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.

Voltage-Controlled High-Bandwidth Terahertz Oscillators Based on Antiferromagnets

Producing compact voltage-controlled frequency generators and sensors operating in the terahertz (THz) regime represents a major technological challenge. Here, we show that noncollinear antiferromagnets (NCAFMs) with kagome structure host gapless self-oscillations whose frequencies are tunable from 0 Hz to the THz regime via electrically induced spin-orbit torques (SOTs). The auto-oscillations' initiation, bandwidth, and amplitude are investigated by deriving an effective theory, which captures the reactive and dissipative SOTs. We find that the dynamics strongly depends on the ground state's chirality, with one chirality having gapped excitations, whereas the opposite chirality provides gapless self-oscillations. Our results reveal that NCAFMs offer unique THz functional components, which could play a significant role in filling the THz technology gap.

Field-Free High-Frequency Exchange-Spring Spin-Torque Nano-Oscillators

Spin-torque nano-oscillators (STNOs) are a type of nanoscale microwave auto-oscillators utilizing spin-torque to generate magnetodynamics with great promise for applications in microwaves, magnetic memory, and neuromorphic computing. Here, we report the first demonstration of exchange-spring STNOs, with an exchange-spring ([Co/Pd]-Co) reference layer and a perpendicular ([Co/Ni]) free layer. This magnetic configuration results in high-frequency (>10 GHz) microwave emission at a zero magnetic field and exchange-spring dynamics in the reference layer and the observation of magnetic droplet solitons in the free layer at different current polarities. Our demonstration of bipolar and field-free exchange-spring-based STNOs operating over a 20 GHz frequency range greatly extends the design freedom and functionality of the current STNO technology for energy-efficient high-frequency spintronic and neuromorphic applications.

Magnon scattering modulated by omnidirectional hopfion motion in antiferromagnets for meta-learning

Neuromorphic computing is expected to achieve human-brain performance by reproducing the structure of biological neural systems. However, previous neuromorphic designs based on synapse devices are all unsatisfying for their hardwired network structure and limited connection density, far from their biological counterpart, which has high connection density and the ability of meta-learning. Here, we propose a neural network based on magnon scattering modulated by an omnidirectional mobile hopfion in antiferromagnets. The states of neurons are encoded in the frequency distribution of magnons, and the connections between them are related to the frequency dependence of magnon scattering. Last, by controlling the hopfion's state, we can modulate hyperparameters in our network and realize the first meta-learning device that is verified to be well functioning. It not only breaks the connection density bottleneck but also provides a guideline for future designs of neuromorphic devices.

Magnetic force microscopy of an operational spin nano-oscillator

Magnetic force microscopy (MFM) is a powerful technique for studying magnetic microstructures and nanostructures that relies on force detection by a cantilever with a magnetic tip. The detected magnetic tip interactions are used to reconstruct the magnetic structure of the sample surface. Here, we demonstrate a new method using MFM for probing the spatial profile of an operational nanoscale spintronic device, the spin Hall nano-oscillator (SHNO), which generates high-intensity spin wave auto-oscillations enabling novel microwave applications in magnonics and neuromorphic computing. We developed an MFM system by adding a microwave probe station to allow electrical and microwave characterization up to 40 GHz during the MFM process. SHNOs-based on NiFe/Pt bilayers with a specific design compatible with the developed system-were fabricated and scanned using a Co magnetic force microscopy tip with 10 nm spatial MFM resolution, while a DC current sufficient to induce auto-oscillation flowed. Our results show that this developed method provides a promising path for the characterization and nanoscale magnetic field imaging of operational nano-oscillators.

Freezing and thawing magnetic droplet solitons

Magnetic droplets are non-topological magnetodynamical solitons displaying a wide range of complex dynamic phenomena with potential for microwave signal generation. Bubbles, on the other hand, are internally static cylindrical magnetic domains, stabilized by external fields and magnetostatic interactions. In its original theory, the droplet was described as an imminently collapsing bubble stabilized by spin transfer torque and, in its zero-frequency limit, as equivalent to a bubble. Without nanoscale lateral confinement, pinning, or an external applied field, such a nanobubble is unstable, and should collapse. Here, we show that we can freeze dynamic droplets into static nanobubbles by decreasing the magnetic field. While the bubble has virtually the same resistance as the droplet, all signs of low-frequency microwave noise disappear. The transition is fully reversible and the bubble can be thawed back into a droplet if the magnetic field is increased under current. Whereas the droplet collapses without a sustaining current, the bubble is highly stable and remains intact for days without external drive. Electrical measurements are complemented by direct observation using scanning transmission x-ray microscopy, which corroborates the analysis and confirms that the bubble is stabilized by pinning.

Magnetic droplets are a type of non-topological magnetic soliton, which are stabilised and sustained by spin-transfer torques for instance. Without this, they would collapse. Here Ahlberg et al show that by decreasing the applied magnetic field, droplets can be frozen, forming a static nanobubble

Giant nonlinear self-phase modulation of large-amplitude spin waves in microscopic YIG waveguides

Nonlinear self-phase modulation is a universal phenomenon responsible, for example, for the formation of propagating dynamic solitons. It has been reported for waves of different physical nature. However its direct experimental observation for spin waves has been challenging. Here we show that exceptionally strong phase modulation can be achieved for spin waves in microscopic waveguides fabricated from nanometer-thick films of magnetic insulator, which support propagation of spin waves with large amplitudes corresponding to angles of magnetization precession exceeding 10°. At these amplitudes, the nonstationary nonlinear dynamic response of the spin system causes an extreme broadening of the spectrum of spin-wave pulses resulting in a strong spatial variation of the spin-wave wavelength and a temporal variation of the spin-wave phase across the pulse. Our findings demonstrate great complexity of nonlinear wave processes in microscopic magnetic structures and importance of their understanding for technical applications of spin waves in integrated devices.

Nonequilibrium sub-10 nm spin-wave soliton formation in FePt nanoparticles

Magnetic nanoparticles such as FePt in the L10 phase are the bedrock of our current data storage technology. As the grains become smaller to keep up with technological demands, the superparamagnetic limit calls for materials with higher magnetocrystalline anisotropy. This, in turn, reduces the magnetic exchange length to just a few nanometers, enabling magnetic structures to be induced within the nanoparticles. Here, we describe the existence of spin-wave solitons, dynamic localized bound states of spin-wave excitations, in FePt nanoparticles. We show with time-resolved x-ray diffraction and micromagnetic modeling that spin-wave solitons of sub-10 nm sizes form out of the demagnetized state following femtosecond laser excitation. The measured soliton spin precession frequency of 0.1 THz positions this system as a platform to develop novel miniature devices.

Evidence for spin current driven Bose-Einstein condensation of magnons

The quanta of magnetic excitations - magnons - are known for their unique ability to undergo Bose-Einstein condensation at room temperature. This fascinating phenomenon reveals itself as a spontaneous formation of a coherent state under the influence of incoherent stimuli. Spin currents have been predicted to offer electronic control of Bose-Einstein condensates, but this phenomenon has not been experimentally evidenced up to now. Here we show that current-driven Bose-Einstein condensation can be achieved in nanometer-thick films of magnetic insulators with tailored nonlinearities and minimized magnon interactions. We demonstrate that, above a certain threshold, magnons injected by the spin current overpopulate the lowest-energy level forming a highly coherent spatially extended state. We quantify the chemical potential of the driven magnon gas and show that, at the critical current, it reaches the energy of the lowest magnon level. Our results pave the way for implementation of integrated microscopic quantum magnonic and spintronic devices.

Magnetization dynamics in artificial spin ice

In this topical review, we present key results of studies on magnetization dynamics in artificial spin ice (ASI), which are arrays of magnetically interacting nanostructures. Recent experimental and theoretical progress in this emerging area, which is at the boundary between research on frustrated magnetism and high-frequency studies of artificially created nanomagnets, is reviewed. The exploration of ASI structures has revealed fascinating discoveries in correlated spin systems. Artificially created spin ice lattices offer unique advantages as they allow for a control of the interactions between the elements by their geometric properties and arrangement. Magnonics, on the other hand, is a field that explores spin dynamics in the gigahertz frequency range in magnetic micro- and nanostructures. In this context, magnonic crystals are particularly important as they allow the modification of spin-wave properties and the observation of band gaps in the resonance spectra. Very recently, there has been considerable progress, experimentally and theoretically, in combining aspects of both fields-artificial spin ice and magnonics-enabling new functionalities in magnonic and spintronic applications using ASI, as well as providing a deeper understanding of geometrical frustration in the gigahertz range. Different approaches for the realization of ASI structures and their experimental characterization in the high-frequency range are described and the appropriate theoretical models and simulations are reviewed. Special attention is devoted to linking these findings to the quasi-static behavior of ASI and dynamic investigations in magnonics in an effort to bridge the gap between both areas further and to stimulate new research endeavors.

Controlled nonlinear magnetic damping in spin-Hall nano-devices

Large-amplitude magnetization dynamics is substantially more complex compared to the low-amplitude linear regime, due to the inevitable emergence of nonlinearities. One of the fundamental nonlinear phenomena is the nonlinear damping enhancement, which imposes strict limitations on the operation and efficiency of magnetic nanodevices. In particular, nonlinear damping prevents excitation of coherent magnetization auto-oscillations driven by the injection of spin current into spatially extended magnetic regions. Here, we propose and experimentally demonstrate that nonlinear damping can be controlled by the ellipticity of magnetization precession. By balancing different contributions to anisotropy, we minimize the ellipticity and achieve coherent magnetization oscillations driven by spatially extended spin current injection into a microscopic magnetic disk. Our results provide a route for the implementation of efficient active spintronic and magnonic devices driven by spin current.

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 nonlinear 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 nanoconstrictions 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 neuromorphic computing, directly compatible with CMOS technology.

Experimental Observation of Single Skyrmion Signatures in a Magnetic Tunnel Junction

We have deterministically created a stable topological spin texture in magnetic tunnel junctions (MTJ) by using pulsed or microwave currents. The spin texture is characterized by a field-dependent intermediate resistance state and a new magnetic resonance. Micromagnetic simulations show that the observations are consistent with the nucleation of a single skyrmion, facilitated by a spatially nonuniform stray field. The unique resonance spectrum is identified as the skyrmion breathing mode and a skyrmion diameter of 75 nm is estimated. This work shows the possibility to create skyrmions in MTJs without the Dzyaloshinskii-Moriya interaction and could lead to noninvasive, on-chip skyrmion measurement.

Backscattering Immunity of Dipole-Exchange Magnetostatic Surface Spin Waves

The existence of backscattering-immune spin-wave modes is demonstrated in magnetic thin films of nanoscale thickness. Our results reveal that chiral magnetostatic surface waves (CMSSWs), which propagate perpendicular to the magnetization direction in an in-plane magnetized thin film, are robust against backscattering from surface defects. CMSSWs are protected against various types of surface inhomogeneities and defects as long as their frequency lies inside the gap of the volume modes. Our explanation is independent of the topology of the modes and predicts that this robustness is a consequence of symmetry breaking of the dynamic magnetic fields of CMSSWs due to the off-diagonal part of the dipolar interaction tensor, which is present both for long- (dipole-dominated) and short-wavelength (exchange-dominated) spin waves. Micromagnetic simulations confirm the robust character of the CMSSWs. Our results open a new direction in designing highly efficient magnonic logic elements and devices employing CMSSWs in nanoscale thin films.

Ultra-fast artificial neuron: generation of picosecond-duration spikes in a current-driven antiferromagnetic auto-oscillator

We demonstrate analytically and numerically, that a thin film of an antiferromagnetic (AFM) material, having biaxial magnetic anisotropy and being driven by an external spin-transfer torque signal, can be used for the generation of ultra-short “Dirac-delta-like” spikes. The duration of the generated spikes is several picoseconds for typical AFM materials and is determined by the inplane magnetic anisotropy and the effective damping of the AFM material. The generated output signal can consist of a single spike or a discrete group of spikes (“bursting”), which depends on the repetition (clock) rate, amplitude, and shape of the external control signal. The spike generation occurs only when the amplitude of the control signal exceeds a certain threshold, similar to the action of a biological neuron in response to an external stimulus. The “threshold” behavior of the proposed AFM spike generator makes possible its application not only in the traditional microwave signal processing but also in the future neuromorphic signal processing circuits working at clock frequencies of tens of gigahertz.

Generation and stability of dynamical skyrmions and droplet solitons

A spin-polarized current in a nanocontact to a magnetic film can create collective magnetic oscillations by compensating the magnetic damping. In particular, in materials with uniaxial magnetic anisotropy, droplet solitons have been observed-a self-localized excitation consisting of partially reversed magnetization that precesses coherently in the nanocontact region. It is also possible to generate topological droplet solitons, known as dynamical skyrmions (DSs). Here, we show that spin-polarized current thresholds for DS creation depend not only on the material's parameters but also on the initial magnetization state and the rise time of the spin-polarized current. We study the conditions that promote either droplet or DS formation and describe their stability in magnetic films without Dzyaloshinskii-Moriya interactions. The Oersted fields from the applied current, the initial magnetization state, and the rise time of the injected current can determine whether a droplet or a DS forms. DSs are found to be more stable than droplets. We also discuss electrical characteristics that can be used to distinguish these magnetic objects.

Investigation of magnetic droplet solitons using x-ray holography with extended references

A dissipative magnetic soliton, or magnetic droplet, is a structure that has been predicted to exist within a thin magnetic layer when non-linearity is balanced by dispersion, and a driving force counteracts the inherent damping of the spin precession. Such a soliton can be formed beneath a nano-contact (NC) that delivers a large spin-polarized current density into a magnetic layer with perpendicular magnetic anisotropy. Although the existence of droplets has been confirmed from electrical measurements and by micromagnetic simulations, only a few attempts have been made to directly observe the magnetic landscape that sustains these structures, and then only for a restricted set of experimental parameter values. In this work we use and x-ray holography technique HERALDO, to image the magnetic structure of the [Co/Ni]x4 multilayer within a NC orthogonal pseudo spin-valve, for different range of magnetic fields and injected electric currents. The magnetic configuration imaged at −33 mA and 0.3 T for devices with 90 nm NC diameter reveals a structure that is within the range of current where the droplet soliton exist based on our electrical measurements and have it is consistent with the expected size of the droplet (∼100 nm diameter) and its spatial position within the sample. We also report the magnetisation configurations observed at lower DC currents in the presence of fields (0–50 mT), where it is expected to observe regimes of the unstable droplet formation.

Dynamics of nonlinear Schrödinger breathers in a potential trap

We consider the evolution of the 2-soliton (breather) of the nonlinear Schrödinger equation on a semi-infinite line with the zero boundary condition and a linear potential, which corresponds to the gravity field in the presence of a hard floor. This setting can be implemented in atomic Bose-Einstein condensates, and in a nonlinear planar waveguide in optics. In the absence of the gravity, repulsion of the breather from the floor leads to its splitting into constituent fundamental solitons, if the initial distance from the floor is smaller than a critical value; otherwise, the moving breather persists. In the presence of gravity, the breather always splits into a pair of "co-hopping" fundamental solitons, which may be frequency locked in the form of a quasi-breather, or unlocked, forming an incoherent pseudo-breather. Some essential results are obtained in an analytical form, in addition to the systematic numerical investigation.

Microwave probe stations with three-dimensional control of the magnetic field to study high-frequency dynamics in nanoscale devices

We present two microwave probe stations with motorized rotary stages for adjusting the magnitude and angle of the applied magnetic field. In the first system, the magnetic field is provided by an electromagnet and can be adjusted from 0 to ∼1.4 T while its polar angle (θ) can be varied from 0° to 360°. In the second system, the magnetic field is provided by a Halbach array permanent magnet, which can be rotated and translated to cover the full range of polar (θ) and azimuthal (φ) angles with a tunable field magnitude up to ∼1 T. Both systems are equipped with microwave probes, bias-Ts, amplifiers, and spectrum analyzers to allow for microwave characterization up to 40 GHz, as well as software to automatically perform continuous large sets of electrical and microwave measurements.

Direct Observation of Zhang-Li Torque Expansion of Magnetic Droplet Solitons

Magnetic droplets are nontopological dynamical solitons that can be nucleated in nanocontact based spin torque nano-oscillators (STNOs) with perpendicular magnetic anisotropy free layers. While theory predicts that the droplet should be of the same size as the nanocontact, its inherent drift instability has thwarted attempts at observing it directly using microscopy techniques. Here, we demonstrate highly stable magnetic droplets in all-perpendicular STNOs and present the first detailed droplet images using scanning transmission X-ray microscopy. In contrast to theoretical predictions, we find that the droplet diameter is about twice as large as the nanocontact. By extending the original droplet theory to properly account for the lateral current spread underneath the nanocontact, we show that the large discrepancy primarily arises from current-in-plane Zhang-Li torque adding an outward pressure on the droplet perimeter. Electrical measurements on droplets nucleated using a reversed current in the antiparallel state corroborate this picture.

Generation and annihilation time of magnetic droplet solitons

Magnetic droplet solitons were first predicted to occur in materials with uniaxial magnetic anisotropy due to a long-range attractive interaction between elementary magnetic excitations, magnons. A non-equilibrium magnon population provided by a spin-polarized current in nanocontacts enables their creation and there is now clear experimental evidence for their formation, including direct images obtained with scanning x-ray transmission microscopy. Interest in magnetic droplets is associated with their unique magnetic dynamics that can lead to new types of high frequency nanometer scale oscillators of interest for information processing, including in neuromorphic computing. However, there are no direct measurements of the time required to nucleate droplet solitons or their lifetime-experiments to date only probe their steady-state characteristics, their response to dc spin-currents. Here we determine the timescales for droplet annihilation and generation using current pulses. Annihilation occurs in a few nanoseconds while generation can take several nanoseconds to a microsecond depending on the pulse amplitude. Micromagnetic simulations show that there is an incubation time for droplet generation that depends sensitively on the initial magnetic state of the nanocontact. An understanding of these processes is essential to utilizing the unique characteristics of magnetic droplet solitons oscillators, including their high frequency, tunable and hysteretic response.

Designing magnetic droplet soliton nucleation employing spin polarizer

We show by means of micromagnetic simulations that spin polarizer in nano-contact (NC) spin torque oscillators as the representative of the fixed layer in an orthogonal pseudo-spin valve can be employed to design and to control magnetic droplet soliton nucleation and dynamics. We found that using a tilted spin polarizer layer decreases the droplet nucleation time which is more suitable for high speed applications. However, a tilted spin polarizer increases the nucleation current and decreases the frequency stability of the droplet. Additionally, by driving the magnetization inhomogenously at the NC region, it is found that a tilted spin polarizer reduces the precession angle of the droplet and through an interplay with the Oersted field of the DC current, it breaks the spatial symmetry of the droplet profile. Our findings explore fundamental insight into nano-scale magnetic droplet soliton dynamics with potential tunability parameters for future microwave electronics.

Spin caloritronic nano-oscillator

Energy loss due to ohmic heating is a major bottleneck limiting down-scaling and speed of nano-electronic devices, and harvesting ohmic heat for signal processing is a major challenge in modern electronics. Here, we demonstrate that thermal gradients arising from ohmic heating can be utilized for excitation of coherent auto-oscillations of magnetization and for generation of tunable microwave signals. The heat-driven dynamics is observed in Y₃Fe₅O₁₂/Pt bilayer nanowires where ohmic heating of the Pt layer results in injection of pure spin current into the Y₃Fe₅O₁₂ layer. This leads to excitation of auto-oscillations of the Y₃Fe₅O₁₂ magnetization and generation of coherent microwave radiation. Our work paves the way towards spin caloritronic devices for microwave and magnonic applications.

Harvesting ohmic heat for signal processing is one of major challenges in modern electronics and spin caloritronics, but not yet well accomplished. Here the authors demonstrate a spin torque oscillator device driven by pure spin current arising from thermal gradient across an Y₃Fe₅O₁₂/Pt interface.

X-ray imaging of spin currents and magnetisation dynamics at the nanoscale

Understanding how spins move in time and space is the aim of both fundamental and applied research in modern magnetism. Over the past three decades, research in this field has led to technological advances that have had a major impact on our society, while improving the understanding of the fundamentals of spin physics. However, important questions still remain unanswered, because it is experimentally challenging to directly observe spins and their motion with a combined high spatial and temporal resolution. In this article, we present an overview of the recent advances in x-ray microscopy that allow researchers to directly watch spins move in time and space at the microscopically relevant scales. We discuss scanning x-ray transmission microscopy (STXM) at resonant soft x-ray edges, which is available at most modern synchrotron light sources. This technique measures magnetic contrast through the x-ray magnetic circular dichroism (XMCD) effect at the resonant absorption edges, while focusing the x-ray radiation at the nanometre scale, and using the intrinsic pulsed structure of synchrotron-generated x-rays to create time-resolved images of magnetism at the nanoscale. In particular, we discuss how the presence of spin currents can be detected by imaging spin accumulation, and how the magnetisation dynamics in thin ferromagnetic films can be directly imaged. We discuss how a direct look at the phenomena allows for a deeper understanding of the the physics at play, that is not accessible to other, more indirect techniques. Finally, we present an overview of the exciting opportunities that lie ahead to further understand the fundamentals of novel spin physics, opportunities offered by the appearance of diffraction limited storage rings and free electron lasers.

Interface-Induced Phenomena in Magnetism

This article reviews static and dynamic interfacial effects in magnetism, focusing on interfacially-driven magnetic effects and phenomena associated with spin-orbit coupling and intrinsic symmetry breaking at interfaces. It provides a historical background and literature survey, but focuses on recent progress, identifying the most exciting new scientific results and pointing to promising future research directions. It starts with an introduction and overview of how basic magnetic properties are affected by interfaces, then turns to a discussion of charge and spin transport through and near interfaces and how these can be used to control the properties of the magnetic layer. Important concepts include spin accumulation, spin currents, spin transfer torque, and spin pumping. An overview is provided to the current state of knowledge and existing review literature on interfacial effects such as exchange bias, exchange spring magnets, spin Hall effect, oxide heterostructures, and topological insulators. The article highlights recent discoveries of interface-induced magnetism and non-collinear spin textures, non-linear dynamics including spin torque transfer and magnetization reversal induced by interfaces, and interfacial effects in ultrafast magnetization processes.

Order of magnitude improvement of nano-contact spin torque nano-oscillator performance

Spin torque nano-oscillators (STNO) represent a unique class of nano-scale microwave signal generators and offer a combination of intriguing properties, such as nano sized footprint, ultrafast modulation rates, and highly tunable microwave frequencies from 100 MHz to close to 100 GHz. However, their low output power and relatively high threshold current still limit their applicability and must be improved. In this study, we investigate the influence of the bottom Cu electrode thickness (t_Cu) in nano-contact STNOs based on Co/Cu/NiFe GMR stacks and with nano-contact diameters ranging from 60 to 500 nm. Increasing t_Cu from 10 to 70 nm results in a 40% reduction of the threshold current, an order of magnitude higher microwave output power, and close to two orders of magnitude better power conversion efficiency. Numerical simulations of the current distribution suggest that these dramatic improvements originate from a strongly reduced lateral current spread in the magneto-dynamically active region.

A 20 nm spin Hall nano-oscillator

Spin Hall nano-oscillators (SHNOs) are an emerging class of pure spin current driven microwave signal generators. Through the fabrication of 20 nm nano-constrictions in Pt/NiFe bilayers, we demonstrate that SHNOs can be scaled down to truly nanoscopic dimensions, with the added benefit of ultra-low operating currents and improved power conversion efficiency. The lateral confinement leads to a strong shape anisotropy field as well as an additional demagnetizing field whose reduction with increasing auto-oscillation amplitude can yield a positive current tunability contrary to the negative tunability commonly observed for localized excitations in extended magnetic layers. Micromagnetic simulations corroborate the experimental findings and suggest that the active magnetodynamic area resides up to 100 nm outside of the nano-constriction.

Breaking of Galilean Invariance in the Hydrodynamic Formulation of Ferromagnetic Thin Films

Microwave magnetodynamics in ferromagnets are often studied in the small-amplitude or weakly nonlinear regime corresponding to modulations of a well-defined magnetic state. However, strongly nonlinear regimes, where the aforementioned approximations are not applicable, have become experimentally accessible. By reinterpreting the governing Landau-Lifshitz equation of motion, we derive an exact set of equations of dispersive hydrodynamic form that are amenable to analytical study even when full nonlinearity and exchange dispersion are included. The resulting equations are shown to, in general, break Galilean invariance. A magnetic Mach number is obtained as a function of static and moving reference frames. The simplest class of solutions are termed uniform hydrodynamic states (UHSs), which exhibit fluidlike behavior including laminar flow at subsonic speeds and the formation of a Mach cone and wave fronts at supersonic speeds. A regime of modulational instability is also possible, where the UHS is violently unstable. The hydrodynamic interpretation opens up novel possibilities in magnetic research.

Spin wave localization in tangentially magnetized films

We present an analytical description of localized spin wave modes that form in a parabolic field minimum in a thin ferromagnetic film. Mode profiles proportional to Hermite functions are eigenfuctions of the applied field and exchange parts of the equations of motion, and also provide a basis for numerical approximation of magnetostatic interactions. We find that the spin wave modes are roughly equally spaced in frequency and have roughly equal coupling to a uniform driving field. The calculated mode frequencies and corresponding profiles of localized spin wave modes are in good agreement with micromagnetic modeling and previously published experimental results on multiple resonances from a series of localized modes detected by ferromagnetic resonance force microscopy.

Magnetic droplet nucleation boundary in orthogonal spin-torque nano-oscillators

Static and dynamic magnetic solitons play a critical role in applied nanomagnetism. Magnetic droplets, a type of non-topological dissipative soliton, can be nucleated and sustained in nanocontact spin-torque oscillators with perpendicular magnetic anisotropy free layers. Here, we perform a detailed experimental determination of the full droplet nucleation boundary in the current–field plane for a wide range of nanocontact sizes and demonstrate its excellent agreement with an analytical expression originating from a stability analysis. Our results reconcile recent contradicting reports of the field dependence of the droplet nucleation. Furthermore, our analytical model both highlights the relation between the fixed layer material and the droplet nucleation current magnitude, and provides an accurate method to experimentally determine the spin transfer torque asymmetry of each device.

Magnetic droplets occur in nanocontact spin-torque oscillators with perpendicular anisotropy, forming part of a family of particle-like magnetic objects, which may be excited for high-frequency applications. Here, the authors determine a current–field phase diagram for magnetic droplet nucleation.

Skyrmion Creation and Manipulation by Nano-Second Current Pulses

Easy creation and manipulation of skyrmions is important in skyrmion based devices for data storage and information processing. We show that a nano-second current pulse alone is capable of creating/deleting and manipulating skyrmions in a spin valve with a perpendicularly magnetized free layer and broken chiral symmetry. Interestingly, for an in-plane magnetized fixed layer, the free layer changes from a single domain at zero current to a Neel wall at an intermediate current density. Reverse the current polarity, the Neel wall changes to its image inversion. A properly designed nano-second current pulse, that tends to convert one type of Neel walls to its image inversion, ends up to create a stable skyrmion without assistance of external fields. For a perpendicularly magnetized fixed layer, the skyrmion size can be effectively tuned by a current density.

Spin-wave-beam driven synchronization of nanocontact spin-torque oscillators

The synchronization of multiple nanocontact spin-torque oscillators (NC-STOs) is mediated by propagating spin waves (SWs). Although it has been shown that the Oersted field generated in the vicinity of the NC can dramatically alter the emission pattern of SWs, its role in the synchronization behaviour of multiple NCs has not been considered so far. Here we investigate the synchronization behaviour in multiple NC-STOs oriented either vertically or horizontally, with respect to the in-plane component of the external field. Synchronization is promoted (impeded) by the Oersted field landscape when the NCs are oriented vertically (horizontally) due to the highly anisotropic SW propagation. Not only is robust synchronization between two oscillators observed for separations larger than 1,000 nm, but synchronization of up to five oscillators, a new record, has been observed in the vertical array geometry. Furthermore, the synchronization can no longer be considered mutual in nature.

Direct observation and imaging of a spin-wave soliton with p-like symmetry

Spin waves, the collective excitations of spins, can emerge as nonlinear solitons at the nanoscale when excited by an electrical current from a nanocontact. These solitons are expected to have essentially cylindrical symmetry (that is, s-like), but no direct experimental observation exists to confirm this picture. Using a high-sensitivity time-resolved magnetic X-ray microscopy with 50 ps temporal resolution and 35 nm spatial resolution, we are able to create a real-space spin-wave movie and observe the emergence of a localized soliton with a nodal line, that is, with p-like symmetry. Micromagnetic simulations explain the measurements and reveal that the symmetry of the soliton can be controlled by magnetic fields. Our results broaden the understanding of spin-wave dynamics at the nanoscale, with implications for the design of magnetic nanodevices.

Injecting spin-polarized current into a ferromagnetic thin film via a nanocontact is expected to generate a radially-symmetric spin wave soliton. Here, the authors use time-resolved x-ray microscopy and micromagnetic simulations to demonstrate the occurrence of p-like symmetry associated with non-uniform magnetic fields in the nanocontact region.

Topological, non-topological and instanton droplets driven by spin-transfer torque in materials with perpendicular magnetic anisotropy and Dzyaloshinskii-Moriya Interaction

The interfacial Dzyaloshinskii-Moriya Interaction can modify the topology of droplets excited by a localized spin-polarized current. Here, we show that, in addition to the stationary droplet excitations with skyrmion number either one (topological) or zero (non-topological), there exists, for a fixed current, an excited mode with a non-stationary time behavior. We call this mode "instanton droplet", which is characterized by time domain transitions of the skyrmion number. These transitions are coupled to an emission of incoherent spin-waves that can be observed in the frequency domain as a source of noise. Our results are interesting from a fundamental point of view to study spin-wave emissions due to a topological transition in current-driven systems, and could open the route for experiments based on magnetoresistance effect for the design of a further generation of nanoscale microwave oscillators.

A three-dimensional spin-diffusion model for micromagnetics

We solve a time-dependent three-dimensional spin-diffusion model coupled to the Landau-Lifshitz-Gilbert equation numerically. The presented model is validated by comparison to two established spin-torque models: The model of Slonzewski that describes spin-torque in multi-layer structures in the presence of a fixed layer and the model of Zhang and Li that describes current driven domain-wall motion. It is shown that both models are incorporated by the spin-diffusion description, i.e., the nonlocal effects of the Slonzewski model are captured as well as the spin-accumulation due to magnetization gradients as described by the model of Zhang and Li. Moreover, the presented method is able to resolve the time dependency of the spin-accumulation.

Direct Observation of a Localized Magnetic Soliton in a Spin-Transfer Nanocontact

We report the direct observation of a localized magnetic soliton in a spin-transfer nanocontact using scanning transmission x-ray microscopy. Experiments are conducted on a lithographically defined 150 nm diameter nanocontact to an ultrathin ferromagnetic multilayer with perpendicular magnetic anisotropy. Element-resolved x-ray magnetic circular dichroism images show an abrupt onset of a magnetic soliton excitation localized beneath the nanocontact at a threshold current. However, the amplitude of the excitation ≃25° at the contact center is far less than that predicted (⪅180°), showing that the spin dynamics is not described by existing models.

Dynamically stabilized magnetic skyrmions

Magnetic skyrmions are topologically non-trivial spin textures that manifest themselves as quasiparticles in ferromagnetic thin films or noncentrosymmetric bulk materials. So far attention has focused on skyrmions stabilized either by the Dzyaloshinskii–Moriya interaction (DMI) or by dipolar interaction, where in the latter case the excitations are known as bubble skyrmions. Here we demonstrate the existence of a dynamically stabilized skyrmion, which exists even when dipolar interactions and DMI are absent. We establish how such dynamic skyrmions can be nucleated, sustained and manipulated in an effectively lossless medium under a nanocontact. As quasiparticles, they can be transported between two nanocontacts in a nanowire, even in complete absence of DMI. Conversely, in the presence of DMI, we observe that the dynamical skyrmion experiences strong breathing. All of this points towards a wide range of skyrmion manipulation, which can be studied in a much wider class of materials than considered so far.

Magnetic skyrmions are particle-like spin textures with non-trivial topology which are stabilized by local magnetic interactions. Here, the authors demonstrate theoretically a class of skyrmions which are stabilized dynamically in the absence of interactions in a nanocontact spin-torque oscillator.

A scenario for magnonic spin-wave traps

Spatially resolved measurements of the magnetization dynamics on a thin CoFeB film induced by an intense laser pump-pulse reveal that the frequencies of resulting spin-wave modes depend strongly on the distance to the pump center. This can be attributed to a laser generated temperature profile. We determine a shift of 0.5 GHz in the spin-wave frequency due to the spatial thermal profile induced by the femtosecond pump pulse that persists for up to one nanosecond. Similar experiments are presented for a magnonic crystal composed of a CoFeB-film based antidot lattice with a Damon Eshbach mode at the Brillouin zone boundary and its consequences are discussed.

Perturbation theory for propagating magnetic droplet solitons

Droplet solitons are strongly nonlinear, inherently dynamic structures in the magnetization of ferromagnets, balancing dispersion (exchange energy) with focusing nonlinearity (strong perpendicular anisotropy). Large droplet solitons have the approximate form of a circular domain wall sustained by precession and, in contrast to single magnetic vortices, are predicted to propagate in an extended, homogeneous magnetic medium. In this work, multiscale perturbation theory is used to develop an analytical framework for investigating the impact of additional physical effects on the behaviour of a propagating droplet. After first developing soliton perturbation theory in the general context of Hamiltonian systems, a number of physical phenomena of current interest are investigated. These include droplet–droplet and droplet–boundary interactions, spatial magnetic field inhomogeneities, spin transfer torque induced forcing in a nanocontact device and damping. Their combined effects demonstrate the fundamental mechanisms for a previously observed droplet drift instability and under what conditions a slowly propagating droplet can be supported by the nanocontact, important considerations for applications. This framework emphasizes the particle-like dynamics of the droplet, providing analytically tractable and practical predictions for modern experimental configurations.

Dynamical skyrmion state in a spin current nano-oscillator with perpendicular magnetic anisotropy

We study the spectral characteristics of spin current nano-oscillators based on the Pt/[Co/Ni] magnetic multilayer with perpendicular magnetic anisotropy. By varying the applied magnetic field and current, both localized and propagating spin wave modes of the oscillation are achieved. At small fields, we observe an abrupt onset of the modulation sidebands. We use micromagnetic simulations to identify this state as a dynamical magnetic skyrmion stabilized in the active device region by spin current injection, whose current-induced dynamics is accompanied by the gyrotropic motion of the core due to the skew deflection. Our results demonstrate a practical route for controllable skyrmion manipulation by spin current in magnetic thin films.

Gilbert damping in noncollinear ferromagnets

The precession and damping of a collinear magnetization displaced from its equilibrium are well described by the Landau-Lifshitz-Gilbert equation. The theoretical and experimental complexity of noncollinear magnetizations is such that it is not known how the damping is modified by the noncollinearity. We use first-principles scattering theory to investigate transverse domain walls (DWs) of the important ferromagnetic alloy Ni80Fe20 and show that the damping depends not only on the magnetization texture but also on the specific dynamic modes of Bloch and Néel DWs in ways that were not theoretically predicted. Even in the highly disordered Ni80Fe20 alloy, the damping is found to be remarkably nonlocal.

Stable magnetic droplet solitons in spin-transfer nanocontacts

Magnetic thin films with perpendicular magnetic anisotropy have localized excitations that correspond to reversed, dynamically precessing magnetic moments, which are known as magnetic droplet solitons. Fundamentally, these excitations are associated with an attractive interaction between elementary spin-excitations and have been predicted to occur in perpendicularly magnetized materials in the absence of damping. Although damping suppresses these excitations, it can be compensated by spin-transfer torques when an electrical current flows in nanocontacts to ferromagnetic thin films. Theory predicts the appearance of magnetic droplet solitons in nanocontacts at a threshold current and, recently, experimental signatures of droplet nucleation have been reported. However, to date, these solitons have been observed to be nearly reversible excitations, with only partially reversed magnetization. Here, we show that magnetic droplet solitons exhibit a strong hysteretic response in field and current, proving the existence of bistable states: droplet and non-droplet states. In the droplet soliton state we find that the magnetization in the contact is almost fully reversed. These observations, in addition to their fundamental interest, are important to understanding and controlling droplet motion, nucleation and annihilation.

Magnetization boundary conditions at a ferromagnetic interface of finite thickness

We develop a systematic approach to derive boundary conditions at an interface between two ferromagnetic materials in the continuous medium approximation. The approach treats the interface as a two-sublattice material, although the final equations connect magnetizations outside of the interface and therefore do not explicitly depend on its structure. Instead, the boundary conditions are defined in terms of some average properties of the interface, which may also have a finite thickness. In addition to the interface anisotropy and symmetric exchange coupling, this approach allows us to take into account coupling resulting from inversion symmetry breaking in the vicinity of the interface, such as the Dzyaloshinskii-Moriya antisymmetric exchange interaction. In the case of negligible interface anisotropy and Dzyaloshinskii-Moriya exchange parameters, the derived boundary conditions represent a generalization of those proposed earlier by Barnaś and Mills and are therefore named 'generalized Barnaś-Mills boundary conditions'. We demonstrate how one could use the boundary conditions to extract parameters of the interface via fitting of appropriate experimental data. The developed theory could be applied to modeling of both linear and non-linear spin waves, including exchange, dipole-exchange, magnetostatic, and retarded modes, as well as to calculations of non-uniform equilibrium micromagnetic configurations near the interface, with a direct impact on the research in magnonics and micromagnetism.

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.

Origin of spectral purity and tuning sensitivity in a spin transfer vortex nano-oscillator

We investigate the microwave characteristics of a spin transfer nano-oscillator (STNO) based on coupled vortices as a function of the perpendicular magnetic field H(⊥). Interestingly, we find that our vortex-based oscillator is quasi-isochronous independently of H(⊥) and for a dc current ranging between 18 and 25 mA. It means that the severe nonlinear broadening usually observed in STNOs can be suppressed on a broad range of bias. Still, the generation linewidth displays strong variations on H(⊥) (from 40 kHz to 1 MHz), while the frequency tunability in current remains almost constant (7  MHz/mA). This demonstrates that isochronicity does not necessarily imply a loss of frequency tunability, which is here governed by the current induced Oersted field. It is not sufficient either to achieve the highest spectral purity in the full range of H(⊥). We show that the observed linewidth broadenings are due to the excited mode interacting with a lower energy overdamped mode, which occurs at the successive crossings between harmonics of these two modes. These findings open new possibilities for the design of STNOs and the optimization of their performance.

Confined dissipative droplet solitons in spin-valve nanowires with perpendicular magnetic anisotropy

Magnetic dissipative droplets are localized, strongly nonlinear dynamical modes excited in nanocontact spin valves with perpendicular magnetic anisotropy. These modes find potential application in nanoscale structures for magnetic storage and computation, but dissipative droplet studies have so far been limited to extended thin films. Here, numerical and asymptotic analyses are used to demonstrate the existence and properties of novel solitons in confined structures. As a nanowire's width is decreased with a nanocontact of fixed size at its center, the observed modes undergo transitions from a fully localized two-dimensional droplet into a two-dimensional droplet edge mode and then a pulsating one-dimensional droplet. These solitons are interpreted as dissipative versions of classical, conservative solitons, allowing for an analytical description of the modes and the mechanisms of bifurcation. The presented results open up new possibilities for the study of low-dimensional solitons and droplet applications in nanostructures.