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In this article we review in detail the magnetic properties of the simple cubic oxides NiO, MnO, and CoO, and also discuss the properties of the more complicated, but related, transition-metal oxides CuO and FeO. The magnetic ordering scheme and the several competing magnetic interactions strongly affect the lattice structure (giving rise to distortions) and hence the vibrational properties. The various interactions of the magnetic moments plus the spin-phonon coupling, which heavily influence the physical properties of these metal monoxides, are discussed thoroughly.

A non-bosonic technique, based on the drone-fermion perturbation method and a high-density expansion, is employed to study the spin-wave (SW) scattering processes in a ferromagnetic thin film with exchange and dipole-dipole interactions. Specifically, the diagrammatic contributions to the spin-spin Green's functions are evaluated within a 1/zperturbation expansion, wherezis the number of spins interacting with any given spin. The results are used to calculate the SW damping at temperatures below the Curie temperatureTC. It is found that, apart from the usual contributions due to three-magnon and four-magnon processes in the film, which are dominant at relatively low temperatures (consistent with boson expansion methods), there is an additional mechanism that becomes important for temperatures above about12TCThis is spin disorder damping, previously studied in bulk magnetic materials; it occurs when a spin wave is scattered by the instantaneous disorder produced when a longitudinal spin component undergoes a large thermal fluctuation. Numerical estimates are presented for thin films of Permalloy and EuO.

By using a microscopic dipole-exchange theory within a Green's function formalism, we study the coupling regime of microwave cavity photons to magnons in nanostructures. The ferromagnetic nanostructures considered are single- and double-layer films, nanowires with rectangular cross-sections, and one-dimensional magnonic crystal arrays of nanowires. In contrast with previous studies of magnon-photon hybrid systems, where either bulklike magnetic samples or macroscopic spheres or films were utilized, a discrete lattice of effective spins is employed to establish a microscopic theory for describing the dependence of the magnon frequencies on the wave vector. We explore hybrid systems derived from the discrete magnons in nanostructures and a selected microwave cavity photon, where strong photon-magnon coupling is expected. This may extend the functionality of the existing hybrid systems or may introduce new functionality. The dependence of the hybridized frequency modes on applied magnetic field are calculated and it is shown that the results are significantly modified compared with those for magnetic bulk materials. In particular, a series of anticrossing phenomena of the cavity mode and multiple magnon modes of ferromagnetic nanostructures are reported. Our findings are important for future applications in integrated hybrid systems for quantum magnonics.

A theoretical analysis is reported for the spin waves in ferromagnetically-ordered magnonic crystals consisting of lateral periodic arrays of composite nanowires. The structure of each nanowire is a vertically-developed multilayer built up according to a quasiperiodic Fibonacci sequence. Each nanowire is separated by a non-magnetic spacer in either direction. The quasiperiodicity in these composite nanowires is addressed in two ways: the geometric variation in a single-component (permalloy) structure and the compositional variation (using cobalt and permalloy). These composite nanowire structures are compared and contrasted with one another. A microscopic approach is used to calculate the spectra of spin-wave bands and band gaps for several generation numbers of the Fibonacci sequence. Comparison of the density of states for these structures is made with that for the periodic cases, which highlights distinct characteristics of the quasiperiodicity. The fractal-like scaling properties of the modes show characteristics analogous to some complex biological systems.

The spin-wave spectra are studied theoretically in periodic magnonic crystals (MCs) of vertically stacked cylindrical nickel nanodisks or nanorings separated by nonmagnetic spacers, resulting in infinitely long segmented nanowire or nanotube MC arrays, respectively. A microscopic or Hamiltonian-based approach is employed for the magnetization dynamics, in which an external magnetic field is applied along the cylinder axis and the periodic length is varied by changing the length of the spacers. The results show a broadening and shift of the spin-wave frequency bands at smaller spacer length due to the strong dipolar inter-element coupling, which also modifies the spatially-inhomogeneous equilibrium magnetization in the finite-length cylindrical elements. The effects are found to be more pronounced in a nanotube MC than in a nanowire MC, mainly because the absence of the core in a nanotube favours vortex states.

The localization behavior and scaling properties of magnetostatic modes propagating on magnetic aperiodic superlattices made up by rare-earth materials is analyzed. Both surface and bulk modes are obtained, considering two different aperiodic rules of stacking: Thue-Morse and Fibonacci. The magnetization is considered to be perpendicular to the superlattice's interfaces. Our model consider as magnetic materials both dysprosium and holmium, at different temperatures. A scaling behavior is observed for the allowed bulk bands, through specific ordering parameters, meaning that the allowed bands have a fractal (or multifractal) structure.

We present a theoretical study for the surface and bulk magnon-polaritons in magnonic crystals (or semi-infinite layered superlattices), which are formed from an array of ferromagnetic materials and nonmagnetic spacers with graphene sheets interposed between them. The external medium is taken to be vacuum. The Fermi energies in the graphene can be varied by employing different electronic doping levels, resulting in a strong influence exerted by the presence of graphene on the surface magnon-polariton modes. These effects include localization of the modes and control of the group velocities of the modes as the Fermi energies of the graphene sheets are varied, along with an important role for the phenomenological damping in the graphene sheets.

A theoretical analysis is described for the spin waves in single- and double-layered nanorings using a microscopic, or Hamiltonian-based, formalism. The calculations, which yield the frequencies and spatially-dependent intensities of the quantized spin waves, are applied to the vortex and onion (bi-domain) states in a single nanoring, as well as to the field-induced switching. In the case of asymmetric double-layered nanorings (with a nonmagnetic spacer) there are coupled spin waves controlled by varying the spacer thickness to change the strength of the inter-ring dipolar interactions. The different possible magnetic states, depending on the applied magnetic field, may involve vortex states (with the same or opposite chirality) in both layers, a vortex state in one layer and onion state in the other, or onion states in both layers. Numerical applications are made to permalloy nanorings with realistic dimensions and magnetic parameter values.

We present a theoretical study for the surface magnon-polaritons in structures formed by graphene layer(s) on an insulating gyromagnetic medium (that can be either ferromagnetic or antiferromagnetic) surrounded by vacuum. We consider different doping levels to vary the Fermi energies in the graphene, including both semi-infinite and slab magnetic samples. Our results reveal a strong influence, exerted by the presence of graphene, on the surface magnon-polariton modes. The effects include control of the group velocities for the modes as the Fermi energies of the graphene sheet are varied, modified nonreciprocal and reciprocal mode propagation properties depending on the type of magnetic material, and distinct localization properties for the emerging surface modes.

We report a facile fabrication method for copper nanoparticle superlattices, based on thermal evaporation of ultrathin layers of copper on solution-processed thin films formed by few-layer graphene platelets. We show that the annealing of these systems in nitrogen without previous exposure to air prompts the heterogeneous nucleation of the Cu layer into nanoparticle superlattices self-assembled along specific crystallographic directions of graphene. Theoretical calculations suggest a lowest formation energy for Cu-nanoparticle arrays aligning along armchair directions, indicating that their self-assembly is energetically more favourable. The possibility of using these superlattices in evanescent waveguiding devices is explored by three-dimensional scanning near-field optical microscopy. The light-confining properties of our systems in the near-field indicate that our nanoparticle superlattices are poised to satisfy the technological demands required by nanophotonics devices.

The dispersion relations for bulk and surface plasmon-polaritons in a semi-infinite 1D photonic crystal interlayered with graphene are calculated in the presence of an applied magnetic field. The results are applied to SiO2 as the constituent material in geometry where the layers are arranged in a periodic array with the same layer thickness. The static magnetic field is applied perpendicular to the plane of layers. Numerical results are presented for the modes in THz range, up to 10 THz, to illustrate the important role of the applied magnetic field on the graphene sheets in modifying the polariton dispersion curves, especially for magnetic fields of the order of 1 T. It is found that the polariton frequencies and band gaps have a sensitive dependence on the electron scattering rate parameter (and hence the applied magnetic field strength) in the graphene sheets. Electromagnetic retardation effects are fully taken into account for the bulk bands, while for the surface modes (which are shown to have a novel non-reciprocal propagation characteristics) it is convenient to focus on the regime where retardation is small

In this work we study the plasmon-polariton spectra in one-dimensional photonic crystals based on the Fibonacci, Thue-Morse and double-period sequences, where we have graphene at the interface of one of the constituent building blocks (A = SiO2/graphene, B = SiO2). The dispersion relations for each quasicrystal are numerically calculated by using a transfer-matrix approach. The spectra of these structures are shown to be fractals (for the bulk bands distribution), obeying a power law in a particular frequency region and these are induced specifically by the quasiperiodic ordering in the unit cells of each system studied. We also report a strong dependence of the width of the bulk bands on the wave vector for this particular frequency region, whereas for large wave vectors the fractal properties in these spectra are absent

A theoretical study is made for the bulk and surface plasmon-polaritons in one-dimensional semi-infinite layered semiconductor photonic crystals with graphene interlayers. The retarded dispersion relations are calculated in a general way and applied to two cases, depending on whether a graphene sheet is present or absent at the first interface of the semi-infinite structure. We apply the result to doped GaAs as the constituent material, considering the layers to be arranged in a periodic fashion with alternating layer thicknesses. Both s- and p-polarized modes are evaluated with the effects of retardation on the polaritons being included in the general expressions. Simplifications, particularly for the surface modes, are studied for the case when retardation effects are small. Through numerical examples, we illustrate the important role of the graphene sheets in modifying the plasmon-polariton properties (focusing on the region near the bulk plasma frequency). A strong dependence on the mode polarization is found.

A systematic investigation is presented for the magnetization dynamics in trilayer nanowires, consisting of two permalloy (${\mathrm{Ni}}_{80}{\mathrm{Fe}}_{20}$) layers separated by a nonmagnetic Ru spacer layer. The width of the wires ranges from 90 to 190 nm. By varying the Ru thickness between 0.7 and 2.0 nm, the interlayer coupling can be effectively controlled, modifying the corresponding magnetic ground state and the spin-wave dynamics. By contrast with previous work on coupled trilayer nanowires with larger widths (270 nm and more), the focus here is on nanowire arrays where the strong shape anisotropy competes with the Ruderman-Kittel-Kasuya-Yosida interactions and biquadratic exchange interactions across the Ru interface, as well as dipolar interactions and Zeeman energy. As a result, the spin-wave spectrum is found to be drastically modified. Ferromagnetic resonance and hysteresis loop measurements are reported over a wide range of applied magnetic fields, showing that the overall magnetization alignment between the permalloy layers may be parallel, antiparallel, or in a spin-flop state, depending on the overall interlayer coupling. The experimental results for different stripe widths are successfully analyzed using a microscopic dipole-dipole theory and micromagnetic simulations.

A microscopic (or Hamiltonian-based) theory is presented for the spin-wave instability thresholds in ferromagnetic nanowires under conditions of parallel pumping with a microwave field. A dipole-exchange Hamiltonian is employed in which the external magnetic field is either longitudinal or transverse to the length of the nanowire. This contrasts with most previous work on nonlinear spin waves which concentrate on situations where a macroscopic (or continuum) theory is appropriate. In nanowire stripes with lateral dimensions of order 100 nm or less, the quantization of the eigenmodes becomes modified due to strong spatial confinement and edge effects, making it appropriate to employ a microscopic dipole-exchange approach analogous to that used recently for ultrathin films. Numerical applications are presented for the dependence of the threshold microwave field amplitude for instability on the static applied field (the analog of the butterfly curves). The cases of longitudinal and transverse applied fields are found to lead to distinctly different behaviors, which are illustrated using EuS and permalloy as materials with different ratios of dipolar to exchange interactions. Structural effects due to the discrete spin-wave branches lead to structural aspects of the butterfly curves that are significantly modified compared with those for ultrathin films due to the edge modes in the nanowires.

A theory is developed for the dipolar spin waves in cylindrical multilayer systems consisting of a core surrounded by any arbitrary number of concentric layers (or tubes). Each layer may be magnetic (either ferromagnetic or antiferromagnetic) or a nonmagnetic spacer. The long-range dipolar fields provide coupling between magnetic layers across the spacer regions, resulting in a coupling between the dipolar modes of the system. A transfer matrix approach is employed to calculate the dispersion relations for the mode frequencies in terms of a longitudinal wave number. Numerical applications are made to multilayer systems that include several layers of the ferromagnet Ni, or the uniaxial antiferromagnet GdAlO3, or both. Particular attention is given to the localized interface modes, which are shown to be strongly modified (for example, in their frequency and wave number cutoff) by the multilayer structure, compared to the behavior found in single magnetic wires and tubes.

The last few years have seen dramatic advances in the growth, fabrication and characterization of low-dimensional materials and nanostructures. Most studies of these artificially engineered materials have been driven by their potential for device applications that involve smaller and smaller physical dimensions. In particular, the dynamical properties of these materials are of fundamental interest for the devices that involve high-frequency operation and/or switching. Consequently, the different excitations, vibrational, magnetic, optical, electronic, and so on, need to be understood from the perspective of how their properties are modified in finite structures especially on the nanometre length scale due to the presence of surfaces and interfaces.

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.

We present a systematic study of the static and dynamic magnetization behavior of interlayer-coupled ${\mathrm{Ni}}_{80}{\mathrm{Fe}}_{20}$(200 \AA{})/Ru(${t}_{\mathrm{Ru}}$)/${\mathrm{Ni}}_{80}{\mathrm{Fe}}_{20}$(100 \AA{}) trilayers as a function of the Ru spacer layer thickness ${t}_{\mathrm{Ru}}$. As ${t}_{\mathrm{Ru}}$ was varied in the range from 0 to 15.8 \AA{}, we observe a strong antiferromagnetic (AFM) exchange coupling between the two ferromagnetic (FM) layers for ${t}_{\mathrm{Ru}}$ = 5 \AA{}, which becomes weak for ${t}_{\mathrm{Ru}}$ = 10 \AA{}. For ${t}_{\mathrm{Ru}}$ = 14.1 \AA{}, the coupled magnetic system changes from AFM to FM ordering. Using broadband ferromagnetic resonance spectroscopy, we have probed the effects of the different coupling mechanisms on both the acoustic and optic magnetic modes. We found that the biquadratic exchange coupling has a negligible effect compared to Ruderman-Kittel-Kasuya-Yosida (RKKY) exchange coupling, while the uniaxial anisotropy at the ${\mathrm{Ni}}_{80}{\mathrm{Fe}}_{20}$/Ru interfaces also plays an important role in determining the behaviors of the modes. A mode anticrossing phenomenon is observed when the RKKY exchange interaction term is above a critical value. A theoretical framework developed is in very good agreement with our experimental results.

A microscopic, or Hamiltonian-based, theory is developed to study the spin-wave instability thresholds for the parametric processes occurring in ultrathin ferromagnetic films under conditions of parallel pumping with a microwave field. Most previous work has focused on spheres or films with dimensions of order several microns or more, and the theoretical interpretation has been in terms of macroscopic (continuum) methods. At smaller size scales, as in ultrathin films with thickness less than about 100 nm, the discreteness of the quantized spin waves and their spatial distributions become modified, making it more appropriate (particularly for the nonlinear dynamics) to employ a microscopic or Hamiltonian-based approach with a lattice of effective spins interacting with one another through the magnetic dipole-dipole and exchange interactions. This work utilizes a similar microscopic approach, but with the effects of microwave pumping included, to calculate the spin-wave instability thresholds for the bands of quantized spin waves in ultrathin films with the saturation magnetization parallel to their surface. Magnetic materials with different ratios of the exchange to dipole-dipole strengths are considered, taking examples for relatively strong, intermediate, and weak exchange. In the case of parallel pumping it is found that the shape of the typical ``butterfly curve,'' as conventionally obtained with macroscopic samples of YIG, becomes modified in these ultrathin films due to the occurrence of several quantized spin-wave bands and their spatial properties.

A finite-temperature perturbation formalism is developed to study the processes of spin-wave interactions in ultrathin ferromagnetic films, including the effects of both the long-range magnetic dipole-dipole interactions and the short-range exchange interactions. By contrast with previous macroscopic methods for evaluating spin-wave interactions, the dipolar terms are treated here within a Hamiltonian method, together with exchange and anisotropy terms, to obtain a theory applicable to ultrathin films at temperatures below the Curie temperature. The contributions to the energy shift and the damping (or reciprocal lifetime) of the dipole-exchange spin waves due to three-magnon and four magnon processes are calculated. Numerical examples are presented.

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.

We present a theory for the spin-wave excitations in bilayer magnetic systems with exchange coupling across the interface between two ferromagnetic films having the same crystallographic structure. The Hamiltonian includes exchange and anisotropy terms within each magnetic film of the composite system, as well as at the interface and at the free surfaces. We examine, in particular, the effect of interface canting between the magnetization directions for each film, and we derive effective pinning parameters and dynamic coupling parameters for the interface as functions of the canting angle. We show that, in the special case when the magnetization directions are antiparal lel in the bilayer system, the two films may be considered as effectively decoupled as regards the spin-wave dynamics. We discuss the relevance of this theory to recent experimental studies of bilayer ferromagnetic systems that exhibit antiferromagnetic interface exchange.

The magnons in the canted rutile-structure antiferromagnet NiF 2 have been studied by Raman scattering. Results are presented for the polarization dependences of the one-magnon spectum over a wide range of temperatures below T N and the two-magnon spectrums at low temperatures. A theoretical analysis of the data, including the important role of the spin canting for the one-magnon properties, is shown to provide good agreement with the measurements.

In this work, we demonstrate how the static and dynamic properties of Ni80Fe20/Ru/Ni80Fe20 nanowires can be tuned by varying the Ru spacer layer thickness. Specifically, changing the Ru thickness we have tuned the Ruderman-Kittel-Kasuya-Yosida exchange interaction, and thus the antiferromagnetic (AFM) strength between the Ni80Fe20 layers. We show that there is a strong correlation between the interlayer coupling and features in ferromagnetic resonance (FMR) modes. We found different mode-softening degree of the FMR curves as function of the strength of AFM coupling, together with a clear frequency gap at around zero field. These experimental results are in qualitative agreement with presented micromagnetic simulations that also include biquadratic interface exchange. Understanding these characteristics may offer insights for reconfigurable vertical magnetic logic devices and microwave filters.

A microscopic theory is employed to investigate the spin wave spectra in metamagnetic materials that consist of ferromagnetically ordered layers, with the intralayer ferromagnetic exchange interactions being much stronger than the weak antiferromagnetic interaction between adjacent layers.

The theory for dipole-exchange spin waves in cylindrical ferromagnetic nanowires, as developed in a previous paper, is extended to include spectral intensities, arbitrary orientation of external magnetic field, and effects of single-ion anisotropy. This allows applications to be made to the nickel nanowires studied experimentally. The dependences of the spin-wave frequencies on the nanowire radius, wave vector, and magnetic field are investigated, and the spatial distribution of the eigenmodes are evaluated to analyze their localization. The spectral intensities are calculated within a Green's function formalism, giving a good insight into data from Brillouin light scattering. The spin-wave frequencies obtained in the case of zero field are compared to the experimental results for nickel, and to results deduced from macroscopic theory under conditions of small surface pinning. Also when the magnetic field is perpendicular to the wire axis, making the magnetization nonuniform, our results provide a good description of the experimental behavior.

This chapter focuses on metallic magnetic multilayers. Ultrathin magnetic films consist of ferromagnetic films (Fe) with inter-film exchange coupling via an intervening non-ferromagnetic layer (Cr), giving the trilayer Fe/Cr/Fe structure. In simple metals such as Cu(OOl) and Ag(OOl), the bilinear exchange coupling exhibits strong oscillations with a short wavelength of the order of two atomic monolayers. The exchange coupling through non-ferromagnetic inter layers in this case is found to be strongly affected by the interface roughness. Realistic interfaces often consist of finite terraces along with other inhomogeneities, which result in variations of the interlayer thickness. There is a preferred non-collinear alignment (at 90°) of the magnetization directions among the ferromagnetic layers (Fe) for values of the non-magnetic spacer thickness where the bilinear exchange term was small. Experimental results show that the Fe/Cr/Fe sample enhances the effect of biquadratic coupling, which aligns the magnetization of the Fe layers at 90° to each other. The bilinear and biquadratic coupling strengths can be extracted by fitting the experimental results with a theory that treats the static and dynamic responses on an equal footing. However, in order to obtain reliable fits between theory and experiment, it is necessary to study the variation of some spin-wave property.

Although the electronic properties of semiconductor superlattices and multi-quantum wells (MQWs) have attracted enormous attention in the last two decades, considerably less work has been done on the optical characterization of these artificial specimens, and this is where exciton-polaritons have an important role. The finite wave vector dependence in the dispersion equation for the total energy of the exciton plays a decisive role in the optical properties of a crystal in the exciton energy region. The bulk exciton-polariton dispersion relation is found by solving Maxwell's equation with the use of the dielectric function. The s-polarized exciton-polariton spectrum is found to be qualitatively similar to the p-polarization case; the minor differences are mainly related to the number of surface and guided modes outside the bulk mode lines. Among the experiments to probe these modes, the most relevant are the photoreflectance (PR) and photoluminescence (PL) studies for GaN thin films.

This chapter discusses the propagation of surface polariton electromagnetic modes (with particular reference to the non-magnetic cases of plasmon- and phonon-polaritons) at single and double interfaces. Surface polaritons are those mixed electromagnetic modes that exist at crystalline surfaces and may be excited by various methods. Their specific properties depend on the characteristics of the materials, normally as described by their dielectric function. Guided optical waves consist of light waves trapped by total internal reflection in a region of a dielectric medium that is characterized by a higher refractive index than its surrounding parts. The most common system is a thin film. Above a cut-off frequency, there are no restrictions on the frequencies of the guided modes, and hence a full spectrum of modes is possible .These are examples of modes that form the basis for the integrated optics technology.

Polaritons are quasi-particle excitations in solids consisting of a photon (the quantum of the electromagnetic field) coupled to an elementary excitation (plasmon, phonon, exciton, magnon, etc.) which polarizes the crystal. Knowledge of the dielectric functions of solids is necessary to understand the concept of polaritons. An exciton-polariton is a propagating mode in a dielectric or semiconductor crystal in which the electromagnetic wave is coupled with the polarization wave of excitons. Experimental evidence for the existence of polaritons was provided first for the phonon-like polariton in cubic GaP. The characteristics of polariton bulk (and also surface) electromagnetic modes in dielectric and semiconductor crystals are closely related to the dielectric properties of the media and, in particular, to the frequency dependence of the relevant dielectric functions. Therefore, it is fundamental to have a proper understanding of the dielectric functions of solids. The dielectric function is the response of a system to an external electric field, and it plays an important role in the study of electromagnetically coupled modes—such as the plasmon-, phonon-, and exciton-polaritons.

Advances in the fabrication of multilayer materials make it possible to reveal novel features of such structures. The techniques include modern layer-growth methods such as molecular-beam epitaxy (MBE) and metal-organic chemical vapor deposition (MOCVD) among others, as well as characterization tools such as X-ray scattering, low-energy electron diffraction (LEED), and neutron diffraction. They have made possible the fabrication of layered materials with sharp, high-quality interfaces, and with dimensions comparable to the electron mean free path and the de Broglie wavelength. They allow for an intriguing new class of artificial periodic or superlattice (SL) and quasiperiodic layered materials in that their macroscopic properties are readily subject to design or control by varying the thickness or composition of the constituent films. A periodic structure or superlattice is a kind of planar or 2D nanostructure in the sense that it still has translational symmetry in directions parallel to the plane interfaces. One may also find more complex SL structures involving differently doped semiconductors.

Measurements are reported for the temperature and polarization dependences of two-magnon Raman light scattering in the rutile-structure antiferromagnet CoF 2 over the temperature range from 4 to 40 K . An effective spin model is employed to obtain a good description of the line shapes and peak frequencies for temperatures up to 0.4 T N . The results are also deduced for the relative values of the two-magnon magneto-optical coupling coefficients.

This chapter summarizes some of the experimental techniques that can be used to study polariton excitations in periodic and quasiperiodic structures. The techniques that are presented in the chapter include Raman scattering, Brillouin light scattering (BLS), and resonant Brillouin scattering (RES). The first application of Raman scattering to plasmons in periodic superlattices was for measurements on doped GaAs/Ala x Ga 1-x As superlattices. The modes corresponded fairly well to the model with 2D charge sheets. It is known that spectra are sensitive to the quasiperiodic structure of the superlattice as well as the phonon properties. The observed acoustic frequencies are shifted depending on the size or stage number of the lattice. By contrast, periodic superlattices typically exhibit peak broadening in similar-sized structures. As in the case of Raman scattering, BLS provides a well-established, non-destructive optical technique. It can yield a great deal of information about magnetism in low-dimensional systems such as thin films, multilayers, and patterned structures. Also, BLS gives information about the dynamical properties of a spin system through the detection of long-wavelength spin waves. RBS is perhaps the most powerful experimental technique to probe exciton-polaritons.

A theoretical study is made of the magnetization versus applied field curves of ferromagnetic/nonmagnetic multilayers constructed according to a Fibonacci quasiperiodic sequence. The ferromagnetic films are assumed to have uniaxial anisotropy and are coupled by both bilinear and biquadratic effective exchange. The effects of quasiperiodicity in the magnetic phases are illustrated numerically for Fe/Cr systems., 5 pages, 3 ps figures, Elsevier Latex2e Style. To appear in Journal of Magnetism and Magnetic Materials (proceedings of the 4th International Symposium on Metallic Multilayers, MML'01, Aachen, June 24-29, 2001)

The localized states of a semi-infinite zigzag graphene sheet are studied using a tight-binding model that allows for the inclusion of either one or two lines of impurities. These impurity lines of atoms are placed in rows labeled as n (n = 1, 2, 3, …), where n = 1 is the free edge. The localized defect modes associated with these impurities are studied analytically and numerically within a tridiagonal matrix formalism. For one impurity line, the modes are analyzed according to the position of that line on the sheet, whereas the modes for two impurities are studied also according to their separation and their positions relative to the edge. When an impurity line is located at the edge (n = 1), it is found that the edge states are modified. When the impurities are positioned away from an edge (n > 1), additional localized modes are found to occur that may be relatively flat in their dispersion.

A combined experimental and theoretical study of the origin of paramagnetic centres in graphene nanoribbons (GNRs) is presented. GNRs were prepared from multi-wall carbon nanotubes by an oxidative method at various temperatures. Increasing the oxidation temperature led to GNRs of shorter length with no noticeable effect on the width. Electron spin resonance showed that the ribbon sizes influence both the spin density and type of paramagnetism, with longer ribbons being more prone to form localized paramagnetic centres and shorter ribbons exhibiting a significant paramagnetic contribution from extended states. The density of states for GNRs was calculated with varying dimensions and chiralities using a Huckel tight-binding method. The formation energies of zigzag edges and vacancies, which are expected to be responsible for paramagnetic centres, were evaluated. Our results indicate that longer GNRs favour formation of vacancies while shorter structures favour zigzag edges. This analysis explains the existence of localized paramagnetic centres in longer GNRs and paramagnetism due to electronic states delocalized along zigzag edges in shorter GNRs.

Calculations are reported for the spin-wave bands and gaps in magnonic crystals formed by patterning one (or both) of the surfaces of ferromagnetic thin films. Specifically, a patterning in terms of a periodic array of rectangular grooves is considered, and the theory employs a microscopic (or Hamiltonian-based) method that incorporates exchange and magnetic dipole–dipole interactions, as well as an external magnetic field. The coupling between different periodic elements of the magnonic crystal involves both exchange and dipolar terms, allowing for control of the spin-wave bands and gaps as the depth and width of the grooves are varied. Numerical examples are given for Permalloy structures, considering the stripe patterning to be on one or two surfaces, and the applicability to Brillouin light scattering is discussed.Calculations are reported for the spin-wave bands and gaps in magnonic crystals formed by patterning one (or both) of the surfaces of ferromagnetic thin films. Specifically, a patterning in terms of a periodic array of rectangular grooves is considered, and the theory employs a microscopic (or Hamiltonian-based) method that incorporates exchange and magnetic dipole–dipole interactions, as well as an external magnetic field. The coupling between different periodic elements of the magnonic crystal involves both exchange and dipolar terms, allowing for control of the spin-wave bands and gaps as the depth and width of the grooves are varied. Numerical examples are given for Permalloy structures, considering the stripe patterning to be on one or two surfaces, and the applicability to Brillouin light scattering is discussed.