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We present a combined Brillouin light scattering (BLS) and micromagnetic simulation investigation of the magnetic-field-dependent spin-wave spectra in a hybrid structure made of permalloy (NiFe) artificial spin-ice (ASI) systems, composed of stadium-shaped nanoislands, deposited on the top of an unpatterned permalloy film with a nonmagnetic spacer layer. The thermal spin-wave spectra were recorded by BLS as a function of the magnetic field applied along the symmetry direction of the ASI sample. Magneto-optic Kerr effect magnetometry was used to measure the hysteresis loops in the same orientation as the BLS measurements. The frequency and the intensity of several spin-wave modes detected by BLS were measured as a function of the applied magnetic field. Micromagnetic simulations enabled us to identify the modes in terms of their frequency and spatial symmetry and to extract information about the existence and strength of the dynamic coupling, relevant only to a few modes of a given hybrid system. Using this approach, we suggest a way to understand if the dynamic coupling between ASI and film modes is present or not, with interesting implications for the development of future three-dimensional magnonic applications and devices.

Roe data of the figures contained in the article enttitled: "Nonreciprocal spin-wave dynamics in Pt/Co/W/Co/Pt multilayers", bublished onPHYSICAL REVIEW B 103, 134404 (2021)

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.

In magnonics, a fast-growing branch of wave physics characterized by low energy consumption, it is highly desirable to create circuit elements useful for wave computing. However, it is crucial to reach the nanoscale so as to be competitive with the electronics, which vastly dominates in computing devices. Here, based on numerical simulations, we demonstrate the functionality of the spin-wave diode and the circulator to steer and manipulate spin waves over a wide range of frequency in the GHz regime. They take advantage of the unidirectional magnetostatic coupling induced by the interfacial Dzyaloshinskii-Moriya interaction, allowing the transfer of the spin wave between thin ferromagnetic layers in only one direction of propagation. Using the multilayered structure consisting of $\mathrm{Py}$ and $\mathrm{Co}$ in direct contact with heavy metal, we obtain submicrometer-size nonreciprocal devices of high efficiency. Thus, our work contributes to the emerging branch of energy-efficient magnonic logic devices, giving rise to the possibility of application as a signal-processing unit in the digital and analog nanoscaled spin-wave circuits.

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

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 report a systematic experimental study on the refraction and reflection of magnetostatic spin-waves at a thickness step between two Permalloy films of different thickness. The transmitted spin-waves for the transition from a thick film to a thin film have a higher wave vector compared to the incoming waves. Consequently, such systems may find use as passive wavelength transformers in magnonic networks. We investigate the spin-wave transmission behavior by studying the influence of the external magnetic field, incident angle, and thickness ratio of the films using time-resolved scanning Kerr microscopy and micro-focused Brillouin light scattering. (C) 2018 The Japan Society of Applied Physics

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.

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 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.

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.

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.

The focusing effect for spin waves excited by a curved micrometer-sized coplanar waveguide transducer on top of a 5-?m-thick epitaxial yttrium iron garnet film is studied by means of the micro-focused Mandelstam-Brillouin light scattering technique and micromagnetic simulations. The curvilinear transducer is designed to focus the backward volume spin waves on the in-plane bias magnetic field applied along the symmetry axis of the transducer. We show that two-dimensional maps of spin wave intensity exhibit nonreciprocal properties without mirror symmetry with respect to the magnetic field direction and the focusing effect. The observed effects are the consequence of nonreciprocity of the backward volume spin waves travelling at an angle toward the bias field direction. © 2018 Author(s).

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.

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

Nanocontact spin-torque oscillators are devices in which the generation of propagating spin waves can be sustained by spin transfer torque. In the present paper, we perform combined electrical and optical measurements in a single experimental setup to systematically investigate the excitation of spin waves by a nanocontact spin-torque oscillator and their propagation in a Ni80Fe20 extended layer. By using microfocused Brillouin light scattering we observe an anisotropic emission of spin waves, due to the broken symmetry imposed by the inhomogeneous Oersted field generated by the injected current. In particular, spin waves propagate on the side of the nanocontact where the Oersted field and the in-plane component of the applied magnetic field are antiparallel, while propagation is inhibited on the opposite side. Moreover, propagating spin waves are efficiently excited only in a limited frequency range corresponding to wavevectors inversely proportional to the size of the nanocontact. This frequency range obeys the dispersion relation for exchange-dominated spin waves in the far field, as confirmed by micromagnetic simulations of similar devices. The present results have direct consequences for spin wave based applications, such as synchronization, computation, and magnonics.

In the emerging field of magnon-spintronics, spin waves are exploited to encode, carry and process information in materials with periodic modulation of their magnetic properties, named magnonic crystals. These enable the redesign of the spin wave dispersion, thanks to its dependence on the geometric and magnetic parameters, resulting in the appearance of allowed and forbidden band gaps for specific propagation directions. In this work, we analyze the spin waves band structure of two-dimensional magnonic crystals consisting of permalloy square antidot lattices with different geometrical parameters. We show that the frequency of the most intense spin-wave modes, measured by Brillouin light scattering, exhibits a universal dependence on the aspect ratio (thickness over width) of the effective nanowire enclosed between adjacent rows of holes. A similar dependence also applies to both the frequency position and the width of the main band gap of the fundamental (dispersive) mode at the edge of the first Brillouin zone. These experimental findings are successfully explained by calculations based on the plane-wave method. Therefore, a unified vision of the spin-waves characteristics in two-dimensional antidot lattices is provided, paving the way to the design of tailored nanoscale devices, such as tunable magnonic filters and phase-shifters, with predicted functionalities.

The Brillouin light scattering technique has been exploited to study the angle-resolved spin wave band diagrams of squared Permalloy antidot lattice. Frequency dispersion of spin waves has been measured for a set of fixed wave vector magnitudes, while varying the wave vector in-plane orientation with respect to the applied magnetic field. The magnonic band gap between the two most dispersive modes exhibits a minimum value at an angular position, which exclusively depends on the product between the selected wave vector magnitude and the lattice constant of the array. The experimental data are in very good agreement with predictions obtained by dynamical matrix method calculations. The presented results are relevant for magnonic devices where the antidot lattice, acting as a diffraction grating, is exploited to achieve multidirectional spin wave emission. (C) 2015 AIP Publishing LLC.

Sub-200 nm patterned magnetic dots are key elements for the design of magnetic switches, memory cells or elementary units of nanomagnetic logic circuits. In this paper, we analyse by micromagnetic simulations the magnetization reversal, the dissipated energy and the excited spin eigenmodes in bistable magnetic switches, consisting of elliptical nanodots with 100×60 nm lateral dimensions. Two different strategies for reversal are considered and the relative results compared: (i) the irreversible switching obtained by the application of an external field along the easy axis, in the direction opposite to the initial magnetization; (ii) the precessional switching accomplished by the application of a short magnetic field pulse, oriented perpendicular to the initial magnetization direction. The obtained results are discussed in terms of deviation from the macrospin behavior, energy dissipation and characteristics of the spectrum of spin eigenmodes excited during the magnetization reversal process. © 2013 Elsevier B.V.

International audience; It is well known that Fe films deposited on a c(2 x 2)-reconstructed ZnSe(001) surface show a strong in-plane uniaxial magnetic anisotropy. Here, the effect of the substrate reconstruction on the magnetic anisotropy of Fe has been studied by in situ Brillouin light scattering. We found that the in-plane uniaxial anisotropy is strongly reduced for Fe films grown on a (1 x 1)-unreconstructed ZnSe substrate while the in-plane biaxial one is nearly unaffected by the substrate reconstruction. Calculations of magnetic anisotropy energies within the framework of ab initio density functional theory reveal that the strong suppression of anisotropy at the (1 x 1) interface occurs due to complex atomic relaxations as well as the competing effects originating from magnetocrystalline anisotropy and dipole-dipole interactions. For both sharp and intermixed c(2 x 2) interfaces, the magnetic anisotropy is enhanced compared to the (1 x 1) case due to the further lowering of symmetry. The theoretical results are in agreement with the experimental findings.

The spin-wave band structure of a two-dimensional square array of NiFe circular antidots (hole diameter 120 nm, periodicity 800 nm) is investigated. Brillouin light scattering experiments and band structure calculations, carried out by means of the dynamical matrix method, provide evidence for either extended or localized magnonic modes. Both families exhibit band gaps at Brillouin zone boundaries, attributed to Bragg reflection. Their calculated magnitude agrees with the one obtained by using an analytical model that takes into account the periodic variation of the internal field. This is in contrast to antidots in photonics and electronics, where the back-reflection is directly caused by the presence of holes. The results are important for advancing research on nanostructured two-dimensional magnonic crystals.

The magnetization states and the reversal mechanisms of 30 nm thick NiFe full and slotted rings, with outer and inner diameter of 1400 nm and 600 nm, respectively, are analysed by magneto-optical Kerr effect and in-field magnetic force microscopy. The evolution of the magnetization configuration is investigated as a function of the applied field intensity. Both the measured hysteresis loops and the MFM images are satisfactorily reproduced by a combined micromagnetic and analytical approach, showing that the presence of the slot in one arm of the ring forces the system to undergo a transition into a flux closure vortex state of well defined chirality. Both the reversal mechanism and the field range where the vortex exists are influenced by the aperture angle of the slot.

The dispersion curves of collective spin-wave excitations in a magnonic crystal consisting of a square array of interacting saturated nanodisks have been measured by Brillouin light scattering along the four principal directions of the first Brillouin zone. The experimental data are successfully compared to calculations of the band diagram and of the Brillouin light scattering cross section, performed through the dynamical matrix method extended to include the dipolar interaction between the disks. We found that the fourfold symmetry of the geometrical lattice is reduced by the application of the external field and therefore equivalent directions of the first Brillouin zone are characterized by different dispersion relations of collective spin waves. The dispersion relations are explained through the introduction of a bidimen- sional effective wave vector that characterizes each mode in this magnonic metamaterial.

The behavior of collective spin excitations in chains of rectangular NiFe dots is studied as a function of interdot separation. Dots have thickness of 40 nm and lateral dimensions of 715 × 450 nm2. They are put side by side along the major axis and the interdot separation is varied in the range 55-625 nm. Brillouin light scattering experiments have been performed at normal incidence (exchanged wave vector q = 0) and with the external magnetic field applied along the chain length. A satisfactory interpretation of the experimental data is achieved by magnonic bands calculations based on the dynamical matrix method. Such calculations have been performed at both the center and the border of the first Brillouin zone, in the case of Bloch wave vector q parallel to the applied field. In this way we can predict the amplitude of modes frequency oscillation (magnonic band), which is an important property to identify the behavior of a one-dimensional magnonic meta-material.

We present a combined experimental and micromagnetic study of spin excitations in chains of dense magnetic dots. The samples consist of long chains of rectangular dots with rounded corners having lateral dimensions of 715 \ifmmode\times\else\texttimes\fi{} 450 nm${}^{2}$ and 1025 \ifmmode\times\else\texttimes\fi{} 450 nm${}^{2}$, respectively. Chains are composed of magnetic elements put side by side along either their major or minor axis with edge-to-edge separation below 100 nm. The frequency dispersion of the spin-wave excitations was measured by Brillouin light-scattering technique as a function of the transferred wave vector directed along the chains of dots and for an external magnetic field applied perpendicularly to the transferred wave vector in the dots plane. Evidence is given of collective excitations in the form of Bloch waves propagating through the chains characterized by magnonic energy bands. Micromagnetic calculations, performed by using the dynamical matrix method, enable us to satisfactorily reproduce the frequency dispersion of collective spin modes as well as to visualize the spatial profile of the dynamic magnetization inside the dots. We also propose a general rule to understand the frequency dispersion of collective modes starting from the relative phase of dynamic magnetization in the facing sides of adjacent dots.

Electron beam lithography has been exploited to prepare arrays of elliptical dots of thickness 40 nm and lateral size 700 300 nm. Arrays of both isolated elements and squared clusters of dots were prepared. The hysteresis cycles of these arrays were measured by magneto-optical Kerr effect. Micromagnetic simulations permitted us to reproduce the magnetization curves and to interpret the magnetization reversal mechanism. This proceeds through the formation of two vortexes, due to the rather large dimensions of the dots. Evidence is given to the influence of inter-dot dipolar coupling within the cluster.

Micro-focused Brillouin light scattering (?-BLS) technique is employed to study the magnetization dynamics of a single elliptical NiFe nanoring. Spin waves spectra, recorded at different positions within the ring, compare very well to the results of dynamical micromagnetic simulations, confirming the exact spatial symmetry and localization region of each of the detected modes. In addition, a comparison with the spectra acquired by conventional Brillouin light scattering on a large array of identical nanorings enables us to show the superiority of ?-BLS for the study of stationary and localised modes within nanomagnets.

Micro-focused Brillouin light scattering has been exploited as a scanning probe technique to investigate the spatial localization and symmetry of magnetic excitations in elliptical nanorings. The interpretation of the experimental data has been achieved using the dynamical matrix method. Special attention is paid to the investigation of the soft-mode involved in the vortex-to-onion transition, to the localization of modes as a function of the external field, and to the to identification of the vortex chirality of a single ring.