Interaction of a shear wave with a moving domain wall in a ferromagnetic crystal with allowance for the external magnetic field

The boundary-value problem of the magnetoelastic wave interaction with a moving domain wall in a ferromagnetic crystal is solved in the nonexchange magnetostatic approximation with allowance for the external magnetic field. It is shown that the difference introduced by magnetic field between the ferromagnetic resonance frequencies of the domains does not cause any noticeably departure of the refraction characteristics of reflected and transmitted waves from those observed at zero frequency mismatch. By contrast, the magnitudes of the transmission and reflection coefficients strongly depend on the external magnetic field and on the mobility of the domain wall. The dependence of the magnitude of the reflection coefficient on the external magnetic field at a fixed angle of shear wave incidence is found to possess two ferromagnetic resonance peaks. The positions and heights of the peaks may vary depending on the mobility of the domain wall.     

On the interaction of a shear wave with a moving domain wall in a nonlinear response of the spin subsystem

A solution of the problem of parametric interaction between a plane monochromatic shear wave and a uniformly moving 180°-domain wall of a garnet-ferrite crystal is obtained in the exchangeless magnetostatic approximation by using the perturbation method under the conditions of a nonlinear response of the spin subsystem. It is shown that in a ferromagnetic resonance with magnetostatic oscillation of stray fields, the nonlinearity of the spin subsystem leads to the excitation of shear waves of triple frequency, which may have amplitudes comparable with that of the incident wave for oscillations doubly localized by a domain wall.     

Shear magnetoelastic modes in a ferromagnetic cylinder

Features of the mode spectrum of shear magnetoelastic waves circulating along the boundary of a ferromagnetic cylinder are discussed in the nonexchange magnetostatic approximation. Depending on the level of the spin-phonon coupling in the crystal and on the frequency, the lowest order normal mode may be either fast or slow relative to the bulk shear wave in an infinite crystal. It is shown that, unlike the lowest order mode, the higher order modes, which primarily depend on the curvature of the boundary, demonstrate a weak nonreciprocity of propagation in directions with opposite azimuths. Conditions for the slow propagation of the lowest order mode, when it is identified with a surface magnetoelastic wave, are only possible sufficiently far away from the cutoff frequency of the mode spectrum in ferromagnetic cylinders with a strong spin-phonon coupling and a small curvature of the boundary.     

A trapped wave in a ferroelectric with a moving strip domain

The existence of a shear homogeneous plane wave trapped by a strip domain moving uniformly in a tetragonal ferroelectric crystal is demonstrated. Using the nonrelativistic quasistatic approximation and a change to the moving frame of reference, the solution is obtained and the dispersion relation is derived for the spatial spectrum of the trapped wave. The uniqueness of the solution is established in the case of the multiple degeneracy of the roots of the characteristic equation when the trapped wave contains an attached wave in the strip domain. The trapped wave is shown to correspond to the antisymmetric mode of the electroacoustic wave of the strip domain at the initial point of the spectrum branch. The specific features of the spatial resonance of the trapped wave with a shear wave obliquely incident on the strip domain are considered.     

Interaction of a shear wave with a moving domain wall in an iron garnet crystal

The boundary-value problem of the interaction of a plane monochromatic shear wave with a moving Bloch wall in an iron garnet crystal is solved in the framework of the nonexchange magnetostatic approximation on the basis of the method of phase invariants for wave problems with moving boundaries. For a shear wave incident on the domain wall, the possibility of the reflectionless birefringence is demonstrated. Numerical results illustrating the resonance properties of the magnetic subsystem are presented. It is established that, at the upper bound of the reflectionless birefringence range, the interaction of the shear wave with the domain wall manifests itself as a degenerate resonance with the solution in the form of two combined antiphase, collinearly propagating shear waves of infinitely large amplitudes, which form a zero resulting field.     

Reflection of spin and spin-elastic waves at the interface of a ferromagnetic half-space

This paper considers the reflection of pure spin and spin-elastic (or magneto-elastic) waves at the interface of a ferromagnetic half-space and a vacuum. For pure spin waves two cases are considered, with exchange effects, and without. It is shown that when exchange effects are taken into account, volume spin waves in the ferromagnetic half space incident at the boundary with the vacuum generate a reflected volume spin wave, and an accompanying compound surface wave propagating along the boundary and consisting of two partial inhomogeneous spin waves in the ferromagnetic half-space and a partial magneto-static inhomogeneous surface wave in the vacuum. When exchange effects are neglected the incident wave generates only a reflected volume wave in the ferromagnetic half-space.

Reflection and transmission of spin-elastic (or magneto-elastic) waves has been considered only in the case of the absence of exchange effects. An incident volume wave generates a volume spin-elastic reflected wave and one inhomogeneous magneto-static accompanying surface wave.

Excitations of the magnetic field are not transmitted into the vacuum in both cases when the exchange effect is neglected. In all cases the reflection of a spin wave has the character of a full internal reflection.     

Mode spectrum of noncollinear electroacoustic boundary-guided waves in a ferroelectric with a moving strip domain

The mode spectrum of electroacoustic boundary waves guided by a strip domain uniformly moving in a 4-mm ferroelectric is considered in the quasi-static approximation. The motion of the strip domain is found to cause the wave vector of the electroacoustic wave to be noncollinear with the guiding boundaries. The frequency dependences of the phase velocity are presented for the symmetric and antisymmetric modes of the electroacoustic wave. These dependences are compared in the reference system fixed to the strip domain and in the laboratory reference system. It is shown that, at low and moderate frequencies, the symmetric mode of the electroacoustic wave is more efficiently localized by a moving strip domain than by a single domain wall.     

Linear mechanism of surface gravity wave generation in horizontally sheared flow

An analysis is presented of a linear mechanism of surface gravity wave generation in a horizontally sheared flow in a fluid layer with free boundary. A free-surface flow of this type is found to be algebraically unstable. The development of instability leads to the formation of surface gravity waves whose amplitude grows with time according to a power law. Flow stability is analyzed by using a nonmodal approach in which the behavior of a spatial Fourier harmonic of a disturbance is considered in a semi-Lagrangian frame of reference moving with the flow. Shear-flow disturbances are divided into two classes (wave and vortex disturbances) depending on the value of potential vorticity. It is shown that vortex disturbances decay with time while the energy of wave disturbances increases indefinitely. Transformation of vortex disturbances into wave ones under strong shear is described.     

Features of a shear elastic wave propagating in an acoustic superlattice of the magnet-ideal diamagnet type: The reflectance

The influence of the inhomogeneous exchange interaction on the conditions of a shear elastic wave reflection from the surface of a bounded magnetic superlattice consisting of ferromagnetic and superconducting layers is studied.     

Spectral properties of electroacoustic waves in a ferroelectric with a moving periodic domain structure

The propagation of shear waves in a tetragonal ferroelectric with a moving superlattice of 180° domain walls (DW) is considered in a quasistatic approximation. It is found that the spectrum of shear waves consists of alternating allowed and forbidden bands in both cases of static and moving superlattices. It is shown that, due to the Doppler shift in the wave eigenfrequencies, the motion of the DW superlattice causes the degenerate roots of the dispersion equation to split and the splitting increases with the vibration mode number. The acoustic nonreciprocity induced by the moving DW superlattice in the ferroelectric is discussed.     

Application of surface and normal ultrasonic waves for measuring the parameters of technical fluids: II. Density measurements

The effect of a fluid on the surface waves moving in a waveguide along its boundary with the fluid is considered. The effect of the shear and volume viscosities of the fluid on the damping coefficient of such a surface wave is estimated. It is shown that the effect of fluids may be neglected at a measurement accuracy of about 10^?3 if their shear viscosities are lower than 0.1 Pa s. At a higher viscosity, corrections that take into account the contribution of viscous losses to the measured damping coefficient of a surface wave should be introduced. A technique for calibrating a density sensor for low-viscosity fluids is described, and the densities of NaCl and saccharose solutions in distilled water are measured. The experimental results agree qualitatively with the theoretical estimates. It is noted that this method of measuring the longitudinal impedance of a fluid can use the same apparatus design in both the principle (pulsed) and the frequency range (1?C10 MHz) for measuring the density, both viscosities, the velocity, and the sound absorption coefficient of a fluid. This design almost coincides with the apparatus used in the means of nondestructive quality control of materials and articles.     

Computational simulation of wave propagation problems in infinite domains

This paper deals with the computational simulation of both scalar wave and vector wave propagation problems in infinite domains. Due to its advantages in simulating complicated geometry and complex material properties, the finite element method is used to simulate the near field of a wave propagation problem involving an infinite domain. To avoid wave reflection and refraction at the common boundary between the near field and the far field of an infinite domain, we have to use some special treatments to this boundary. For a wave radiation problem, a wave absorbing boundary can be applied to the common boundary between the near field and the far field of an infinite domain, while for a wave scattering problem, the dynamic infinite element can be used to propagate the incident wave from the near field to the far field of the infinite domain. For the sake of illustrating how these two different approaches are used to simulate the effect of the far field, a mathematical expression for a wave absorbing boundary of high-order accuracy is derived from a two-dimensional scalar wave radiation problem in an infinite domain, while the detailed mathematical formulation of the dynamic infinite element is derived from a two-dimensional vector wave scattering problem in an infinite domain. Finally, the coupled method of finite elements and dynamic infinite elements is used to investigate the effects of topographical conditions on the free field motion along the surface of a canyon.     

Two-dimensional shear wave speed and crawling wave speed recoveries from in vitro prostate data

The crawling wave experiment was developed to capture a shear wave induced moving interference pattern that is created by two harmonic vibration sources oscillating at different but almost the same frequencies. Using the vibration sonoelastography technique, the spectral variance image reveals a moving interference pattern. It has been shown that the speed of the moving interference pattern, i.e., the crawling wave speed, is proportional to the shear wave speed with a nonlinear factor. This factor can generate high-speed artifacts in the crawling wave speed images that do not actually correspond to increased stiffness. In this paper, an inverse algorithm is developed to reconstruct both the crawling wave speed and the shear wave speed using the phases of the crawling wave and the shear wave. The feature for the data is the application to in vitro prostate data, while the features for the algorithm include the following: (1) A directional filter is implemented to obtain a wave moving in only one direction; and (2) an L(1) minimization technique with physics inspired constraints is employed to calculate the phase of the crawling wave and to eliminate jump discontinuities from the phase of the shear wave. The algorithm is tested on in vitro prostate data measured at the Rochester Center for Biomedical Ultrasound and University of Rochester. Each aspect of the algorithm is shown to yield image improvement. The results demonstrate that the shear wave speed images can have less artifacts than the crawling wave images. Examples are presented where the shear wave speed recoveries have excellent agreement with histology results on the size, shape, and location of cancerous tissues in the glands.     

Nonlinear magnetoacoustic interactions in weak ferromagnets

The pinning and interaction of a single domain wall with normal magnetoelastic waves excited during its motion in a single-crystal yttrium orthoferrite plate, were discovered and investigated by a method based on the magneto-optical Faraday effect. The dependences of the bending wave amplitude and the spectra of shear waves, which can be excited by a moving domain wall, were calculated. The results obtained are interpreted with allowance for the interactions of excited oscillations in both the magnetic and elastic subsystems of the orthoferrite.     

Scattering of a Rayleigh surface acoustic wave by a small-size inhomogeneity in a solid half-space

We use the Born approximation of the perturbation method to solve the problem of scattering of a harmonic Rayleigh surface acoustic wave by a weak-contrast inhomogeneity that is small compared with the wavelength and is located in a solid half-space near its boundary. The material of the inhomogeneity differs from the material of the half-space only in its density. The Rayleigh wave incident on the inhomogeneity is excited by a monochromatic surface force source acting normally to the half-space boundary. We derive expressions for the displacement fields in the scattered spherical compressional and shear (SV- and SH-polarized) waves. Scattering of the Rayleigh wave into a Rayleigh wave is studied in detail. We find expressions for the vertical and horizontal components of the displacement vector in the scattered Rayleigh wave as well as its radiated power. It is shown that the field of the scattered surface wave is mainly formed by vertical oscillations of the inhomogeneity in the field of the incident wave. In this case, the radiated power for the scattered Rayleigh wave formed by vertical motion of the inhomogeneity in the incident-wave field depends on the depth of the inhomogeneity as the fourth power of the function describing the well-known depth dependence of the vertical displacements in the Rayleigh surface wave. Correspondingly, the dependence of the radiated power for the scattered Rayleigh wave formed by horizontal motion of the inhomogeneity depends on its location depth as the fourth power of the depth dependence of the horizontal displacements in the Rayleigh surface wave. We perform calculations of the ratio between the powers of the scattered and incident Rayleigh waves for different ratios between the velocities of the compressional and shear waves in a solid. It is shown that the radiated power for the scattered surface wave decreases sharply with increasing depth of the subsurface-inhomogeneity location. Thus, the scattering of a Rayleigh wave into a Rayleigh wave is fairly efficient only when the location depth of the inhomogeneity does not exceed about one-third of the wavelength of the shear wave in an elastic medium.     

Theory of ferromagnetic resonances in thin wires

A phenomenological theory of ferromagnetic resonances in a ferromagnetic metallic cylinder magnetized along its axis is based on the simultaneous solution of the equation of motion and Maxwell's equations. A general relaxation term in the equation of motion is used. The boundary conditions correspond to the dynamic surface anisotropy with the preferred direction parallel to the static magnetization. It is shown that the solution yields an infinite number of resonance modes of different spatial symmetry. Formulas for the surface impedance and the relative absorption of individual modes are derived. The effect of the finite radius of the cylinder on the resonance, antiresonance and spin wave resonance behaviour is discussed.     

移动边界问题的时空域正则区域迭代配点法

考虑热传导方程的移动边界问题,其定解区域随着时间而变化.构造一种时空域上的高精度数值算法求解1+1维移动边界问题.在时空域上假设一个初始移动边界位置,构成移动边界问题的不规则计算区域,选择一个适当的正则区域(矩形区域)完全覆盖所计算的不规则区域,在正则区域上利用移动边界约束条件和固定边界条件,采用时空域重心插值配点法求...     

Thickness-shear modes and magnetoelastic waves in a longitudinally magnetized ferromagnetic plate

Magnetoelastic (ME) waves and thickness-shear modes in the ferromagnetic plate are studied. Coupled vibrations of magnetization and shear elastic deformations excited simultaneously by a variable magnetic field propagate in two mutually perpendicular directions: parallel and normal to a surface. For parameters characteristic of isotropic ferromagnet with the sample magnetization and Zeeman field parallel to the surface, resonant frequencies of shear modes are computed and their dispersion law is examined. It is shown that the dependence of dimensional resonances frequencies on wave number k_z of ME wave propagating along saturating field direction occurs. The possibility of excitation of ME waves with different k_z explains multimode character of thickness ME resonances.     

Spin orientation and excitation of magnetic nanocluster on metal surface

The spin orientation and excitation of the ferromagnetic nanocluster on the magnetic metal surface are studied numerically. We show that localized magnetic excitation modes are generated by the spin fluctuation of the cluster, when the ferromagnetic interaction J′ between the cluster and the metal surface is small and the spins in the cluster are oriented in the opposite direction with those of the metal surface by the external field. This magnetic structure is similar to the domain wall (DW) structure of a ferromagnetic wire, both sides of which connect with metal surfaces. As the interaction J′ increases, the sign of the thermal average of the spins in the cluster changes, i.e., the spin-flip takes place. In this time, the magnetic fluctuation of the cluster becomes large and the magnetic excitation energies, except for that of one excitation mode, overlap with the excitation spectrum of the spin wave. We also show that, by the overlap, sharp peaks and dips occur in the excitation spectrum of the spin wave.     

Spin-polarized electron energy loss spectroscopy of high energy, large wave vector spin waves in ultrathin fcc Co films on Cu(001)

The realm of high energy, large wave vector spin waves in ultrathin films and at surfaces is unexplored because a suitable method was not available up to now. We present experimental data for an 8 ML thick Co film deposited on Cu(001) which show that spin-polarized electron energy loss spectroscopy can be used to measure spin-wave dispersion curves of ultrathin ferromagnetic films up to the surface Brillouin zone boundary.