Ferrimagnetic resonance spectra of magnetic bubble films at low microwave frequencies

Magnetic bubble films exhibit a number of ferrimagnetic resonance modes due to the spatial variation of the anisotropy. The resonance frequencies have been measured as a function of the applied bias fieldH ₀. In the lower field range the magnetization of the transient layer, which has negative anisotropy, is not yet parallel toH ₀. In this range the resonance frequencies are shifted to higher values due to pinning effects. In films grown by the vertical dipping method an additional layer on top of the transient layer is observed within which the magnetization rotates from the direction in the transient layer to that of the bulk of the film. In films grown by horizontal dipping no such layer could be detected. Each ferrimagnetic resonance mode excites transverse elastic waves in the film due to the magnetoelastic interaction and thus gives rise to elastic resonances of the whole crystal, film and substrate. These elastic resonances lead to a fine-structure of the ferrimagnetic resonances. The observed fine-structure vanishes periodically with frequency and from this behaviour the thickness of the magnetic film and of the transient layer has been determined.     

Self-diffusion at grain boundaries with a disordered atomic structure

A change in the free energy of a grain boundary is analyzed in the case when lattice vacancies come to the boundary and are then delocalized in its disordered atomic structure. It is shown that the free energy of the boundary is minimized at some excess atomic volume Δv _b =Δv _b ^* , whose value depends on the energy of vacancy formation in the crystal lattice and the boundary energy. The formation of a metastable localized grain-boundary vacancy as a result of thermal fluctuations of the density in a group of n ₀=\gM_v/Δv _b atoms (\gM_v is the vacancy volume), followed by the jump of an adjacent atom into this vacancy, is taken as an elementary event of grain-boundary diffusion. Expressions for the activation energy of diffusion and the diffusion coefficient are derived for equilibrium (Δv _b =Δv _b ^* ) and nonequilibrium (Δv _b >Δv _b ^* ) boundaries.     

Parametric interaction of space-charge waves in asymmetric thin-film <Emphasis Type="Italic">n</Emphasis>-GaAs structures

Based on a theory developed previously, parametric interaction between space-charge waves in thin-film semiconductor structures with negative differential conductivity is analyzed. The analysis is carried out in the approximation that the drift flux of charge carriers has a rigid boundary and under the assumption that the frequency of low-frequency pumping equals the cutoff frequency f _c of waves being amplified (f _c roughly equals 30 GHz in our case). For asymmetric structures, a general multimode set of coupled equations is reduced to a pair of differential equations for the excitation amplitudes of the fundamental space-charge mode at the signal frequency ω_s and idler frequency ω_i=ω_s−ω_p. The equations are solved numerically for n-GaAs-based structures, and the solution obtained is discussed.     

Nonadiabatic effects in the phonon spectra of superconductors

The nonadiabatic corrections to the self-energy part Σ_s(q, ω) of the phonon Green’s function are studied for various values of the phonon vectors q resulting from electron-phonon interactions. It is shown that the long-range electron-electron Coulomb interaction has no direct influence on these effects, aside from a possible renormalization of the corresponding constants. The electronic response functions and Σ_s(q, ω) are calculated for arbitrary vectors qand energy ω in the BCS approximation. The results obtained for q=0 agree with previously obtained results. It is shown that for large wave numbers q, vertex corrections are negligible and Σ_s(q, ω) possesses a logarithmic singularity at ω=2Δ, where Δ is the superconducting gap. It is also shown that in systems with nesting, Σ_s(Q, ω) (where Q is the nesting vector) possesses a square-root singularity at ω=2Δ, i.e., exactly of the same type as at q=0. The results are used to explain the recently published experimental data on phonon anomalies, observed in nickel borocarbides in the superconducting state, at large q. It is shown, specifically, that in these systems nesting must be taken into account in order to account for the emergence of a narrow additional line in the phonon spectral function S(q, ω)≈−π ⁻¹ Im D _s (q, ω), where D _s (q, ω) is the phonon Green’s function, at temperatures T<T _c . Zh. éksp. Teor. Fiz. 115, 1799–1817 (May 1999)     

Thermal expansion anomalies in TbVO4 due to the cooperative Jahn-Teller effect

The thermal expansion anomalies in TbVO₄ due to the cooperative Jahn-Teller effect were studied experimentally and theoretically. Characteristic magnetoelastic anomalies were observed in the curves of Δa/a and Δc/c of the cell parameters at T<T _c. Calculations of the magnetoelastic contribution to Δa/a and Δc/c from fully symmetric and and low-symmetry ɛ^δ modes were performed using the general crystal-field formalism, and the values of the magnetoelastic coefficient B ^δ were obtained from spectroscopic and spontaneous-deformation data. It is shown that the thermal expansion of TbVO₄ in both the tetragonal and orthorhombic phases can be described well on the basis of a general model based on a single set of interaction parameters. Fiz. Tverd. Tela (St. Petersburg) 40, 1663–1666 (September 1998)     

An oscillator using high order Lamb wave modes

An oscillator using high order Lamb wave modes is presented. Due to the multimode property of Lamb waves, high frequency oscillators using high order mode Lamb waves can be fabricated. To select the operating mode of the Lamb wave oscillator, a high order mode selector is inserted into the feedback loop. An oscillator using the 13th antisymmetric mode (a₁₃) in Lamb wave is achieved in experiments and the oscillating frequency is 5.30 times higher than that of the a₀ mode excited by the interdigital transducer.     

Time reversal technique for health monitoring of metallic structure using Lamb waves

Time reversal active sensing using Lamb waves is investigated for health monitoring of a metallic structure. Experiments were conducted on an aluminum plate to study the time reversal behavior of A₀ and S₀ Lamb wave modes under narrow band and broad band pulse excitation. Damage in the form of a notch was introduced in the plate to study the changes in the characteristics of the time reversed Lamb wave modes experimentally. Time–frequency analysis of the time reversed signal was carried out to extract the damage information. A measure of damage based on wavelet transform was derived to quantify the hidden damage information in the time reversed signal. It has been shown that time reversal can be used to achieve temporal recompression of Lamb waves under broadband signal excitation. Further, the broad band excitation can also improve the resolution of the technique in detecting closely located defects. This is demonstrated by picking up the reflection of waves from the edge of the plate, from a defect close to the edge of the plate and from defects located near to each other. This study shows the effectiveness of Lamb wave time reversal for temporal recompression of dispersive Lamb waves for damage detection in health monitoring applications.     

Nonlinear interactions of acoustic modes in ferromagnets near magnetoacoustic resonance: Effective elastic constants

The magnetoelastic contribution ΔĈ ₍₃₎ to the effective third-order elastic constants Ĉ ₍₃₎ ^ef is determined; it describes the additional elastic anharmonicity induced by nonlinear spin-spin and spin-phonon interactions in ferromagnets. In the vicinity of magnetoacoustic resonance, this anharmonicity can be manifested in three-frequency elastic wave interactions, producing magnetoacoustic mode-frequency transformation effects. It is shown that these effects are magnified in resonance as the result of a huge increase (by several orders of magnitude) in the dynamic elastic constants ΔĈ ₍₃₎. Quantitative estimates are obtained for yttrium iron garnet. Fiz. Tverd. Tela (St. Petersburg) 40, 2080–2084 (November 1998)     

Magnetoelasticity,rotational invariance and magnetoacoustic birefringence in CeAl2

A thorough experimental investigation of elastic and magnetoelastic properties for CeAl₂ is given. The temperature dependence of the various elastic modes is accounted for with a magnetoelastic coupling of the strain components to crystal field split magnetic ions. Large magnetic field effects for thec ₄₄-mode in various geometries are observed. The rotational invariant magnetoelastic interaction is deduced from the experiment and quantitatively accounted for. Magnetoacoustic analoga of the Faraday and Cotton-Mouton-Voigt effect are observed for the first time in the paramagnetic phase.     

铌锌酸铅-钛酸铅薄层中Lamb波模式的交叉特性

以[001]_c和[011]_c极化的铌锌酸铅-钛酸铅晶体为研究对象, 利用子波理论对其无限大自由薄层中传播的Lamb波的色散及模式交叉特性进行了研究. 发现只有[001]_c极化的晶体中的对称与反对称模式Lamb波之间出现了多次交叉, 并且变化规律与铌镁酸铅-钛酸铅的情形相同. Lamb波的A₀和S₀模式的交叉是由准纵向剪切波慢度曲线的多值关系引起的, 此时其x₃方向的波数在一定范围内存在一对非纯虚数的复共轭根. 利用此结论推导出A₀和S₀模式交叉时弹性常数需要满足的条件, 为判断正交、四方对称性晶体中Lamb波的A₀和S₀模式是否交叉提供了一种直观、简便的方法.     

Dispersion of the sound velocity in iron borate under nuclear magnetoacoustic resonance

The frequency dependence of the velocity of coupled magnetoelastic waves in the weak ferromagnet FeBO₃ is investigated experimentally and theoretically. An anomalous frequency dependence of the transverse sound velocity is observed for a single-domain sample under conditions of nuclear magnetoacoustic resonance, when the frequency of sound excited in the sample is close to the NMR frequency of Fe⁵⁷ nuclei. It is shown that the observed dependence is associated with a considerable effect of nonequilibrium states of the nuclear spin system on the renormalization of elastic constants due to effective magnetoelastic coupling.     

Temperature anomalies in the nonlinear magnetoacoustic properties of manganese-zinc spinel single crystals

The absorption of a magnetoelastic wave and the nonlinear resonance interaction of counterpropagating magnetoelastic waves in a manganese-zinc spinel single crystal have been investigated near the conjectured spin-reorientational transition. The convolution signal vanishes near T _tr=291 K; this is explained by the relaxational dynamics of the magnetic mode near the transition. The increase in the strength of the field corresponding to the maximum of the convolution with decreasing temperature is explained by a change in the demagnetizing field. Fiz. Tverd. Tela (St. Petersburg) 39, 652–655 (April 1997)     

Matter-wave propagation in optical lattices

Coherent propagation of atomic-matter waves in a one-dimensional optical lattice is studied. Wave packets of cold two-level atoms propagate simultaneously in two optical potentials in a dressed-state basis. Three regimes of the wave-packet propagation are specified by the quantity Δ² /ω _D , where Δ and ω _D are the dimensionless atom–laser detuning and the Doppler shift, respectively. At Δ² /ω _D ≫ 1, the propagation is essentially adiabatic, at Δ² /ω _D ≪ 1, it is (almost) resonant, and at Δ² ≃ ω _D , the wave packets propagate nonadiabatically, splitting at each node of the standing wave. The latter means that the atom makes a transition from one potential to the other one when crossing each node, and the probability of that transition is given by a Landau–Zener-like formula. All the regimes of propagation are studied with δ-like and Gaussian wave packets in the momentum and position spaces. Varying the control parameters, we can create wave packets trapped in a well of optical potentials and moving ballistically in a given direction in close analogy with point-like atoms. Within some range of the parameters, we force the atom to move in a pure quamtum-mechanical manner in such a way that a part of the packet is trapped in a well, and the other part propagates ballistically. The propagation modes are found to be characterized by different types of time evolution of the uncertainty product and the Wigner function.     

Director dynamics near the nematic-smectic-A phase transition

The Landau-de Gennes model for the free energy of a nematic liquid crystal near the phase transition to the smectic A-phase is used to determine the frequency dependence of the fluctuation corrections to the Frank elastic constants. It is shown that the interaction of the fluctuations of the smectic order parameter and the director results in corrections to all the Frank elastic constants. In the low-frequency limit (ω→0), the corrections to the Frank elastic constants K ₂₂ and K ₃₃ are the largest, and decrease to zero in the infinite-frequency limit. The correction to K ₁₁ is negative, and vanishes in both limits. The absolute value of the correction to K ₁₁ is the largest at frequencies in the megahertz range. It is shown that in oriented nematics the interaction of the smectic fluctuations and the director limits deviations of the director from the direction of preferred orientation, as a result of which relaxation of both inhomogeneous and homogeneous distortions of the director field can be observed. It is also shown that this gives rise to a frequency interval in the megahertz range in which shear waves begin to propagate in the nematic. The propagation speed of these waves is roughly a hundred times smaller than that of sound and strongly depends on the direction of propagation. Zh. éksp. Teor. Fiz. 114, 2022–2033 (December 1998)     

Laser-induced circumferential waves on hollow cylinder and their interaction with defects by finite element method

A three dimensional (3-D) finite element model for simulating laser induced circumferential wave on a hollow cylinder is developed based on the thermoelastical mechanism, which can take any laser source into account and simulate the interactions between circumferential wave and defects in the hollow cylinder. The model is verified by a control calculation. The results show that the waveforms of circumferential wave are in very good agreement with those available in literature, not only on the arrival time and shape but also on the amplitudes of A ₀, S ₀ and A₁ modes. Using the model, circumferential waves on the surfaces of two series hollow cylinders are simulated, one with same thickness but different outer radius, and the other with the same outer radius but different thickness. The results show that a new mode appears in circumferential wave, compared with Lamb wave in plate. With increase of thickness or radius, the amplitude of the new mode reduces. Another conclusion is that with increase of the thickness of the hollow cylinder, the circumferential wave evolves gradually to the cylindrical Rayleigh waveform, which results from the attenuation of the coupling effect between the outer and inner surface. Moreover, the circumferential waves generated on a hollow cylinder with a surface defect are also simulated, and the results indicate that in the circumferential waves obtained at the point beyond the defect, the amplitude of A ₀ mode decreases and its dispersion enhances. More importantly, a new bipolar waveform corresponding to the interaction of S ₀ mode with the defect appears, its amplitude is larger than three times of that of S ₀ mode. As a result, we consider that the new bipolar waveform will be the optimal feature to nondestructively detect the surface defect on the hollow cylinder.     

Quadrupole interactions in MoCl5 intercalated in graphite

The time-differential perturbed angular correlation technique was used to investigate quadrupole interactions following the decay of⁹⁹Mo as a probe in the intercalation compound graphite-molybdenum pentachloride. Analysis of the 740-(44) 141 keV γ-γ correlation in⁹⁹Tc reveals the presence of two sites with static electric field gradient interactions, one of which corresponds to a moderately damped (δ∼16%), high-frequency interaction (v _q∼630 MHz), the other to a heavily damped (δ∼28%), low-frequency (v _q∼283 MHz) component.     

Prolonged acousto-optic interaction with Lamb waves in crystalline plates

The propagation and acousto-optic interaction of Lamb modes in an anisotropic plate of tellurium dioxide (TeO2) are studied numerically and analytically. In the case of a Y-cut X-propagating TeO2 plate, the very high elastic anisotropy of the crystal greatly modifies the dispersion curves, giving rise to their multiple oscillations. The existence ranges of backward Lamb modes increase with the mode order contrary to the case of isotropic plates. The quasi-collinear light scattering by Lamb waves is considered. Owing to the structure of Lamb wave field, a simultaneous light diffraction at two different optical frequencies can take place while Lamb waves are excited only at the single frequency. It is demonstrated with the Z-cut (110)-propagating plate that a small change in the acoustic frequency can result in a significant shift in the frequency of the scattered light.     

Lattice mechanical properties of noble and transition metals

A model pseudopotential depending on an effective core radius but otherwise parameter free is used to study the interatomic interactions, phonon dispersion curves (inq and r-space analysis), phonon density of states, mode Grüneisen parameters, dynamical elastic constants (C ₁₁,C ₁₂ andC ₄₄), bulk modulus (B), shear modulus (C′), deviation from Cauchy relation (C ₁₂–C ₄₄), Poisson’s ratio (σ), Young’s modulus (Y), behavior of phonon frequencies in the elastic limit independent of the direction (Y ₁), limiting value in the [110] direction (Y ₂), degree of elastic anisotropy (A), maximum frequencyω _max, mean frequency 〈ω〉, 〈ω ²〉^1/2=(〈ω〉/〈ω ⁻¹〉)^1/2, fundamental frequency 〈ω ²〉, and propagation velocities of the elastic constants in Cu, Ag, Au, Ni, Pd, and Pt. The contribution of s-like electrons is calculated in the second-order perturbation theory for the model potential while that of d-like electrons is taken into account by introducing repulsive short-range Born-Mayer like term. Very recently proposed screening function due to Sarkar et al. has been used to obtain the screened form factor. The theoretical results are compared with experimental findings wherever possible. A good agreement between theoretical investigations and experimental findings has proved the ability of our model potential for predicting a large number of physical properties of transition metals.     

Convexity of internal energy of cubic crystal deformed to orthorhombic structure

A generalized set of strain variablesq _r ^N , has been defined to develop the expression for a generalized set of second order and third-order elastic moduliC _rs ^N andC _rst ^N for a cubic crystal deformed to orthorhombic structure. The HessainC _rs ^N δq_rδq_s andC _rst ^N δq_rδq_sδq_t (r=1, 2……6; summation convention) are calculated in the new variables and compared withG-strength andS-strength, for both positive and negative loading environment. The convexity of the internal energy relative to various choice of strain measure is examined considering up to third degree terms in the internal energy expression. The computational results forbcc iron is presented according to the new moduli. The stable ranges thus obtained for iron under hydrostatic compressive and tensile stresses is found to generate the classical stable range, green-stable range and stretch-stable range as the specific cases. However,bcc iron does not seem to follow any conventional stable ranges under hydrostatic compression, where the present generalized stable range is found satisfactory.     

Effect of upflowing field-aligned electron beams on the electron cyclotron waves in the auroral magnetosphere

The role of low density upflowing field-aligned electron beams (FEBs) on the growth rate of the electron cyclotron waves at the frequencies ω _r < Ω_e, propagating downward in the direction of the Earth’s magnetic field, has been analysed in the auroral region at ω _e/Ω_e < 1 where ω _e is the plasma frequency and Ω_e is the gyrofrequency. The FEBs with low to high energy (E _b) but with low temperature (T _‖b) have no effect on these waves. The FEBs with E _b < 1 keV and T _‖b (> 1.5 keV) have been found to have significant effect on the growth rate. Analysis has revealed that it is mainly the T _‖b which inhibits the growth rate (magnitude) and the range of frequency (bandwidth) of the instability mainly in the higher frequency spectrum. The inhibition in the growth rate and bandwidth increases with increase in T _‖b. The FEBs with less E _b (giving drift velocity) reduce growth rate more than the beams with larger E _b. The inhibition of growth rate increases with the increase in the ratio ω _e/Ω_e indicating that the beams are more effective at higher altitudes.