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Parametric spin wave excitation allows studying a variety of nonlinear phenomena, such as magnon scattering. In patterned micro- and nanostructures the magnon spectra is discrete and translational symmetry is broken, which means allowable scattering channels differ from those in continuous films. An example is non-degenerate scattering by which high-power transverse field pumping creates two magnons with distinct frequencies around half the pumping frequency. Through micromagnetics simulations, we show under certain conditions that combining two pumping frequencies generates new magnon modes through a process of stimulated magnon scattering. Such processes are found to depend on the film geometry and sequence of the pumping fields., Comment: 6 pages, 5 figures

We present a computational study of the parametric excitation of spin waves in thin film disks with a mode-resolved approach. The method involves projecting out the time-dependent magnetization, computed using micromagnetics simulations, onto the spatial profile of the eigenmodes that are obtained from the linearization of the equations of motion. Unlike spectral analysis in the frequency domain, the projection allows for the analysis of transient mode dynamics under parametric excitation. We apply this method to parallel pumping of quantized spin wave modes in in-plane magnetized thin-film disks, where phenomena such as frequency pulling, mutual phase locking, and higher-order magnon scattering processes are identified., Comment: 12 pages, 11 figures

Magnons are elementary excitations in magnetic materials and undergo nonlinear multimode scattering processes at large input powers. In experiments and simulations, we show that the interaction between magnon modes of a confined magnetic vortex can be harnessed for pattern recognition. We study the magnetic response to signals comprising sine wave pulses with frequencies corresponding to radial mode excitations. Three-magnon scattering results in the excitation of different azimuthal modes, whose amplitudes depend strongly on the input sequences. We show that recognition rates above 95\% can be attained for four-symbol sequences using the scattered modes, with strong performance maintained with the presence of amplitude noise in the inputs.

The spectral signatures of magnetic skyrmions under microwave field excitation are of fundamental interest and can be an asset for high frequency applications. These topological solitons can be tailored in multilayered thin films, but the experimental observation of their spin wave dynamics remains elusive, in particular due to large damping. Here, we study Pt/FeCoB/AlO$_x$ multilayers hosting dense and robust skyrmion lattices at room temperature with Gilbert damping of $\sim 0.02$. We use magnetic force microscopy to characterise their static magnetic phases and broadband ferromagnetic resonance to probe their high frequency response. Micromagnetic simulations reproduce the experiments with accuracy and allow us to identify distinct resonant modes detected in the skyrmion lattice phase. Low ($<$ 2 GHz) and intermediate frequency ($2-8$ GHz) modes involve excitations localised to skyrmion edges in conjunction with precession of the uniform background magnetisation, while a high frequency ($>$ 12 GHz) mode corresponds to in-phase skyrmion core precession emitting spin waves into uniform background with wavelengths in the 50--80 nm range commensurate with the lattice structure. These findings could be instrumental in the investigation of room temperature wave scattering and the implementation of novel microwave processing schemes in reconfigurable arrays of solitons., Comment: Main text and supplemetary information, 31 pages in total, 18 figures

The development of spintronic oscillators is driven by their potential applications in radio frequency telecommunication and neuromorphic computing. In this work, we propose a spintronic oscillator based on the chiral coupling in thin magnetic films with patterned anisotropy. With an in-plane magnetized disk imprinted on an out-of-plane magnetized slab, the oscillator takes a polar vortex-like magnetic structure in the disk stabilized by a strong Dzyaloshinskii-Moriya interaction. By means of micromagnetic simulations, we investigate its oscillatory properties under applied spin current and, by placing an ensemble of oscillators in the near vicinity, we demonstrate their synchronization with different resonant frequencies. Finally, we show their potential application in neuromorphic computing using a network with six oscillators.

A theoretical study of delayed feedback in a spin-torque nano-oscillator model is presented. The feedback acts as a modulation of the supercriticality, which results in changes in the oscillator frequency through a strong nonlinearity, amplitude modulations, and a rich modulation sideband structure in the power spectrum at long delays. Modulation sidebands persist at finite temperatures but some of the complex structure is lost through the finite coherence time of the oscillations., Comment: 7 pages, 7 figures. This is the version of the article before peer review or editing, as submitted by an author to Journal of Physics D: Applied Physics. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at https://doi.org/10.1088/1361-6463/abaf26

We use time-resolved measurement and modeling to study the spin-torque induced motion of a domain wall in perpendicular anisotropy magnets. In disc of diameters between 70 and 100 nm, the wall drifts across the disc with pronounced back-and-forth oscillations that arise because the wall moves in the Walker regime. Several switching paths occur stochastically and lead to distinct switching durations. The wall can cross the disc center either in a ballistic manner or with variably marked oscillations before and after the crossing. The crossing of the center can even occur multiple times if a vertical Bloch line nucleates within the wall. The wall motion is analyzed using a collective coordinate model parametrized by the wall position $q$ and the tilt $\phi$ of its in-plane magnetization projection. The dynamics results from the stretch field, which describes the affinity of the wall to reduce its length and the wall stiffness field describing the wall tendency to reduce dipolar energy by rotating its tilt. The wall oscillations result from the continuous exchange of energy between to the two degrees of freedom $q$ and $\phi$. The stochasticity of the wall dynamics can be understood from the concept of the retention pond: a region in the $q-\phi$ space in which walls are transiently bound to the disc center. Walls having trajectories close to the pond must circumvent it and therefore have longer propagation times. The retention pond disappears for a disc diameter of typically 40 nm: the wall then moves in a ballistic manner irrespective of the dynamics of its tilt. The propagation time is then robust against fluctuations hence reproducible., Comment: submitted to Phys. Rev. B

We propose a time-delay oscillator with Mackey-Glass nonlinearity based on a pinned magnetic domain wall in a thin film nanostrip. Through spin transfer torques, electric currents applied along the strip cause the domain wall to deform and displace away from a geometrical pinning site, which can be converted into a nonlinear transfer function through a suitable choice of a readout. This readout serves as a delay signal, which is subsequently fed back into the applied current with amplification. With micromagnetics simulations, we study the role of the readout position, time delay, and feedback gain on the dynamics of this domain wall. In particular, we highlight regimes in which self-sustained oscillations and complex transients are possible., Comment: 5 pages, 7 figures

Quantum oxide materials possess a vast range of properties stemming from the interplay between the lattice, charge, spin and orbital degrees of freedom, in which electron correlations often play an important role. Historically, the spin-orbit coupling was rarely a dominant energy scale in oxides. It however recently came to the forefront, unleashing various exotic phenomena connected with real and reciprocal-space topology that may be harnessed in spintronics. In this article, we review the recent advances in the new field of oxide spin-orbitronics with a special focus on spin-charge interconversion from the direct and inverse spin Hall and Edelstein effects, and on the generation and observation of topological spin textures such as skyrmions. We highlight the control of spin-orbit-driven effects by ferroelectricity and give perspectives for the field., Comment: Submitted to Nature Reviews Materials

We present an experimental study of vortex dynamics in magnetic nanocontacts based on pseudo spin valves comprising the Co$_2$MnGe Heusler compound. The films were grown by molecular beam epitaxy, where precise stoichiometry control and tailored stacking order allowed us to define the bottom ferromagnetic layer as the reference layer, with minimal coupling between the free and reference layers. 20-nm diameter nanocontacts were fabricated using a nano-indentation technique, leading to self-sustained gyration of the vortex generated by spin-transfer torques above a certain current threshold. By combining frequency- and time-domain measurements, we show that different types of spin-transfer induced dynamics related to different modes associated to the magnetic vortex configuration can be observed, such as mode hopping, mode coexistence and mode extinction appear in addition to the usual gyration mode.

We show experimentally through time-resolved conductance measurements that magnetization reversal through domain wall motion in sub-100 nm diameter magnetic tunnel junctions is dominated by two distinct stochastic effects. The first involves the incubation time related to domain wall nucleation, while the second results from stochastic motion in the Walker regime. Micromagnetics simulations reveal several contributions to temporal pinning of the wall near the disk center, including Bloch point nucleation and wall precession. We show that a reproducible ballistic motion is recovered when Bloch and N\'eel wall profiles become degenerate in energy in optimally sized disks, which enables quasi-deterministic motion.

Ultrathin ferromagnets with frustrated exchange and the Dzyaloshinskii-Moriya interaction can support topological solitons such as skyrmions and antiskyrmions, which are metastable and can be considered particle-antiparticle counterparts. When spin-orbit torques are applied, the motion of an isolated antiskyrmion driven beyond its Walker limit can generate skyrmion-antiskyrmion pairs. Here, we use atomistic spin dynamics simulations to shed light on the scattering processes involved in this pair generation. Under certain conditions a proliferation of these particles and antiparticles can appear with a growth rate and production asymmetry that depend on the strength of the chiral interactions and the dissipative component of the spin-orbit torques. These features are largely determined by scattering processes between antiskyrmions, which can be elastic or result in bound states or annihilation., Comment: 7 pages, 6 figures

Antiferromagnetic materials are promising platforms for next-generation spintronics owing to their fast dynamics and high robustness against parasitic magnetic fields. However, nanoscale imaging of the magnetic order in such materials with zero net magnetization remains a major experimental challenge. Here we show that non-collinear antiferromagnetic spin textures can be imaged by probing the magnetic noise they locally produce via thermal populations of magnons. To this end, we perform nanoscale, all-optical relaxometry with a scanning quantum sensor based on a single nitrogen-vacancy (NV) defect in diamond. Magnetic noise is detected through an increase of the spin relaxation rate of the NV defect, which results in an overall reduction of its photoluminescence signal under continuous laser illumination. As a proof-of-concept, the efficiency of the method is demonstrated by imaging various spin textures in synthetic antiferromagnets, including domain walls, spin spirals and antiferromagnetic skyrmions. This imaging procedure could be extended to a large class of intrinsic antiferromagnets and opens up new opportunities for studying the physics of localized spin wave modes for magnonics., Comment: 7 pages, 5 figures

An implementation of a lattice-based approach for computing the topological skyrmion charge is provided for the open source micromagnetics code MuMax3. Its accuracy with respect to an existing method based on finite difference derivatives is compared for three different test cases. The lattice-based approach is found to be more robust for finite-temperature dynamics and for nucleation and annihilation processes in extended systems., Comment: 9 pages, 5 figures

We present an analytical model to account for the inertial dynamics of a magnetic vortex. The model is based on a deformation of the core profile based on the D\"oring kinetic field, whereby the deformation amplitudes are promoted to dynamical variables in a collective-coordinate approach that provides a natural extension to the Thiele model. This extended model accurately describes complex transients due to inertial effects and the variation of the effective mass with velocity. The model also provides a quantitative description of the inertial dynamics leading up to vortex core reversal, which is analogous to the Walker transition in domain wall dynamics.

Harnessing chaos or intrinsic nonlinear behaviours from dynamical systems is a promising avenue for the development of unconventional information processing technologies. However, the exploitation of such features in spintronic devices has not been attempted despite the many theoretical and experimental evidence of nonlinear behaviour of the magnetization dynamics in nanomagnetic systems. Here, we propose a first step in that direction by unveiling and characterizing the patterns and symbolic dynamics originating from the nonlinear chaotic time-resolved electrical signals generated experimentally by a nanocontact vortex oscillator (NCVO). We use advanced filtering methods to dissociate nonlinear deterministic patterns from thermal fluctuations and show that the emergence of chaos results in the unpredictable alternation of simple oscillatory patterns controlled by the NCVO's core-polarity switching. With phase-space reconstruction techniques, we perform a symbolic analysis of the time series to assess the level of complexity and entropy generated in the chaotic regime. We find that at the centre of its incommensurate region, it can exhibit maximal entropy and complexity. This suggests that NCVOs are promising nonlinear nanoscale source of entropy that could be harnessed for information processing., Comment: 16 pages, 10 figures

We have conducted experiments to probe how the dynamics of nanocontact vortex oscillators can be modulated by an external signal. We explore the phase-locking properties in both the commensurate and chaotic regimes, where chaos appears to impede phase-locking while a more standard behavior is seen in the commensurate phase. These different regimes correspond to how the periodicity of the vortex core reversal relates to the frequency of core gyration around the nanocontact; a commensurate phase appears when the reversal rate is an integer fraction of the gyration frequency, while a chaotic state appears when this ratio is irrational. External modulation where the power spectral density exhibits rich features, appears due to the modulation between the external source frequency, gyration frequency, and core reversal frequency. We explain these features with first- or second-order modulation between the three frequencies. Phase-locking is also visible between the external source frequency and internal vortex modes (gyration and core reversal modes)., Comment: 11 pages, 7 figures

We present an experimental study of spin-torque driven vortex self-oscillations in magnetic nanocontacts. We find that above a certain threshold in applied currents, the vortex gyration around the nanocontact is modulated by relaxation oscillations, which involve periodic reversals of the vortex core. This modulation leads to the appearance of commensurate but also more interestingly here, incommensurate states, which are characterized by devil's staircases in the modulation frequency. We use frequency- and time-domain measurements together with advanced time-series analyses to provide experimental evidence of chaos in incommensurate states of vortex oscillations, in agreement with theoretical predictions., Comment: 5 pages, 4 figures

From the pioneering work of Winter [Phys. Rev. 124, 452 (1961)], a magnetic domain wall of Bloch type is known to host a special wall-bound spin-wave mode, which corresponds to spin-waves being channeled along the magnetic texture. Using micromagnetic simulations, we investigate spin-waves travelling inside Bloch walls formed in thin magnetic media with perpendicular-to-plane magnetic anisotropy and we show that their propagation is actually strongly nonreciprocal, as a result of dynamic dipolar interactions. We investigate spin-wave non-reciprocity effects in single Bloch walls, which allows us to clearly pinpoint their origin, as well as in arrays of parallel walls in stripe domain configurations. For such arrays, a complex domain-wall-bound spin-wave band structure develops, some aspects of which can be understood qualitatively from the single-wall picture by considering that a wall array consists of a sequence of up/down and down/up walls with opposite non-reciprocities. Circumstances are identified in which the non-reciprocity is so extreme that spin-wave propagation inside individual walls becomes unidirectional., Comment: 7 pages, 5 figures

The interfacial Dzyaloshinskii-Moriya interaction (DMI) is important for chiral domain walls (DWs) and for stabilizing magnetic skyrmions. We study the effects of introducing increasing thicknesses of Ir, from zero to 2 nm, into a Pt/Co/Ta multilayer between the Co and Ta. We observe a marked increase in magnetic moment, due to the suppression of the dead layer at the interface with Ta, but the perpendicular anisotropy is hardly affected. All samples show a universal scaling of the field-driven domain wall velocity across the creep and depinning regimes. Asymmetric bubble expansion shows that DWs in all of the samples have the left-handed N\'{e}el form. The value of in-plane field at which the creep velocity shows a minimum drops markedly on the introduction of Ir, as does the frequency shift of the Stokes and anti-Stokes peaks in Brillouin light scattering measurements. Despite this qualitative similarity, there are quantitative differences in the DMI strength given by the two measurements, with BLS often returning higher values. Many features in bubble expansion velocity curves do not fit simple models commonly used to date, namely a lack of symmetry about the velocity minimum and no difference in velocities at high in-plane field. These features are explained by the use of a model in which the depinning field is allowed to vary with in-plane field in a way determined from micromagnetic simulations. This theory shows that velocity minimum underestimates the DMI field, consistent with BLS returning higher values. Our results suggest that the DMI at an Ir/Co interface has the same sign as the DMI at a Pt/Co interface.

Skyrmions and antiskyrmions in magnetic ultrathin films are characterised by a topological charge describing how the spins wind around their core. This topology governs their response to forces in the rigid core limit. However, when internal core excitations are relevant, the dynamics become far richer. We show that current-induced spin-orbit torques can lead to phenomena such as trochoidal motion and skyrmion-antiskyrmion pair generation that only occurs for either the skyrmion or antiskyrmion, depending on the symmetry of the underlying Dzyaloshinskii-Moriya interaction. Such dynamics are induced by core deformations, leading to a time-dependent helicity that governs the motion of the skyrmion and antiskyrmion core. We compute the dynamical phase diagram through a combination of atomistic spin simulations, reduced-variable modelling, and machine learning algorithms. It predicts how spin-orbit torques can control the type of motion and the possibility to generate skyrmion lattices by antiskyrmion seeding.

We revisit the description of ferromagnetic domain wall dynamics through an extended one-dimensional model by allowing flexural distortions of the wall during its motion. This is taken into account by allowing the domain wall center and internal angle to be functions of position in the direction parallel to the wall. In the limit of small applied fields, this model accounts for the nonreciprocity in the propagation of wall modes and their stability in the presence of the Dzyaloshinskii-Moriya interaction and in-plane magnetic field., Comment: 8 pages, 8 figures

A theoretical study of delayed feedback in spin-torque nano-oscillators is presented. A macrospin geometry is considered, where self-sustained oscillations are made possible by spin transfer torques associated with spin currents flowing perpendicular to the film plane. By tuning the delay and amplification of the self-injected signal, we identify dynamical regimes in this system such as chaos, switching between precession modes with complex transients, and oscillator death. Such delayed feedback schemes open up a new field of exploration for such oscillators, where the complex transient states might find important applications in information processing., Comment: 5 pages, 7 figures

We investigate the Gilbert damping and the magnetization switching of perpendicularly magnetized FeCoB-based free layers embedded in tunnel junctions adequate for spin-torque operated memories. We study the influence of the boron content in MgO / FeCoB /Ta systems alloys on their Gilbert damping after crystallization annealing. Increasing the boron content from 20 to 30\% increases the crystallization temperature, thereby postponing the onset of elemental diffusion within the free layer. This reduction of the interdiffusion of the Ta atoms helps maintaining the Gilbert damping at a low level of 0.009 without any penalty on the anisotropy and the magneto-transport properties up to the 400$^\circ$C annealing required in CMOS back-end of line processing. In addition, we show that dual MgO free layers of composition MgO/FeCoB/Ta/FeCoB/MgO have a substantially lower damping than their MgO/FeCoB/Ta counterparts, reaching damping parameters as low as 0.0039 for a 3 \r{A} thick Tantalum spacer. This confirms that the dominant channel of damping is the presence of Ta impurities within the FeCoB alloy. On optimized tunnel junctions, we then study the duration of the switching events induced by spin-transfer-torque. We focus on the sub-threshold thermally activated switching in optimal applied field conditions. From the electrical signatures of the switching, we infer that once the nucleation has occurred, the reversal proceeds by a domain wall sweeping though the device at a few 10 m/s. The smaller the device, the faster its switching. We present an analytical model to account for our findings. The domain wall velocity is predicted to scale linearly with the current for devices much larger than the wall width. The wall velocity depends on the Bloch domain wall width, such that the devices with the lowest exchange stiffness will be the ones that host the domain walls with the slowest mobilities., Comment: Submitted to the proceedings of TMRC 2017

A theoretical study of the current-driven dynamics of magnetic skyrmions in disordered perpendicularly-magnetized ultrathin films is presented. The disorder is simulated as a granular structure in which the local anisotropy varies randomly from grain to grain. The skyrmion velocity is computed for different disorder parameters and ensembles. Similar behavior is seen for spin-torques due to in-plane currents and the spin Hall effect, where a pinning regime can be identified at low currents with a transition towards the disorder-free case at higher currents, similar to domain wall motion in disordered films. Moreover, a current-dependent skyrmion Hall effect and fluctuations in the core radius are found, which result from the interaction with the pinning potential., Comment: 5 pages, 5 figures

The topologically protected magnetic spin configurations known as skyrmions offer promising applications due to their stability, mobility and localization. In this work, we emphasize how to leverage the thermally driven dynamics of an ensemble of such particles to perform computing tasks. We propose a device employing a skyrmion gas to reshuffle a random signal into an uncorrelated copy of itself. This is demonstrated by modelling the ensemble dynamics in a collective coordinate approach where skyrmion-skyrmion and skyrmion-boundary interactions are accounted for phenomenologically. Our numerical results are used to develop a proof-of-concept for an energy efficient ($\sim\mu\mathrm{W}$) device with a low area imprint ($\sim\mu\mathrm{m}^2$). Whereas its immediate application to stochastic computing circuit designs will be made apparent, we argue that its basic functionality, reminiscent of an integrate-and-fire neuron, qualifies it as a novel bio-inspired building block., Comment: 41 pages, 20 figures

We study the current-driven skyrmion expulsion from magnetic nanostrips using micromagnetic simulations and analytic calculations. We explore the threshold current density for the skyrmion expulsion, and show that this threshold is determined by the critical boundary force as well as the spin-torque parameters. We also find the dependence of the critical boundary force on the magnetic parameters; the critical boundary force decreases with increasing the exchange stiffness and perpendicular anisotropy constants, while it increases with increasing Dzyaloshinskii-Moriya interaction and saturation magnetization constants. Using a simple model describing the skyrmion and locally-tilted edge magnetization, we reveal the underlying physics of the dependence of the critical boundary force on the magnetic parameters based on the relation between the scaled Dzyaloshinskii-Moriya-interaction parameter and the critical boundary force. This work provides a fundamental understanding of the skyrmion expulsion and the interaction between the skymion and boundaries of devices and shows that the stability of the skyrmion in devices can be related to the scaled Dzyaloshinskii-Moriya-interaction parameter of magnetic materials., Comment: 8 pages, 9 figures

A theoretical study on how synchronization and resonance-like phenomena in superparamagnetic tunnel junctions can be driven by spin-transfer torques is presented. We examine the magnetization of a superparamagnetic free layer that reverses randomly between two well-defined orientations due to thermal fluctuations, acting as a stochastic oscillator. When subject to an external ac forcing this system can present stochastic resonance and noise-enhanced synchronization. We focus on the roles of the mutually perpendicular damping-like and field-like torques, showing that the response of the system is very different at low and high-frequencies. We also demonstrate that the field-like torque can increase the efficiency of the current-driven forcing, specially at sub-threshold electric currents. These results can be useful for possible low-power, more energy efficient, applications., Comment: 9 pages, 7 figures

The Dzyaloshinskii-Moriya interaction in ultrathin ferromagnets can result in nonreciprocal propagation of spin waves. We examine theoretically how spin wave power flow is influenced by this interaction. We show that the combination of the dipole-dipole and Dzyaloshinskii-Moriya interactions can result in unidirectional caustic beams in the Damon-Eshbach geometry. Morever, self-generated interface patterns can also be induced from a point-source excitation., Comment: 6 pages, 5 figures

We study ns scale spin-torque-induced switching in perpendicularly magnetized tunnel junctions (pMTJ). Although the switching voltages match with the macrospin instability threshold, the electrical signatures of the reversal indicate the presence of domain walls in junctions of various sizes. In the antiparallel (AP) to parallel (P) switching, a nucleation phase is followed by an irreversible flow of a wall through the sample at an average velocity of 40 m/s with back and forth oscillation movements indicating a Walker propagation regime. A model with a single-wall locally responding to the spin-torque reproduces the essential dynamical signatures of the reversal. The P to AP transition has a complex dynamics with dynamical back-hopping whose probability increases with voltage. We attribute this back-hopping to the instability of the nominally fixed layers.

A theory for the spin wave eigenmodes of a Dzyaloshinskii domain wall is presented. These walls are N\'eel-type domain walls that can appear in perpendicularly-magnetized ultrathin ferromagnets in the presence of a sizeable Dzyaloshinskii-Moriya interaction. The mode frequencies for spin waves propagating parallel and perpendicular to the domain wall are computed using a continuum approximation. In contrast to Bloch-type walls, it is found that the spin wave potential associated with Dzyaloshinskii domain walls is not reflectionless, which leads to a finite scattering cross-section for interactions between spin waves and domain walls. A gap produced by the Dzyaloshinskii interaction emerges, and consequences for spin wave driven domain wall motion and band structures arising from periodic wall arrays are discussed.

We study the magnetization dynamics in a nanocontact magnetic vortex oscillators as function of temperature. Low temperature experiments reveal that the dynamics at low and high currents differ qualitatively. At low currents, we excite a temperature independent standard oscillation mode, consisting in the gyrotropic motion of a free layer vortex about the nanocontact. Above a critical current, a sudden jump of the frequency is observed, concomitant with a substantial increase of the frequency versus current slope factor. Using micromagnetic simulation and analytical modeling, we associate this new regime to the creation of a vortex-antivortex pair in the pinned layer of the spin valve. The vortex-antivortex distance depends on the Oersted field which favors a separation, and on the exchange bias field, which favors pair merging. The pair in the pinned layer provides an additional spin torque altering the dynamics of the free layer vortex, which can be quantitatively accounted for by an analytical model.

Spin waves in perpendicularly-magnetized Pt/Co/AlO$_x$/Pt ultrathin films with varying Co thicknesses (0.6-1.2 nm) have been studied with Brillouin light spectroscopy in the Damon-Eshbach geometry. The measurements reveal a pronounced nonreciprocal propagation, which increases with decreasing Co thicknesses. This nonreciprocity is attributed to an interfacial Dzyaloshinskii-Moriya interaction (DMI), which is significantly stronger than asymmetries resulting from surface anisotropies for such modes. Results are consistent with an interfacial DMI constant $D_s = -1.7 \pm 0.11$ pJ/m, which favors left-handed chiral spin structures. This suggests that such films below 1 nm in thickness should support novel chiral states like skyrmions., Comment: 5 pages, 3 figures, 1 table

The consequences of nonlinear anisotropic damping, driven by the presence of Rashba spin-orbit coupling in thin ferromagnetic metals, are examined for the dynamics of topological magnetic solitons such as domain walls, vortices, and skyrmions. The damping is found to affect Bloch and N\'eel walls differently in the steady state regime below Walker breakdown and leads to a monotonic increase in the wall velocity above this transition for large values of the Rashba coefficient. For vortices and skyrmions, a generalization of the damping tensor within the Thiele formalism is presented. It is found that chiral components of the damping affect vortex- and hedgehog-like skyrmions in different ways, but the dominant effect is an overall increase in the viscous-like damping., Comment: 8 pages, 3 figures

The channeling of spin waves with domain walls in ultrathin ferromagnetic films is demonstrated theoretically and through micromagnetics simulations. It is shown that propagating excitations localized to the wall, which appear in the frequency gap of bulk spin wave modes, can be guided effectively in curved geometries and can propagate in close proximity to other channels with no perceptible scattering or loss in coherence. For N\'eel-type walls arising from an interfacial Dzyaloshinskii-Moriya interaction, the channeling is strongly nonreciprocal and group velocities can exceed 1 km/s in the long wavelength limit for certain propagation directions., Comment: 5 pages, 4 figures

The flow of in-plane current through ultrathin magnetic heterostructures can cause magnetization switching or domain wall nucleation owing to bulk and interfacial effects. Within the magnetic layer, the current can create magnetic instabilities via spin transfer torques (STT). At interface(s), spin current generated from the spin Hall effect in a neighboring layer can exert torques, referred to as the spin Hall torques, on the magnetic moments. Here, we study current induced magnetization switching in perpendicularly magnetized CoFeB/MgO heterostructures with a heavy metal (HM) underlayer. Depending on the thickness of the HM underlayer, we find distinct differences in the inplane field dependence of the threshold switching current. The STT is likely responsible for the magnetization reversal for the thinner underlayer films whereas the spin Hall torques cause the switching for thicker underlayer films. For the latter, we find differences in the switching current for positive and negative currents and initial magnetization directions. We find that the growth process during the film deposition introduces an anisotropy that breaks the symmetry of the system and causes the asymmetric switching. The presence of such symmetry breaking anisotropy enables deterministic magnetization switching at zero external fields.

The dynamics of individual magnetic skyrmions confined in ultrathin film dots is studied theoretically. The systems considered are transition metal ferromagnets possessing perpendicular magnetic anisotropy and particular attention is given to the dynamic response of the skyrmions to perpendicular driving fields. By using micromagnetics simulations, it is shown that breathing modes can hybridize with geometrically-quantized spin wave eigenmodes of the circular dots considered, leading to distinct features in the power spectrum that differ to the behavior expected for uniformly magnetized systems. The field dependence of the breathing modes offers a direct means of detecting and characterizing such skyrmion states in experiment., Comment: 7 pages, 7 figures

We present an experimental study of phase-locking in a stochastic magnetic oscillator. The system comprises a magnetic tunnel junction with a superparamagnetic free layer, whose magnetization dynamics is driven with spin torques through an external periodic driving current. We show that synchronization of this stochastic oscillator to the input current is possible for current densities below $3 \times 10^6$ A/cm$^2$, and occurs for input frequencies lower than the natural mean frequency of the stochastic oscillator. We show that such injection-locking is robust and leads to a drastic reduction in the phase diffusion of the stochastic oscillator, despite the presence of a frequency mismatch between the oscillator and the excitation.

Ultrathin metallic ferromagnets on substrates with strong spin-orbit coupling can exhibit induced chiral interactions of the Dzyaloshinskii-Moriya (DM) form. For systems with perpendicular anisotropy, the presence of DM interactions has important consequences for current-driven domain-wall motion and underpins possible spintronic applications involving skyrmions. We show theoretically how spin textures driven by the DM interaction allow nonreciprocal channeling of spin waves, leading to measurable features in magnetic wires, dots, and domain walls. Our results provide methods for detecting induced DM interactions in metallic multilayers and controlling spin wave propagation in ultrathin nanostructures., Comment: 7 pages, 4 figures

We determine the temperature profile in magnetic nanocontacts submitted to the very large current densities that are commonly used for spin-torque oscillator behavior. Experimentally, the quadratic current-induced increase of the resistance through Joule heating is independent of the applied temperature from 6 K to 300 K. The modeling of the experimental rate of the current-induced nucleation of a vortex under the nanocontact, assuming a thermally-activated process, is consistent with a local temperature increase between 150 K and 220 K. Simulations of heat generation and diffusion for the actual tridimensional geometry were conducted. They indicate a temperature-independent efficiency of the heat sinking from the electrodes, combined with a localized heating source arising from a nanocontact resistance that is also essentially temperature-independent. For practical currents, we conclude that the local increase of temperature is typically 160 K and it extends 450 nm about the nanocontact. Our findings imply that taking into account the current-induced heating at the nanoscale is essential for the understanding of magnetization dynamics in nanocontact systems., Comment: 5 pages, 5 figures

Power dissipation is one of the most important factors limiting the future miniaturisation of integrated circuits. The capability of controlling magnetic states with a low voltage through magnetoelectric coupling in magnetostrictive/piezoelectric systems may pave the way toward ultra low-power electronics. Although the former effect has been demon-strated in several multiferroic heterostructures, the incorporation of such complex geometries into practical magnetic memory and logic nanodevices has been lacking. Here, we demonstrate the room temperature control of a domain wall gate with an electric field in a nanowire consisting of a laterally polarized piezoelectric bar inducing a giant strain in a ferromagnetic spin-valve. We propose to use such novel domain wall gate as an elementary brick to generate a complete set of boolean logic functions or stabilize domain walls in high density memory applications., Comment: 16 pages, 4 figures

Vortex-based spin-torque oscillators can be made from extended spin valves connected to an electrical nanocontact. We study the implementation of frequency shift keying modulation in these oscillators. Upon a square modulation of the current in the 10 MHz range, the vortex frequency follows the current command, with easy identification of the two swapping frequencies in the spectral measurements. The frequency distribution of the output power can be accounted for by convolution transformations of the dc current vortex waveform, and the current modulation. Modeling indicates that the frequency transitions are phase coherent and last less than 25 ns. Complementing the multi-octave tunability and first-class agility, the capability of frequency shift keying modulation is an additional milestone for the implementation of vortex-based oscillators in RF circuit., Comment: 6 pages, 5 figures

Spin-transfer torques in magnetic nanocontacts can lead to self-sustained magnetization oscillations that involve large-amplitude gyrotropic vortex motion. This dynamics consists of a steady state orbit around the nanocontact, which is made possible because the intrinsic magnetic damping is compensated by spin torques. In this article, we present an analytical theory of the power spectrum of these oscillations based on a rigid-vortex model. The appearance of vortex oscillations in nanocontacts is not associated with a Hopf bifurcation: there is no critical current and the only precondition for steady-state oscillations at finite currents is the existence of a vortex in the system, in contrast with conventional spin-torque oscillators that involve large-angle magnetization precession. The oscillation frequency is found to depend linearly on the applied current and inversely proportional to the orbital radius. By solving the associated Langevin problem for the vortex dynamics, the lineshape and linewidth for the power spectrum are also obtained. Under typical experimental conditions, a Lorentzian lineshape with a current-independent linewidth is predicted. Good quantitative agreement between the theory and recent experiments is shown., Comment: 12 pages, 6 figures

We study spin-torque induced oscillations of MgO magnetic tunnel junctions in the time domain. By using the Hilbert transform on the time traces, we obtain for the first time a direct experimental measure of the coupling between the power and the phase fluctuations. We deduce the power restoration rate and we obtain low values for the coupling strength, which is consistent with the weak frequency dependence on the applied voltage., Comment: 3 pages, 3 figures

We study the agility of current-tunable oscillators based on a magnetic vortex orbiting around a point contact in spin-valves. Theory predicts frequency-tuning by currents occurs at constant orbital radius, so an exceptional agility is anticipated. To test this, we have inserted an oscillator in a microwave interferometer to apply abrupt current variations while time resolving its emission. Using frequency shift keying, we show that the oscillator can switch between two stabilized frequencies differing by 25% in less than ten periods. With a wide frequency tunability and a good agility, such oscillators possess desirable figures of merit for modulation-based rf applications., Comment: 3 pages, 3 figures

We present a theoretical study of the influence of magnetic viscosity on current-driven domain wall dynamics. In particular we examine how domain wall depinning transitions, driven by thermal activation, are influenced by the adiabatic and nonadiabatic spin-torques. We find the Arrhenius law that describes the transition rate for activation over a single energy barrier remains applicable under currents but with a current-dependent barrier height. We show that the effective energy barrier is dominated by a linear current dependence under usual experimental conditions, with a variation that depends only on the nonadiabatic spin torque coefficient beta., Comment: 8 pages, 4 figures

We present an experimental and theoretical study of the low-field dynamics of current-driven vortex oscillations in nanocontacts based on spin-valve multilayers. These oscillations appear as low-frequency (250-500 MHz) excitations in the electrical power spectrum which arise from to variations in the giant-magnetoresistance. We show that the vortex oscillations, once nucleated at large fields applied perpendicular to the film plane, persist at zero applied magnetic fields. Some training effects on the oscillation frequency and linewidth also observed for small in-plane magnetic fields., Comment: 6 pages, 7 figures