In-plane Wave Research Articles

Ferromagnetic resonance saturation and second order Suhl spin wave instability processes in thin Permalloy films

High power ferromagnetic resonance (FMR) loss versus static field H profiles and the corresponding spin wave instability threshold microwave field amplitude hcrit vs H butterfly curves were measured for in-plane magnetized thin Permalloy films of thicknesses 35, 57, 74, 104, and 123nm at a nominal pumping frequency of 9.11GHz. Cavity loading and calibration issues that proved to be problematic in past attempts to obtain accurate resonance saturation data over the full FMR profile in ferrites and metal films were resolved through a careful decoupling of the pump field and a full cavity response calibration. The FMR profiles show a drop in the loss peak, a shift in the peak to lower field, a broadening, and the development of a foldover-like asymmetry as the power is increased. The butterfly curves show a minimum hcrit at the low power FMR field and a smooth rounded increase on either side, except for a small kink on the low field side associated with the shift and asymmetry development. Apart from the kink, the second order Suhl spin wave instability theory, suitably modified for thin films, provided good fits to the butterfly curve data through the use of a single spin wave linewidth ΔHk value for each data set. The ΔHk values ranged from 16to35Oe, with the implied critical mode in-plane wave vectors always directed parallel to the static field. These spin wave linewidths translate into Gilbert damping parameter αk values in the 0.002–0.005 range, the same order as expected for intrinsic magnon-electron scattering losses in metal ferromagnets. These αk values are about a factor of 2 smaller than those implied by the low power FMR linewidths. The FMR in-plane precession cone angles at threshold were on the order of 3°–6°.

Analytical prediction and experimental measurement for mode conversion and scattering of plate waves at non-symmetric circular blind holes in isotropic plates

A model for guided wave scattering from non-symmetric blind holes in isotropic plates using Poisson and Mindlin plate wave theories for in-plane and flexural wave modes, respectively, is presented. It makes use of the wave function expansion technique and coupling conditions at the defect boundary in order to evaluate the scattered far fields of the three fundamental guided wave modes. The results were compared to other analytical models as well as experimental measurements for mode conversion from S0 to A0. Measurements agreed well with predictions confirming the validity of the model, highlighting at the same time the strong frequency dependence of the scattering and mode conversion behaviour.

Intervalley splitting and intersubband transitions inn-typeSi∕SiGequantum wells: Pseudopotential vs. effective mass calculation

Intervalley mixing between conduction-band states in low-dimensional $\mathrm{Si}∕\mathrm{Si}\mathrm{Ge}$ heterostructures induces splitting between nominally degenerate energy levels. The symmetric double-valley effective mass approximation and the empirical pseudopotential method are used to find the electronic states in different types of quantum wells. A reasonably good agreement between the two methods is found, with the former being much faster computationally. Aside from being an oscillatory function of well width, the splitting is found to be almost independent of in-plane wave vector, and an increasing function of the magnitude of interface gradient. While the model is defined for symmetric envelope potentials, it is shown to remain reasonably accurate for slightly asymmetric structures such as a double quantum well, making it acceptable for simulation of multilayer intersubband optical devices. Intersubband optical transitions are investigated under both approximations and it is shown that in most cases valley splitting causes linewidth broadening, although under extreme conditions, transition line doublets may result.

Propagation and localization of two-dimensional in-plane elastic waves in randomly disordered layered piezoelectric phononic crystals

Two-dimensional in-plane wave propagation and localization in the disordered layered piezoelectric phononic crystals with material 6 mm are investigated taking the electromechanical coupling into account. The electric field is approximated as quasi-static. The analytical solutions of elastic waves are obtained. The 6 × 6 transfer matrix between two consecutive unit cells is obtained by means of the mechanical and electrical continuity conditions. The expressions of the localization factor and localization length in the disordered periodic structures are presented by regarding the variables of the mechanical and electrical fields as the elements of the state vector. The numerical results of the localization factors and localization lengths are presented for two kinds of disordered piezoelectric phononic crystals, i.e. ZnO–PZT–5H and PVDF–PZT–5H piezocomposites. It is seen from the results that the incident angle of elastic waves and the thickness of the piezoelectric ceramics have significant effects on the wave localization characteristics. For different piezoelectric phononic crystals, the effects of the incident angle are very different. Moreover, with the increase of the disorder degree, the localization phenomenon is strengthened.

Ultrasonic system for in-plane paper characterisation

. Some of these previous studies investigated plate wave’s propagation in paper, in an attempt to obtain correlations with mechanical properties using contactless methods due to the impossibility of using traditional contact techniques [1,2,7] . Other researchers have developed on-line systems that can measure certain properties in a moving web [3,8-10] . Ultrasonic analysis is a very interesting technique because it is fast, non-destructive and is very sensitive to the cellulose-fibre-based structure of the paper . In this paper a computer-controlled, fully-automated ultrasonicbased system composed of a measuring head and peripheral hardware was conceived. The system performs ultrasonic velocity measurements in the plane of the paper sheet which can be used to establish the tensile stiffness index (TSI). This parameter has an increased acceptance as a measure of paper strength properties [2] . Once TSI for the different orientations is known, the tensile stiffness orientation angle (TSO), defined by the orientation of the maximum of the TSI plot and the paper machine direction, can be evaluated. Another important factor in the paper industry is the use of mineral fillers that are applied for economic reasons, because fillers impart to paper specific properties. Bulk, air permeability, porosity, light scattering, stiffness, gloss and printability are some of the paper properties that are dependent on mineral fillers and on filler level [10] . Paper strength is reduced by filler incorporation, due to the reduction in bonded area of cellulose fibres. Mineral fillers have very different elastic properties from cellulose fibre, so the overall elastic property of the paper with fillers is different from a paper that has only cellulose fibres. Due to the good linear correlation between the mineral filler content in paper and ultrasonic velocities, the prediction of the elastic properties variation can be achieved. 2. Background The measurement of ultrasonic velocities is a powerful technique for non-destructive analysis of the mechanical properties of materials. Typically, the propagation velocity of a plane wave through a material is equal to the square root of the Young’s modulus divided by the mass density. So, the Young’s modulus can be obtained from velocity measurements. In our case we are interested in the analysis of planar materials. These are defined as plates that have lateral dimensions larger than the wavelength of in-plane bulk waves and whose thickness is small compared to the wavelength of out-ofplane bulk waves [11]

Strong Dependence of Spin Direction and Wave Function Localization on In-plane Wave Vector in Wide Modulation-doped Quantum Wells

An important mechanism in spintronics is spin-splitting induced by structure and/or bulk inversion asymmetry. These effects are frequently assumed to depend on two parameters usually denoted by α and β respectively, and α is assumed to be proportional to some average electric field. We here demonstrate that the spatial dependence of the electric field gives very important effects absent in simpler models. These effects are particularly clear in wide modulation-doped quantum wells where there are two weakly interacting electron gases in the interface regions. Using an 8 × 8 k . p matrix approach we obtain anticrossings between interacting subbands at which the spin direction and/or wave function localization are found to be strong functions of the in-plane wave vector.

Study on band gaps of elastic waves propagating in one-dimensional disordered phononic crystals

Band gaps of elastic waves, both in-plane and anti-plane waves, propagating along arbitrary direction in one-dimensional disordered phononic crystals are studied in this paper. The localization of wave propagation due to random disorder is discussed by introducing the concept of the localization factor. As a special case between ordered and disordered structures, we analyze the properties of the band gaps of phononic crystals with quasi-periodicity (i.e. phononic quasicrystals). Compared with the periodic structure, phononic quasicrystals involve more bands with localization of wave motion. The transmission coefficients are also calculated and the results show the same behaviors as the localization factor does. Therefore, the localization factor may act as an accurate and efficient parameter to characterize band structures of both ordered and disordered (including quasi-periodic) phononic crystals.

Efficient switching of Rashba spin splitting in wide modulation-doped quantum wells

The authors demonstrate that the size of the electric-field-induced Rashba spin splitting in an 80nm wide modulation-doped InGaSb quantum well can depend strongly on the spatial variation of the electric field. In a slightly asymmetric quantum well it can be an order of magnitude stronger than for the average uniform electric field. For even smaller asymmetry spin subbands can have wave functions and/or expectation values of the spin direction that are completely changed as the in-plane wave vector varies. The Dresselhaus effect [Phys. Rev. 100, 580 (1955)] can give an anticrossing at which the spin rapidly flips.

Optically nonlinear phonon–polariton modes in a three-layered structure

A theory is presented for the propagation of phonon–polariton modes arising when phonons are coupled to electromagnetic waves in multilayered structures. A multi-layered structure consists of a thin film surrounded symmetrically by a bounding media. Numerical calculations are given for s -polarized phonon–polariton modes in the case where the bounding media are assumed to be semi-infinite layers with nonlinear dielectric functions of ionic crystal type supporting optical phonon modes and the thin film is characterized by a Kerr-type nonlinear dielectric function. The phonon–polaritons were found to have distinct branches characteristic of optical phonons and showing features that are different from those of plasmon–polaritons [S. Baher, M.G. Cottam, Surf. Rev. Lett. 10 (2003) 13]. The parameters that modify the modes are the in-plane wave vector, the thickness of the film, the phonon frequency and the nonlinearity of each layer. It was found that by increasing the film thickness and nonlinearity coefficient, the curves move to the left and the number of the branches increases without changing the pattern of the curves.

Investigation of band structures for 2D non-diagonal anisotropic photonic crystals using a finite element method based eigenvalue algorithm

A finite element method based eigenvalue algorithm is developed for the analysis of band structures of two-dimensional non-diagonal anisotropic photonic crystals under the in-plane wave propagation. The characteristics of band structures for the square and triangular lattices consisting of anisotropic materials are examined in detail and the intrinsic effect of anisotropy on the construction of band structures is investigated. We discover some interesting relationships of band structures for certain directions of the wave vector in the first Brillouin zone and present a theoretical explanation for this phenomenon. The complete band structures can be conveniently constructed by means of this concept.

Localised bending modes in split ring resonators

We present band diagrams for in-plane elastic waves propagating within a doubly periodic structure involving split ring resonators (SRR). From the Navier equations we derive that the lowest resonant frequencies are associated with localised bending modes solutions of a fourth-order differential equation in thin-bridges, which are responsible for the appearance of a low frequency stop band. Potential applications lie in the design of earthquake resistant systems.

Measuring in-plane mechanical properties of plate-like samples using phonographic pickups

An affordable acoustic method to estimate mechanical film characteristics with in-plane shear and longitudinal waves was developed. A 23 kHz (24% FBW, −3 dB) signal was excited into thin plate-like samples with a piezoceramic pickup (Ronette ST105/Tonar) and received with an inductive pickup (Shure M92E). Signal-to-noise ratios of 12–27 dB were obtained corresponding to a two-way insertion loss of −105.5, −94.5 dB (shear, long). From the time-of-flight the phase velocity of the wave was estimated. This actuation–detection scheme can excite in-plane acoustic waves in the sample. An in-plane mode purity of −45 dB was recorded. Laser Doppler vibrometry showed that the waves were truly in-plane. The method showed good repeatability with a standard deviation of 2 m s−1 (0.17%) for shear and 5 m s−1 (0.22%) for longitudinal waves. Elastic and shear moduli as well as the Poisson ratio were determined for 174 ± 2 µm thick Mylar® and 184 ± 2 µm thick (795 ± 10 kg m−3) coated paper samples (24 ± 0.5 °C and 40 ± 5% RH). The estimated in-plane moduli for the Mylar® showed a 30% offset, but exhibited the same ratio, compared to the sample manufacturer values (ASTM D 882 test). The effect of heating the sample (140 ± 1 °C) was studied and changes in the dynamic mechanical moduli of the samples on the order of 3% were detected.

Ferromagnetic resonance force microscopy studies of arrays of micron size permalloy dots

The dynamic magnetic properties of micron-sized permalloy disks have been investigated using magnetic resonance force microscopy. From local spectroscopy data, information about the global sample properties is obtained. The experimental results are in good agreement with theoretical predictions, which account for magnetostatic modes with quantized in-plane wave vector. Ferromagnetic resonance spectral features due to the permalloy dots in close proximity to the micromagnetic probe tip provide two-dimensional images of the sample.

Conformal coverage for two-dimensional arrays of microcavites with quasi-three dimensional confinement by distributed Bragg reflectors

Different from conventional three-dimensional confined microcavity fabrication method in which micropillar microcavities were obtained through the etching of planar semicoductor microcavities, we adopted the conformal coverage to fabricate two-dimensional arrays of quasi three-dimensional confined optical microcavities providing both vertical and lateral optical confinement by the distributed Bragg reflectors (DBRs). Our microcavity samples were directly deposited on the patterned substrates with two-dimensional arrays of air holes. The SEM and cross-section TEM images show that the periodicity of the patterned substrate was still kept after deposition while the growth of DBRs along the sidewalls occurred simultaneously, which provided the transverse optical confinement. In order to probe the optical modes of this kind of microcavities, room temperature photoluminescence signals from prepared microcavities were detected. Three resonant modes were presented and exhibited obvious angular dependence. We attributed these phenomena to quantization of the in-plane wave vector components confined by lateral DBRs.

Propagation of in-plane elastic waves in a composite panel

The paper presents certain results of the analysis of in-plane elastic wave propagation in a composite panel. This problem is solved by the use of the Spectral Element Method. In the current approach the composite panel is modelled by a 36-node spectral membrane finite elements with nodes defined at Gauss–Lobatto–Legendre points. As approximation polynomials the fifth order orthogonal Lagrange polynomials have been used. In order to calculate the element characteristic stiffness and mass matrices the Gauss–Lobatto quadrature has been applied. Numerical calculations are carried out for various orientations of reinforcing fibres within the panel as well as for various volume fractions of the fibres. It is shown that propagation of in-plane elastic waves in composite materials is a more complex phenomenon than in the case of isotropic materials. The velocities of the elastic waves and also the direction of propagation are functions of the fibre orientation and the relative volume fraction of the fibres.

Brillouin light scattering studies of the mechanical properties of ultrathin low-k dielectric films

In an effort to reduce RC time delays that accompany decreasing feature sizes, low-k dielectric films are rapidly emerging as potential replacements for silicon dioxide (SiO2) at the interconnect level in integrated circuits. The main challenge in low-k materials is their substantially weaker mechanical properties that accompany the increasing pore volume content needed to reduce k. We show that Brillouin light scattering is an excellent nondestructive technique to monitor and characterize the mechanical properties of these porous films at thicknesses well below 200nm that are pertinent to present applications. Observation of longitudinal and transverse standing wave acoustic resonances and the dispersion that accompany their transformation into traveling waves with finite in-plane wave vectors provides for a direct measure of the principal elastic constants that completely characterize the mechanical properties of these ultrathin films. The mode amplitudes of the standing waves, their variation within the film, and the calculated Brillouin intensities account for most aspects of the spectra. We further show that the values obtained by this method agree well with other experimental techniques such as nanoindentation and picosecond laser ultrasonics.

Dresselhaus spin-orbit coupling effect on dwell time of electrons tunneling through double-barrier structures

We investigated the effect of the Dresselhaus spin-orbit coupling on the dwell time of electrons tunneling through double-barrier structures with or without an external electric field. The results indicate that obvious resonant features exist in the time domain. In the presence of the Dresselhaus spin-orbit coupling, both the transmission and the dwell time of the resonant peaks of the spin-up and spin-down electrons split. There is a great difference between the dwell time of the electrons with opposite spin orientations, which reaches the maxima at the resonant energies, and becomes greater under a larger in-plane wave vector. The results also indicate that structural asymmetry and external electric fields can greatly affect the dwell time of the electrons.

A surface optical phonon assisted transition in a semi-infinite superlattice with a cap layer

Using the transfer matrix method and Fermi's golden rule, we calculate the intersubband transition rates between surface electronic states due to different surface optical phonon modes (SOPMs) for a semi-infinite superlattice (SL) with a cap layer in the dielectric continuum approximation. The influence of various structural configurations on surface electron–phonon scattering is given in detail. The calculated results show that the surface electron–phonon scattering rates are markedly influenced by the magnitude of the in-plane electronic wave vector k‖ and have a complicated dependence on the constituent layers of the SL, the substrate as well as the cap layer. It is found that the magnitude of in-gap electron transition rates essentially depends on the attenuation length of the localized electronic states and SOPMs.

Propagation of in-plane waves in an isotropic panel with a crack

The paper presents certain results of the analysis of wave propagation in an isotropic panel with damage in the form of a fatigue crack. This problem is solved by the use of the spectral element method. In the current approach the panel is modelled by a number of 36-node spectral membrane finite elements with nodes defined at appropriate Gauss–Lobatto–Legendre points. As approximation polynomials the 5th order orthogonal Lagrange polynomials have been used. In order to calculate the element characteristic stiffness and mass matrices the Gauss–Lobatto quadrature has been applied. The crack can be of an arbitrary length, depth, and location. The elastic behaviour of the panel at the crack location is simulated as a line spring with a varying stiffness along the crack length. Numerical calculations are carried out for various locations of the crack in the panel as well as for the panel with stiffeners. The problem of the identification of the crack from the transmitted and reflected waves is also considered in the paper.

Rashba spin splitting in biased semiconductor quantum wells

Rashba spin splitting (RSS) in biased semiconductor quantum wells is investigated theoretically based on the eight-band envelope function model. We find that at large wave vectors, RSS is both nonmonotonic and anisotropic as a function of in-plane wave vector, in contrast to the widely used linear and isotropic model. We derive an analytical expression for RSS, which can correctly reproduce such nonmonotonic behavior at large wave vectors. We also investigate numerically the dependence of RSS on the various band parameters and find that RSS increases with decreasing band gap and subband index, increasing valence band offset, external electric field, and well width. Our analytical expression for RSS provides a satisfactory explanation to all these features.