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Many recent papers report on the interest of spin waves for applications. This paper revisits the propagating spin wave spectroscopy when using inductive transceivers connected to a network analyzer. The spin wave conduit can be made of a non-reciprocal material. The formalism offers a method to understand, design and optimize devices harnessing propagating spin waves, including when a unidirectional energy flow is desired. The concept of the mismatch of helicity between the spin wave and the magnetic field radiated by antennas is first clarified. Owing to the form of the susceptibility tensor reflecting the precession ellipticity, there exists specific orientations of the wavevector for which a perfect helicity mismatch is reached. The spin waves with this orientation and this direction of wavevector are "dark" in the sense that they do not couple with the inductive antenna. This leads to single-sided wavevector generation, that should not to be confused with a unidirectional emission of energy. A method to calculate the antenna-to-antenna transmission parameter is then provided. Analytical approximations are then applied on situations that illustrate the respective role of the direction of the spin wave wavevector versus that of the group velocity. The often-encountered cases of spin waves possessing either a V-shaped or a flat dispersion relation are revisited. These reciprocal dispersion relations lead to amplitude non-reciprocity because of the helicity mismatch phenomenon. Conversely, for spin waves with a line-shaped dispersion relation, a quasi-unidirectional emission of spin waves occurs. This situation can be obtained when using the acoustical spin waves of synthetic antiferromagnets when the wavevector is close to parallel to the applied field. We finally show that this configuration can be harnessed to design reconfigurable frequency filters.

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

We report on the first experimental demonstration of majority logic operation using spin waves in a scaled device with an in-line input and output layout. The device operation is based on the interference of spin waves generated and detected by inductive antennas in an all-electrical microwave circuit. We demonstrate the full truth table of a majority logic function with the ability to distinguish between strong and weak majority, as well as an inverted majority function by adjusting the operation frequency. Circuit performance projections predict low energy consumption of spin wave based compared to CMOS for large arithmetic circuits., Comment: This project has received funding from the European Union's Horizon 2020 research and innovation program under grant agreement No. 801055 "Spin Wave Computing for Ultimately-Scaled Hybrid Low-Power Electronics" - CHIRON

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 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.

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

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

Spin waves are excitations in ferromagnetic media that have been proposed as information carriers in hybrid spintronic devices with much lower operation power than conventional charge-based electronics. Their wave nature can be exploited in majority gates by using interference for computation. However, a scalable spin-wave majority gate that can be co-integrated alongside conventional electronics is still lacking. Here, we demonstrate a sub-micron inline spin-wave majority gate with fan-out. Time-resolved imaging of the magnetization dynamics by scanning transmission x-ray microscopy illustrates the device operation. All-electrical spin-wave spectroscopy further demonstrates majority gates with sub-micron dimensions, reconfigurable input and output ports, and frequency-division multiplexing. Challenges for hybrid spintronic computing systems based on spin-wave majority gates are discussed., Comment: This project has received funding from the European Union's Horizon 2020 research and innovation program under grant agreement No. 801055 "Spin Wave Computing for Ultimately-Scaled Hybrid Low-Power Electronics" - CHIRON

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

We simulate the spin torque-induced reversal of the magnetization in thin disks with perpendicular anisotropy at zero temperature. Disks typically smaller than 20 nm in diameter exhibit coherent reversal. A domain wall is involved in larger disks. We derive the critical diameter of this transition. Using a proper definition of the critical voltage, a macrospin model can account perfectly for the reversal dynamics when the reversal is coherent. The same critical voltage appears to match with the micromagnetics switching voltage regardless of the switching path.

Using broadband ferromagnetic resonance, we measure the damping parameter of [Co(5 \r{A})/Pt(3 \r{A})]${\times 6}$ multilayers whose growth was optimized to maximize the perpendicular anisotropy. Structural characterizations indicate abrupt interfaces essentially free of intermixing despite the miscible character of Co and Pt. Gilbert damping parameters as low as 0.021 can be obtained despite a magneto-crystalline anisotropy as large as $10^6~\textrm{J/m}^3$. The inhomogeneous broadening accounts for part of the ferromagnetic resonance linewidth, indicating some structural disorder leading to a equivalent 20 mT of inhomogenity of the effective field. The unexpectedly relatively low damping factor indicates that the presence of the Pt heavy metal within the multilayer may not be detrimental to the damping provided that intermixing is avoided at the Co/Pt interfaces.

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

We study the generation of propagating spin waves in Ta/CoFeB waveguides by spin-orbit torque antennas and compare them to conventional inductive antennas. The spin-orbit torque was generated by a transverse microwave current across the magnetic waveguide. The detected spin wave signals for an in-plane magnetization across the waveguide (Damon-Eshbach configuration) exhibited the expected phase rotation and amplitude decay upon propagation when the current spreading was taken into account. Wavevectors up to about 6 rad/$\mu$m could be excited by the spin-orbit torque antennas despite the current spreading, presumably due to the non-uniformity of the microwave current. The relative magnitude of generated anti-damping spin-Hall and Oersted fields was calculated within an analytic model and it was found that they contribute approximately equally to the total effective field generated by the spin-orbit torque antenna. Due to the ellipticity of the precession in the ultrathin waveguide and the different orientation of the anti-damping spin-Hall and Oersted fields, the torque was however still dominated by the Oersted field. The prospects for obtaining a pure spin-orbit torque response are discussed, as are the energy efficiency and the scaling properties of spin-orbit torque antennas., Comment: 20 pages, 5 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

Strong ferromagnetic interlayer exchange couplings $J$ in perpendicularly magnetized systems are becoming increasingly desirable for applications. We study whether ferromagnetic interlayer exchange couplings can be measured by a combination of broadband ferromagnetic resonance methods and magnetometry hysteresis loops. For this we model the switching and the eigenexcitations in bilayer systems comprising a soft layer coupled to a thicker harder layer that possesses higher perpendicular magnetic anisotropy. For large $J >0$ the switching fields are essentially independent of $J$ but the frequency of the optical eigenmode of the bilayer and the linewidth of the acoustical and optical eigenmode are directly sensitive to the coupling. We derive a corpus of compact analytical expressions to analyze these frequencies, their linewidth and discuss the meaning thereof. We illustrate this corpus on a system mimicking the fixed layers of a magnetic tunnel junction meant for spin torque applications.

We study the evolution of perpendicularly magnetized tunnel junctions under 300 to 400 $^{\circ}$C annealing. The hysteresis loops do not evolve much during annealing and they are not informative of the underlying structural evolutions. These evolutions are better revealed by the frequencies of the ferromagnetic resonance eigenmodes of the tunnel junction. Their modeling provides the exchange couplings and the layers' anisotropies within the stack which can serve as a diagnosis of the tunnel junction state after each annealing step. The anisotropies of the two CoFeB-based parts and the two Co/Pt-based parts of the tunnel junction decay at different rates during annealing. The ferromagnet exchange coupling through the texture-breaking Ta layer fails above 375$^{\circ}$C. The Ru spacer meant to promote a synthetic antiferromagnet behavior is also insufficiently robust to annealing. Based on these evolutions we propose optimization routes for the next generation tunnel junctions.

We study whether a direct measurement of the absolute temperature of a Magnetic Tunnel Junction (MTJ) can be performed using the high frequency electrical noise that it delivers under a finite voltage bias. Our method includes quasi-static hysteresis loop measurements of the MTJ, together with the field-dependence of its spin wave noise spectra. We rely on an analytical modeling of the spectra by assuming independent fluctuations of the different sub-systems of the tunnel junction that are described as macrospin fluctuators. We illustrate our method on perpendicularly magnetized MgO-based MTJs patterned in 50*100 nm2 nanopillars. We apply hard axis (in-plane) fields to let the magnetic thermal fluctuations yield finite conductance fluctuations of the MTJ. Instead of the free layer fluctuations that are observed to be affected by both spin-torque and temperature, we use the magnetization fluctuations of the sole reference layers. Their much stronger anisotropy and their much heavier damping render them essentially immune to spin-torque. We illustrate our method by determining current-induced heating of the perpendicularly magnetized tunnel junction at voltages similar to those used in spin-torque memory applications. The absolute temperature can be deduced with a precision of +/- 60 K and we can exclude any substantial heating at the spin-torque switching voltage., Comment: 10 pages, 6 figures

We develop an all electrical experiment to perform the broadband phase-resolved spectroscopy of propagating spin waves in micrometer sized thin magnetic stripes. The magnetostatic surface spin waves are excited and detected by scaled down to 125 nm wide inductive antennas, which award ultra broadband wavevector capability. The wavevector selection can be done by applying an excitation frequency above the ferromagnetic resonance. Wavevector demultiplexing is done at the spin wave detector thanks to the rotation of the spin wave phase upon propagation. A simple model accounts for the main features of the apparatus transfer functions. Our approach opens an avenue for the all electrical study of wavevector-dependent spin wave properties including dispersion spectra or non-reciprocal propagation., Comment: 5 pages, 3 figures

Half Metal Magnets are of great interest in the field of spintronics because of their potential full spin-polarization at the Fermi level and low magnetization damping. The high Curie temperature and predicted 0.7eV minority spin gap make the Heusler alloy Co2MnSi very promising for applications.We investigated the half-metallic magnetic character of this alloy using spin-resolved photoemission, ab initio calculation and ferromagnetic resonance. At the surface of Co2MnSi, a gap in the minority spin channel is observed, leading to 100% spin polarization. However, this gap is 0.3 eV below the Fermi level and a minority spin state is observed at the Fermi level. We show that a minority spin gap at the Fermi energy can nevertheless be recovered either by changing the stoichiometry of the alloy or by covering the surface by Mn, MnSi or MgO. This results in extremely small damping coefficients reaching values as low as 7x 10-4.

We use spin-torque resonance to probe simultaneously and separately the dynamics of a magnetic domain wall and of magnetic domains in a nanostripe magnetic tunnel junction. Thanks to the large associated resistance variations we are able to analyze quantitatively the resonant properties of these single nanoscale magnetic objects. In particular, we find that the magnetic damping of both domains and domain walls is doubled compared to the damping value of their host magnetic layer. We estimate the contributions to damping arising from dipolar couplings between the different layers in the junction and from the intralayer spin pumping effect. We find that they cannot explain the large damping enhancement that we observe. We conclude that the measured increased damping is intrinsic to large amplitudes excitations of spatially localized modes or solitons such as vibrating or propagating domain walls

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

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

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 experimentally study the motion of atoms interacting with a periodically pulsed near resonant standing wave. For discrete pulse frequencies we observe a comb-like momentum distribution. The peaks have widths of 0.3 recoil momenta and a spacing which is an integer multiple of the recoil momentum. The atomic population is trapped in ground states which periodically evolve to dark states each time the standing wave is switched on., Comment: 4 pages, 3 figures. LaTeX/RevTeX (uses psfig). Submitted to Phys. Rev. Lett