arXiv subjects

Mykola Dvornik

Publications and source records attributed to Mykola Dvornik.

At least 19 recordsLinked to original sources

arXiv2020

Frequency Stability of Spin-Hall Nano-Oscillators with Realistic Grain Structure

Nano-constriction spin-Hall nano-oscillators (NC-SHNOs) are one of the most promising alternatives among the microwave spintronics devices. They can provide highly coherent and widely tuneable microwave signals and can be fabricated at low temperatures, which makes them compatible with back-end-of-the-line CMOS processing. For its applications, the frequency stability of each device is crucial, in particular for synchronization of oscillator arrays. In this work, we focus on the influence of a realistic grain structure on the SHNO frequency stability using both measurements as well as micromagnetic simulations. Grains in the thin ferromagnetic metal films can influence the output characteristic of the SHNO since the exchange coupling is reduced locally at the grain boundaries. This work provides a novel micromagnetic simulation method, for systematic investigation of frequency instability or variability from device-to-device. Experimentally, a device-to-device frequency variability of ~270 MHz was found and in some extreme cases, a double-mode oscillation was observed in the high current operation range. This oscillation behavior was reproduced in simulations, where the inclusion of grains resulted in a frequency variability of ~100 MHz and double-mode oscillations for some particular configurations. The double modes are consistent with a partial decoupling, or non-coherent operation, of two oscillating regions located at the nano-constriction edges.

cond-mat.mes-hall↗

arXiv2020

Impact of intra-grain spin wave reflections on nano-contact spin torque oscillators

We investigate the origin of the experimentally observed varying current-frequency nonlinearity of the propagating spin wave mode in nano-contact spin torque oscillators. Nominally identical devices with 100 nm diameter are characterized by electrical microwave measurements and show large variation in the generated frequency as a function of drive current. This quantitative and qualitative device-to-device variation is described in terms of continuous and discontinuous nonlinear transitions between linear current intervals. The thin film grain microstructure in our samples is determined using atomic force and scanning electron microscopy to be on the scale of 30 nm. Micromagnetic simulations show that the reflection of spin waves against the grain boundaries results in standing wave resonance configurations. For a simulated device with a single artificial grain, the frequency increases linearly with the drive current until the decreased wavelength eventually forces another spin wave anti-node to be formed. This transition results in a discontinuous step in the frequency versus current relation. Simulations of complete, randomly generated grain microstructures additionally shows continuous nonlinearity and a resulting device-to-device variation in frequency that is similar to the experimental levels. The impact of temperature from 4 K to 300 K on the resonance mode-transition nonlinearity and frequency noise is investigated using simulations and it is found that the peak levels of the spectral linewidth as a function of drive current agrees quantitatively with typical levels found in experiments at room temperature.

cond-mat.mes-hall↗

arXiv2020

Giant voltage control of spin Hall nano-oscillator damping

Spin Hall nano-oscillators (SHNOs) are emerging spintronic devices for microwave signal generation and oscillator based neuromorphic computing combining nano-scale footprint, fast and ultra-wide microwave frequency tunability, CMOS compatibility, and strong non-linear properties providing robust large-scale mutual synchronization in chains and two-dimensional arrays. While SHNOs can be tuned via magnetic fields and the drive current, neither approach is conducive for individual SHNO control in large arrays. Here, we demonstrate electrically gated W/CoFeB/MgO nano-constrictions in which the voltage-dependent perpendicular magnetic anisotropy, tunes the frequency and, thanks to nano-constriction geometry, drastically modifies the spin-wave localization in the constriction region resulting in a giant 42 % variation of the effective damping over four volts. As a consequence, the SHNO threshold current can be strongly tuned. Our demonstration adds key functionality to nano-constriction SHNOs and paves the way for energy-efficient control of individual oscillators in SHNO chains and arrays for neuromorphic computing.

physics.app-ph↗

arXiv2019

Micromagnetic Modeling of Telegraphic Mode Jumping in Microwave Spin Torque Oscillators

The time domain stability of microwave spin torque oscillators (STOs) has been investigated by systematic micromagnetic simulations. A model based on internal spin wave reflection at grain boundaries with reduced exchange coupling was implemented and used to study the oscillator under quasi-stable operating conditions. Telegraphic mode jumping between two operating frequencies (23.3 and 24.1 GHz) was observed in the time domain with characteristic dwell times in the range of 10-100 ns. The oscillating volume was shown to have a different shape at the distinct operating frequencies. The shape difference is governed by spin wave reflections at the grain boundaries. The resulting non-linear behavior of the oscillator was shown to be a collective effect of spin wave scattering at different locations within a few spin wavelengths from the nano-contact.

cond-mat.mes-hall↗

arXiv2019

Spin-Orbit-Torque Driven Propagating Spin Waves

Spin-orbit torque (SOT) can drive sustained spin wave (SW) auto-oscillations in a class of emerging microwave devices known as spin Hall nano-oscillators (SHNOs), which have highly non-linear properties governing robust mutual synchronization at frequencies directly amenable to high-speed neuromorphic computing. However, all demonstrations have relied on localized SW modes interacting through dipolar coupling and/or direct exchange. As nanomagnonics requires propagating SWs for data transfer, and additional computational functionality can be achieved using SW interference, SOT driven propagating SWs would be highly advantageous. Here, we demonstrate how perpendicular magnetic anisotropy can raise the frequency of SOT driven auto-oscillations in magnetic nano-constrictions well above the SW gap, resulting in the efficient generation of field and current tunable propagating SWs. Our demonstration greatly extends the functionality and design freedom of SHNOs enabling long range SOT driven SW propagation for nanomagnonics, SW logic, and neuro-morphic computing, directly compatible with CMOS technology.

physics.app-ph↗

arXiv2019

Spatial Mapping of Torques within a Spin Hall Nano-oscillator

Time-resolved scanning Kerr microscopy (TRSKM) was used to study precessional magnetization dynamics induced by a radio frequency (RF) current within a Al$_2$O$_3$/Py(5 nm)/Pt(6 nm)/Au(150 nm) spin Hall nano-oscillator structure. The Au layer was formed into two needle-shaped electrical contacts that concentrated the current in the centre of a Py/Pt mesa of 4 $μ$m diameter. Due to the spin Hall effect, current within the Pt layer drives a spin current into the Py layer, exerting a spin transfer torque (STT). By injecting RF current, and exploiting the phase-sensitivity of TRSKM and the symmetry of the device structure, the STT and Oersted field torques have been separated and spatially mapped. The STT and torque due to the in-plane Oersted field are observed to exhibit minima at the device centre that is ascribed to spreading of RF current that is not observed for DC current. Torques associated with the RF current may destabilise the position of the self-localised bullet mode excited by the DC current, and inhibit injection locking. The present study demonstrates the need to characterise both DC and RF current distributions carefully.

cond-mat.mes-hall↗

arXiv2018

Two-dimensional mutual synchronization in spin Hall nano-oscillator arrays

Spin Hall nano-oscillators (SHNOs) utilize pure spin currents to drive local regions of magnetic films and nanostructures into auto-oscillating precession. If such regions are placed in close proximity to each other they can interact and sometimes mutually synchronize, in pairs or in short linear chains. Here we demonstrate robust mutual synchronization of two-dimensional SHNO arrays ranging from 2 x 2 to 8 x 8 nano-constrictions, observed both electrically and using micro-Brillouin Light Scattering microscopy. The signal quality factor, $Q=f/Δf$, increases linearly with number of mutually synchronized nano-constrictions ($N$), reaching 170,000 in the largest arrays. While the microwave peak power first increases as $N^2$, it eventually levels off, indicating a non-zero relative phase shift between nano-constrictions. Our demonstration will enable the use of SHNO arrays in two-dimensional oscillator networks for high-quality microwave signal generation and neuromorphic computing.

cond-mat.mes-hall↗

arXiv2018

Mutual synchronization of constriction-based spin Hall nano-oscillators in weak in-plane fields

We study mutual synchronization in double nanoconstriction-based spin Hall nano-oscillators (SHNOs) under weak in-plane fields ($μ_0H_\mathrm{IP}$ = 30-40 mT) and also investigate its angular dependence. We compare SHNOs with different nano-constriction spacings of 300 and 900 nm. In all devices, mutual synchronization occurs below a certain critical angle, which is higher for the 300 nm spacing than for the 900 nm spacing, reflecting the stronger coupling at shorter distances. Alongside the synchronization, we observe a strong second harmonic consistent with predictions that the synchronization may be mediated by the propagation of second harmonic spin waves. However, although Brillouin Light Scattering microscopy confirms the synchronization, it fails to detect any related increase of the second harmonic. Micromagnetic simulations instead explain the angular dependent synchronization as predominantly due to magneto-dipolar coupling between neighboring SHNOs.

physics.app-ph↗

arXiv2018

Time resolved imaging of the non-linear bullet mode within an injection-locked nano-contact spin Hall nano-oscillator

Injection of a radio frequency (RF) current was used to phase lock the SHNO to the TRSKM. The out of plane magnetization was detected by means of the polar magneto optical Kerr effect (MOKE). However, longitudinal MOKE images were dominated by an artifact arising from the edges of the Au NCs. Time resolved imaging revealed the simultaneous excitation of a non-linear `bullet' mode at the centre of the device, once the DC current exceeded a threshold value, and ferromagnetic resonance (FMR) induced by the RF current. However, the FMR response observed for sub-critical DC current values exhibits an amplitude minimum at the centre, which is attributed to spreading of the RF spin current due to the reactance of the device structure. This FMR response can be subtracted to yield images of the bullet mode. As the DC current is increased above threshold, the bullet mode appears to increase in size, suggesting increased translational motion. The reduced spatial overlap of the bullet and FMR modes, and this putative translational motion, may impede the injection locking and contribute to the reduced locking range observed within NC-SHNO devices. This illustrates a more general need to control the geometry of an injection-locked oscillator so that the autonomous dynamics of the oscillator exhibit strong spatial overlap with those resulting from the injected signal.

cond-mat.mes-hall↗

arXiv2018

Mapping out the spin-wave modes of constriction-based spin Hall nano-oscillators in weak in-plane fields

We experimentally study the auto-oscillating spin-wave modes in NiFe/$β-$W constriction-based spin Hall nano-oscillators as a function of bias current, in-plane applied field strength, and azimuthal field angle, in the low-field range of 40-80 mT. We observe two different spin-wave modes: i) a linear-like mode confined to the minima of the internal field near the edges of the nanoconstriction, with weak frequency dependencies on the bias current and the applied field angle, and ii) a second, lower frequency mode that has significantly higher threshold current and stronger frequency dependencies on both bias current and the external field angle. Our micromagnetic modeling qualitatively reproduces the experimental data and reveals that the second mode is a spin-wave bullet and that the SHNO mode hops between the two modes, resulting in a substantial increase in linewidths. In contrast to the linear-like mode, the bullet is localized in the middle of the constriction and shrinks with increasing bias current. Utilizing intrinsic frequency doubling at zero field angle we can reach frequencies above 9 GHz in fields as low as 40 mT, which is important for the development of low-field spintronic oscillators with applications in microwave signal generation and neuromorphic computing.

cond-mat.mes-hall↗

arXiv2018

Anomalous nonlinearity of the magnonic edge mode

Nonlinearity of magneto-dynamics is typically described by a single constant, $\mathcal{N}$, with positive and negative values indicating repulsion and attraction of magnons, respectively. In thin magnetic films with easy-plane magnetic anisotropy, magnon attraction is typically achieved for an in-plane magnetization. At sufficient stimulus, e.g. via application of spin transfer torque, the attraction can give rise to self-localized magnetic solitons, such as spin wave bullets, which shrink as their amplitude increases. In contrast, for an oblique magnetization above a certain critical angle, the repulsion of magnons only allows for propagating modes, which expand when pumped more strongly. Here we demonstrate, both analytically and using micromagnetic simulations, that such a dichotomic description is inadequate for magnonic edge modes, which naturally appear in confined magnetic systems. In particular, we demonstrate that the confinement potential of such modes is nonlinear in nature and its contribution makes $\mathcal{N}$ non-monotonically dependent on their amplitude. As a prominent example, edge modes show compression and expansion for negative and positive $\mathcal{N}$, yet remain localized. In striking contrast to the extended geometries, edge magnons might also repeal even for an in-plane magnetization.

cond-mat.mes-hall↗

arXiv2018

Damping's effect on the magnetodynamics of spin Hall nano-oscillators

We study the impact of spin wave damping ($α$) on the auto-oscillation properties of nano-constriction based spin Hall nano-oscillators (SHNOs). The SHNOs are based on a 5 nm Pt layer interfaced to a 5 nm Py$_{100-x-y}$Pt$_{x}$Ag$_{y}$ magnetic layer, where the Pt and Ag contents are co-varied to keep the saturation magnetization constant (within 10 %), while $α$ varies close to a factor of three. We systematically investigate the influence of the Gilbert damping on the magnetodynamics of these SHNOs by means of electrical microwave measurements. Under the condition of a constant field, the threshold current scales with the damping in the magnetic layer. The threshold current as a function of field shows a parabolic-like behavior, which we attribute to the evolution of the spatial profile of the auto-oscillation mode. The signal linewidth is smaller for the high-damping materials in low magnetic fields, although the lowest observed linewidth was measured for the alloy with least damping.

cond-mat.mes-hall↗

arXiv2017

Tunable spin pumping in exchange coupled magnetic trilayers

Magnetic thin films at ferromagnetic resonance (FMR) leak angular momentum, which may be absorbed by adjacent layers. This phenomenon, known as spin pumping, is manifested by an increase in the resonance linewidth ($ΔH$), and the closely related Gilbert damping. Another effect of this transfer of spin currents is a dynamical and long-range coupling that can drive two magnetic layers into a collective precession when their FMR frequencies coincide. A collective behavior is also found in magnetic trilayers with interlayer exchange coupling (IEC). In this study we investigate the interplay between IEC and spin pumping, using Co/Cu/Py pseudo-spin values. We employ broadband FMR spectroscopy to explore both the frequency and coupling-strength dependence of $ΔH$. Our observations show that there exists a cut-off frequency, set by the IEC strength, below which the precession is truly collective and the spin pumping is suppressed. These results demonstrate that it is possible to control the spin pumping efficiency by varying the frequency or the interlayer exchange coupling.

cond-mat.mes-hall↗

arXiv2017

On the origin of magnetization auto-oscillations in constriction-based spin Hall nano-oscillators

We use micromagnetic simulations to map out and compare, the linear and auto-oscillating modes in constriction-based spin Hall nano-oscillators as a function of applied magnetic field with varying magnitude and out-of-plane angle. We demonstrate that for all possible applied field configurations the auto-oscillations emerge from the localized linear modes of the constriction. For field directions tending towards the plane, these modes are of the so-called "edge" type, i.e. localized at the opposite sides of the constriction. When the magnetization direction instead approaches the film normal, the modes transform to the so-called "bulk" type, i.e. localized inside the constriction with substantially increased precession volume, consistent with the re-distribution of the magnetic charges from the sides to the top and bottom surfaces of the constriction. In general, the threshold current of the corresponding auto-oscillations increases with the applied field strength and decreases with its out-of-plane angle, consistent with the behavior of the internal field and in good agreement with a macrospin model. A quantitative agreement is then achieved by taking into account the strongly non-uniform character of the system via a mean-field approximation. Both the Oe field and the spin transfer torque from the drive current increase the localization and decrease the frequency of the observed mode. Furthermore, the anti-symmetric Oe field breaks the lateral symmetry, favoring the localized mode at one of the two constriction edges, in particular for large out-of-plane field angles where the threshold current is significantly increased and the edge demagnetization is suppressed.

cond-mat.mes-hall↗

arXiv2016

Homodyne-detected ferromagnetic resonance of in-plane magnetized nano-contacts: composite spin wave resonances and their excitation mechanism

This work provides a detailed investigation of the measured in-plane field-swept homodyne-detected ferromagnetic resonance (FMR) spectra of an extended Co/Cu/NiFe pseudo spin valve stack using a nanocontact (NC) geometry. The magnetodynamics are generated by a pulse-modulated microwave current and the resulting rectified dc mixing voltage, which appears across the NC at resonance, is detected using a lock-in amplifier. Most notably, we find that the measured spectra of the NiFe layer are composite in nature and highly asymmetric, consistent with the broadband excitation of multiple modes. Additionally, the data must be fit with two Lorentzian functions in order to extract a reasonable value for the Gilbert damping of the NiFe. Aided by micromagnetic simulations, we conclude that (i) for in-plane fields the rf Oersted field in the vicinity of the NC plays the dominant role in generating the observed spectra, (ii) in addition to the FMR mode, exchange dominated spin waves are also generated, and (iii) the NC diameter sets the mean wavevector of the exchange dominated spin wave, in good agreement with the dispersion relation.

cond-mat.mes-hall↗

arXiv2015

Phenomenological description of the nonlocal magnetization relaxation in magnonics, spintronics, and domain-wall dynamics

A phenomenological equation called Landau-Lifshitz-Baryakhtar (LLBar) equation, which could be viewed as the combination of Landau-Lifshitz (LL) equation and an extra "exchange damping" term, was derived by Baryakhtar using Onsager's relations. We interpret the origin of this "exchange damping" as nonlocal damping by linking it to the spin current pumping. The LLBar equation is investigated numerically and analytically for the spin wave decay and domain wall motion. Our results show that the lifetime and propagation length of short-wavelength magnons in the presence of nonlocal damping could be much smaller than those given by LL equation. Furthermore, we find that both the domain wall mobility and the Walker breakdown field are strongly influenced by the nonlocal damping.

cond-mat.mtrl-sci↗

arXiv2014

The design and verification of Mumax3

We report on the design, verification and performance of mumax3, an open-source GPU-accelerated micromagnetic simulation program. This software solves the time- and space dependent magnetization evolution in nano- to micro scale magnets using a finite-difference discretization. Its high performance and low memory requirements allow for large-scale simulations to be performed in limited time and on inexpensive hardware. We verified each part of the software by comparing results to analytical values where available and to micromagnetic standard problems. mumax3 also offers specific extensions like MFM image generation, moving simulation window, edge charge removal and material grains.

physics.comp-ph↗

arXiv2014

Thermodynamically self-consistent non-stochastic micromagnetic model for the ferromagnetic state

In this work, a self-consistent thermodynamic approach to micromagnetism is presented. The magnetic degrees of freedom are modeled using the Landau-Lifshitz-Baryakhtar theory, that separates the different contributions to the magnetic damping, and thereby allows them to be coupled to the electron and phonon systems in a self-consistent way. We show that this model can quantitatively reproduce ultrafast magnetization dynamics in Nickel.

cond-mat.mtrl-sci↗