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Optical heterodyne detection is a powerful technique for characterizing a wide range of physical excitations. Here, we use two types of optical heterodyne detection techniques (fundamental and parametric pumping) to microscopically characterize the high-frequency auto-oscillations of single and multiple nano-constriction spin Hall nano-oscillators (SHNOs). To validate the technique and demonstrate its robustness, we study SHNOs made from two different material stacks, NiFe/Pt and W/CoFeB/MgO, and investigate the influence of both the RF injection power and the laser power on the measurements, comparing the optical results to conventional electrical measurements. To demonstrate the key features of direct, non-invasive, submicron, spatial, and phase-resolved characterization of the SHNO magnetodynamics, we map out the auto-oscillation magnitude and phase of two phase-binarized SHNOs used in Ising Machines. This proof-of-concept platform establishes a strong foundation for further extensions, contributing to the ongoing development of crucial characterization techniques for emerging computing technologies based on spintronics devices, Comment: 7 pages

Antiferromagnets (AFMs) are promising materials for future high-frequency field-free spintronic applications. Self-localized spin structures can enhance their capabilities and introduce new functionalities to AFM-based devices. Here we consider a domain wall (DW), a topological soliton that bridges a connection between two ground states, similar to a Josephson junction (JJ) link between two superconductors. We demonstrate the similarities between DWs in bi-axial AFM with easy-axis primary anisotropy, driven by a spin current, and long Josephson junctions (LJJs). We found that the Bloch line (BL) in DWs resembles the fluxon state of JJs, creating a close analogy between the two systems. We propose a scheme that allows us to create, move, read, and delete such BLs. This transmission line operates at room temperature and can be dynamically reconfigured in contrast to superconductors. Results of a developed model were confirmed by micromagnetic simulations for Cr$_2$O$_3$ and DyFeO$_3$, i.e., correspondingly with weak and strong in-plane anisotropy. Overall, the proposed scheme has significant potential for use in magnetic memory and logic devices., Comment: 8 pages, 5 figures; Published in Physical Review Applied

Ferromagnetic materials dominate as the magnetically active element in spintronic devices, but come with drawbacks such as large stray fields, and low operational frequencies. Compensated ferrimagnets provide an alternative as they combine the ultrafast magnetization dynamics of antiferromagnets with a ferromagnet-like spin-orbit-torque (SOT) behavior. However to use ferrimagnets in spintronic devices their advantageous properties must be retained also in ultrathin films (t < 10 nm). In this study, ferrimagnetic Gdx(Fe87.5Co12.5)1-x thin films in the thickness range t = 2-20 nm were grown on high resistance Si(100) substrates and studied using broadband ferromagnetic resonance measurements at room temperature. By tuning their stoichiometry, a nearly compensated behavior is observed in 2 nm Gdx(Fe87.5Co12.5)1-x ultrathin films for the first time, with an effective magnetization of Meff = 0.02 T and a low effective Gilbert damping constant of {\alpha} = 0.0078, comparable to the lowest values reported so far in 30 nm films. These results show great promise for the development of ultrafast and energy efficient ferrimagnetic spintronic devices., Comment: 7 Pages, 4 Figures

Magnonics is a field of science that addresses the physical properties of spin waves and utilizes them for data processing. Scalability down to atomic dimensions, operations in the GHz-to-THz frequency range, utilization of nonlinear and nonreciprocal phenomena, and compatibility with CMOS are just a few of many advantages offered by magnons. Although magnonics is still primarily positioned in the academic domain, the scientific and technological challenges of the field are being extensively investigated, and many proof-of-concept prototypes have already been realized in laboratories. This roadmap is a product of the collective work of many authors that covers versatile spin-wave computing approaches, conceptual building blocks, and underlying physical phenomena. In particular, the roadmap discusses the computation operations with Boolean digital data, unconventional approaches like neuromorphic computing, and the progress towards magnon-based quantum computing. The article is organized as a collection of sub-sections grouped into seven large thematic sections. Each sub-section is prepared by one or a group of authors and concludes with a brief description of the current challenges and the outlook of the further development of the research directions., Comment: 74 pages, 57 figures, 500 references

We demonstrate the compositional effect on the magnetodynamic and auto-oscillations properties of Ni100-xFex/Pt (x= 10 to 40) nanoconstriction based spin Hall nano-oscillators. Using spin-torque ferromagnetic resonance (ST-FMR) performed on microstrips, we measure a significant reduction in both damping and spin Hall efficiency with increasing Fe content, which lowers the spin pumping contribution. The strong compositional effect on spin Hall efficiency is primarily attributed to the increased saturation magnetization in Fe-rich devices. As a direct consequence, higher current densities are required to drive spin-wave auto-oscillations at higher microwave frequencies in Fe-rich nano-constriction devices. Our results establish the critical role of the compositional effect in engineering the magnetodynamic and auto-oscillation properties of spin Hall devices for microwav eand magnonic applications.

Controlling the directionality of spin waves is a key ingredient in wave-based computing methods such as magnonics. In this paper, we demonstrate this particular aspect by using an all-optical point-like source of continuous spin waves based on frequency comb rapid demagnetization. The emitted spin waves contain a range of k-vectors and by detuning the applied magnetic field slightly off the ferromagnetic resonance (FMR), we observe X-shaped caustic spin-wave patterns at $70^{\circ}$ propagation angles as predicted by theory. When the harmonic of the light source approaches theFMR, the caustic pattern gives way to uniaxial spin-wave propagation perpendicular to the in-plane component of the applied field. This field-controlled propagation pattern and directionality of optically emitted short-wavelength spin waves provide additional degrees of freedom when designing magnonic devices., Comment: 5 pages, 4 figures

We demonstrate sustained coherent emission of spin waves in NiFe films using rapid demagnetization from high repetition rate femtosecond laser pulse trains. As the pulse separation is shorter than the magnon decay time, magnons having a frequency equal to a multiple of the 1 GHz repetition-rate are coherently amplified. Using scanning micro-Brillouin Light Scattering (BLS) we observe this coherent amplification as strong peaks spaced 1 GHz apart. The BLS counts vs. laser power exhibit a stronger than parabolic dependence consistent with counts being proportional to the square of the magnetodynamic amplitude, and the demagnetization pulse strength being described by a Bloch law. Spatial spin wave mapping demonstrates how both localized and propagating spin waves can be excited, and how the propagation direction can be directly controlled. Our results demonstrate the versatility of BLS spectroscopy for rapid demagnetization studies and enable a new platform for photo-magnonics where sustained coherent spin waves can be utilized., Comment: 7 pages, 7 figures

We demonstrate field and current controlled magnetodynamics in nanocontact spin-torque nano-oscillators (STNOs) based on orthogonal magnetic tunnel junctions (MTJs). We systematically analyze the microwave properties (frequency $f$, linewidth $\Delta f$, power $P$, and frequency tunability $df/dI$) with their physical origins---perpendicular magnetic anisotropy (PMA), damping-like and field-like spin transfer torque (STT), and voltage-controlled magnetic anisotropy (VCMA). These devices present several advantageous characteristics: high emission frequencies ($f> 20$ GHz), high frequency tunability ($df/dI=0.25$~GHz/mA), and zero-field operation ($f\sim 4$ GHz). Furthermore, a detailed investigation of $f(H, I)$ reveals that $df/dI$ is mostly governed by the large VCMA (287~fJ/(V$\cdot$m)), while STT plays a negligible role., Comment: 13 pages, 4 figures

The inertial effects of magnetic solitons play a crucial role in their dynamics and stability. Yet governing their inertial effects is a challenge for their use in real devices. Here, we show how to control the inertial effects of magnetic droplet solitons. Magnetic droplets are strongly nonlinear and localized autosolitons than can form in current-driven nanocontacts. Droplets can be considered as dynamical particles with an effective mass. We show that the dynamical droplet bears a second excitation under its own inertia. These excitations comprise a chiral profile, and appear when the droplet resists the force induced by the Oersted field of the current injected into the nanocontact. We reveal the role of the spin torque on the excitation of these chiral modes and we show how to control these modes using the current and the field., Comment: 10 pages

Ni$_{0.8}$Fe$_{0.2}$ (Py) and Py alloyed with Cu exhibit intriguing ultrafast demagnetization behavior, where the Ni magnetic moment shows a delayed response relative to the Fe, an effect which is strongly enhanced by Cu alloying. We have studied a broad range of Cu concentrations to elucidate the effects of Cu alloying in Py. The orbital/spin magnetic moment ratios are largely unaffected by Cu alloying, signifying that Cu-induced changes in the ultrafast demagnetization are not related to spin-orbit interactions. We show that magnon diffusion can explain the delayed Ni response, which we attribute to an enhanced magnon generation rate in the Fe sublattice relative to the Ni sublattice. Furthermore, Py exhibits prominent RKKY-like exchange interactions, which are strongly enhanced between Fe atoms and diminished between Ni atoms by Cu alloying. An increased Fe magnon scattering rate is expected to occur concurrently with this increased Fe-Fe exchange interaction, supporting the results obtained from the magnon diffusion model.

Spin torque and spin Hall effect nanooscillators generate high intensity spin wave auto oscillations on the nanoscale enabling novel microwave applications in spintronics, magnonics, and neuromorphic computing. For their operation, these devices require externally generated spin currents either from an additional ferromagnetic layer or a material with a high spin Hall angle. Here we demonstrate highly coherent field and current tunable microwave signals from nanoconstrictions in single 15 and 20 nm thick permalloy layers. Using a combination of spin torque ferromagnetic resonance measurements, scanning microBrillouin light scattering microscopy, and micromagnetic simulations, we identify the autooscillations as emanating from a localized edge mode of the nanoconstriction driven by spin orbit torques. Our results pave the way for greatly simplified designs of auto oscillating nanomagnetic systems only requiring a single ferromagnetic layer., Comment: 11 pages, 2 figures

We demonstrate low-operational-current W/Co$_{20}$Fe$_{60}$B$_{20}$/MgO spin Hall nano-oscillators (SHNOs) on highly resistive silicon (HiR-Si) substrates. Thanks to a record high spin Hall angle of the $\beta$-phase W ($\theta_{SH}$ = -0.53), a very low threshold current density of 3.3 $\times$ 10$^{7}$ A/cm$^2$ can be achieved. Together with their very wide frequency tunability (7-28 GHz), promoted by a moderate perpendicular magnetic anisotropy, this makes HiR-Si/W/CoFeB based SHNOs potential candidates for wide-band microwave signal generation. Their CMOS compatibility offers a promising route towards the integration of spintronic microwave devices with other on-chip semiconductor microwave components., Comment: 6 pages, 4 figures

Using He+ ion irradiation, we demonstrate how the magnetodynamic properties of both ferromagnetic layers in all-perpendicular [Co/Pd]/Cu/[Co/Ni] spin valves can be tuned by varying the He+ ion fluence. As the perpendicular magnetic anisotropy of both layers is gradually reduced by the irradiation, different magnetic configurations can be achieved from all-perpendicular, through orthogonal, to all in-plane. In addition, both the magnetic damping and the inhomogeneous broadening of the Co/Ni layer improve substantially with increasing fluence. GMR of the spin valve is negatively affected and decreases linearly from an original value of 1.14% to 0.4% at the maximum fluence of 50*10^14 He+/cm^2., Comment: 5 Pages, 4 Figures

Short wave-length exchange-dominated propagating spin waves will enable magnonic devices to operate at higher frequencies and higher data transmission rates.1 While GMR based magnetic nano-contacts are highly efficient injectors of propagating spin waves2,3, the generated wave lengths are 2.6 times the nano-contact diameter4, and the electrical signal strength remains much too weak for practical applications. Here we demonstrate nano-contact based spin wave generation in magnetic tunnel junction stacks, and observe large discrete frequency steps consistent with the hitherto ignored possibility of second and third order propagating spin waves with wave lengths of 120 and 74 nm, i.e. much smaller than the 150 nm nano-contact. These higher-order propagating spin waves will not only enable magnonic devices to operate at much higher frequencies, but also greatly increase their transmission rates and spin wave propagating lengths, both proportional to the much higher group velocity.

Recent studies have revealed that domain walls in magnetic nanostructures can serve as compact, energy-efficient spin-wave waveguides for building magnonic devices that are considered promising candidates for overcoming the challenges and bottlenecks of today's CMOS technologies. However, imprinting long strip-domain walls into magnetic nanowires remains a challenge, especially in curved geometries. Here, through micromagnetic simulations, we present a method for writing strip-domain walls into curved magnetic nanowires using spin-orbit torque. We employ Y-shaped magnetic nanostructures as well as an S-shaped magnetic nanowire to demonstrate the injection process. In addition, we verify that the Y-shaped nanostructures that incorporate strip-domain walls can function as superior spin-wave multiplexers, and that spin-wave propagation along each conduit can be controllably manipulated. This spin-wave multiplexer based on strip-domain walls is expected to become a key signal-processing component in magnon spintronics., Comment: main manuscript: 38 pages and 8 figures; supplemental material: 21 pages, 12 figures, and 1 table

Recent experiments performed in current-driven nano-contacts with strong perpendicular anisotropy have shown that spin-transfer torque can drive self-localized spin waves [1, 2] that above a certain threshold intensity can condense into a highly nonlinear magnetodynamic and nano-sized state known as a magnetic droplet soliton [3]. Here we demonstrate analytically, numerically, and experimentally that at sufficiently large driving currents, and for a spin polarization that is tilted away from the film normal, the circular droplet soliton can become unstable to periodic excitations of its perimeter. We furthermore show that these perimeter excitation modes (PEMs) are parametrically excited when the fundamental droplet soliton precession frequency is close to twice the frequency of one or more of the PEMs. As a consequence, for increasing applied fields, progressively higher PEMs can be excited. Quantitative agreement with experiment confirms this picture., Comment: Submitted to PRB

Super-harmonic injection locking of single nano-contact (NC) spin-torque vortex oscillators (STVOs) subject to a small microwave current has been explored. Frequency locking was observed up to the fourth harmonic of the STVO fundamental frequency $f_{0}$ in microwave magneto-electronic measurements. The large frequency tunability of the STVO with respect to $f_{0}$ allowed the device to be locked to multiple sub-harmonics of the microwave frequency $f_{RF}$, or to the same sub-harmonic over a wide range of $f_{RF}$ by tuning the DC current. In general, analysis of the locking range, linewidth, and amplitude showed that the locking efficiency decreased as the harmonic number increased, as expected for harmonic synchronization of a non-linear oscillator. Time-resolved scanning Kerr microscopy (TRSKM) revealed significant differences in the spatial character of the magnetization dynamics of states locked to the fundamental and harmonic frequencies, suggesting significant differences in the core trajectories within the same device. Super-harmonic injection locking of a NC-STVO may open up possibilities for devices such as nanoscale frequency dividers, while differences in the core trajectory may allow mutual synchronisation to be achieved in multi-oscillator networks by tuning the spatial character of the dynamics within shared magnetic layers., Comment: 21 pages, 8 figures

Time-resolved scanning Kerr microscopy has been used to directly image the magnetization dynamics of nano-contact (NC) spin-torque vortex oscillators (STVOs) when phase-locked to an injected microwave (RF) current. The Kerr images reveal free layer magnetization dynamics that extend outside the NC footprint, where they cannot be detected electrically, but which are crucial to phase-lock STVOs that share common magnetic layers. For a single NC, dynamics were observed not only when the STVO frequency was fully locked to that of the RF current, but also for a partially locked state characterized by periodic changes in the core trajectory at the RF frequency. For a pair of NCs, images reveal the spatial character of dynamics that electrical measurements show to have enhanced amplitude and reduced linewidth. Insight gained from these images may improve understanding of the conditions required for mutual phase-locking of multiple STVOs, and hence enhanced microwave power emission., Comment: 10 pages, 3 figures

We report the observation of a Pt layer thickness dependence on the induced interfacial Dzyaloshinskii-Moriya interaction in ultra-thin Pt($d_{\text{Pt}}$)/CoFeB films. Taking advantage of the large spin-orbit coupling of the heavy metal, the interfacial Dzyaloshinskii-Moriya interaction is quantified by Brillouin light scattering measurements of the frequency non-reciprocity of spin-waves in the ferromagnet. The magnitude of the induced Dzyaloshinskii-Moriya coupling is found to saturate to a value $0.45$ mJ$/$m${}^2$ for Pt thicknesses larger than $\sim 2$ nm. The experimental results are explained by analytical calculations based on the 3-site indirect exchange mechanism that predicts a Dzyaloshinskii-Moriya interaction at the interface between a ferromagnetic thin layer and a heavy metal. Our findings open up a way to control and optimize chiral effects in ferromagnetic thin films through the thickness of the heavy metal layer.

We demonstrate how magnetic droplet soliton pairs, nucleated by two separated nano-contact (NC) spin torque oscillators, can merge into a single droplet soliton. A detailed description of the magnetization dynamics of this merger process is obtained by micromagnetic simulations: A droplet pair with a steady-state in-phase spin precession is generated through the spin-transfer torque effect underneath two separate NCs, followed by a gradual expansion of the droplets volume and the out phase of magnetization on the inner side of the two droplets, resulting in the droplets merging into a larger droplet. This merger occurs only when the NC separation is smaller than a critical value. A transient breathing mode is observed before the merged droplet stabilizes into a steady precession state. The precession frequency of the merged droplet is lower than that of the droplet pair, consistent with its larger size. Merged droplets can again break up into droplet pairs at high enough magnetic field with a strong hysteretic response., Comment: accepted by Physical Review B

Spin transfer torque (STT) affords magnetic nanodevices the potential to act as memory, computing, and microwave elements operating at ultra-low currents and at a low energy cost. Spin transfer torque is not only effective in manipulating well-known magnetic structures, such as domain walls and vortices, but can also nucleate previously unattainable nano-magnetic objects, such as magnetic droplets and skyrmions. While the droplet and the skyrmion are both solitons, the former is inherently dynamic and non-topological, whereas the latter is static but topologically protected. Here we show that it is possible to combine these properties into a novel topologically protected dynamical skyrmion, which adds additional degrees of freedom, and functionality, to both droplet and skyrmion based applications. Unlike static skyrmions, the dynamical skyrmion can be nucleated and sustained without Dzyaloshinskii-Moriya interaction (DMI) or dipole-dipole interaction (DDI), and is a generic soliton solution independent of STT and damping once nucleated. In the presence of large DMI, the dynamical skyrmion experiences strong breathing with particular promise for skyrmion-based memory and microwave applications.

We report on the magnetization depth profile of a hybrid exchange spring system in which a Co/Pd multilayer with perpendicular anisotropy is coupled to a CoFeB thin film with in-plane anisotropy. The competition between these two orthogonal anisotropies promotes a strong depth dependence of the magnetization orientation. The angle of the magnetization vector is sensitive both to the strength of the individual anisotropies and to the local exchange constant, and is thus tunable by changing the thickness of the CoFeB layer and by substituting Ni for Pd in one layer of the Co/Pd stack. The resulting magnetic depth profiles are directly probed by element specific x-ray magnetic circular dichroism (XMCD) of the Co, Fe, and Ni layers located at different average depths. The experimental results are corroborated by micromagnetic simulations.

We have observed distinct temperature-dependent magnetization reversal modes in a perpendicular (Co/Pd)4/Co/Cu/(Co/Ni)4/Co pseudo-spin-valve, which are correlated with spin-transport properties. At 300 K, magnetization reversal occurs by vertically correlated domains. Below 200 K the hysteresis loop becomes bifurcated due to laterally correlated reversal of the individual stacks. The magnetic configuration change also leads to higher spin disorders and a significant increase in the giant magnetoresistance effect. First order reversal curve measurements reveal that the coupled state can be re-established through field cycling, and allow direct determination of the interlayer coupling strength as a function of temperature., Comment: 16 pages, 4 figures, 1 table

We discuss the coherence of magnetic oscillations in a magnetic tunnel junction-based spin-torque oscillator as a function of external field angle. Time-frequency analysis shows mode-hopping between distinct oscillator modes, which arises from linear and nonlinear couplings in the Landau-Lifshitz-Gilbert equation, analogous to mode-hopping observed in semiconductor ring lasers. These couplings and therefore mode-hopping are minimized near the current threshold for antiparallel (AP) alignment of free layer with reference layer magnetization. Away from the AP alignment, mode-hopping limits oscillator coherence., Comment: To appear in Phys. Rev. Lett. Note the paper accompany Suppl info

The thermally-driven formation and evolution of vertex domains is studied for square artificial spin ice. A self consistent mean field theory is used to show how domains of ground state ordering form spontaneously, and how these evolve in the presence of disorder. The role of fluctuations is studied, using Monte Carlo simulations and analytical modelling. Domain wall dynamics are shown to be driven by a biasing of random fluctuations towards processes that shrink closed domains, and fluctuations within domains are shown to generate isolated small excitations, which may stabilise as the effective temperature is lowered. Domain dynamics and fluctuations are determined by interaction strengths, which are controlled by inter-element spacing. The role of interaction strength is studied via experiments and Monte Carlo simulations. Our mean field model is applicable to ferroelectric `spin' ice, and we show that features similar to that of magnetic spin ice can be expected, but with different characteristic temperatures and rates., Comment: 20 pages, 12 figures. Submitted to New Journal of Physics

Quenched disorder affects how non-equilibrium systems respond to driving. In the context of artificial spin ice, an athermal system comprised of geometrically frustrated classical Ising spins with a two-fold degenerate ground state, we give experimental and numerical evidence of how such disorder washes out edge effects, and provide an estimate of disorder strength in the experimental system. We prove analytically that a sequence of applied fields with fixed amplitude is unable to drive the system to its ground state from a saturated state. These results should be relevant for other systems where disorder does not change the nature of the ground state., Comment: The manuscript has been reworked. To be published in Phys. Rev. Lett