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We report the experimental observation of the spin-wave moirc edge and cavity modes using Brillouin light scattering spectromicroscopy in a nanostructured magnetic moirc lattice consisting of two twisted triangle antidot lattices based on an yttrium iron garnet thin film. Spin-wave moirc edge modes are detected at an optimal twist angle and with a selective excitation frequency. At a given twist angle, the magnetic field acts as an additional degree of freedom for tuning the chiral behavior of the magnon edge modes. Micromagnetic simulations indicate that the edge modes emerge within the original magnonic band gap and at the intersection between a mini flatband and a propagation magnon branch. Our theoretical estimate for the Berry curvature of the magnon-magnon coupling suggests a nontrivial topology for the chiral edge modes and confirms the key role played by the dipolar interaction. Our findings shed light on the topological nature of the magnon edge mode for emergent moirc magnonics., Physical Review X, 13 (2), ISSN:2160-3308

Spin-current and spin-wave-based devices have been considered as promising candidates for next-generation information transport and processing and wave-based computing technologies with low-power consumption. Spin pumping has attracted tremendous attention and has led to interesting phenomena, including the line width broadening, which indicates damping enhancement due to energy dissipation. Recently, chiral spin pumping of spin waves has been experimentally realized and theoretically studied in magnetic nanostructures. Here, we experimentally observe by Brillouin light scattering (BLS) microscopy the line width broadening sensitive to magnetization configuration in a hybrid metal-insulator nanostructure consisting of a Co nanowire grating dipolarly coupled to a planar continuous YIG film, consistent with the results of the measured hysteresis loop. Tunable line width broadening has been confirmed independently by propagating spin-wave spectroscopy, where unidirectional spin waves are detected. Position-dependent BLS measurement unravels an oscillating-like behavior of magnon populations in Co nanowire grating, which might result from the magnon trap effect. These results are thus attractive for reconfigurable nanomagnonics devices.

Micro-focused Brillouin–Mandelstam light scattering technique and micromagnetic simulations were used to study surface (SSW) and backward volume (BVSW) spin waves (SW) interference under excitation by curvilinear focusing transducers placed oppositely to each other on a top of a tangentially magnetized yttrium iron garnet (YIG) film. It is shown that due to anisotropic propagation, the 2D interference patterns for both SSW and BVSW focused beams are nonreciprocal. Due to chromatic aberration and caustics formation of the focusing transducers, the interference pattern of the focused SW beams depends on the excitation frequency and is sensitive to local nonuniformities in the YIG film. The obtained results demonstrate the possibility to use curvilinear SW focusing transducers for information technologies based on magnonic optics.

The role of three-dimensionality in a ferromagnetic medium in ruling the propagation properties of spin-waves (SW) has been one of the main focuses of the research activity in recent years. In this context, we investigate the evolution of the SW dispersion (frequency vs wave vector) induced by a progressive vertical undulation of a ferromagnetic film. The geometric undulation is taken along a single direction and is periodic with constant period, while the amplitude (differential maximum height with respect to the film thickness) is gradually increased from 0 to 60 nm. We study the characteristic modification of the internal effective field and link it to the resulting SW dispersions and spatial profile. These systems display at once features both of a planar film and a discretized medium, and the dispersion curves change not only when SWs propagate along the undulation direction, but also perpendicular to it. We discuss the geometric and magnetic conditions for having either the invariance of the SW group velocity with respect to even major changes in the undulation, or a large group velocity for some edge modes. We address a potential dual-band activity, namely the simultaneous propagation of two independent SW-signals, with separated frequency bands and disjoint oscillation regions.

In this work, we study experimentally by broadband ferromagnetic resonance measurements, the dependence of the spin-wave excitation spectra on the magnetic applied field in CoFeB meander-shaped films. Two different orientations of the external magnetic field were explored, namely parallel or perpendicular to the lattice cores. The interpretation of the field dependence of the frequency and spatial profiles of major spin-wave modes were obtained by micromagnetic simulations. We show that the vertical segments lead to the easy-axis type of magnetic anisotropy and support the in-phase and out-of-phase spin-wave precession amplitude in the vertical segments. The latter could potentially be used for the design of tunable metasurfaces or in magnetic memories based on meandering 3D magnetic films., 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 studied both experimentally and theoretically the reprogrammable spin wave band structure in Permalloy(10 nm)/Cu(5 nm)/Permalloy(30 nm) nanowire arrays of width w = 280 nm and inter-wire separation in the range from 80 to 280 nm. We found that, depending on the inter-wire separation, the anti-parallel configuration, where the magnetizations of the two Permalloy layers point in opposite directions, is stabilized over specific magnetic field ranges thus enabling us to directly compare the band structure with that of the parallel alignment. We show that collective spin waves of the Bloch type propagate through the arrays with different magnonic bandwidths as a consequence of the interplay between the intra- and inter-nanowire dynamic dipolar interactions. A detailed understanding, e.g. whether they have a stationary or propagating character, is achieved by considering the phase relation (in-phase or out-of-phase) between the dynamic magnetizations in the two ferromagnetic layers and their average value. This work opens the path to magnetic field-controlled reconfigurable layered magnonic crystals that can be used for future nanoscale magnon spintronic devices.

We present a detailed study of the spin-wave dynamics in single Pt/Co/W and double Pt/Co/W/Co/Pt ferromagnetic layer systems. The dispersion of spin waves was measured by wavevector-resolved Brillouin light scattering spectroscopy while the in-plane and out-of-plane magnetization curves were measured by alternating gradient field magnetometry. The interfacial Dzyaloshinskii-Moriya interaction induced nonreciprocal dispersion relation was demonstrated for both single and double ferromagnetic layers and explicated by numerical simulations and theoretical formulas. The results indicate the crucial role of the order of layers deposition on the magnetic parameters. A significant difference between the perpendicular magnetic anisotropy constant in double ferromagnetic layer systems conduces to the decline of the interlayer interactions and different dispersion relations for the spin-wave modes. Our study provides a significant contribution to the realization of the multifunctional nonreciprocal magnonic devices based on ultrathin ferromagnetic/heavy-metal layer systems., Comment: This version of the manuscript is a prereview first-submission version. 10 pages, 4 figures

Exploring the third dimension in magnonic systems is essential for the investigation of alternative physical phenomena and for the control of spin-wave propagation at the nanoscale. Here, the characteristics of spin waves in vertical meander-shaped ${\mathrm{Co}}_{40}{\mathrm{Fe}}_{40}{\mathrm{B}}_{20}$ thin films consisting of nanosegments located at 90\ifmmode^\circ\else\textdegree\fi{} angles with respect to each other are investigated by Brillouin-light-scattering spectroscopy over four Brillouin zones in reciprocal space. We reveal the dispersion relations and the periodic character of several dispersive branches as well as alternating frequency bands, where spin waves are allowed or forbidden to propagate. Between each couple of successive modes, frequency band gaps exist only for wave numbers k = 2m\ensuremath{\pi}/a, where m is an integer number and a is the size of the meander unit cell, whereas the spectra show propagating modes in the orthogonal film segments for all the other wave numbers. Micromagnetic simulations and analytical calculations are used to understand and explain the results in terms of the mode spatial localization and symmetry. We show that the width and the center frequency of the magnonic band gaps can be controlled by changing the geometrical parameters of the meander-shaped film. The investigated samples behave as three-dimensional waveguides where spin waves propagate in the film segments located at 90\ifmmode^\circ\else\textdegree\fi{} angles with respect to each other, thus making possible vertical spin-wave transport for multilayer magnonic architectures and signal processing.

Publisher Copyright: © 2021 The Author(s). Published by IOP Publishing Ltd. Magnonics is a budding research field in nanomagnetism and nanoscience that addresses the use of spin waves (magnons) to transmit, store, and process information. The rapid advancements of this field during last one decade in terms of upsurge in research papers, review articles, citations, proposals of devices as well as introduction of new sub-topics prompted us to present the first roadmap on magnonics. This is a collection of 22 sections written by leading experts in this field who review and discuss the current status besides presenting their vision of future perspectives. Today, the principal challenges in applied magnonics are the excitation of sub-100 nm wavelength magnons, their manipulation on the nanoscale and the creation of sub-micrometre devices using low-Gilbert damping magnetic materials and its interconnections to standard electronics. To this end, magnonics offers lower energy consumption, easier integrability and compatibility with CMOS structure, reprogrammability, shorter wavelength, smaller device features, anisotropic properties, negative group velocity, non-reciprocity and efficient tunability by various external stimuli to name a few. Hence, despite being a young research field, magnonics has come a long way since its early inception. This roadmap asserts a milestone for future emerging research directions in magnonics, and hopefully, it will inspire a series of exciting new articles on the same topic in the coming years.

Unidirectional information transport plays a key role in optics, microwave technology, electronic logic circuits and devices. Spin waves (SWs) are considered to be a promising candidate for the next-generation logic devices, which have many advantages such as low-energydissipation and compatibility with radio-frequency-based electronic devices. Unidirectional SWs have been demonstrated in magnetic thin films theoretically and experimentally, offering a great opportunity to realize unidirectional transport of spin information. In this article, we review several methods for emitting and measuring unidirectional SWs, such as using the nonreciprocity provided by magnetostatic surface SWs and interfacial Dzyaloshinskii–Moriya interactions. Unidirectional SWs can also be excited by magnetic nanowire arrays as well as spatially defined spin textures. Finally, we review some magnonic logic devices based on unidirectional SWs, such as spin-wave diodes.

Spin-charge interconversion phenomena at the interface between magnetic materials and topological insulators (TIs) are attracting enormous interest in the research effort towards the development of fast and ultra-low power devices for the future information and communication technology. We report a large spin-to-charge conversion efficiency in Au/Co/Au/Sb2Te3/Si(111) heterostructures based on Sb2Te3 TIs grown by metal organic chemical vapor deposition on 4 inches Si(111) substrates. By conducting room temperature spin pumping ferromagnetic resonance, we measure an inverse Edelstein Effect length {\lambda}IEE up to 0.75 nm, a record value for 3-dimensional chalcogenide-based TIs heterostructures. Our results open the path toward the use of chemical methods to produce TIs on large area Si substrates and characterized by highly performing spin-charge conversion, thus marking a milestone toward future technology-transfer., Comment: Main text: 28 pages, 5 figures and 2 tables. Supplementary information are also included in the file with additional 12 pages

We present a systematic experimental and theoretical investigation of the magnonic band structure in dense arrays of both asymmetric and symmetric cross-section trilayered Fe(10 nm)/Cu( $t$)/Py(10 nm) nanowires (NWs). The Cu spacer thickness ($t$) is varied in the range between 0 and 10 nm. The frequency dispersion of collective spin-wave excitations in the above trilayered NW arrays has been studied by the Brillouin light-scattering technique while sweeping the wave vector perpendicularly to the nanowire length over four Brillouin zones of the reciprocal space. The experimental results have been quantitatively reproduced by an original numerical model that includes a two-dimensional Green's function description of the dipole field of the dynamic magnetization and exchange coupling between the layers. We found that, depending on $t$, the Py and Fe magnetic layers within the same nanowire are coupled by either the interlayer exchange or dipolar interactions. This has an impact on both the magnetization reversal and the collective dynamical properties of the artificial crystal. In particular, it is possible to stabilize a magnetization configuration where the layer magnetization vectors point in the same or in the opposite direction over a field range that varies with the Cu thickness. In addition, several modes are detected whose propagation properties (i.e., stationary or dispersive) through the array depend on static magnetization configuration as well as on the relative phase (in-phase or out-of-phase) of dynamic magnetizations between the two layers within the same nanowire.

Magnonic crystals (MCs) are materials with periodically modulated magnetic properties wherethe spin waves (SWs) band structure consists of intervals of allowed SW frequencies and forbiddengaps in which there are no allowed magnonic states. [...]

Magnetic films with a periodic pattern were considered for controlling spin waves (SWs) from 1976. The concept of magnonic crystals (MCs) was proposed as an SW counterpart of photonic crystals. The MC can be formed from a magnetic material with periodic distribution of the constituent materials or periodic modulation of some magnetic parameters or other parameters relevant to the propagation of SWs, such as the external magnetic field, geometry, temperature, or a surrounding of the homogeneous ferromagnetic medium. The chapter provides an overview of the theoretical results on the magnonic band structure in three-dimensional (3D) MCs. The most challenging problem related to experimental studies on 3D MCs is the fabrication of a high-quality structure with periodicity along three directions in the nanoscale. The research on 3D MCs was concentrated on the calculation of the magnonic band structure and influence of the material and geometrical parameters on the magnonic bandgaps. The chapter concludes with prospects for further development toward 3D MCs.

Magnonic quasicrystals can be used to manipulate spin waves, offering possibilities beyond those of periodic magnonic crystals. The authors investigate one-dimensional magnonic Fibonacci quasicrystals and demonstrate the existence of collective spin waves over a broad range of wave vectors. The spin-wave spectra here are tunable by changing magnetic field amplitude (for continuous band-structure adjustment), magnetization configuration (for reprogrammability), or the dimensions of the elements (for scalability). Beyond being fundamentally interesting, these properties show that magnonic quasicrystals are promising for tomorrow's spintronic, microwave, and magnonic technologies.

Magnon spintronics is a prosperous field that promises beyond-CMOS technology based on elementary excitations of the magnetic order that act as information carriers for future computational architectures. Unidirectional propagation of spin waves is key to the realization of magnonic logic devices. However, previous efforts to enhance the magnetostatic surface spin wave nonreciprocity did not realize (let alone control) purely unidirectional propagation. Here we experimentally demonstrate excitation of unidirectional exchange spin waves by a nanoscale magnetic grating consisting of Co nanowires fabricated on an ultrathin yttrium iron garnet film. We explain and model the nearly perfect unidirectional excitation by the chirality of the magneto-dipolar interactions between the Kittel mode of the nanowires and the exchange spin waves of the film. Reversal of the magnetic configurations of film and nanowire array from parallel to antiparallel changes the direction of the excited spin waves. Our results raise the prospect of a chiral magnonic logic without the need to involve fragile surface states.

We investigate magnonic band structure in thin homogeneous permalloy film decorated with periodic array of elliptically shaped permalloy dots and separated by non-magnetic Pt spacer. We demonstrated experimentally formation of the magnonic band structure for Damon-Eshbach wave propagating in permalloy film with the band gap opened at the Brillouin zone border and band splitting at smaller wavenumbers, due to the Bragg interference and interaction of propagating wave of the continuous film with a standing resonant mode of the nano-ellipses, respectively. The shape anisotropy of the permalloy nanodots allows to control the spin wave dynamics through the switch between two states of the magnetization with respect to the underneath film magnetization, thus enabling magnonic band structure reprogrammability. With numerical analysis we show, that predominant role in formation of the magnonic band structure is played by a vertical dynamic coupling between propagating wave in the film and magnetization oscillations in the nanodots., Comment: 7 pages, 8 figures

Using Brillouin light scattering spectroscopy and dynamical matrix method calculations, we study collective spin waves in dense arrays of periodically double-side width-modulated Permalloy nanowires. Width modulation is achieved by creating a sequence of triangular notches on the two parallel nanowire sides, with a periodicity of p=1000 nm, and tunable relative displacement (D) of the notches sequence on the two lateral sides. Both symmetric (D=0) and asymmetric (D= 250 and 500 nm) width-modulated nanowires were investigated. We have found that the detected modes have Bloch-type character and belong to a doublet deriving from the splitting of the modes characteristics of the nanowire with homogeneous width. Interestingly, the amplitude of the magnonic band, the frequency difference of the doublet, as well as their relative scattering intensity, can be efficiently controlled by increasing D rather than having single- or symmetric (D=0) double-side width-modulation.

Active manipulation of spin waves is essential for the development of magnon-based technologies. Here, we demonstrate programmable spin-wave filtering by resetting the spin structure of pinned 90° Néel domain walls in a continuous CoFeB film with abrupt rotations of uniaxial magnetic anisotropy. Using micro-focused Brillouin light scattering and micromagnetic simulations, we show that broad 90° head-to-head or tail-to-tail magnetic domain walls are transparent to spin waves over a broad frequency range. In contrast, magnetic switching to a 90° head-to-tail configuration produces much narrower and strongly reflecting domain walls at the same pinning locations. Based on these results, we propose a magnetic spin-wave valve with two parallel domain walls. Switching the spin-wave valve from an open to a closed state changes the transmission of spin waves from nearly 100 to 0%. Active control over spin-wave transport through programmable domain walls could be utilized in magnonic logic devices or non-volatile memory elements., Magnon-based spintronic devices crucially rely on the capability of spin wave manipulation. Here the authors achieve active control of spin wave transmission by programming a pinned 90 degree Néel domain wall in a continuous CoFeB/BaTiO3 film with abrupt rotations of uniaxial magnetic anisotropy.

We measure and analyze the chirality of Dzyaloshinskii-Moriya-interaction (DMI) stabilized spin textures in multilayers of $\mathrm{Ta}|{\mathrm{Co}}_{20}{\mathrm{F}}_{60}{\mathrm{B}}_{20}|\mathrm{MgO}$. The effective DMI is measured experimentally using domain wall motion measurements, both in the presence (using spin-orbit torques) and absence of driving currents (using magnetic fields). We observe that the current-induced domain wall motion yields a change in effective DMI magnitude and opposite domain wall chirality when compared to field-induced domain wall motion (without current). We explore this effect, which we refer to as current-induced DMI, by providing possible explanations for its emergence, and explore the possibility of its manifestation in the framework of recent theoretical predictions of DMI modifications due to spin currents.

We present the results of advanced micromagnetic simulations, performed using the open-source GPU-accelerated code MuMax3, on spin waves excitation and propagation in two-dimensional magnonic crystals consisting of Permalloy ( $\text{Ni}_{\text{80}}\text{Fe}_{\text{20}}$ ) square antidot lattices. The magnonic band structure of samples having a fixed periodicity $a = 200\ \text{nm}$ and different sides of the square holes, ranging from 30 to 90 nm, has been analyzed in both the magnetostatic surface wave and backward volume wave configurations, encompassing the first three artificial Brillouin zones. A careful analysis of both the dispersive character and the spatial profile of the most prominent eigenmodes permits interpretation of the main features of the transmission spectra of the simulated samples, which can be considered tunable magnonic filters. General conclusions are drawn about the choice of the optimal geometry for the design of signal processing devices based on square antidot lattices.

We have experimentally and numerically investigated the dispersion of collective spin waves propagating through arrays of longitudinally magnetized nanowires (NWs) with a periodically modulated width. Two nanowire arrays with single-side modulation and different periodicities of modulation were studied and compared to the nanowires with a homogeneous width. The spin-wave dispersion, measured up to the third Brillouin zone of the reciprocal space, revealed the presence of two dispersive modes for the width-modulated NWs, whose amplitude of the magnonic band depends on the modulation periodicity, and a set of nondispersive modes at higher frequency. These findings are different from those observed in homogeneous width NWs where only the lowest mode exhibits sizeable dispersion. The measured spin-wave dispersion has been satisfactorily reproduced by means of the dynamical matrix method. The results presented in this work are important in view of the possible realization of tunable frequency magnonic devices.

We report the observation of a Pt layer thickness dependence on the induced interfacial DzyaloshinskiiMoriya interaction in ultrathin Pt(d(Pt))/CoFeB films. Taking advantage of the large spin-orbit ...

We have studied, experimentally and theoretically, the effect of a layering sequence on the magnonic band structure in dense arrays of both asymmetric- and symmetric cross-section tri-layered Py/Cu/Fe and Fe/Cu/Py nanowires. The spin-wave dispersion for these artificial crystals has been measured with Brillouin light scattering (BLS) spectroscopy. We also carried out numerical simulations of the dispersion using an original model employing a 2D Green's function description of the dynamic dipole field of the precessing magnetization. The presence of the Cu spacer exchange-decouples the two magnetic layers, which stabilizes two equilibrium states of static magnetization. These are the parallel and antiparallel states, for which the static magnetization vectors for the layers are either co-aligned or anti-aligned to each other, respectively. These states are stable in a range of applied fields that depend on the layer width and their ordering in the stack. The magnetization configurations and layers sequence, as well as the presence of acoustic (in-phase) and optic (out-of-phase) spin-wave modes, have a significant impact on the magnonic band structure both in terms of the frequency positions of the dispersive and stationary modes and on their spatial profiles.

The propagation of spin waves in antidot lattices with line defects has been studied by both microfocused Brillouin light scattering and micromagnetic simulations. The samples under investigation are NiFe square antidot lattices with circular holes of 250 nm of diameter, periodicity of 700 nm and thickness of 60 nm. Line defects have been introduced in the antidot lattices by removing one row (column) of holes every three rows (columns). Microfocused BLS has been used in order to map out the intensity profile of the main eigenmodes which are excited by a microwave current injected into a coplanar waveguide deposited on top of the sample surface. The comparison between micromagnetic simulations and ?-BLS measurements shows a good agreement not only for the measured frequency but also for the spatial profiles of the modes with the highest intensity in BLS spectra. These eigenmodes extend along the channels between dots rows and their frequency is different in presence of row- or column-defects because of the modification of the internal field felt by the precessing spins. © 2013 Elsevier B.V.

The excitation of spin waves by a microwave current injected into a coplanar waveguide with finite-width ground lines on a continuous Permalloy film is investigated both experimentally and numerically. Phase sensitive micro-focused Brillouin light scattering has been employed to reveal the spatial profile of the propagating spin waves in the magnetostatic surface wave geometry. The experimental results have been satisfactorily reproduced by means of micromagnetic simulations. The exciting microwave field used in this simulation has the spatial profile defined by the coplanar waveguide and user-defined periodic boundary conditions were employed in order to simulate the extended system. The resulting space and time dependent evolution of the magnetization has been analyzed by means of one and two dimensional fast Fourier transform algorithm in order to obtain the spatial profile and the frequency spectrum of the excited spin waves as well as their dispersion relations. Evidence is given to asymmetric emission from the two sides of the coplanar waveguide due to the symmetry breaking related to the sense of precession of the dynamical magnetization, as well as to the near-field effects of the extended spin wave emitter.

Single- or multi-layered planar magnetic dots, with lateral dimensions ranging from tens to hundreds of nanometers, are used as elemental switches in current and forthcoming devices for information and communication technology (ICT), including magnetic memories, spin-torque oscillators and nano-magnetic logic gates. In this review article, we will first discuss energy dissipation during irreversible switching protocols of dots of different dimensions, ranging from a few tens of nanometers to the micrometric range. Then we will focus on the fundamental energy limits of adiabatic (slow) erasure and reversal of a magnetic nanodot, showing that dissipationless operation is achievable, provided that both dynamic reversibility (arbitrarily slow application of external fields) and entropic reversibility (no free entropy increase) are insured. However, recent theoretical and experimental tests of magnetic-dot erasure reveal that intrinsic defects related to materials imperfections such as roughness or polycrystallinity, may cause an excess of dissipation if compared to the minimum theoretical limit. We will conclude providing an outlook on the most promising strategies to achieve a new generation of power-saving nanomagnetic logic devices based on clusters of interacting dots and on straintronics.

We have investigated both experimentally and numerically the magnonic band structure of arrays of closely spaced Fe/permalloy nanowires (NWs) with an L-shape cross-section using the Brillouin light scattering technique and GPU-based micromagnetic simulations. NWs consist of a 340 nm wide and 10 nm thick permalloy layer covered by a 170 nm wide Fe overlayer. The thickness of the latter was varied in the range from 0 to 10 nm in order to analyze its influence on the magnonic band structure. We found that both the frequency and the spatial profile of the most intense and dispersive mode, can be efficiently tuned by the presence of the thin Fe NW overlayer. In particular, by increasing the Fe thickness, one observes a substantial frequency increase, while the spatial profile of the mode narrows and moves to the permalloy NW portion not covered by Fe. In addition, the presence of the Fe overlayer causes a significant increase of the number of detected modes and a change of their intensity in the Brillouin spectra as a function of the Bloch wave number. These results show that it is possible to engineer the band structure of magnonic crystals consisting of bi-layered, L-shaped, NWs by a careful control of the overlayer thickness.

An efficient way for the control of spin wave propagation in a magnetic medium is the use of periodic patterns known as magnonic crystals (MCs). However, the fabrication of MCs especially bi-components, with periodicity on nanoscale, is a challenging task due to the requirement for sharp interfaces. An alternative method to circumvent this problem is to use homogeneous ferromagnetic film with modified periodically surrounding. The structure is also suitable for exploiting nonreciprocal properties of the surface spin waves. In this work, we demonstrate that the magnonic band structure forms in thin permalloy film due to dynamical magnetostatic coupling with Ni stripes near its surface. We show, that the band gap width can be systematically tuned by the changing interlayer thickness between film and stripes. We show also the effect of nonreciprocity, which is seen at the band gap edge shifted from the Brillouin zone boundary and also in nonreciprocal interaction of propagating spin waves in Py film with the standing spin waves in Ni stripes. Our findings open possibility for further investigation and exploitation of the nonreciprocity and band structure in magnonic devices., 12 pages, 5 figures

The magnetic anisotropies of a patterned, exchange biased ${\mathrm{Fe}}_{50}{\mathrm{Mn}}_{50}\text{/}{\mathrm{Ni}}_{80}{\mathrm{Fe}}_{20}$ system are studied using ferromagnetic resonance, supplemented by Brillouin light scattering experiments and Kerr magnetometry. The exchange biased bilayer is partially etched into an antidot geometry so that the system approximates a ${\mathrm{Ni}}_{80}{\mathrm{Fe}}_{20}$ layer in contact with antidot structured ${\mathrm{Fe}}_{50}{\mathrm{Mn}}_{50}$. Brillouin light scattering measurements of the spin wave frequency dependence on the wave vector reveal a magnonic band gap as expected for a periodic modulation of the magnetic properties. Analysis of the ferromagnetic resonance spectra reveals eightfold and fourfold contributions to the magnetic anisotropy. Additionally, the antidot patterning decreases the magnitude of the exchange bias and modifies strongly its angular dependence. Softening of all resonance modes is most pronounced for the applied magnetic field aligned within ${10}^{\ensuremath{\circ}}$ of the antidot axis, in the direction of the bias. Given the degree to which one can tailor the ground state, the resulting asymmetry at low frequencies could make this an interesting candidate for applications such as selective/directional microwave filtering and multistate magnetic logic.

Magnetostatic coupling in arrays of closely spaced magnetic elements is becoming an important issue in the path to the fabrication of spintronic devices. Dense chains of rounded-corners rectangular particles (dots) of lateral size 1025 9 450 nm 2, with interdot spacing variable in the range between 55 and 700 nm, have been patterned by deep UV lithography, followed by the lift-off of two permalloy films of thickness 20 and 40 nm. Magneto-optical Kerr effect (MOKE) and magnetic force microscopy (MFM) experiments, together with micromagnetic simulations, were per- formed to study the dependence of the magnetization configuration on the dipolar coupling. Both MOKE measurements and MFM images clearly show that, at remanence, the magnetic state of isolated particles of thickness 20 nm takes the form of a distorted single domain (C-state or S-State configurations). Instead, when the particle thickness is double (40 nm), closure states characterized by one, two or three vortices occur at remanence. However, when the 40 nm thick dots are placed in chains along the easy axis (head to tail), as the separation is progressively reduced, the single domain state is stabilized at remanence. On the other hand, when the 40 nm thick particles are placed side by side in chains the effect of dipolar interactions is to favour the nucleation of vortex states. For small inter-element separation, there is only one vortex per particle and it has the same chirality in adjacent particles, due to the dipolar interaction. Different from this, for the 20 nm thick samples and sub-100 nm separation, adjacent particles are single-domain but with antiparallel magnetization in neighbour elements, like in an artificial antiferromagnet.

We demonstrate the role of spin-polarized current pulse in activating only a subset of spin-wave normal modes in laterally confined magnetic systems. In order to derive selection rules based on geometrical considerations, the study was carried out by comparing the results of two different micromagnetic frameworks (a classical finite-difference time-domain scheme and the dynamical matrix method) and considering nanopillar devices of elliptical and circular cross-sections in different magnetic ground states (onion, S, and vortex states). The analogies and the differences existing between the mode activation process driven by spin-torque and that obtained by a magnetic field pulse are also addressed.

We present a combined experimental investigation of magnetic normal modes in an antidot lattice using both Brillouin light scattering and broadband ferromagnetic resonance. It was fabricated on a silicon substrate using optical ultraviolet lithography. The sample consisted of a 30-nm-thick Ni80Fe20 squared antidot array with circular holes whose diameter and edge-to-edge spacing are 250 and 150 nm, respectively. Experiments were performed as a function of the applied magnetic field ¿0Hext in the range from -100 to 100 mT, with Hext applied along both the square lattice axis and its diagonal. Several peaks were observed in both the Brillouin light scattering and ferromagnetic resonance spectra, and their evolution with the intensity and the direction of the applied field Hext was measured. Micromagnetic simulations enabled us to identify the modes in terms of their symmetry obtaining a good quantitative agreement with the measured frequencies. In addition, we show how the inhomogeneity of the internal field affected the properties of the magnetic eigenmodes and their localization in different regions of the antidot lattice.

Micro-focused and conventional Brillouin light scattering techniques have been exploited to investigate the spectrum of magnetic excitations (eigenmodes) of elliptical permalloy nanorings in the vortex ground state. The interpretation of the experimental data has been achieved using the dynamical matrix method. A careful comparison of the calculated frequency and profiles of magnetic modes with the experimental data, allowed us to identify the character of the different modes in terms of spatial symmetry and localization. In particular, the spatial extent of each mode was directly visualized by measurement of two-dimensional maps of the mode intensity over the ring surface.

We report an experimental investigation of the magnetic normal modes in large-area Ni80Fe20 antidot arrays fabricated on commercially available silicon substrates using deep ultraviolet lithography at 248 nm exposing wavelength. The effect of the lattice symmetry (square, rhombic and honeycomb) on the magnetic normal modes of the arrays has been investigated by both Brillouin light scattering and broadband ferromagnetic resonance using a vector network analyzer. For all the measured samples, the eigenfrequencies show an angular symmetry which is consistent with the lattice arrangement of the holes. Interpretation of the experimental results was achieved by micromagnetic simulations which enabled us to calculate both the frequencies of the modes and the corresponding spatial profile, correlating their angular evolution with the magnetic ground state.

The authors acknowledge support by the European Union (FPVII (2007-2013) under G.A. n.318287 LANDAUER, and by MIUR-PRIN 2010–11 Project 2010ECA8P3 “DyNanoMag.”. M.P. and P.V. acknowledge funding from the Spanish Ministry of Economy and Competitiveness (Project No. MAT2012-36844); M.P. acknowledges support by Spanish Ministry of Economy and Competitiveness (grant BES-2013-063690). Bistable nanomagnetic switches are extensively used in storage media and magnetic memories, associating each logic state to a different equilibrium orientation of the magnetization. Here we consider the issue of the minimum energy required to change the information content of nanomagnetic switches, a crucial topic to face fundamental challenges of current technology, such as power dissipation and limits of scaling. The energy dissipated during a reset operation, also known as “Landauer erasure”, has been accurately measured at room temperature by vectorial magneto-optical measurements in arrays of elongated Permalloy nanodots. Both elliptical and rectangular dots were analysed, with lateral sizes ranging from several hundreds to a few tens of nanometers and thickness of either 10 nm or 5 nm. The experimental results show a nearly linear decrease of the dissipated energy with the dot volume, ranging from three to one orders of magnitude above the theoretical Landauer limit of kBT×ln(2). These experimental findings are corroborated by micromagnetic simulations showing that the significant deviations from the ideal macrospin behavior are caused by both inhomogeneous magnetization distribution and edge effects, leading to an average produced heat which is appreciably larger than that expected for ideal nanoswitches. Postprint

Spin-Hall oscillators (SHO) are promising sources of spin-wave signals for magnonics applications, and can serve as building blocks for magnonic logic in ultralow power computation devices. Thin magnetic layers used as “free” layers in SHO are in contact with heavy metals having large spin-orbital interaction, and, therefore, could be subject to the spin-Hall effect (SHE) and the interfacial Dzyaloshinskii-Moriya interaction (i-DMI), which may lead to the nonreciprocity of the excited spin waves and other unusual effects. Here, we analytically and micromagnetically study magnetization dynamics excited in an SHO with oblique magnetization when the SHE and i-DMI act simultaneously. Our key results are: (i) excitation of nonreciprocal spin-waves propagating perpendicularly to the in-plane projection of the static magnetization; (ii) skyrmions generation by pure spin-current; (iii) excitation of a new spin-wave mode with a spiral spatial profile originating from a gyrotropic rotation of a dynamical skyrmion. These results demonstrate that SHOs can be used as generators of magnetic skyrmions and different types of propagating spin-waves for magnetic data storage and signal processing applications.

We report the experimental observation of Snell's law for magneto-static spin waves in thin ferromagnetic Permalloy films by imaging incident, refracted and reflected waves. We use a thickness step as the interface between two media with different dispersion relation. Since the dispersion relation for magneto-static waves in thin ferromagnetic films is anisotropic, deviations from the isotropic Snell's law known in optics are observed for incidence angles larger than 25\textdegree{} with respect to the interface normal between the two magnetic media. Furthermore, we can show that the thickness step modifies the wavelength and the amplitude of the incident waves. Our findings open up a new way of spin wave steering for magnonic applications.

In the developing field of magnonics,it is very important to achieve tailoring of spin wave propagation by both a proper combination of materials with different magnetic properties and their nanostructuring on the submicrometric scale. We have exploited deep ultra-violet lithography, in combination with tilted shadow deposition technique, to fabricate arrays of closely spaced bi-layer nanowires (NWs), with separation d=100 nm and periodicity a=440 nm, having bottom and top layers made of Permalloy and Iron, respectively. The NWs have either rectangular cross section (bottom and upper layers of equal width) or L-shaped cross section (upper layer of half width). The frequency dispersion of collective spin wave excitations in the above bi-layered NWs arrays has been measured by the Brillouin light scattering technique while sweeping the wave vector perpendicularly to the wire length over three Brillouin zones of the reciprocal space. For the rectangular NWs, the lowest frequency fundamental mode, characterized by a quasi- uniform profile of the amplitude of the dynamic magnetization across the NW width, exhibits a sizeable and periodic frequency dispersion. A similar dispersive mode is also present in L-shaped NWs, but the mode amplitude is concentrated in the thin side of the NWs. The width and the center frequency of the magnonic band associated with the above fundamental modes has been analyzed, showing that both can be tuned by varying the external applied field. Moreover, for the L-shaped NWs it is shown that there is also a second dispersive mode,at higher frequency,characterized by an amplitude concentrated in the thick side of the NW. These experimental results have been quantitatively reproduced by an original numerical model that includes two-dimensional Green's function of the dipole field of the dynamic magnetization and interlayer exchange coupling between the layers., 17 pages, 5 figures

Using the Vectorial Magneto-Optic Kerr Effect (V-MOKE) and numerical simulations, we have investigated the magnetization reversal process in arrays of 15-nm-thick Permalloy nanometer-scale dots, having elliptical shape and eccentricity, varying from 1 to 2.5. V-MOKE hysteresis loops revealed that the magnetization reversal is incoherent for elements with eccentricity of 1 and 1.5, while it becomes an almost perfect coherent magnetization rotation for elements with eccentricity equal to 2 and 2.5. In the latter case, the V-MOKE loops agree well with those predicted by the Stoner-Wohlfarth model for particles with uniaxial magnetic anisotropy. We were able to reproduce the V-MOKE results with micromagnetic simulations, gaining a deeper insight into the magnetic configurations that develop during the reversal process. (c) 2006 Elsevier B.V. All rights reserved.

Experimental results and theoretical calculations are presented for the static and dynamic magnetic properties of a weak exchange-spring symmetric FeTaN/FeSm/FeTaN trilayer. Static properties were investigated by means of alternating gradient field and magneto-optic Kerr effect magnetometries. The frequencies of three spin wave modes were measured by inelastic light scattering from long wavelength thermal spin waves. The combined analysis of spin wave frequencies and magnetometry data provides a consistent set of exchange, anisotropy and film thickness parameters.

The magnetic field dependences of the frequencies of standing spin-wave modes in a tangentially magnetized array of thin rectangular permalloy dots (800 × 550 nm) were measured experimentally by a Brillouin light scattering technique and calculated theoretically using an approximate size-dependent quantization of the spin-wavevector components in the dipole-exchange dispersion equation for spin waves propagating in a continuous magnetic film. It was found that the inhomogeneous internal bias magnetic field of the dot has a strong influence on the profiles of the lowest spin-wave standing modes. In addition, the dynamic magnetization distributions found for both longitudinally and transversely magnetized long magnetic stripes gives a good approximation for mode distributions in a rectangular dot magnetized along one of its in-plane sides. An approximate analytic theory of exchange-dominated spin-wave modes, strongly localized along the dot edge that is perpendicular to the bias magnetic field, is developed. A good quantitative agreement with the results of the BLS experiment is found.

Brillouin light scattering has been exploited in situ to study spin waves in ultrathin Co/GaAs(0 0 1) films of different thickness in the range between 1 and 7 nm, i.e. both before and after the bcc–hcp phase transition. A marked evolution of the in-plane anisotropy has been observed in connection with the structural transformation. Measurements of the spin-wave frequency as a function of the in-plane direction and of the intensity of the applied magnetic field, as well as of the incidence angle of light, enabled us to determine the magnetic parameters of the films, including the in-plane anisotropy constants.

The structural and magnetic properties of FeTaN/FeSm/FeTaN multilayers, deposited by dc magnetron sputtering, have been investigated as function of the alloy layers thickness. Structural and morphological characterizations, accomplished by transmission electron microscopy, X-ray reflectivity and grazing-incidence X-ray diffraction, account for a well-defined layered structure of the multilayers with a limited interface roughness. The magnetization reversal process is examined experimentally using magneto-optical Kerr vector magnetometry by measuring the longitudinal and transverse hysteresis loops. It is found that, for soft layer thickness above 3.2 nm, the magnetization reversal occurs via the formation of a stable exchange-spring state in which the magnetic moments of the outermost soft layer gradually rotates away from the unswitched underlying hard layer.

A detailed Brillouin light scattering (BLS) investigation of spin waves in Co(20 nm)/Cr(d Cr )/Co(20 nm) symmetric trilayer with wedge-shaped Cr interlayer has been carried out. Results showed that the interlayer exchange coupling oscillates, with antiferromagnetic peaks near the Cr layer thickness of 0.7 and 2.5 nm. These oscillations can be satisfactorily reproduced by a calculation based on the RKKY theory. An independent confirmation of the results obtained by BLS has been derived by measuring the saturation field of the longitudinal hysteresis loop as a function of the Cr thickness by magneto-optic Kerr effect magnetometry. Using the magnetic parameter determined by the above analysis, we have calculated the Brillouin cross section for the different Cr spacer thickness obtaining a very good agreement with the measured spectra.

We employed micro-focused Brillouin light scattering to study the amplification of the thermal spin wave eigenmodes by means of a pure spin current, generated by the spin-Hall effect, in a transversely magnetized Pt(4nm)/NiFe(4nm)/SiO2(5nm) layered nanowire with lateral dimensions 500x2750 nm2. The frequency and the cross section of both the center (fundamental) and the edge spin wave modes have been measured as a function of the intensity of the injected dc electric current. The frequency of both modes exhibits a clear redshift while their cross section is greatly enhanced on increasing the intensity of the injected dc. A threshold-like behavior is observed for a value of the injected dc of 2.8 mA. Interestingly an additional mode, localized in the central part of the nanowire, appears at higher frequency on increasing the intensity of the injected dc above the threshold value. Micromagnetic simulations were used to quantitatively reproduce the experimental results and to investigate the complex non-linear dynamics induced by the spin-Hall effect, including the modification of the spatial profile of the spin wave modes and the appearance of the extra mode above the threshold., 13 pages, 4 figures in journal of applied physics 2015