Comments on the paper “phonon lifetimes in fused quartz at low temperatures”

By comparing their results to those given in our previous paper [2] Jackson et al. pointed out a disagreement in Brillouin scattering measurements of the lifetime of thermal phonons in vitreous silica at 2.4 K. A careful analysis leads us to the conclusion that both the values given by these authors and their accuracy are not substantially different from ours. The consistency between these measurements and the values obtained from theory and from the extrapolation of ultrasonic results is examined.     

Brillouin scattering studies of rare gas solids

Abstract

The scattering of light by elementar excitations in the matter is results in two phenomena, discriminated by the zero wavevector frequency of the excitation: if this frequency is zero, one deals with Brillouin scattering, and with Raman scattering in the other case. Brillouin scattering results from the interaction of light with thermal excitations (acoustic phonons in a crystal) of a material, or, from a classical point of view, with density waves. Contrary to Raman scattering, the selection rules allow always the observation of at least one mode. It is a powerful technic in the study of rare gases under pressure: at ambient temperature, rare gases crystallize in the face centered cubic structure (except helium which structure was recently found to be hexagonal) and are therefore Raman and infrared inactive.

Experimental results will be reviewed on rare gases and rare gas mixtures in the fluid phase, like He-Ne and He-H₂. These results will be discussed in relation with recent measurements of the frequency of global oscillations of Jupiter.     

Pressure dependence of phonon energies at critical points in the Brillouin zone in KTaO3 measured with differential second order raman scattering

Wavelength modulated Raman scattering was used to study the effects of pressure on the second order spectrum of KTaO₃. The pressure results lend support to previous identifications of structures in the second order differential Raman spectrum in terms of pairs of phonons from critical points in the Brillouin zone. Using these identification mode Grüneisen parameters are obtained for several vibrational modes. Strong anharmonic behavior of of the TA(X) mode is observed when we correlate the results from pressure measurements with previous studies of the effects of temperature.     

Temperature dependence of hypersonic attenuation in NaCl and KCl crystals

The usual theories of ultrasonic attenuation (Landau-Rumer and Akhiezer) are in disagreement with experiments involving hypersonic phonons (Brillouin scattering). This is shown here by measurements on NaCl and KCl. We observe a Tⁿ dependence with n approximately equal to 2.8, and an attenuation increasing with temperature in the low and high temperature range respectively. An extension of the Landau-Rumer and Akhiezer theories to hypersonic frequencies is proposed. Our theoretical expressions give a good account of the temperature dependence of the attenuation in the whole temperature range.     

Brillouin scattering study of phase transitions in T1Ins2

The temperature dependence of the elastic coefficients of T1InS₂ has been investigated by Brillouin scattering measurements. For longitudinal phonons propagating in the (001) plane the variation of ΔC_∼∼(T_c−T) was found below the ferroelectric transition point (T_c=189 K). For propagation perpendicular to the (001) plane (C₃₃ mode) clear anomalies were observed at T=213 K and T=195 K. Between these temperatures the Brillouin peaks show broadening, which is attibuted to a coupling between the acoustic mode and an overdamped mode.     

Phonon lifetimes in fused quartz at low temperatures

Thermal Brillouin scattering from fused quartz has been observed with high resolution at low temperatures. At 2.4 K the longitudinal phonons of ν = 33 GHz are very well-defined excitations, with a lifetime of (2.0±.2)×10^-7 sec. This value is in substantial disagrement with those reported by Pelous and Vacher¹.     

Soft modes below the incommensurate transition in K2SeO4

A coordinated series of Raman and Brillouin scattering measurements were carried out in K₂SeO₄ with emphasis on temperatures near and below the incommensurate structural phase transition (T_i=129 K). Below the lock-in phase transition (T_c=99 K) Raman scattering from both the amplitude mode and the phase mode analog was observed. However, only the amplitude mode could be followed into the incommensurate phase. Details of the amplitude mode frequency and damping are reported for temperatures considerably closer to T_i than previously possible. Our results do not confirm the diverging linewidth extrapolated from earlier Raman work. We also report here the first Brillouin scattering results in K₂SeO₄. Although substancial interaction effects between the acoustic phonons and the soft amplitude mode are evident near T_i, the coupled mode lineshapes can be well described without the introduction of a relaxing self energy for the soft mode. Finally, limits on the characteristics of the phason are drawn from our failure to observe it directly in the incommensurate phase.     

Observation of Brillouin scattering in mixed InxGa1−xP crystals

Brillouin scattering is observed in the In_xGa_1?xP solid solution with 0.38 ? × ? 0. The composition dependences of the longitudinal and transverse acoustic phonons propagating along the [111] direction are investigated and compared with the expressions derived by Lakshmi et al. from the random element isodisplacement theory. Pronounced broadening of the Brillouin peaks is observed with the increasing amount of In in GaP.     

Zone edge phonons in CdS1−xSex

Zone edge phonons of mixed CdS_1?xSe_x have been studied by mean of infrared absorption and Raman scattering techniques. In the A point of the Brillouin zone, it has been shown that transverse acoustical phonons have a one mode behaviour, and that optical phonons have a two modes behaviour. CdS and CdSe zone center phonons can combined and give a LO(CdS) + LO(CdSe) Raman peak in addition to the 2LO(CdS) and 2LO(CdSe) peaks; this is not the case for phonons from the edge of the Brillouin-zone where no CdS + CdSe combination can take place.     

Anharmonic dynamical behaviour in bcc zirconium

We present inelastic neutron scattering measurements of the low energy and strongly damped phonons in the high temperature bcc phase of zirconium. These phonons were investigated at different scattering vectors but equivalent phonon wave vectors in different Brillouin zones or along different but equivalent paths in the same Brillouin zone. Neither the observed differences in intensity nor in line shapes can be explained by the coherent one-phonon scattering law . This leads to an apparent violation of the fundamental symmetry of lattice dynamics. Taking into account the strong anharmonicity of these phonons, interferences between one- and multi-phonon scattering are held responsible for these effects. Measurements in different scattering planes reveal that due to the symmetry of the bcc lattice, these effects can only be observed in certain directions. Received: 24 December 1997 / Received in final form: 9 March 1998 / Accepted: 19 March 1998     

Guided acoustic wave Brillouin scattering in photonic crystal fibers

We experimentally investigate guided acoustic wave Brillouin scattering in several photonic crystal fibers by use of the so-called fiber loop mirror technique and show a completely different dynamics with respect to standard all-silica fibers. In addition to the suppression of most acoustic phonons, we show that forward Brillouin scattering in photonic crystal fibers is substantially enhanced only for the fundamental acoustic phonon because of efficient transverse acousto-optic field overlap. The results of our numerical simulations reveal that this high-frequency phonon is indeed trapped within the fiber core by the air-hole microstructure, in good agreement with experimental measurements.     

A polarizable point ion model for partially covalent semiconductors

Theoretical models of the lattice dynamics of sapphire (α — Al₂O₃), based on the assumption of rigid ions, have been fitted to measured phonons at theΓ-point of the Brillouin zone. Short range interactions were taken into account by assuming 2-body interactions between touching ions. Additional 3-body interactions could not improve the fit significantly. Calculated dispersion curves are presented and compared with inelastic neutron scattering data. A good agreement for branches along the trigonal axis can be stated.     

Spin-phonon interactions near the one-dimensional antiferromagnetic ordering in CsNiCl3

The velocity of 10 MHz and 27 GHz longitudinal phonons propagating along the c-axis in the one-dimensional antiferromagnet CsNiCl₃ has been measured using ultrasonic and Brillouin light scattering techniques, respectively. An anomalous change in phonon velocity near the one-dimensional magnetic ordering temperature due to the spin-phonon interaction has been observed in both cases.     

Light scattering as a form of modulation spectroscopy

In the conventional modulation spectroscopy the optical constants of a solid are modulated by means of an external parameter (stress, electric field, etc). As a result of the presence of elemental excitations in the solid (usually phonons) a spontaneous modulation of the optical constants takes place at the frequency of the excitations. This modulation can be observed in light scattering experiments (Raman and Brillouin). Such measurements yield information about the frequency and density of states of the excitations (conventional Raman and Brillouin measurements), about their interaction with electronic states, and about the electronic transitions themselves (resonant scattering experiments). The theory of resonant Raman and Brillouin scattering in semiconductors will be discussed in connection with that of other modulation experiments (piezoreflectance, stress induced birefringence). Another closely related phenomenon, that of spatial-dispersion-induced birefringence will also be presented.     

Resonant Raman scattering spectra in a ZnCdSe/ZnSe structure with a quantum well and open nanowires

Resonance Raman scattering (RS) spectra of a ZnCdSe/ZnSe sample containing a single quantum well and quantum well-based open nanowires were studied at T=300 K. The longitudinal optical (LO) phonons involved in the formation of the observed spectra of the quantum-well and nanowire regions differ noticeably in energy. The LO phonon energies in the structures under study were calculated taking into account the compositional effect (doping of Cd into ZnSe) and biaxial strain. When excited in the exciton resonance region, RS is shown to occur via free (extended) excitonic states with the involvement of LO phonons of the ZnCdSe strained layer with final wave vectors near the Brillouin zone center. When excited below the excitonic resonance in the ZnCdSe layer, resonance scattering via localized exciton states provides a noticeable contribution to the observed RS lines. Because of the finite size of a localized state, phonons with large wave vectors are involved in these scattering processes. The RS lines produced under excitation in the excitonic region of the thick barrier layers are due to scattering from the ZnSe barrier phonons.     

Pressure Dependence of Acoustic Modes in AgGaSe 2

The pressure dependence of the transverse acoustic TA[0 0 1] and TA[1 0 0] phonons and the low-frequency optical v 3 phonons of AgGaSe 2 has been measured at pressures up to 4.3 GPa by inelastic neutron scattering. The strong frequency decreases in the whole Brillouin zone of the TA modes show generally a weak nonlinearity. Depending on the wavevector, the softening prior to the phase transition at 2.6 GPa also affects the optical mode to a less extent.     

Raman spectra of fosterite

The normal modes of the Raman-active phonons in the center of the Brillouin zone in a natural monocrystal of Mg₂SiO₄ were measured by using Raman scattering. All of the modes predicted by group theory were observed and measured. Some deviations from previously published values in synthetic samples were observed for the low energy phonons.     

Electron-phonon interaction due to interchain coupling in Nb3Sn

Using the Weger-Labbé-Friedel model the electron-phonon coupling in Nb₃Sn for scattering between orthogonal families of Nb-chains is calculated. It is shown that interchain coupling may cause the softening of the shear modulus C₄₄ with decreasing temperature. This mechanism gives rise to a softening over the whole Brillouin zone of all those acoustical phonons the long wavelength behaviour of which depends on C₄₄. A Fermi energy of 17 meV is necessary to fit the experimental data.