free layer by the orientation of angular polarizer of the nano pillar device. We fixed the angular polarizer as 0°, 30°, 60°, 90° and the corresponding switching time is 6.53 ns, 4.36 ns, 2.25 ns and 1.21 ns respectively for an applied current density of 5 × 10{sup 11} Am{sup −2}.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Spin-torque ferromagnetic resonance measurements utilizing spin Hall magnetoresistance in W/Co 40 Fe 40 B 20 /Mg O structures

Here, we study the magnetic properties of W/Co 40 Fe 40 B 20 (CoFeB)/MgO films using the spin-torque ferromagnetic resonance (ST-FMR) technique. This study takes the advantage of the spin Hall magnetoresistance (SMR) for generating an oscillating resistance, which is one of the necessary requirements for obtaining mixing voltage in the ST-FMR technique. We have measured both the as-grown and the annealed samples with different CoFeB layer thicknesses, which include the in-plane and out-of-plane magnetic anisotropies. The spectra for these two types of anisotropies show distinct signatures. By analyzing the ST-FMR spectra, we extract the effective anisotropy field for both types of samples. In addition, we investigate the influence of CoFeB thickness and annealing on the Gilbert damping constant. Our experiments show that by taking advantage of SMR, the ST-FMR measurement acts as an effective tool with high sensitivity for studying the magnetic properties of ultrathin magnetic films.

42 ENGINEERING↗

High-Frequency Dynamics Modulated by Collective Magnetization Reversal in Artificial Spin Ice

Spin-torque ferromagnetic resonance arises in heavy metal-ferromagnet heterostructures when an alternating charge current is passed through the bilayer stack. The methodology to detect the resonance is based on the anisotropic magnetoresistance, which is the change in the electrical resistance due to different orientations of the magnetization. In connected networks of ferromagnetic nanowires, known as artificial spin ice, the magnetoresistance is rather complex owing to the underlying collective behavior of the geometrically frustrated magnetic domain structure. Here, we demonstrate spin-torque ferromagnetic resonance investigations in a square artificial spin-ice system and correlate our observations to magneto-transport measurements. The experimental findings are described using a simulation approach that highlights the importance of the correlated dynamics response of the magnetic system. Here, our results open the possibility of designing reconfigurable microwave oscillators and magnetoresistive devices based on connected networks of nanomagnets.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗