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Magnetic skyrmion-based spin-torque nano-oscillators (STNOs) have attracted significant interest because of their potential applications as microwave signal emitters and integrability in the existing CMOS process flow. However, the stable circular motion of the skyrmion in the nanodisk is affected by the Magnus force, which can destroy and annihilate the skyrmion at the nanodisk edge, thereby limiting the application of the maximum oscillation frequency. To overcome this problem, we investigated the influence of a modified magnetized structure at the edge of the nanodisk on the oscillation dynamics of skyrmions, in which the modified magnetized profile is acquired by local modification of the magnetic material parameters, and these skyrmions can move along the tilting magnetization formatted wall. It was found that the upper threshold for steady skyrmion oscillations can be improved by approximately two times compared to the standard structure without modified edge magnetization profiles. Based on the effective field analysis, we confirmed that the spatial distribution of the tilting moment at the edge layer changed the effective field distribution and caused a non-monotonic change in the upper threshold current with the modified region width. Our results may provide an optional route for designing future skyrmion-based STNOs with better performance in the communication and computing areas. [ABSTRACT FROM AUTHOR]

In this work, micromagnetic simulations demonstrate that a steady oscillation mode accompanied by magnetic domain splitting and the creation and annihilation of meron can be excited by spin-polarized currents. It is found that the in-plane magnetic anisotropy and Dzyaloshinskii-Moriya interaction (DMI) have a greater influence on the oscillation frequency. The oscillation frequency can vary from 3 GHz to 31 GHz by controlling anisotropy strength under a fixed current density. By changing DMI strength, the oscillation frequency varies from 9 to 13.6 GHz and from 29.7 to 37 GHz. Compared with ferromagnetic skyrmion-based spin-torque oscillators (STOs), the STOs based on this magnetic domain and meron further increase the oscillation frequency. Our results may provide theoretical support for the research and development of future high-frequency STOs.

It is well-known that a spin-transfer torque caused by a dc electric current can excite in a two-dimensional ferromagnetic film exchange-dominated magnetic solitons, often called "spin-wave bullets", under the condition of a negative nonlinear shift of spin wave frequency. In this work, we demonstrate that in a quasi-one-dimensional (1D) case, e.g., in a nanowire spin-Hall oscillator, it is possible to excite a stable dissipative magnetic soliton, which is dominated by the dipole-dipole interaction. This dissipative magnetic soliton can be described in the framework of a 1D Ginzburg-Landau auto-oscillator model, and has the shape similar to that of the exchange-dominated spin wave bullet, but with a different spatial localization law. The influence of the dipolar interaction makes possible the stabilization of a dissipative soliton in a relatively large (micron-sized) active area of the oscillator, which is in a sharp contrast with the two-dimensional case, where the excitation of a stable spin-wave bullet was observed only in relatively small active areas having typical sizes of the order of 100 nm. The characteristics and possible applications of these dipole-dominated spin wave bullets are discussed. [ABSTRACT FROM AUTHOR]

This paper presents a steady auto-oscillation in a spin-torque oscillator using MgO-based magnetic tunnel junction (MTJ) with a perpendicular polarizer and a perpendicular free layer. As the injected d.c. current varied from 1.5 to 3.0 mA under a weak magnetic field of 290 Oe, the oscillation frequency decreased from 1.85 to 1.3 GHz, and the integrated power increased from 0.1 to 74 pW. A narrow linewidth down to 7 MHz corresponding to a high Q factor of 220 was achieved at 2.7 mA, which was ascribed to the spatial coherent procession of the free layer magnetization. Moreover, the oscillation frequency was quite sensitive to the applied field, about 3.07 MHz/Oe, indicating the potential applications as a weak magnetic field detector. These results suggested that the MgO-based MTJ with perpendicular magnetic easy axis could be helpful for developing spin-torque oscillators with narrow-linewidth and high sensitive. [ABSTRACT FROM AUTHOR]

We propose a novel setup for a spin-torque oscillator reader in magnetic hard disk drive technology. Two adjacent bit tracks are to be read simultaneously, leading to high data transfer rate and increased resilience to noise as the lateral size of the oscillator device is allowed to remain larger than the bit width. We perform micromagnetic simulations of an example system and find that the magnetization response has a clear unimodal character, which enables for detection of two bit values at the same time. We analyze the frequency of the device under the influence of two different external fields and conduct a simulation of a successful dynamic readout. We estimate the signal linewidth and signal-to-noise ratios of the setup and show that it may be potentially beneficial for magnetic readout applications. [ABSTRACT FROM AUTHOR]

Spin-torque oscillators (STOs) are the candidates for a novel class of magnetic field sensors, suitable especially for magnetic media read head purposes. While a number of investigations on the STO readout ability have been reported, comparatively little attention has been paid to the issue of its behavior in highly inhomogeneous magnetic fields, i.e., generated by densely stored magnetic media. We examine the theoretical limits for the STO technology usage for sensor applications, using both a general auto-oscillator model and a micromagnetic simulations framework. We find that the deterioration of the output signal may lead to significant readout errors already for the bit width of a few nanometers, which is close to the current state-of-the-art in the data storage industry. [ABSTRACT FROM PUBLISHER]

Current-induced spin-transfer torque can induce magnetization precession in gigahertz ranges, which enables various microwave devices. In most cases, this current-induced precession requires an additional external magnetic field, which is detrimental for device applications. In this work, we show that the current-induced precession is realized even without an external field when the magnetic layer has conical magnetization, caused by the second order easy-axis magnetic anisotropy. We theoretically derive the oscillation frequency and output power and confirm their validity by macrospin simulations. We find that the ratio of the second to the first anisotropy constants is key to determine the maximum frequency and power. Our results will be helpful for the applications of microwave devices utilizing spin-transfer torques and provide a design rule of such devices. [ABSTRACT FROM AUTHOR]

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. Our results show how a linear mode coupling, which is necessary for observed mode-hopping to occur, arises through coupling to a magnon bath. The acquired temperature dependence of this coupling implies that the manifold of orbits and fixed points may shift with temperature. [ABSTRACT FROM AUTHOR]

The spin-torque oscillator (STO) is the most important component in microwave-assisted magnetic recording (MAMR). To realize MAMR, a small injected STO current is mandatory, as are large amplitude and stable oscillations. In this paper, an isolated STO element (without the write head) and an STO integrated into a write head were analyzed using micromagnetic analysis. First, the integrated STO was used and the optimum injected currents ( $J_{{\textrm {opt}}}\text{s} ) that excite high-frequency magnetic fields were derived for various Gilbert damping factors ( \alpha \texts ) and saturation magnetization ( 4\pi M_s ) in the field generating layer. Second, $J_{{\textrm {opt}}}\text{s}$ were derived for various isolated STO structures. The effect of the material characteristics on $J_{{\textrm {opt}}}$ was also investigated. [ABSTRACT FROM PUBLISHER]

We present micromagnetic simulations at various grain sizes of four-layer exchange-coupled composite microwave-assisted magnetic recording (MAMR) systems that have maximized areal density capability using the Nelder–Mead simplex algorithm. We restrict our media to have crystalline KuV/kT $> \,\, \sim 100$ . Our optimized MAMR designs show roughly 120 Gb/in2 areal density growth per nanometer of grain pitch reduction and achieve an areal density of 37% larger than a publicly available 700 Gb/in2 conventional perpendicular recording reference at a similar grain size and write width. We analyze all 26 optimization variables to identify common trends indicative of high-performance MAMR media. Our principle goal is to help media designers optimize media for MAMR performance, and to project how this optimization changes with the grain size. Balancing write-ability, noise performance, thermal stability, and resonance-matching characteristics is most important. [ABSTRACT FROM AUTHOR]

Synchronization of two nanopillar oscillators driven by spin torque and coupled through the magnetic dipolar interaction. The dominant mode in each oscillator is gyrotropic motion of the vortex core in an elliptical orbit about the free layer disk center. The dynamic properties of this mode is investigated by solution the coupled Thiele equations with both nanopillar oscillators having identical dimensions, but with a current mismatch. It is noticed that there is a range in the current difference where the oscillators will be synchronized where the vortex gyrotropic motion will be frequency-locked with the radii of gyrotropic motion equal for both disks. There is, however, a phase shift between the gyrotropic motion with the smaller current disk lagging the higher current disk by a few degrees. [ABSTRACT FROM AUTHOR]

Microwave-assisted magnetic recording (MAMR) employs a spin-torque oscillator (STO) to assist a standard magnetic writer field in switching grains of a magnetic recording medium. The STO field has different polarization angles at different positions, resulting in different mixes of in-media-plane and out-of-media-plane (vertical) field components. We find that the vertical component of the STO field degrades the writing process, increasing jitter, decreasing low-frequency signal-to-noise ratio, decreasing magnetic write width, and decreasing areal density capability. This is not due to postwrite erasure, but rather is part of the write process itself. Simple vector considerations illuminate the cause for this degradation. Consequently, experimental and modeling approaches that estimate MAMR switching-field reduction using only in-media-plane oscillating fields will erroneously overestimate the impact of the ac fields in the magnetic recording process. [ABSTRACT FROM AUTHOR]

In this paper, we show that the dynamics of injection-locked Spin Hall Effect Spin-Torque Oscillator (SHE-STO) cluster can be exploited as a robust primitive computational operator for non-Boolean associative computing. A cluster of SHE-STOs can be locked to a common frequency and phase with an injected ac current signal. DC input to each STO from external stimuli can conditionally unlock some of them. Based on the input dc signal, the degree of synchronization of SHE-STO cluster is detected by CMOS interface circuitry. The degree of synchronization can be used for associative computing/matching. We present a numerical simulation model of SHE-STO devices based on Landau–Lifshitz–Gilbert equation with spin-transfer torque term and Spin Hall Effect. The model is then used to analyze the frequency and phase locking properties of injection-locked SHE-STO cluster. Results show that associative computing based on the injection locked SHE-STO cluster can be energy efficient and relatively immune to device parameter variations and thermal noise. [ABSTRACT FROM PUBLISHER]

The state diagram of spin-torque oscillator (STO) with perpendicular reference layer (REF) and planar field generation layer (FGL) was studied by a macrospin model and a micro-magnetic model. The state diagrams are calculated versus the current density, external field and external field angle. It was found that the oscillation in FGL could be controlled by current density combined with external field so as to achieve a wide frequency range. An optimized current and applied field region was given for microwave assisted magnetic recording (MAMR), considering both frequency and output field oscillation amplitude. The results of the macro-spin model were compared with those of the micro-magnetic model. The macro-spin model was qualitatively different from micro-magnetics and experimental results when the current density was large and the FGL was non-uniform. [ABSTRACT FROM AUTHOR]

We investigated the high-power spin–torque oscillator in a half-metallic Heusler alloy Co 2 MnSi spin-valve nanopillars with perpendicular magnetization under external magnetic field using micromagnetic simulations. Our simulations show that the narrow optimum current of magnetization precession in the Heusler-based spin valve is broadened by introducing the surface anisotropy. The linear decrease of frequency with the out-of-plane magnetic field is obtained in our simulation. Additionally, the in-plane magnetic field dependence of frequency shows a parabolic curve which is explained by the magnetization trajectory tilting. Furthermore, we also discussed the decrease of output power using the excitation of non-uniform magnetization precession in the in-plane magnetic fields. [ABSTRACT FROM AUTHOR]

Abstract: 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. [Copyright &y& Elsevier]

Abstract: 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). [Copyright &y& Elsevier]

High-data-transfer-rate readers beyond 3 Gbit/s composed of spin-torque oscillators (STOs) are considered and the signal-to-noise ratios (SNRs) of the output signals under the thermal magnetization fluctuations are calculated by using the recent nonlinear theories. The “STO Reader” senses the media field as a modulation in the oscillation frequency, enabling high-data-transfer rates beyond the limit of ferromagnetic relaxation. The output (digital) signal is obtained by frequency modulation (FM) detection, which is commonly used in communication technologies. As the problem of rapid phase diffusion in nonlinear STOs caused by the thermal fluctuations is overcome by employing a delay detection method, the sufficiently large SNRs are expected even in nonlinear STOs less than 30\times 30\ \nm^2 in size. The prompt response of the STO frequency (phase) to the media field and the high-data-transfer rate beyond 5 Gbit/s are shown by micromagnetic simulation. The frequency transition of STO in less than 1 ns under the pulse field is also confirmed by experiment. [ABSTRACT FROM AUTHOR]

A macro-spin simulation has been carried out to study the thermal stability of a spin-torque oscillator (STO) connected in parallel with a capacitance. To study the impact of realistic thermal fluctuation on an STO, a stochastic magnetic field vector is added into the Landau-Lifshitz-Gilbert-Slonczewski (LLGS) equation. From the numerical solution, it is found that the addition of capacitance positively influences the thermal stability of the system, and can improve the quality factor of the microwave power spectrum even in the presence of thermal fluctuation. The results of I-V phase shift under different conditions suggest that there may exist an optimum capacitance for which the thermal stability of the system can be most enhanced. [ABSTRACT FROM AUTHOR]

This paper formulates a general analytic approach to the theory of microwave generation in magnetic nano-structures driven by spin-polarized current and reviews analytic results obtained in this theory. The proposed approach is based on the universal model of an auto-oscillator with negative damping and nonlinear frequency shift. It is demonstrated that this universal model, when applied to the case of a spin-torque oscillator (STO) based on a current-driven magnetic nano-pillar or nano-contact, gives adequate description of most of the experimentally observed properties of STO. In particular, the model describes the power and frequency of the generated microwave signal as functions of the bias current and magnetic field, predicts the magnitude and properties of the generation linewidth, and explains the STO behavior under the influence of periodic and stochastic external signals: frequency modulation, phase-locking to external signals, mutual phase-locking in an array of STO, broadening of the generation linewidth near the generation threshold, etc. The proposed nonlinear auto-oscillator theory is rather general and can be used not only for the development of practical nano-sized STO, but, also, for the description of nonlinear auto-oscillating systems of any physical nature. [ABSTRACT FROM PUBLISHER]

We present a micromagnetic modeling study of microwave assisted magnetic recording (MAMR) on a typical exchange-coupled four-layer media. With the help of an alternating current (ac) magnetic field, the switching field can be reduced, especially at the media resonant frequency. Typical hysteresis loop measurements employ a depth-invariant ac field; however, the field generated from a spin-torque oscillator (STO) varies with spacing. Considering this depth variance, the switching field reduction becomes less than observed with a depth-invariant ac field. Furthermore, we find an even smaller switching field reduction when using a realistic magnetic writer and STO fields to record a dc track on randomly magnetized grains. Consequently, we conclude that MAMR hysteresis loops employing a depth-invariant ac field significantly overestimate the ac field’s contribution to grain switching in an actual recording situation. [ABSTRACT FROM AUTHOR]

• High frequency oscillations about 65 GHz by the influence of in-plane magnetic field. • Frequency tunability from 15 to 68 GHz by current or the direction of in-plane field. • Frequency tunability from 35 to 65 GHz by varying magnitude of the in-plane field. • Enhancement of power by varying the current and the direction of in-plane field. We show the possibility of high-frequency oscillations in a spin-torque oscillator that consists of an in-plane magnetized free and pinned layers in the presence of in-plane magnetic field by numerically solving the associated Landau-Lifshitz-Gilbert-Slonczewski (LLGS) equation. We discover that frequency can be tuned significantly by tuning the direction of the in-plane magnetic field. Further, we observe the oscillation frequencies as high as 65 GHz for appropriate in-plane magnetic field angles. We also show the tunability of microwave frequency from ~ 15 GHz to ~ 68 GHz by tuning the magnitude of the direct current or the in-plane field angle and from ~ 35 GHz to ~ 65 GHz by varying the strength of the in-plane magnetic field. The power is proved to be enhanced by the in-plane field angle and current. [ABSTRACT FROM AUTHOR]

Micromagnetic simulations were carried out to obtain stable oscillation of a spin transfer torque oscillator (STO) inserted into the gap between the main pole and trailing shield of a write head. We assumed a spin injection layer with in-plane anisotropy. Results show that reducing the magnetostatic interaction between the write head and the STO is the key to obtaining stable STO oscillation. [ABSTRACT FROM AUTHOR]

We studied the effect of injecting a low-frequency (0.5–1 GHz) ac signal on the natural oscillations of a nano-oxide layer-based nanocontact magnetoresistive spin-torque oscillator with multiple Fe50Co50 nanocontacts. We observed a frequency modulation effect with odd-numbered side bands having low amplitudes. Also, no frequency shift at main spectral peak's frequency, typical with nonlinear frequency modulation, was observed. We could not completely explain this behavior, but we propose that this could be related to the internal dynamics of constricted domain walls. [ABSTRACT FROM AUTHOR]

• Magnetization states of 2 recording layers (RLs) are detected layer-selectively. • A spin-torque oscillator (STO) is used as a read device. • The STO induces and detects state-dependent ferromagnetic resonance (FMR) in each RL. • The RLs are designed to suppress interlayer interference caused by dipolar fields. • The changes in STO oscillation occur on a 1-ns timescale shown by moving the STO. We use micromagnetic simulation to demonstrate layer-selective detection of magnetization directions from magnetic dots having two recording layers by using a spin-torque oscillator (STO) as a read device. This method is based on ferromagnetic resonance (FMR) excitation of recording-layer magnetizations by the microwave field from the STO. The FMR excitation affects the oscillation of the STO, which is utilized to sense the magnetization states in a recording layer. The recording layers are designed to have different FMR frequencies so that the FMR excitation is selectively induced by tuning the oscillation frequency of the STO. Since all magnetic layers interact with each other through dipolar fields, unnecessary interlayer interferences can occur, which are suppressed by designing magnetic properties of the layers. We move the STO over the magnetic dots, which models a read head moving over recording media, and show that changes in the STO oscillation occur on the one-nanosecond timescale. [ABSTRACT FROM AUTHOR]

Abstract: A theory of generation linewidth of a spin-torque oscillator (STO) based on an in-plane-magnetized nano-pillar with an anisotropic “free” magnetic layer has been developed. It is predicted that by choosing the direction of the in-plane bias magnetic field along the “hard” anisotropy axis of the STO “free” layer and the magnitude of this field to be four times larger than the anisotropy field () it would be possible to compensate the nonlinear phase noise and to achieve the minimum value of the generation linewidth, characteristic for an auto-oscillator without a nonlinear frequency shift. [Copyright &y& Elsevier]