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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.

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.

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.

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 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.

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.

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.

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.

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

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.

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

Brillouin light scattering has been utilized to study the field dependence of resonant spin-wave modes in layered NiFe(30 nm)/Cu(10 nm)/NiFe(15 nm)/Cu(10 nm)/NiFe(30 nm) nanowires of rectangular cross section, 150 nm wide and formed in arrays that are spaced laterally by 400 nm. The major and minor longitudinal hysteresis curves have been measured by the magneto-optical Kerr effect technique, with applied field parallel to the length of the nanowires. The light-scattering spectra were recorded as a function of the magnetic field strength, encompassing both the parallel and antiparallel alignments of the middle stripe with respect to the magnetization direction of the outermost ones. The field ranges for the antiparallel state are different from those for the parallel case, while the mode frequencies change abruptly at the parallel-to-antiparallel transition field (and vice versa). The modes detected in the antiparallel state are found to have only a weak dependence on the applied magnetic field, whether along the major or minor hysteresis curves, while in the parallel state the mode frequencies monotonically increase with the applied magnetic field. The experimental results have been successfully interpreted, across the whole range of the magnetic fields investigated, in terms of the mode localizations across the width and in the layered structure. This was accomplished by means of a microscopic (Hamiltonian-based) theory, which has been extended here to the case of non parallel magnetic ground states. (C) 2015 Elsevier B.V. All rights reserved.

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.

Brillouin light scattering (BLS) and the surface magneto-optical Kerr effect (SMOKE) provide two well established, non-destructive, optical techniques whose combined use can yield a great deal of information about magnetism in low-dimensional systems, such as thin films, multilayers, and patterned structures. The former technique gives information on the high-frequency dynamical properties of a spin system, through detection of long-wavelength spin waves, while the latter permits easy and direct access to the orientation of the magnetization and to its evolution with the applied magnetic field. Both techniques can be implemented in situ, to study thin magnetic films and nanostructures in ultrahigh-vacuum conditions. In this article the main characteristics of both BLS and the SMOKE are discussed and a few experiments carried out at GHOST laboratory, Perugia University, are presented, with emphasis given to the complementarity of the two techniques.

The structural and magnetic properties of ultrathin Fe films, grown by e-beam evaporation on a Cu(1 0 0) single crystal, have been studied. The low-energy electron diffraction patterns account for a pseudomorphic growth of fcc-Fe(1 0 0) up to a thickness of a few nanometers, followed by a Pitsch transformation, consisting of bcc-Fe(1 1 0) domains. The magnetic properties of the films were investigated in situ by the combined use of surface magneto-optical Kerr effect and Brillouin light scattering. A ferromagnetic behaviour was detected for film thickness below about 1 nm and above 3 nm. A careful determination of the magnetic parameters and of the anisotropy constants of the ferromagnetic films was achieved by studying the dependence of the spin-wave frequency on the angle of incidence of light, on the intensity of the applied magnetic field and on its direction on the surface plane.

We report on the structural and magnetic properties of thin Fe films grown on the Cu(1 1 0) surface. In-plane grazing-incidence X-ray diffraction has been used to measure the lateral lattice spacing of the Fe films. Complementary information about the structure of the topmost layers has been obtained by means of Auger and photoelectron diffraction. The Fe film grows pseudomorphic with the substrate up to a thickness of about 0.8 nm. The diffraction feature of a new phase is observed at 1.6 nm, with a corresponding interplanar distance close to the bulk body centered cubic (bcc) Fe one, which is eventually recovered at higher thickness (6.4 nm). From comparison between X-ray diffraction and photoelectron diffraction, it is suggested that the bcc-like Fe grows on the (1 0 0) surface with its [1 1 0] axis oriented along the [0 0 1] substrate direction. The photoelectron diffraction data also indicate a strong faceting in the [1 1 0] substrate direction. This morphology is believed to contribute to the in-plane uniaxial magnetic anisotropy observed by Kerr effect and Brillouin light scattering from spin waves.

It is shown experimentally that collective Bloch spin waves are able to propagate in a dense periodic array of nanowires with step-modulated thickness along the periodicity direction. The spin wave dispersion (frequency versus wave vector k) was measured using the Brillouin light scattering technique by sweeping the wave vector perpendicularly to the wire length. Remarkably, the mode measured at the lowest frequency exhibits an oscillating dispersion and its frequency is up-shifted with respect to the homogeneous-thickness wires of the same width. The modes located at higher frequencies have negligible dependencies on the wave number, i.e. are practically dispersionless. Complementary ferromagnetic resonance measurements enabled us to independently measure the whole set of modes at k = 0, showing a good agreement with the Brillouin light scattering data. These results have been successfully reproduced in a numerical simulation employing a two-dimensional Green's function description of the dynamic dipole field of the precessing magnetization. The theory also allowed visualizing the non-trivial distribution of dynamic magnetization across the wire cross-section and estimating the Brillouin light scattering cross-section. The analysis of these intensities suggests complicated magneto-optical coupling between the light and the dynamic magnetization in the arrays of nanowires with step-modulated thickness. This work can stimulate the design, tailoring, and characterization of three-dimensional magnonic crystals. © 2014 IOP Publishing Ltd.

Brillouin light scattering (BLS) has been used to investigate the elastic properties of polycrystalline AIN films, about 1 μ m thick, grown by DC-reactive magnetron sputtering on Si 3 N 4 coated (100)-Si substrates. Taking advantage from the detection of a number of different acoustic modes, a complete elastic characterization of the films has been achieved. The elastic constants c 11 and c 66 have been selectively determined from detection of the longitudinal and of the shear horizontal bulk modes, respectively, travelling parallel to the film surface. The three remaining elastic constants, namely c 44 , c 33 and c 13 , have been obtained from detection of the Rayleigh surface wave and of the longitudinal bulk wave propagating at different angles from the surface normal. The values of the elastic constants of these sputtered AIN films depend on the deposition conditions and on the microstructural properties of the films, especially oxygen contamination and quality of texture. In the case of the films with the best degree of texture and the lowest oxygen content, the values of the elastic constants are rather close to those previously determined in epitaxial A1N films grown at high temperature by MOCVD. This demonstrates that sputter deposition at relatively low temperature can be used to grow high quality A1N films on Si and is of great importance in view of the integration of these films in the technology of IC semiconductors.

with q2 n = q2 nx + q2 ny + q2 nz and n = 1,2, . . . . After Eq. (4) the symbols qx , qy , and qz should be replaced by qnx , qny , and qnz, respectively. The changes do not affect the numerical calculations presented in Sec. V performed at qnx = 0 for the generic nth backward modes that have a qny component much larger than qnx . The article J. Jorzick, S. O. Demokritov, C. Mathieu, B. Hillebrands, B. Bartenlian, C. Chappert, F. Rousseaux, and A. N. Slavin, Phys. Rev. 60, 15194 (1999) is cited twice, both as Ref. 12 and as Ref. 15.

The Brillouin light scattering technique has been exploited in situ to study the magnetic properties of ultrathin Fe films, grown on a Cu(1 1 1) single crystal substrate, during the FCC/BCC phase transition. A determination of the magnetic parameters and of the anisotropy constants was achieved.

We present a combined experimental and theoretical study of the spin wave band structure in two-dimensional magnonic crystals consisting of square arrays of either circular permalloy dots (disks) or antidots (holes). The spin wave dispersion has been measured by means of Brillouin light scattering spectroscopy, spanning the wave vector over several Brillouin zones in the reciprocal space of the artificial crystals. The experimental data are satisfactorily interpreted thanks to band structure calculations carried out using the dynamical matrix method. In the case of the array of disks, the frequency dispersion of the different eigenmodes in any direction in the reciprocal space can be explained introducing the concept of a bidimensional effective wave vector. In the case of the antidot array, two families of propagating modes, having extended and localized character, exhibit bandgaps at Brillouin zone boundaries. The bandgap formation is discussed in terms of Bragg reflection as well as of the inhomogeneity of the internal magnetic field experienced by precessing spins.

Brillouin light scattering was applied to measure the evolution of spin waves in exchange-coupled [Co/Pd]-NiFe films with out-of-plane/in-plane magnetic anisotropy. Tunable tilting of the magnetization has important effects on the spin wave frequency gap: a substantial increase is observed with decreasing the soft NiFe thickness, while seemingly insignificant tilting angles cause a strong reduction with respect to a film with only the hard [Co/Pd] component. The spin wave frequency is reproduced also in samples, with increased thickness of the upper Pd layer, where a sudden modification in the tilting at the hard/soft interface is caused by the weakening of interlayer exchange.

Magnonic crystals, materials with periodic modulation of their magnetic properties, represent the magnetic counterpart of photonic, phononic and plasmonic crystals, and have been largely investigated in recent years because of the possibility of using spin waves as a new means for carrying and processing information over a very large frequency bandwidth. Here, we review recent Brillouin light scattering studies of 2D magnonic crystals consisting of single- and bi-component arrays of interacting magnetic dots or antidot lattices. In particular, we discuss the principal properties of the magnonic band diagram of such systems, with emphasis given to its dependence on both magnetic and the geometrical parameters. Thanks to the possibility of tailoring their band structure by means of several degrees of freedom, planar magnonic crystals offer a good opportunity to design an innovative class of nanoscale microwave devices.

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.

In this chapter, the basics of microfocused Brillouin light scattering from spin waves are reviewed. The focus is on the details of the experimental setup, its performances and potentialities, and to the possible future developments of this technique. Some recent results from low-dimensional magnetic systems are also reviewed covering the following areas: (a) detection and mapping of thermal spin waves from single magnetic nanostructures (single-layer elliptical rings and multilayer rectangles); (b) spin waves excited by microwave currents in plain films, magnetic waveguides, and magnonic crystals; and (c) spin waves excited by the spin-transfer torque effect in nanocontact systems with an extended layer.

The static and dynamic magnetic properties of a FeTaN/FeSm/FeTaN trilayer are investigated by alternating gradient field magnetometry and Brillouin light scattering. Evidence is given for a strong in-plane uniaxial anisotropy induced by a magnetic field applied during deposition. The spin-wave spectrum consists of different modes, with either surface or bulk character. A nonreciprocal behavior of the spin-wave frequency due to the exchange field exerted on the FeTaN layer at the FeSm interface is observed.

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.

The Brillouin light scattering cross section from a thick magnetic multilayer has been calculated using a theoretical model based on a macroscopic partial waves approach for the calculation of the normal modes. Special attention has been paid to analyzing the effect of inclusion of the second order magneto-optic constant in addition to the first order one (corresponding to Voigt and Faraday effects, respectively). This model has been exploited to analyze the experimental Brillouin spectra measured from a several nm thick Ni/Cu bilayer. Both surface and bulk standing spin waves have been experimentally detected for different incident angles and applied magnetic fields (including field reversal). The measured spectra can be satisfactorily reproduced by our model, allowing the determination of magnetic and magneto-optic parameters of the samples.

A compact ultrahigh-vacuum chamber, specially designed to allow in situ Brillouin light-scattering (BLS) and surface magneto-optical Kerr-effect measurements has been set up. Experimental results relative to both the structure and the magnetic properties of ultrathin Fe films grown by e-beam evaporation on a Cu(110) single crystal are presented. Low-energy electron diffraction patterns account for epitaxial growth of fcc Fe(110) up to 4–6 A, followed by a transition to a more disordered state, consisting of bcc Fe domains. The BLS analysis enabled us to study the dependence of the spin-wave frequency on the angle of incidence of light, on the intensity of the magnetic field, and on its direction on the surface plane.

Collective spin excitations in a planar array of interacting submicron magnetic squared dots have been studied by the Brillouin light-scattering technique. The dispersion curves of collective spin modes are characterized by periodical oscillations determined by the width of the artificial Brillouin zone. Because of the uniaxial symmetry introduced by the application of an external magnetic field ${H}_{0}$, the dynamical coupling and the frequency dispersion of collective modes are different when the wave vector is perpendicular or parallel to ${H}_{0}$. An analytical model has been exploited to calculate the dispersion of collective spin modes by numerically solving eigenvalue/eigenfunction problem for a band matrix which originates from linearized Landau-Lifshitz magnetic torque equation. A very good agreement between calculation and experiment was found. In addition, a micromagnetic approach has been exploited to achieve an independent evaluation of the collective modes frequency and a visualization of their spatial profile on a limited $(3\ifmmode\times\else\texttimes\fi{}3)$ array of dots.

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.

The Brillouin light-scattering technique has been applied to study collective spin waves in a dense array of dipolarly coupled ${\text{Ni}}_{80}{\text{Fe}}_{20}$ stripes of alternating widths, during the magnetization reversal process. Both the saturated ``ferromagnetic'' state, where the magnetizations of wide and narrow stripes are parallel, and the ``antiferromagnetic'' state, characterized by an antiparallel alignment of the static magnetization in adjacent stripes, have been analyzed. The experimental data provide strong evidence of sustained collective excitations in the form of Bloch waves with permitted and forbidden magnonic energy bands. The measured frequencies as a function of the exchanged wave vector have been satisfactorily reproduced by numerical simulations which enabled us to calculate the spatial profiles of the Bloch waves, showing that some of the modes are preferentially localized in either the wide or the narrow stripes. We estimated the expected light-scattering cross section for each mode at different magnetic ground states, achieving a good agreement with the measured intensities. The alternating-width stripes system studied here represents a one-dimensional artificial magnonic crystal with a complex base and can be considered as a model system for reprogrammable dynamical response, where the band structure of collective spin waves can be tailored by changing the applied magnetic field.

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.