Magnons in surface-rearranged ferromagnetic thin films

By a Green function approach, spin waves in a surface-rearranged ferromagnetic thin film are derived both analytically and numerically. Heisenberg exchange, bulk and surface anisotropy between nearest neighbors and external magnetic field are taken into account for an sc film with {001} surfaces. Because of the anisotropies, the dynamical matrix defined from the Green function equations is not Hermitian, so we generalize the Bogoliubov canonical transformation to derive the spin wave spectrum. The spin waves propagating inside the film result from the superposition of two sine or hyperbolic sine waves. The amplitude and polarization of spin waves are shown to be quite sensitive to the details of the surface rearrangements, whereas spin wave energies are not so sensitive to such rerrangements, except when soft modes occur in the unrearranged configuration. In that case, we show that when the surface rearrangement is taken into account, soft modes disappear in the spin wave spectrum.     

Calculation of nonlinear modes guided by multilayer dielectric structures using the resonance technique

A simple and easily programmable approach based on the resonance method has been developed for analysing optical waves guided by complicated configurations such as multilayer dielectric structures with arbitrary nonlinear media. In this formulation both TE and TM polarizations are considered. In the present paper, as an example of the resonance technique application, the five-layer waveguiding configuration, including two arbitrary nonlinear media along with a linear film of arbitrary profile, is treated. Numerical results are presented in the form of guided power versus propagation constant for various parameters of the problem.     

Nano scale computational architectures with Spin Wave Bus

We propose and analyze a new kind of nano scale computational architectures using spin waves as a physical mechanism for device interconnection. Information is encoded into the phase of spin waves propagating in a ferromagnetic film — a Spin Wave Bus. We describe several possible logic devices utilizing spin waves. The performance of the proposed devices is illustrated by numerical modeling based on the experimental data for spin wave excitation and propagation in NiFe film. The key advantage of the proposed architectures is that information transmission is accomplished without charge transfer. Potentially, the architectures with Spin Wave Bus may be beneficial in terms of power consumption and resolve the interconnect problem. Another expected benefit is in the enhanced logic functionality. Using phase logic, it is possible to realize a number of logic functions in one device. These advantages make the architectures with a Spin Wave Bus very promising for application in ultra-high-density integrated circuits (more than 10¹⁰ devices per square inch).     

Numerical modelling of TE and TM modes in lossy nonlinear optical waveguides

The intensity-dependent characteristics of nonlinear TE and TM waves in a thin film bounded by lossy nonlinear media are analysed by the finite-element method. In this approach, the power-dependent complex propagation constants and local complex electromagnetic field distributions of lossy nonlinear TE and TM waves are obtained directly from the given lossy nonlinear waveguides, without any approximations. Numerical results for these modes in a lossy nonlinear waveguiding system with different absorption coefficients are given. It is shown that the complex dispersion relations, for both TE and TM modes, are strongly power dependent.     

Hysteresis of the characteristics of magnetostatic waves in ferrite films with stripe domains whose magnetization vectors are oriented close to the plane of the film

The propagation of zero-exchange spin waves (magnetostatic waves) is investigated in yttrium iron garnet films having a regular stripe domain structure with almost in-plane orientation of the domain magnetization vectors. The characteristics of the waves are studied for magnetizations of the film parallel and perpendicular to projections of the [111] crystallographic axes onto the plane of the film. It is established, in contrast with films having the domain magnetization vectors oriented close to the normal to the plane of the film, that both the propagation of magnetostatic waves and the variation of the parameters of the domain structure exhibit a distinctly pronounced hysteretic character as the magnetizing field is varied. The hysteresis of the amplitude-frequency response, equiphase, and dispersion curves of the magnetostatic waves is investigated. The authors examine how the hysteresis of these parameters is related to the hysteresis of the domain structure. The spectrum of magnetostatic waves is found to have an interval of wavelengths (wave numbers) that are not excited in the unsaturated film when the applied field is close to the saturation value, and this phenomenon as well exhibits hysteresis. Zh. éksp. Teor. Fiz. 114, 1430–1450 (October 1998)     

Observation of spin-wave envelope solitons in periodic magnetic film structures

The formation and propagation of light and dark microwave spin-wave envelope solitons in a periodic magnetic film structure have been observed. The periodic structure was manufactured on the basis of the single-crystal film of iron-yttrium garnet and a lattice of copper strips placed on the surface of the film perpendicularly to the propagation direction of carrying spin waves. The solitons are generated at frequencies corresponding to the band gap in the spectrum of the spin waves of the periodic structure, which is due to the first Bragg resonance.     

Spin-wave spectroscopy and application of its methods to heterostructures of silicon dioxide with Co nanoparticles on a GaAs substrate

A method has been developed for determining magnetic and electrical characteristics of film nanostructures containing magnetic nanoparticles from dispersion curves of surface spin waves propagating in these nanostructures. The dispersion curves of spin waves are determined by the dynamics of the spin component described by the generalized Landau-Lifshitz equations and an alternating electromagnetic field induced by a spin wave. Since spin waves are very sensitive to inhomogeneity of magnetic parameters, spin disorder, and conductivity of an object near or inside which these waves propagate, they can be used for determining magnetic and electrical characteristics of the objects under investigation. The developed calculation method, which can be employed both in spin-wave spectroscopy and in analysis of dispersion curves obtained by other methods, has been used for determining parameters of heterostructures consisting of a SiO₂ film with Co nanoparticles on a GaAs substrate. It has been found from the shape of dispersion curves of the surface spin waves that, in the film near the interface, spins of the nanoparticles are close to a ferromagnetic ordering, whereas near the free surface, the spin orientation of nanoparticles is more chaotic. It has been revealed that a conducting layer is formed in GaAs, and the SiO₂(Co) film near the interface has an increased conductivity.     

Total reflection of ultrasound from a ferromagnetic plate with surface pinning of the spins

Using the effective transfer matrix for coupled elastic and spin waves, formulas are derived for the amplitudes of reflection and transmission of right-hand polarized elastic waves incident, in a direction along the normal, on a transversely magnetized ferromagnetic film with homogeneous conditions for pinning of the spins on the surfaces of the film. It is shown that a series of lines with reflectance maxima appears, to the extent of the magnetoelastic coupling, near the magnetoacoustic resonance. The shapes of the spectral line contours and the effect of the thickness of the film and damping are analyzed. The possibility of a similar effect in other polariton systems is discussed.     

Eigen electromagnetic waves of a coaxial waveguiding structure filled by a non‐uniform dissipative plasma with azimuthal magnetic field

This paper studies the propagation and spatial attenuation of high‐frequency eigen‐symmetric and dipolar electromagnetic waves along a coaxial plasma–metal waveguiding structure that contains a slightly axial and strong radial non‐uniform cylindrical plasma slab in an external azimuthal non‐uniform magnetic field. The influence of such parameters as the effective electron collision frequency, the direct current value producing the external azimuthal magnetic field, parameters that characterize plasma density radial profile, and waveguide geometric parameters on the dispersion, spatial attenuation, and radial field structure of the waves is considered. The regions of waveguiding structure parameters where the electromagnetic wave properties can be effectively controlled are studied and analyzed.     

Transmission enhancement by conversion of evanescent waves into propagating waves

The convolution between spatial modes of two different parts of an optical system can convert evanescent waves into propagating waves. This principle is applied to different optical systems for analyzing various effects in transmission enhancements experiments. We discuss here the differences between the present principle which is related to broadening of resonances and the near-field optical microscopy based on a tunneling effect by a tip detector. The present analysis is applied in particular to two systems: a) transmission enhancement in one slit by coupling the transmitted radiation with transversal Fabry–Pérot electromagnetic (EM) modes, and b) transmission enhancement by coupling between a metallic film with arrays of holes and surface plasmons (SP). The present approach gives more information on transmission enhancement phenomena than that obtained by conventional treatments and can also solve certain disagreements between different theories. The differences between the present process of converting evanescent waves into propagating waves, and that related to the new development of getting a super-resolution by an hyperlens are discussed. PACS 41.20.Jb; 73.20.Mf; 42.79.Dj     

Spin wave dynamics and the determination of intrinsic damping in locally excited Permalloy thin films

Time-resolved scanning Kerr effect microscopy has been used to study magnetization dynamics in Permalloy thin films excited by transient magnetic pulses generated by a micrometer-scale transmission line structure. The results are consistent with magnetostatic spin wave theory and are supported by micromagnetic simulations. Magnetostatic volume and surface spin waves are measured for the same specimen using different bias field orientations and can be accurately calculated by k-space integrations over all excited plane wave components. A single damping constant of Gilbert form is sufficient to describe both scenarios. The nonuniform pulsed field plays a key role in the spin wave dynamics, with its Fourier transform serving as a weighting function for the participating modes. The intrinsic Gilbert damping parameter alpha is most conveniently measured when the spin waves are effectively stationary.     

Sensitivity of integrated optical sensors based on a prism coupler

Errors of registration of complex mode propagation constant increments for the sensors with a film waveguiding structure deposited on the base of the prism coupler are investigated. Possibilities for minimization of mean square errors of the registration by choosing parameters of the waveguiding structure and the exciting light beam are determined. As an example, the optimized sensor of ammonia concentration in air is analysed.     

Gap plasmon polariton structure for very efficient microscale-to-nanoscale interfacing

The seamless transition between microscale photonics and nanoscale plasmonics requires overpassing different waveguiding mechanisms and a few orders of magnitude in the lateral dimension. Exploiting gap plasmon-polariton waves both at the microscale and nanoscale with an ultrashort (few micrometers) nonadiabatic tapered gap plasmon waveguide, we show theoretically that very high-power transfer efficiency (approximately 70%) is achieved. The same mechanism may be used to harvest impinging light waves and direct them into a nanohole or slit to exhibit an anomalous transmission without the conventional periodic structures. The interplay of plasmonic and oscillating modes is analyzed.     

Dissipation of the spin wave energy in magnetic multilayer films

It is shown that the penetration of standing spin waves into a layer with high damping is one of the channels of energy dissipation of these waves. The line broadening of spin wave modes due to this layer increases with the mode index and may be much larger than the natural linewidth associated with a layer having low damping. The linewidths of spin wave modes are found to be anisotropic, which is due to the dependence of the penetration depth of spin waves into the high-damping layer on the orientation of the external magnetic field with respect to the film. A theoretical model is proposed, which is consistent with the experimental data.     

Dispersion characteristics of spin waves in planar periodic structures based on ferromagnetic films

A technique for calculating the dispersion characteristics of planar periodic magnetic structures is suggested. It is based on joint application of the spin-wave mode analytical approach and the transfer matrix formalism. The dispersion characteristics of a planar periodic waveguiding medium representing a thin ferromagnetic film with an array of metallic strips (metallic grating) on its surface are calculated. It is shown that the dispersion characteristics of planar periodic structures based on ferromagnetic films depend, not only on the geometry of the waveguiding system, but also on the surface anisotropy of the initial film.     

Waveguide interaction of light with spin waves in a ferromagnetic film

We discuss the results of a theoretical analysis of the waveguide interaction of light and spin waves. Both linear and quadratic magnetooptical effects are taken into account. The features of the interaction are considered for the three principal types of spin waves: waves in a normally magnetized ferromagnetic film, and longitudinal and transverse waves in a tangentially magnetized film. Isotropic and anisotropic diffraction processes are considered. Numerical estimates of the intensity and frequency properties of the diffraction scattering are given for a number of situations of practical interest. The effect of a strong constant magnetic field on the interaction of light and spin waves is considered.Translated from Izvestiya Vyssnikh Uchebnykh Zavednii, Fizika, No. 4, pp. 5–31, April, 1989.     

Plasmon mechanism of light transmission through a metal film or a plasma layer

It is shown that a smooth metal film (or a plasma layer) can be made transparent for an electromagnetic wave when two identical subwavelength diffraction gratings are placed on both sides of the film. The electromagnetic wave transmission through the metal film is caused by excitation of evanescent surface waves (plasmons) and their transformation into propagating waves at the gratings. A model which is developed analytically shows that the problem of the wave transmission is physically equivalent to the problem of excitation of two coupled resonators of evanescent waves which are formed at the two film surfaces.     

Interaction between large and small signals in a resonant transmission line based on magnetostatic waves

The influence of a large signal on the characteristics of a small signal near the frequency of the former is experimentally studied for the case of their simultaneous propagation through a resonant transmission line based on backward volume magnetostatic waves. The effects observed are caused by the excitation of spin waves in a ferromagnetic film at different large-signal frequencies and by the back influence of excited spin-wave packets on the amplitude and phase characteristics of the small signal.     

Magneto-optical effects in ultrathin structures at transversal magnetization

Procedures based on the Yeh’s 4 × 4 matrix formalism for the treatment of the electromagnetic interactions in multilayers at transversal magnetization and at an arbitrary angle of incidence are described. With the restriction to the magneto-optical effects linear in the magnetization the characteristic matrix for magnetic layer is derived. The reflection and transmission coefficients are obtained in the case of magnetic ultrathin film on substrate. The magneto-optical thin film waveguides at transversal magnetization are analysed in details and the dispersion relations for guided modes in a single layer, a bilayer, a sandwich and the approach to expand this way for waveguiding conditions in multilayers are presented. Work partially sponsored by Grant Agency of the Czech Republic, reg. No. 202/98/0235 and Ministry of Education in the frame of KONTAKT program, reg. No. ME 175/1998.     

Magnonics: Experiment to prove the concept

An experimental scheme for studying spin wave propagation across thin magnetic film samples is proposed. The scheme is based upon the creation of picosecond pulses of strongly localized effective magnetic field via ultrafast optical irradiation of a specially deposited exchange bias or exchange spring layer. The spin waves are excited near the irradiated surface before propagating across the thickness of the sample. They are then detected near the other surface either within the finite optical skin depth using the linear magneto-optical Kerr effect in metallic samples or by the magnetic second harmonic generation. The experiment can facilitate investigations of propagating spin waves with wavelengths down to several nanometers and frequencies in excess of hundreds of Gigahertz. An experiment upon a periodically layered nanowire (a finite cross-section magnonic crystal) is numerically simulated, although the sample might equally well be a continuous film or an array of elements (e.g. nanowires) that either have uniform composition or are periodically layered as in a magnonic crystal. The experiments could be extended to study domain wall-induced spin wave phase shifts and can be used for the creation of spin wave magnetic logic devices.