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

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

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

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

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

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

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

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

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

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

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

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

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

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.

Brillouin light scattering (BLS) was exploited to study the spin wave properties of spin-valve (SV) type samples basically consisting of two 5 nm-thick NiFe layers (separated by a Cu spacer of 5 nm), differently biased through the interface exchange coupling with an antiferromagnetic IrMn layer. Three samples were investigated: a reference SV sample, without IrMn (reference); one sample with an IrMn underlayer (10 nm thick) coupled to the bottom NiFe film; one sample with IrMn underlayer and overlayer of different thickness (10 nm and 6 nm), coupled to the bottom and top NiFe film, respectively. The exchange coupling with the IrMn, causing the insurgence of the exchange bias effect, allowed the relative orientation of the NiFe magnetization vectors to be controlled by an external magnetic field, as assessed through hysteresis loop measurements by magneto-optic magnetometry. Thus, BLS spectra were acquired by sweeping the magnetic field so as to encompass both the parallel and antiparallel alignment of the NiFe layers. The BLS results, well reproduced by the presented theoretical model, clearly revealed the combined effects on the spin dynamic properties of the dipolar interaction between the two NiFe films and of the interface IrMn/NiFe exchange coupling. (C) 2015 AIP Publishing LLC.

In these last years, experimental [1] and theoretical [2] studies of bilayer composed by a heavy metal film coupled with a thin ferromagnet have opened a route on the development of a more efficient category of spintronic devices. In those samples, the spin-orbit interaction in the Pt/Py bilayer drove the magnetic state to precessional states when the magnetic losses were fully compensated by the torque due to the spin-hall effect generated by the current flowing in the heavy metal. Here, we study a different geometry to excite propagating spin-waves and get the synchronization between two spin-hall oscillators (see Fig. 1). The structure has dimensions 1.5 μm × 3.0 μm with rectangular shape. The used system is composed by two contacts placed in the center of the device 400nm away from each other, while the two pairs of tips are 100nm and 200nm away for the two spin-Hall oscillators SHO-1 and SHO-2 respectively (see Fig.1a). The Gold (Au) triangular contacts (thickness of 150 nm) are positioned above the bilayer composed by CoFeB(1nm)/ Pt(8nm) (see Fig. 1b). The current is injected (along the x-direction) via the two Gold contacts deposited over the ferromagnet (CoFeB). When the current is injected only through a contact, localized modes and propagating spin waves have been observed when the magnetic field was applied in-plane or out of plane, respectively [2]. With this in mind, the device described above has been studied to obtain the synchronization between two spin-hall oscillators when the current is injected through the two contacts at once. We have performed a systematic study based on micromagnetic simulations to understand the origin of the excited modes and the dynamical behavior as a function of field amplitude and current. Fig. 2a summarizes the oscillation frequency of the excited mode as a function of the current, for different external fields (H=200, 400, 600, and 800mT) applied out of plane. Those results are referred to the current region where the two oscillators are synchronized. Fig. 2b shows the snapshots of the magnetization for the points A, B, C and D as displayed in Fig. 2a. As the field is reduced, the wavelength of the excited spin-waves increases. In fact, while for H=800mT a clear identification of the two sources of spin-waves can be observed, at H=200mT the wavelength of the propagating modes becomes comparable with the distance between the two oscillators giving rise to an excitation pattern where the two contacts cannot be identified anymore (the excited spin-waves exhibit an elliptical polarization). Our results show how spin-Hall nanoscillators can find application as high tunable spin-wave emitters for magnonic applications where spin waves are used for transmission and processing information on nanoscale. In the full paper, the possibility to obtain synchronized bullet modes by applying in-plane magnetic field will be also demonstrated.

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.

Electron beam (e-beam) and X-ray lithographic techniques have been used to fabricate permalloy (Ni80Fe20) and nickel rectangular and triangular dots and antidots on an area of (1×1) mm2. Dot dimensions and spacings range from 500 nm to 1 µm and from 250 nm to 50 nm, respectively. The changes of the magnetic properties induced by patterning have been studied by means of magneto-optic Kerr effect (MOKE) magnetometry and the Brillouin light scattering (BLS) technique.

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.

Ni/Cu multilayers were grown by RF sputtering. The crystal orientation, the thickness of the elemental layers and the interface quality were analysed by X-ray diffraction in the θ –2 θ configuration. Magnetic anisotropy was investigated by both a static and a dynamic technique, namely magneto–optical Kerr effect (MOKE) and Brillouin light scattering (BLS). Longitudinal MOKE loops accounted for the in-plane orientation of the magnetization, while polar loops were used to determine the out-of-plane anisotropy fields, showing the existence of a minor second-order contribution in addition to the first-order one. BLS was then exploited to detect thermal excited spin waves through inelastic scattering of light. The out-of-plane anisotropy fields evaluated by this high-frequency dynamic technique compare well with the first-order values obtained by analysis of polar MOKE hysteresis cycles.

Cu/Ni/Cu heterostructures have been in situ deposited on the 7×7 reconstructed Si(111) surface. A number of complementary techniques, such as in situ low-energy, medium-energy and Kikuchi electron diffraction and ex situ X-ray diffraction, were used in order to characterise the growth process and the structural properties of the films. It is found that the growth mode of metallic films is characterised by the presence of twinned islands induced by the 7×7 reconstruction of the Si(111) substrate. This work can stimulate further application of the metal–metal epitaxy on silicon to grow high quality ultrathin magnetic films to be integrated in microelectronic devices.

Surface magneto-optical Kerr effect (SMOKE) magnetometry in the temperature range 10–300 K was exploited to investigate the magnetic properties of high-quality Cu/Ni/Cu/Si(1 1 1) epitaxial heterostructures with thickness of the Ni layer, d Ni , between 10 and 60 A. For a fixed temperature, the equilibrium direction of the magnetization is parallel or perpendicular to the film surface, depending on the Ni thickness, because of the competition among shape anisotropy, magnetoelastic anisotropy and interface anisotropy. No reorientation of the magnetization could be observed as a function of temperature, for any of the specimens analyzed, while a large variation of the loop squareness and coercivity was found. This last variation has been qualitatively explained using a theoretical model based on a Green's function technique, valid for a monodomain film with a coherent rotation of the magnetization.

Epitaxial Cu/Fe/Cu trilayers with Fe film thickness between 4 and 110 A have been deposited on the 7×7 reconstructed surface of Si(111) single crystal. The structural and chemical characterization of Fe films was accomplished by in situ low energy electron diffraction, Kikuchi electron diffraction and Auger electron spectroscopy. As the Fe thickness exceeds about 6–8 A, a fcc–bcc phase transition occurs by the appearance of bcc(110) domains in the Kurdjumov–Sachs orientation. The structural transformation is also confirmed by ex situ X-ray diffraction experiments in the θ–2θ configuration. The evolution of the magnetic properties with the Fe film thickness has been studied by means of surface magneto-optic Kerr effect. Hysteresis loops measurements in the longitudinal configuration show a marked increase of the saturation signal which can be associated with the structural fcc–bcc phase transition of Fe.

A comprehensive investigation of rotatable anisotropy in a Fe${}_{0.8}$Ga${}_{0.2}$ thin film with a stripe domain structure has been performed comparing static and dynamic measurements. The stripes' domain formation and their rotation under a transverse magnetic field have been imaged by magnetic force microscopy. The rotatable anisotropy field ${H}_{\mathrm{rot}}$ was determined by fitting the frequency evolution of the dipole-dominated magnetostatic spin-wave mode versus the in-plane orientation of the stripe domains, measured by Brillouin light scattering in the absence of any dc or ac magnetic field. We obtained ${H}_{\mathrm{rot}}\ensuremath{\approx}1.35$ kOe, which is nearly ten times larger than the crystallographic in-plane anisotropy field. By applying a dc magnetic field along the stripes' axis, ${H}_{\mathrm{rot}}$ decreases, and eventually vanishes for saturated in-plane magnetization. At remanence, we established a quantitative relationship between static and dynamic properties, that is, the stripes' rotation angle and the in-plane angle dependence of spin-wave frequency.

The magnetic field dependence of the magnetic eigenmode frequencies in 150 nm wide layered permalloy nanowires (NWs) has been studied by the Brillouin light scattering technique. The NWs have the following layering structure Py(30 nm)/Cu(10 nm)/Py(d)/Cu(10 nm)/Py(30 nm) with fixed thickness of the top and bottom stripe and differ by the thickness d of the middle Py stripe (with d = 15, 30, 60 nm). The magnetic field, applied along the length of the wires, has been swept from positive to negative saturation thus exploring both the ferromagnetic and the antiferromagnetic relative orientation of the magnetization in the middle stripe with respect to the outermost ones. In conjunction with the transition between the two different ground states, the mode frequencies undergo an abrupt variation. Moreover the mode frequencies in the antiferromagnetic state are relatively insensitive to the applied field strength. The experimental results (frequencies versus magnetic field strength) have been successfully interpreted by means of a microscopic (Hamiltonian-based) theory which incorporates both the exchange and dipole–dipole interactions as well as effects of single-ion anisotropy and an external magnetic field applied parallel to the NW axis. This model was extended to account for parallel and antiparallel magnetization orientations in the layered NWs, enabling us to also calculate the probability amplitude of each spin-wave eigenmode at any position in the trilayered NWs.

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.

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.

Two-dimensional arrays of bicomponent structures made of cobalt and permalloy elliptical dots with thickness of 25 nm, length 1 mu m, and width of 225 nm, have been prepared by a self-aligned shadow deposition technique. Brillouin light scattering has been exploited to study the frequency dependence of thermally excited magnetic eigenmodes on the intensity of the external magnetic field, applied along the easy axis of the elements. Several modes have been observed while sweeping the field along the major and minor hysteresis loops, encompassing both the parallel and the antiparallel alignment of the magnetization in adjacent permalloy and cobalt dots. Micromagnetic simulations based on the dynamic matrix method enabled us to successfully reproduce the measured evolution of the frequencies with the field, as well as to identify the spatial profiles of the modes. A marked difference in the field dependence of the frequency of some modes has been observed for parallel and antiparallel magnetization configurations, suggesting the possibility of tuning the dynamic response in a reprogrammable way. The role of both static and dynamic magnetic coupling in determining the mode frequency is discussed in detail by studying the frequency evolution as a function of the gap size between the dots.

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.

We have investigated the magnetization configurations of ferromagnetic rectangular particles with lateral dimensions 1025 × 450 nm2 and two different thicknesses: 10 and 40 nm. For each thickness, we analyzed both an array consisting of isolated particles and a second one where the nanomagnets are put head-to-tail, with 85 nm interdot spacing, forming long chains of closely-spaced elements. Magneto-optical Kerr effect measurements and in-field magnetic force microscopy experiments were performed to achieve a deep comprehension of the magnetization reversal process. It is shown that inter-particle dipolar coupling substantially modifies the reversal mechanism in the case of the largest thickness, where it can delay or even suppress the occurrence of closure configurations of the magnetization (with one or more vortices), that are typical of isolated nanomagnets.

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 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 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.