Attenuation Of Longitudinal Sound Waves Research Articles

Some Anomalies in Magnetoacoustic Attenuation in Pyrolytic Graphite

We have measured the temperature and frequency dependences of the giant quantum attenuation of longitudinal sound waves in pyrolytic graphite, in particular in the situation of simultaneous absorption due to electrons and holes. The sound wave vector q was applied in parallel to the c -axis, and the magnetic field vector H was in a plane containing the c -axis. We have found that the slopes of the plots of the attenuation coefficient α( T , f , H p ) versus temperature T and α( T , f , H p ) versus frequency f at the peak field H p ∼19 kG are anomalously large at θ<10^°. The magnitude of α( T , f , H p ) is also very large. Here θ is the angle between q and H . On the basis of Kuramoto's theory, these data are analyzed in terms of the correlation effect on α( T , f , H ). The result suggests that some modifications of the theory are required to explain all aspects of the present anomalies.

Anomalous frequency dependence of giant quantum attenuation in Bismuth below 1 K

Giant quantum attenuation of longitudinal sound waves in Bi has been measured at temperatures down to 8 mK for the case that the electron ( n = 0, s = + 1) and hole ( n = 1, s = − 1) Landau levels cross simultaneously Fermi level at a field of about 90 kOe. The temperature and frequency dependences of the peak attenuation due to these two levels are expressed by α p ∝ T -μω ν with μ ⋍ 1 and ν ⋍ 1 at T > 1 K. When T ≲ 1 K the value of μ decreases by decreasing temperature and below 0.1 K, α p takes almost constant value. At T ≲ 0.5 K, ν becomes larger than 1 and maximum value of ν observed is 2 at T ∼ 0.05 K. These features of the attenuation peak at very low temperatures are consistent with what are expected in the fluctuation region of the gas-liquid type transition of the electron-hole system.

Acoustic behaviour of amorphous selenium

The attenuation of longitudinal sound waves in amorphous selenium has been measured at frequencies of 15 and 25 MHz and in the range of temperature between 10 and 310 K. It is shown that absorption exhibits a minimum around Tτ150 K, while a pronounced maximum takes place around 30 K. Such a behaviour is briefly discussed in the frame of acoustic properties of amorphous material below the glass temperature. It is shown that the experimental results can be described, almost qualitatively, in terms of a recently proposed theoretical model involving a stochastic resonance that seems to be characteristic of the disordered systems.

Spin Splitting Factor and Deformation Potential Tensor Components of Holes in Antimony

From the measurements of the giant quantum attenuation of longitudinal sound waves, the anisotropy of the spin splitting factor γ (the ratio of the spin splitting to the Landau splitting) for the holes in principal ellipsoid in antimony has been determined for two cases, H // a binary-trigonal plane and H // a bisectrix-trigonal plane. The values of γ obtained for H along the binary ( x -), bisectrix ( y -) and trigonal ( z -) axes are as follows: γ x h =0.43, γ y h =0.80, and γ z h =0.74. The deformation potential tensor components D h i i h for the principal hole-ellipsoid have also been determined from an analysis of line shapes of the attenuation curves. The results obtained are as follows: | D x x h |=4.7 eV, | D y y h | ∼1.6 eV, | D z z h |=0.62 eV, and D y y h / D x x h ∼-0.34.

Effects of Magnetic Field Dependence of Deformation Potentials upon Line Shapes of the Giant Quantum Attenuation of Sound Waves in Bismuth

The magnetic field dependence of line shapes of the giant quantum attenuation of longitudinal sound waves in bismuth has been investigated in rather weak magnetic fields but in a low Landau quantum number region. It is shown that when the energy interval between an electron Landau level and a hole level located in the neighborhood of the Fermi level decreases, the attenuation peak on the lower field side of the twin peaks is greatly enhanced in height and sharpened in width, but the temperature dependence of the attenuation coefficient of the lower field peak is almost normal. This apparently anomalous angular dependence of the line shape can be well explained by taking account of peculiar field dependence of the deformation potentials which was overlooked in existing theories of the giant quantum attenuation of sound waves in semimetals.

Nonlinear ultrasonic attenuation in glasses

Measurements of the attenuation of longitudinal sound waves of frequencies between 730 MHz and 1400 MHz were made on a borosilicate glass at temperatures from 0.4 K to 2 K. For high acoustic intensity J the absorption decreases with decreasing temperature. At low temperatures the attenuation is strongly dependent on the acoustic input power and was found to be proportional to J − 1 2 indicating a saturation of the absorption. For low acoustic intensities ( J ⪅ 2 × 10 −7 W/cm 2) an increase of the attenuation with decreasing temperature below T < 0.6 K was observed. The experimental results are compared with recent data in vitreous silica and can qualitatively be described by current theories based on a tunneling model.

Anomalous ultrasonic attenuation in vitreous silica at low temperatures

The attenuation of longitudinal sound waves of 750 and 970 MHz has been determined in vitreous silica down to 0.4 K. The unsaturated attenuation observed at the smallest incident acoustic intensities allows a quantitative comparison with the “tunneling model” for glasses.

Further Study of the Occurrence of the Excitonic Phase Transition in Bismuth under Strong Magnetic Fields by Ultrasonic Attenuation

A previous measurement of the anomalous temperature dependence of the giant quantum attenuation of longitudinal sound waves in bismuth under strong magnetic fields was extended down to 1.06 K, and further evidence for the occurrence of the excitonic phase transition was obtained. The plot of sound attenuation versus temperature in the anomalous case showed a roundish convex curve near a maximum located at a point a little below T c , a temperature parameter to be identified with the phase transition point. This temperature dependence of the attenuation is well explained in terms of the critical fluctuation and a modified form of Maki-Nakanishi's formula of the attenuation of the excitonic state in the absence of field. The transition temperature, the critical exponent and other parameters to specify the anomalous attenuation curve near T c are evaluated for several cases of a parameter related to the energy difference between the hole and electron Landau levels in the normal state.

Ultrasonic attenuation due to polarization domain relaxation processes in the transverse spin density wave phase of antiferromagnetic chromium

Measurements of the field dependence of the ultrasonic attenuation of longitudinal sound waves in the frequency range 10 MHz to 300 MHz propagating in the transverse spin density wave phase of a single Q single crystal of chromium interpreted in terms of a relaxation model for thermally activated polarization domains and provide an independent indication that their volume in this sample is of the order of 10-15 to 10-16 cm3.

Electron-phonon interaction in aluminum from ultrasonic attenuation measurements

The attenuation of longitudinal soundwaves in normal and superconducting aluminum has been measured, yielding the electronic contribution to the normal state attenuation. The electron-phonon interaction constant is found to be in good agreement with the calculated constant based on Pippard's theory. The experiments support our assumption of an isotropic deformation parameterKx, using Segall's and Ashcroft's modifications of the Harrison model of the Fermi surface.

Giant Quantum Attenuation of Sound Waves in Antimony. I. Deformation Potential Constants and Spin Splitting Factors of Electrons

The giant quantum attenuation of longitudinal sound waves in antimony was investigated in pulsed magnetic fields up to 170 kG, at temperatures of about 1.6 K and at sound wave frequencies of 60 and 100 Mc/s. The values of the deformation potential tensor components for the electrons in the principal pocket obtained from an amplitude analysis are as follows: | D x x (e) |=6.1 eV, | D y y (e) |=7.9 eV, | D z z (e) |=0.44 eV, and D x x (e) / D y y (e) =-0.77, where x -, y - and z -axis refer to a binary, a bisectrix and the trigonal axis respectively. A determination of the anisotropy of spin splitting factors (spin splitting/Landau splitting) of the electrons is made for two cases of H ∥ x y -plane and H ∥ y z -plane.

Magnetic Phase Diagram of MnF2from Ultrasonic and Differential Magnetization Measurements

The magnetic phase diagram of Mn${\mathrm{F}}_{2}$, in the $H\ensuremath{-}T$ plane, is determined in magnetic fields up to 200 kG directed along the [001] and [100] directions. The magnetic phase transitions appear as anomalies in the ultrasonic attenuation and/or the differential magnetization. Near the various second-order phase transitions, the attenuation of longitudinal sound waves exhibits $\ensuremath{\lambda}$ anomalies, whereas near the spin-flop transition (which is a first-order transition) the ultrasonic attenuation exhibits a sharp spike and/or an abrupt increase, depending on the mode of propagation. The spin-flop transition is accompanied by a spike in the differential magnetic moment. The N\'eel temperature is ${T}_{N}=(67.33\ifmmode\pm\else\textpm\fi{}0.03)\ifmmode^\circ\else\textdegree\fi{}$K, and the triple point for H\ensuremath{\parallel}[001] is at ${T}_{3}=(64.9\ifmmode\pm\else\textpm\fi{}0.1)\ifmmode^\circ\else\textdegree\fi{}$K and ${H}_{3}=119\ifmmode\pm\else\textpm\fi{}2$ kG. The field at the spin-flop transition (for H\ensuremath{\parallel}[001]) increases monotonically with temperature from 92\ifmmode\pm\else\textpm\fi{}1.5 kG at 4.2\ifmmode^\circ\else\textdegree\fi{}K to 119\ifmmode\pm\else\textpm\fi{}2 kG at the triple point. The curvature, at ${T}_{N}$, of the antiferromagnetic-paramagnetic boundary with H\ensuremath{\parallel}[001] is $\frac{{d}^{2}T}{d{H}^{2}}=\ensuremath{-}(3.2\ifmmode\pm\else\textpm\fi{}0.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}\ifmmode^\circ\else\textdegree\fi{}$K/${\mathrm{G}}^{2}$. The curvature, at ${T}_{N}$, for the antiferromagnetic-paramagnetic boundary with H\ensuremath{\parallel}[100] is smaller by about an order of magnitude. The various phase boundaries are compared with the predictions of the molecular-field theory and other theoretical models.

Giant Quantum Attenuation of Sound Waves in Bismuth. I. Spin Splitting Factors of Electrons and Holes

The giant quantum attenuation of longitudinal sound waves in bismuth was investigated in pulsed magnetic fields up to 170 kG, at a temperature of 1.65°K and at sound wave frequencies of 60 and 100 Mc/s. The angle between the sound wave vector q and the magnetic field vector H was varied by rotating a sample. By combining data in a previous paper with the present ones the anisotropy of the spin splitting factor for electrons in the principal pocket is completely determined for two cases H ∥ X Y -plane and H ∥ Y Z -plane, where X -, Y - and Z -axis refer to a binary, a bisectrix and the trigonal axis, respectively. The Baraff theory is successfully applied to interpret the anisotropy, and values of some parameters in the theory are determined. The hole spin splitting factor for the case H ∥ Z -axis is found conclusively to be (1.86±0.02).

Ultrasonic Attenuation in Normal and Superconducting Indium

Measurements of the electron contribution to the attenuation of longitudinal sound waves propagating in normal and superconducting indium have been made up to 330 MHz. Data have been obtained for propagation along the principal crystallographic axes as well as for a number of directions in the (010) plane. The results exhibit considerable deviation from free-electron behavior. The limiting slopes of the attenuation versus frequency are highly anisotropic, and for quasi-longitudinal modes include a significant contribution which vanishes within approximately 30 mdeg of ${T}_{c}$. This drop is in addition to the less sudden drop associated with the BCS attenuation for longitudinal waves. Comparison of the measurements with simple calculations based on a modified free-electron model suggests that the effect of the crystal potential on the Fermisurface topology is largely responsible for the observed attenuation behavior.

Magnetoacoustic Effect in Potassium

The attenuation of longitudinal sound waves in the presence of a transverse magnetic field has been measured in potassium and fitted with the free-electron theory using the mean free path of the electrons as a parameter to be determined. A discrepancy is found, which is though to have the same origin as the anomalous magnetoresistance found by other workers in this material.

High-Frequency Sound Absorption in Superconductors

Theoretical and numerical results for the attenuation of high-frequency sound waves in superconductors are presented. Explicit calculations are given for the attenuation of longitudinal sound waves with wavelengths both large and small compared with the electron mean free path in pure superconductors and in superconductors containing magnetic impurities. Extensions to more general situations are discussed. The contribution due to the disruption of Cooper pairs by phonons is examined as a function of impurity concentration.

Viscoelastic relaxations in solutions of poly(glutamic acid) and gelatin at ultrasonic frequencies.

AbstractComplex shear viscosity η* = η′ – iη″ of poly (L‐glutarmic acid) solution was measured by the torsional crystal method at 50 kc./sec. as a function of pH. A sharp peak was found at the midpoint of the helix‐coil transition region in both η′ and η″. The relaxation time is calculated from η′ and η″ assuming a single relaxation process and the peak value at the midpoint of transition is estimated at 10−6 sec. Such behavior agrees well with the prediction from the theory of Schwarz. The attenuation of longitudinal sound waves at,3 Me./sec. was measured as a function of pH for solutions of poly(glutamic acid), glutamic acid, and gelatin. A small attenuation peak was observed for the three solutions, the peak height being almost, the same for them. The peak is interpreted in terms of the dissociation reaction of side chains.

Magnetoacoustic Study of the Rhenium Fermi Surface

The magnetic field dependence of the attenuation of longitudinal sound waves with frequencies up to 1 kMc/sec has been studied in very pure rhenium. Ordinary (transverse-field) dimensional resonances, open-orbit resonances, ordinary and giant Landau-level oscillations, longitudinal-field resonances, and cyclotron resonances were observed. Much of the data are consistent with only slight modifications to the 5th-through 8th-zone Fermi-surface sheets calculated by Mattheiss. The dominant signal in the dimensional-resonance data, which yields an isotropic caliper of 0.121 ${\mathrm{\AA{}}}^{\ensuremath{-}1}$ in the basal plane, probably results from the $\ensuremath{\Gamma}$-centered cavity of the 8th-zone electron sheet. A Landau-level period is observed whose corresponding area is that included by the isotropic caliper. Effective masses obtained from giant Landau-level oscillations and acoustic cyclotron resonance are in reasonable agreement with existing data. The longitudinal-field resonances yield values of the extremal and elliptic limiting point values of $\frac{\ensuremath{\partial}A}{\ensuremath{\partial}{k}_{z}}$, where $A$ is the cross-sectional area of the Fermi surface in the plane normal to ${\mathbf{k}}_{z}$.

Attenuation of longitudinal sound waves in potassium in an oblique magnetic field

The absorption edge for Doppler shifted cyclotron resonance of longitudinal sound waves in potassium is found to agree with the prediction of the free electron model, demonstrating that the ground state of this material does not possess a spin density wave aligned parallel to the magnetic field.

Electronic Attenuation of Longitudinal Soundwaves in Aluminium

AbstractThe frequency dependence of the difference between the attenuation of longitudinal soundwaves in a perpendicular magnetic field and in zero field is used in an experimental analysis of three parameters in the electron‐phonon interaction. The parameters are the electron mean free path and the magnitude of the interaction in zero and infinite field. The first parameter is compared with the mean free path deduced from electrical size effects. The interaction parameter in zero field is found to be in fair agreement with theoretical estimates. In high fields the interaction is not localized at the fermi surface, and it is found that symmetrically shaped orbits having an electron group velocity normal to the magnetic field, contribute most strongly to the attenuation.