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A theoretical analysis is made for the quantized spin waves in single-layered ferromagnetic nanorings with the added effect of interfacial Dzyaloshinski–Moriya interactions (DMI). A microscopic, or Hamiltonian-based, formalism is employed that includes competing terms for the symmetric (bilinear) exchange interactions, the antisymmetric DMI, the magnetic dipole–dipole interactions, and applied magnetic field. It is found that, in our model, the transition field value between vortex and onion states is shifted by the inclusion of DMI effects. Significantly, the spin-wave frequencies are also modified with the effects being largest in the onion state close to the transition field. We present combined analytical and numerical results obtained for the static and dynamical magnetization, including the frequencies and amplitudes (with relative phase) of the spin waves when interfacial DMI is present.

A spin-wave (SW) theory that includes the long-range dipole–dipole interactions is presented for monolayers of van der Waals (vdW) ferromagnets for which the magnetic ions lie on a two-dimensional honeycomb lattice. The dipolar interactions provide an additional anisotropy in these materials, along with the Ising exchange interaction and/or single-ion anisotropies that typically stabilize the two-dimensional magnetic ordering. Analytical results for the linearized SW energies are obtained for the ferromagnets in two geometries: complete films and finite-width stripes (or ribbons). In both cases it is found that the inclusion of the dipole–dipole interactions leads to a shift and sometimes a splitting of the magnetic modes in the vdW structure. Also, in the latter case, where the edges are assumed to be along the zigzag lattice directions, the dipole–dipole interactions are found to play a role, as well as the exchange interactions, in modifying the localized edge SWs. Numerical examples are given, including applications to the ferromagnet CrI3.

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.

An overall comparative study is made of the spin-phonon interactions in several rutile-structure transition-metal difluorides, specifically FeF₂, MnF₂, NiF₂, and CoF₂, in terms of recent developments obtained experimentally using inelastic light scattering spectroscopy and theoretically using a modified mean-field approach to estimate spin-pair correlation functions. New experimental data are presented here and interpreted within an extended and comprehensive theoretical treatment to yield estimates for the spin-phonon coupling coefficients and the relative magnitudes of the magneto-optical coupling coefficients. С использованием последних результатов экспериментально с применением спектроскопии неупругого рассеяния света и теоретически методом модифицированного среднеполевого подхода для оценки корреляционных функций спиновой пары проведено полное сравнительное исследование спин-фононных взаимодействий в нескольких дифлуоридах переходных металлов рутиловой структуры, в частности FeF₂, MnF₂, NiF₂ и CoF₂. С целью получения оценок коэффициентов спин-фононной связи и относительных величин коэффициентов магнитооптической связи представлены новые экспериментальные данные, которые интерпретируются в рамках всестороннего расширенного теоретического описания З використанням останніх результатів експериментально зі застосуванням спектроскопії непружного розсіяння світла та теоретично методом модифікованого середньопольового підходу для оцінки кореляційних функцій спінової пари проведено повне порівняльне дослідження спін-фононних взаємодій в декількох діфлуоридах перехідних металів рутилової структури, зокрема FeF₂, MnF₂, NiF₂ та CoF₂. З метою отримання оцінок коефіцієнтів спін-фононного зв’язку та відносних величин коефіцієнтів магнітооптичного зв’язку представлено нові експериментальні данні, які інтерпретуються в рамках всебічного розширеного теоретичного опису.

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.

A theoretical account is given for the non-classical properties of magnons in ultra-thin ferromagnetic films with in-plane magnetization under the conditions of parallel pumping. A microscopic or Hamiltonian-based approach with a lattice of effective spins interacting through the magnetic dipole–dipole and exchange interactions is used. With the Zeeman energies of the static applied field and the microwave pumping field included, the total Hamiltonian is transformed from spin operators to boson creation and annihilation operators. Using a representation of coherent magnon states, we obtain the explicit results for the temporal evolution of the magnon occupation number as well as the magnon squeezing. In particular, it is shown that the manipulation of the collapse-and-revival phenomena for the average number of magnons and the properties of the magnon squeezing is made possible by controlling the nonlinearity in the system through the microwave pumping field.

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.

A theoretical study is reported for the effects of an external magnetic field on the spin-wave dynamics of finite-length nanotubes, where the end effects are important as well as radial variations. By using a microscopic (or Hamiltonian-based) formalism, the frequencies and spatial amplitudes of the dipole-exchange spin waves are calculated for two orientations of the applied magnetic field. When the magnitude of this field is varied there is a switching between different magnetic ordering states and a modification to the spin-wave modes. For a longitudinal field (along the nanotube axis) there is competition between the bottleneck (or bamboo) state and a twisted bottleneck state with vortex components at the ends, having either the same or opposite chirality. For a transverse field the equilibrium spin orientations are tilted relative to the nanotube axis and vary with respect to their position in the finite-length nanotube. The resulting effect on the spin waves is studied as the transverse field is increased from a low value: initially the field inhibits the vortex states and eventually it produces an overall spin reorientation. Numerical calculations are presented for permalloy and nickel nanotubes with realistic dimensions and magnetic field values.

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.

A microscopic (or Hamiltonian-based) theory is employed for the spin-wave instability thresholds of nonlinear processes in ultrathin ferromagnetic stripes and films under perpendicular pumping with an intense microwave field. The spatially-quantized linear spin waves in these nanostructures may participate in parametric processes through the three-magnon interactions (the first-order Suhl process) and the four-magnon interactions (the second-order Suhl process) when pumped. By contrast with most previous studies of spin-wave instabilities made for larger samples, where macroscopic (or continuum) theories involving Maxwell's equations for magnetic dipolar effects are used, a discrete lattice of effective spins is employed. Then a dipole-exchange spin Hamiltonian is employed to investigate the behavior of the quantized spin waves under perpendicular pumping, when modifications due to the more extensive spatial confinement and edges effects in these nanostructures become pronounced. The instability thresholds versus applied magnetic field are calculated, with emphasis on the size effects and geometries of the nanostructures and on the different relative strengths of the magnetic dipole-dipole and exchange interactions in materials. Numerical results are presented using parameters for Permalloy, YIG, and EuS.

Theoretical studies are reported for the non-classical quantum statistical behavior of bosonic excitations in obliquely-magnetized nanowires under condition of microwave pumping. A dipole-exchange Hamiltonian is employed in which the external magnetic field is transverse to the length of the ferromagnetic nanowire, causing the magnetization to be canted away from the symmetry axis. Using a coherent magnon states representation we obtain explicit results for the temporal evolution of the magnon creation and annihilation operators. Applications are presented in the perpendicular pumping configuration for the initial collapse and then revival of the magnon occupation number, the super-Poissonian magnon-counting statistics, and the magnon squeezing. It is found that all of these processes are enhanced by having an oblique-magnetization state in the nanowire. For comparison, we also present results when the microwave pumping field is in the orientation parallel to the magnetization. It is found that the parallel and perpendicular microwave pumping configurations lead to important differences in the time dependences.

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 investigate theoretically the quantum dynamics and statistics of magnons in a cavity–magnon system, where the magnons in a single yttrium iron garnet (YIG) sphere are coupled to microwave cavity photons. Under the rotating wave approximation, the Hamiltonian of the system is solved analytically. By using the coherent magnon state representation, we show that the magnon Kerr nonlinearity, which originates in the magnetocrystalline anisotropy in the YIG sample, could yield a periodic sub-Poissonian distribution and quadrature squeezing effects in the magnons. The generation and manipulation of these nonclassical quantum statistical properties of the magnons can be controlled by scaling the size of the YIG sample.

The coherent magnon state representation is employed to investigate the quantum-statistical behavior of the nonlinear excitation of magnons in ferromagnets. Both the long-range magnetic dipole-dipole and short-range exchange interactions are included, along with a static longitudinal applied field and a microwave pumping field in the perpendicular orientation. Within a microscopic (or Hamiltonian-based) approach the total Hamiltonian is transformed from spin operators to a normal-mode set of boson creation and annihilation operators. When the three-magnon interactions are included, it is found that the microwave pumping field may be used to control the nonlinear statistical properties of the system. From a study of the time evolution of the system we deduce the average number of magnons, the super-Poissonian statistical behavior, and the occurrence of magnon squeezing. We also compare the results with the case where the microwave pumping field is in the parallel orientation, and it is found that there are important differences in the time dependence.

Calculations are reported for the spin-wave instabilities in a ferromagnetic nanowire with circular cross section, as well as nanotubes, under conditions of parallel microwave pumping. The quantized spin waves are characterized by a one-dimensional wave vector along the nanowire and the external applied magnetic field is taken to be parallel to the longitudinal axis. In nanowires with lateral dimensions less than about 200 nm, the spatial quantization of the eigenmodes become predominant and our theory employs a microscopic (or Hamiltonian-based) dipole-exchange method analogous to that used recently for ultrathin films and nanowire stripes with rectangular cross section. Numerical applications are made to wires with different radii and comparisons are presented with nanowires having square cross sections. When our nanowire results are compared with those for macroscopic samples or for ultrathin films, it is found that the “butterfly curves” (threshold field vs. applied field) are significantly modified and show more structural features.

A microscopic, or Hamiltonian-based, theory is outlined for studying the spin-wave instability thresholds of the parametric processes occurring in ferromagnetic nanostructures under conditions of pumping with a microwave eld. Most previous work has concentrated on spheres or lms with dimensions of order several μm or more, with the theoretical interpretation being made in terms of macroscopic (or continuum) methods. At smaller length scales, as in ultrathin lms and nanowires with thickness or lateral dimensions less than about 100 nm, the discreteness of the quantized spin waves and their spatial distributions become modi ed, making it more appropriate to employ a microscopic approach to the nonlinear dynamics with a lattice of e ective spins interacting through the magnetic dipole dipole and exchange interactions. E ects of microwave pumping (in either the parallel or perpendicular con guration) are incorporated in calculations for the instability thresholds of the quantized spin-wave bands in di erent nanostructures and materials.

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.

Theoretical studies are reported for the quantum-statistical properties of microwave-driven multi-mode magnon systems as represented by ferromagnetic nanowires with a stripe geometry. Effects of both the exchange and the dipole-dipole interactions, as well as a Zeeman term for an external applied field, are included in the magnetic Hamiltonian. The model also contains the time-dependent nonlinear effects due to parallel pumping with an electromagnetic field. Using a coherent magnon state representation in terms of creation and annihilation operators, we investigate the effects of parallel pumping on the temporal evolution of various nonclassical properties of the system. A focus is on the interbranch mixing produced by the pumping field when there are three or more modes. In particular, the occupation magnon number and the multi-mode cross correlations between magnon modes are studied. Manipulation of the collapse and revival phenomena of the average magnon occupation number and the control of the cross correlation between the magnon modes are demonstrated through tuning of the parallel pumping field amplitude and appropriate choices for the coherent magnon states. The cross correlations are a direct consequence of the interbranch pumping effects and do not appear in the corresponding one- or two-mode magnon systems.

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