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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

A mathematical model of oscillatory systems control with liquid dampers is considered which differs from the classical ones by replacing the first derivative of such a fractional derivative that is between numbers 0 and 2 other than unity. Using the methods of constructing Letov controllers, a control law is constructed that ensures the asymptotic stability of the closed system and minimizes the quadratic functional. The results are illustrated by a specific numerical example.

Almost any use of a superconductor implies a nonequilibrium state. Remarkably, the non-equilibrium states induced by a microwave stimulus and the dynamics of magnetic flux quanta (Abrikosov vortices) can give rise to strikingly contrary effects: A sufficiently high-power electromagnetic field of GHz frequency can stimulate superconductivity, whereas fast vortex motion can trigger an instability abruptly quenching the superconducting state. Here, we advance or delay such dynamical quenching of the vortex state in Nb thin films by tuning the power and frequency of the microwave ac stimulus added to a dc bias current. The experimental findings are supported by time-dependent Ginzburg-Landau simulations and they can be explained qualitatively based on a model of "breathing mobile hot spots", implying a competition of heating and cooling of quasiparticles along the trajectories of moving fluxons whose core sizes vary in time. In addition, we demonstrate universality of the stimulation effect on the thermodynamic and transport properties of type II superconductors., Comment: 11 pages. 7 figures

We explore the dynamics of spiral spin waves in Permalloy nano-elements with variable aspect ratio of geometric dimensions, and their potential use as improved spin wave emitters with no or little biasing field required. Numerical results show that above a certain thickness, propagating spiral waves can be obtained in circular and square shaped elements in a flux closure state. VNA-FMR experiments on 20 nm (thin) and 80 nm (thick) samples confirm two type of spectra corresponding to different dispersions for thinner and thicker elements. We show that, for the thicker films, the vortex core region acts as a source of large amplitude spiral spin waves, which dominate over other modes. In case of the thinner elements, these modes are critically damped. For different shapes of the patch, we show that a rich collection of confined propagating modes can also be excited, modifying the final wave front and enriching the potential of the nano-dot as a spin wave emitter. We give an explanation for the intense spiral modes from the perspective of a balance of dipolar and exchange energies in the sample., Comment: 12 pages, 9 figures

In the mixed state of type II superconductors penetrated by an external magnetic field in the form of a lattice of Abrikosov vortices the dc resistance is known to increase with increasing velocity of the vortex lattice. Accordingly, vortex pinning sites impeding the vortex motion are widely used to preserve the low-dissipative response of the system. Here, while subjecting superconducting Nb films with nanogrooves to a combination of dc and ac current stimuli and tuning the number of mobile and pinned vortices by varying the magnetic field around the so-called matching values, we observe a completely opposite effect. Namely, the vortex-related microwave excess loss for mobile vortices becomes smaller than for pinned vortices in a certain range of power levels at ac current frequencies above 100\,MHz. While a theoretical description of the observed effect is yet to be elaborated we interpret our findings in terms of a competition of the effective cooling of the system by the quasiparticles leaving the vortex cores with the conventional Joule heating caused by the current flow., Comment: 5 pages, 3 figures

We analyze shot noise in a magnetic tunnel junction with a two-level quantum dot attached to the magnetic electrodes. The considerations are limited to the case when some transport channels are suppressed at low temperatures. Coupling of the two dot's levels to the electrodes are assumed to be generally different and also spin-dependent. To calculate the shot noise we apply the approach based on the full counting statistics. The approach is used to account for experimental data obtained in magnetic tunnel junctions with organic barriers. The experimentally observed Fano factors correspond to the super-Poissonian statistics, and also depend on relative orientation of the electrodes' magnetic moments. We have also calculated the corresponding spin shot noise, which is associated with fluctuations of spin current.

Spin waves have been studied experimentally and by simulations in 1000 nm side equilateral triangular Permalloy dots in the Buckle state (B, with in-plane field along the triangle base) and the Y state (Y, with in-plane field perpendicular to the base). The excess of exchange energy at the triangles edges creates channels that allow effective spin wave propagation along the edges inthe B state. These quasi one-dimensional spin waves emitted by the vertex magnetic charges gradually transform from propagating to standing due to interference and(as pointed out by simulations) areweakly affected by smallvariations of the aspect ratio(from equilateral to isosceles dots) or by interdot dipolar interaction present in our dot arrays. Spin waves excited in the Y state have mainly a two-dimensional character.Propagation of the spin waves along the edge states in triangular dots opens possibilities for creation of new and versatile spintronic devices., Comment: 9 pages with 7 figures

Broadband magnetization response of equilateral triangular 1000 nm Permalloy dots has been studied under an in-plane magnetic field, applied parallel (buckle state) and perpendicular (Y state) to the triangles base. Micromagnetic simulations identify edge spin waves (E-SWs) in the buckle state as SWs propagating along the two adjacent edges. These quasi one-dimensional spin waves emitted by the vertex magnetic charges gradually transform from propagating to standing due to interference and are weakly affected by dipolar interdot interaction and variation of the aspect ratio. Spin waves in the Y state have a two dimensional character. These findings open perspectives for implementation of the E-SWs in magnonic crystals and thin films., Comment: 8 pages + 4 figures

The time dependent transient lateral photovoltaic effect has been studied with us time resolution and with chopping frequencies in the kHz range, in lithographically patterned 21 nm thick, 5, 10 and 20 um wide and 1500 um long Co lines grown over naturally passivated p-type Si (100). We have observed a nearly linear dependence of the transitorial response with the laser spot position. A transitorial response with a sign change in the laser-off stage has been corroborated by numerical simulations. A qualitative explanation suggests a modification of the drift-diffusion model by including the in uence of a local inductance. Our findings indicate that the microstructuring of position sensitive detectors could improve their space-time resolution., Comment: 4 pages, 4 figures

We report on room temperature magnetoresistance and low frequency noise in sub-100nm elliptic CoFeB/MgO/CoFeB magnetic tunnel junctions with ultrathin (0.9nm) barriers. For magnetic fields applied along the hard axis, we observe current induced magnetization switching between the antiparallel and parallel alignments at DC current densities as low as 4*106A/cm2. We attribute the low value of the critical current to the influence of localized reductions in the tunnel barrier, which affects the current distribution. The analysis of random telegraph noise, which appears in the field interval near a magnetization switch, provides an estimate to the dimension of the pseudo pinholes that trigger the magnetization switching via local spin torque. Micromagnetic simulations qualitatively and quantitatively reproduce the main experimental observations.

We demonstrate that shot noise in Fe/MgO/Fe/MgO/Fe double-barrier magnetic tunnel junctions is determined by the relative magnetic configuration of the junction and also by the asymmetry of the barriers. The proposed theoretical model, based on sequential tunneling through the system and including spin relaxation, successfully accounts for the experimental observations for bias voltages below 0.5V, where the influence of quantum well states is negligible. A weak enhancement of conductance and shot noise, observed at some voltages (especially above 0.5V), indicates the formation of quantum well states in the middle magnetic layer. The observed results open up new perspectives for a reliable magnetic control of the most fundamental noise in spintronic structures., Comment: 8 pages, 4 figures

We observed unexpected resonant response in [Fe/Cr]_(10) multilayers epitaxially grown on MgO(100) substrates which exists only when both ac current and dc magnetic field are simultaneously applied. The magnitude of the resonances is determined by the multilayer magnetization proving their intrinsic character. The reduction of interface epitaxy leads to non-linear dependence of the magnitude of resonances on the alternating current density. We speculate that the existence of the interface transition zone could facilitate the subatomic vibrations in thin metallic films and multilayers grown on bulk insulating substrates., Comment: 6 pages, 5 figures

We investigate electronic transport in epitaxial Fe(100)/MgO/Fe/MgO/Fe double magnetic tunnel junctions with soft barrier breakdown (hot spots). Specificity of these junctions are continious middle layer and Nitrogen doping of the MgO barriers which provides soft breakdown at biases about 0.5V. In the junctions with hot spots we observe quasi-periodic changes in the resistance as a function of bias voltage which point out formation of quantum well states in the middle Fe continuous free layer. The room-temperature oscillations have been observed in both parallel and antiparallel magnetic configurations and for both bias polarizations. A simple model of tunneling through hot spots in the double barrier magnetic junction is proposed to explain qualitatively this effect., Comment: 11 pages, 4 figures

We report on the strong influence of Carbon doping on 1/f noise in fully epitaxial Fe/MgO(100)12ML/Fe magnetic tunnel junctions in comparison with undoped junctions with a large density of barrier defects. Carbon influences the relaxation of defects, the reconstruction of the interface and the symmetry transformation of interface resonance states, which are suggested to contribute to the strong reduction of the 1/f noise. Our study demonstrates that doping with light elements could be a versatile tool to improve the electron transport and noise in epitaxial magnetic tunnel junctions with large density of barrier defects., Comment: 8 pages, 3 figures

We report on room temperature low frequency noise due to magnetic inhomogeneities/domain walls (MI/DWs) in elliptic submicron FeCoB/MgO/FeCoB magnetic tunnel junctions with an area between 0.0245 and 0.0675{\mu}m2. In the smaller area junctions we found an unexpected random telegraph noise (RTN1), deeply in the parallel state, possibly due to stray field induced MI/DWs in the hard layer. The second noise source (RTN2) is observed in the antiparallel state for the largest junctions. Strong asymmetry of RTN2 and of related resistance steps with current indicate spin torque acting on the MI/DWs in the soft layer at current densities below 5x10^5 A/cm2., Comment: 12 pages, 4 figures

We investigate the magnetization dynamics in circular Permalloy dots with spatially separated magnetic vortices interconnected by domain walls (double vortex state). We identify a novel type of quasi one-dimensional (1D) localised spin wave modes confined along domain walls, connecting each of two vortex cores with two edge half-antivortices. Variation of the mode eigenfrequencies with the dot size is in quantitative agreement with the developed model, which considers a dipolar origin of the localized 1D spin waves or so-called Winter\'s magnons [J.M. Winter, Phys.Rev. 124, 452 (1961)]. These spin waves are analogous to the displacement waves of strings, and could be excited in a wide class of patterned magnetic nanostructures possessing domain walls, namely in triangular, square, circular or elliptic magnetic dots.

Alloying Fe electrodes with V, through reduced FeV/MgO interface mismatch in epitaxial magnetic tunnel junctions with MgO barriers, notably suppresses both nonmagnetic (parallel) and magnetic (antiparallel) state 1/f noise and enhances tunnelling magnetoresistance (TMR). A comparative study of the room temperature electron transport and low frequency noise in Fe1-xVx/MgO/Fe and Fe/MgO/Fe1-xVx MTJs with 0 <= x <= 0.25 reveals that V doping of the bottom electrode for x < 0.1 reduces in nearly 2 orders of magnitude the normalized nonmagnetic and magnetic 1/f noise. We attribute the enhanced TMR and suppressed 1/f noise to strongly reduced misfit and dislocation density., Comment: 12 pages, 3 figures

We report on detailed broadband ferromagnetic resonance measurements of azimuthal and radial spin wave excitations in circular Permalloy dots in the vortex ground state. Dots with aspect ratio (Beta =height over radius) varied from 0.03 to 0.1 were explored. We found that for Beta exceeding approximately 0.05, variation of the spin wave eigenfrequencies with Beta deviates from the predicted dependence. The frequency splitting of two lowest azimuthal modes was observed. The experimentally observed dependence of the frequency splitting on beta was reasonably well described by dynamic splitting model accounting the spin-waves and, vortex gyrotropic mode interaction.

Permalloy magnetic tunnel junctions. Complementary low frequency noise measurements are used to understand the conductance results. The obtained data indicate the breakdown of the Coulomb blockade for thickness of the asymmetric silicon layer exceeding 1.2\AA . The crossover in the conductance, the dependence of the tunnelling magnetoresistance with the bias voltage and the noise below 80K correspond to 1 monolayer coverage. Interestingly, the zero bias magnetoresistance remains nearly unaffected by the presence of the silicon layer. The proposed model uses Larkin-Matveev approximation of tunnelling through a single impurity layer generalized to 3D and takes into account the variation of the barrier shape with the bias voltage. The main difference is the localization of all the impurity levels within a single atomic layer. In the high thickness case, up to 1.8\AA, we have introduced a phenomenological parameter, which reflects the number of single levels on the total density of silicon atoms., Comment: 10 pages, 13 figures

The broadband ferromagnetic resonance (FMR) linewidth of the free layer of magnetic tunnel junctions is used as a simple diagnostic of the quality of the magnetic structure. The FMR linewidth increases near the field regions of free layer reversal and pinned layer reversal, and this increase correlates with an increase in magnetic hysteresis in unpatterned films, low frequency noise in patterned devices, and previous observations of magnetic domain ripple by use of Lorentz microscopy. Postannealing changes the free layer FMR linewidth indicating that considerable magnetic disorder, originating in the exchange-biased pinned layer, is transferred to the free layer., Comment: 13 pages, 4 figures

Ferromagnetic resonance and static magnetic properties of CoFe/Al2O3/CoFe/Py and CoFe/Al2O3/CoFeB/Py magnetic tunnel junctions and of 25nm thick single-layer Permalloy(Py) films have been studied as a function of temperature down to 2K. The temperature dependence of the ferromagnetic resonance excited in the Py layers in magnetic tunnel junctions shows knee-like enhancement of the resonance frequency accompanied by an anomaly in the magnetization near 60K. We attribute the anomalous static and dynamic magnetic response at low temperatures to interface stress induced magnetic reorientation transition at the Py interface which could be influenced by dipolar soft-hard layer coupling through the Al2O3 barrier.

Domain-wall magnetoresistance and low-frequency noise have been studied in epitaxial antiferromagnetically-coupled [Fe/Cr(001)]_10 multilayers and ferromagnetic Co line structures as a function of DC current intensity. In [Fe/Cr(001)]_10 multilayers a transition from excess to suppressed domain-wall induced 1/f noise above current densities of j_c ~ 2*10^5 A/cm^2 has been observed. In ferromagnetic Co line structures the domain wall related noise remains qualitatively unchanged up to current densities exceeding 10^6A/cm^2. Theoretical estimates of the critical current density for a synthetic Fe/Cr antiferromagnet suggest that this effect may be attributed to current-induced domain-wall motion that occurs via spin transfer torques.

We report on room temperature 1/f noise in fully epitaxial Fe(45nm)/MgO(2.6nm)/Fe(10nm) magnetic tunnel junctions (MTJs) with and without carbon doping of the Fe/MgO bottom interface. We have found that the normalized noise (Hooge factor) asymmetry between parallel and antiparallel states may strongly depend on the applied bias and its polarity. Both types of MTJs exhibit record low Hooge factors being at least one order of magnitude smaller than previously reported., Comment: 9 pages, 3 figures

Low temperature (10K) high voltage bias dynamic conductivity (up to 2.7V) and shot noise (up to 1V) were studied in epitaxial Fe(100)/Fe-C/MgO(100)/Fe(100) magnetic tunnel junctions, as a function of the magnetic state. The junctions show large tunnel magnetoresistance (185% at 300K and 330% at 4K). Multiple sign inversion of the magnetoresistance is observed for bias polarity when the electrons scan the electronic structure of the bottom Fe-C interface. The shot-noise shows a Poissonian character. This demonstrates a pure spin dependent direct tunneling mechanism and validates the high structural quality of the MgO barrier.

We report on tunnelling magnetoresistance (TMR), current-voltage (IV) characteristics and low frequency noise in epitaxially grown Fe(110)/MgO(111)/Fe(110) magnetic tunnel junctions (MTJs) with dimensions from 2x2 to 20x20 um2. The evaluated MgO energy barrier (0.50+/-0.08 eV), the barrier width (13.1+/-0.5 angstrom) as well as the resistance times area product (7+/-1 Mohmsum2) show relatively small variation, confirming a high quality epitaxy and uniformity of all MTJs studied. The noise power, though exhibiting large variation, was observed to be roughly anticorrelated with the TMR. Surprisingly, for the largest junctions we observed a strong enhancement of the normalized low-frequency noise in the antiparallel magnetic configuration. This behaviour could be related to an interplay between the magnetic state and the local barrier defects structure of the epitaxial MTJs, Comment: 9 pages and 3 figures

We report the experimental observation of sub-Poissonian shot noise in single magnetic tunnel junctions, indicating the importance of tunneling via impurity levels inside the tunnel barrier. For junctions with weak zero-bias anomaly in conductance, the Fano factor (normalized shot noise) depends on the magnetic configuration being enhanced for antiparallel alignment of the ferromagnetic electrodes. We propose a model of sequential tunneling through nonmagnetic and paramagnetic impurity levels inside the tunnel barrier to qualitatively explain the observations., Comment: 5 pages, 5 figures

Superconducting films in perpendicular magnetic field are found to rectify alternating currents. The effect has been observed both in plain and nanostructured superconducting films (niobium and lead). The rectified voltage appears both along and transverse to alternating current and strongly depends on the magnetic field. Rectification phenomena is based on the property of superconductors to have permanent circulating currents in magnetic field (vortices) and to develop electric fields at high enough currents. In contrast to previous findings, at higher current frequencies no asymmetric pinning sites are needed to produce rectification and related guided flux motion., Comment: 15 pages, 4 figures, PDF file

For antiferromagnetically coupled Fe/Cr multilayers the low field contribution to the resistivity, which is caused by the domain walls, is strongly enhanced at low temperatures. The low temperature resistivity varies according to a power law with the exponent about 0.7 to 1. This behavior can not be explained assuming ballistic electron transport through the domain walls. It is necessary to invoke the suppression of anti-localization effects (positive quantum correction to conductivity) by the nonuniform gauge fields caused by the domain walls., Comment: 5 pages with 3 figures

In order to probe the influence of the surface-induced anisotropy on the impurity spin magnetization, we measure the anomalous Hall effect in thin AuFe films at magnetic fields up to 15 T. The observed suppression of the anomalous Hall resistivity at low fields as well as the appearance of a minimum in the differential Hall resistivity at higher fields can be explained by our theoretical model which takes into account the influence of a polycrystalline film structure on the surface-induced anisotropy. Our results imply that the apparent discrepancy between different experimental results for the size effects in dilute magnetic alloys can be linked to a different microstructure of the samples., Comment: 4 pages, 3 figures, E-mail addresses: devreese@uia.ua.ac.be, fomin@uia.ua.ac.be

Tunnel and point contact experiments have been made in a URu$_2$Si$_2$ single crystal along the c-axis. The experiments were performed changing temperature and contact size in a low temperature scanning tunneling microscope. A resonance develops at the Fermi level at $T\sim 60$ K. This resonance splits and becomes asymmetric when the 17.5 K phase transition is crossed. These results are consistent with the existence of Kondo like bound states of the U$^{4+}$ ionic configurations and the conduction electrons. Below the transition, these configurations are split by the development of quadrupolar ordering. The peak separation can be interpreted as a direct measurement of the order parameter. Measurements on a policrystalline UAu_2Si_2$ sample are also reported, with a comparative study of the behavior of both materials., Comment: 4 pages (Latex) + 2 postscript figures