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A comprehensive experimental and theoretical study of indirect gap optical absorption in bulk Ge is presented. While this topic has been the subject of intense studies from the early days of semiconductor physics, the resonant aspect of the absorption received very little attention until now. This is a unique property of Ge related to the proximity of the direct and indirect gaps. The absorption coefficient was measured over the entire spectral range between the two gaps for comparison with theory. It is shown that the standard textbook expressions, obtained by assuming intermediate states with constant energy, are in very poor agreement with experiment. A theory first proposed by Hartman [R. L. Hartman, Phys. Rev. 127, 765 (1962)], which takes into account the energy dependence of the intermediate states, provides a much better account of the photon-energy dependence of the absorption, but the prediction of the experimental absorption strength requires the incorporation of excitonic effects. The latter, however, have only been considered by Elliott [R. J. Elliott, Phys. Rev. 108, 1384 (1957)] in the limit of constant intermediate state energy. A generalization to the case of energy-dependent intermediate states, consistent with Hartman's theory, is presented here. The basic qualitative difference with the classical Elliott theory is that the excitonic character of the intermediate states affects the computed absorption, generating an additional resonant enhancement that is confirmed by the experimental data. The generalized theory presented here agrees very well with the experimental absorption using independently determined band structure parameters.

Brillouin spectroscopy of porous Si $(\ensuremath{\pi}$-Si) formed on p-type (100) Si has revealed two acoustic-phonon peaks associated with the surface and film modes of the thick porous slab. They exhibit relatively large peak widths that are attributed to fractons. Longitudinal wave guiding is enhanced in high porosity $\ensuremath{\pi}$-Si due to its very low sound velocities compared with Si. Unlike opaque semiconductors where ripple scattering is dominant, the elasto-optic contribution to the scattering mechanism is found to be significant in $\ensuremath{\pi}$-Si. Both phonon velocities show appreciable negative dispersion due to a porosity gradient.

Although NiO is often considered the classic example of an antiferromagnetic insulator, recent investigations have revealed unexplained features of the magnon spectrum. The present study of the temperature and polarization behavior of first-order magnetic Raman scattering reveals that the polarization selection rules are not described by the generally accepted antisymmetric scattering tensor. The inclusion of quadratic magneto-optic coupling terms can explain the symmetry of the scattering tensor, but does not lead to results consistent with the accepted [112] spin alignment direction. {copyright} {ital 1998} {ital The American Physical Society}

Brillouin spectra of ferroelectric ${\mathrm{PbHPO}}_{4}$ (${\mathit{T}}_{\mathit{c}}$=310 K) and its deuterated isomorph ${\mathrm{PbDPO}}_{4}$ (${\mathit{T}}_{\mathit{c}}$=462 K) have been measured as a function of temperature across their transition temperatures. Certain longitudinal acoustic waves are found to exhibit anomalous propagation in the vicinity of ${\mathit{T}}_{\mathit{c}}$. The relaxation times, ${\mathrm{\ensuremath{\tau}}}_{0}$, for a noninteracting dipole are evaluated from the Brillouin shifts, based on a phenomenological approach. The ${\mathrm{\ensuremath{\tau}}}_{0}$ values are the same in both ${\mathrm{PbHPO}}_{4}$ and ${\mathrm{PbDPO}}_{4}$, indicating that the ferroelectric transition is driven by an order-disorder relaxation mode. This study also reveals that the paraelectric phase symmetry is, on a macroscopic scale, centrosymmetric.

Resonant Raman scattering was used to study an InSb/${\mathrm{In}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Al}}_{\mathit{x}}$Sb strained-layer superlattice and the InSb and ${\mathrm{In}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Al}}_{\mathit{x}}$Sb parent materials. Resonant enhancement peaks were observed in epilayer films in the regions of the ${\mathit{E}}_{1}$ and ${\mathit{E}}_{1}$+${\mathrm{\ensuremath{\Delta}}}_{1}$ optical gaps. In the superlattice, two sets of peaks observed in the plots of the Raman cross section versus exciting photon energy are shown to originate from the independent electronic transitions in the alternating layers. The calculated resonance Raman profiles for two phonons in the alloy layers are in reasonable agreement with experiment. Estimates of the strain and confinement effects in these layers were made and these agree with the observed differences from the parent materials.

Raman scattering has been used to study a variety of InSb/In 1-x Al x Sb strained-layer superlattices grown by magnetron sputter epitaxy. The observed frequencies of zone-folded longitudinal acoustic phonons agree well with those calculated using Rytov's theory of acoustic vibrations in layered media. The intensities of these phonons do not coincide with those calculated within the regime of the photoelastic mechanism for light scattering because the exciting light energy is close to resonance with superlattice electronic transitions. The longitudinal optic phonons in In 1-x Al x Sb layers exhibit two-mode behavior and their shift due to the intralayer strain is discussed

Resonant Raman scattering was used to probe the electronic structure of InSb/In 1-x Al x Sb strained-layer superlattices in the region of the E 1 and E 1 +Δ 1 optical gaps. The two sets of peaks observed in the plots of the Raman cross section versus photon energy are shown to originate from the independent electronic transitions in the alternating layers. Estimates of the strain and confinement effects were made and these agree with the observed differences from bulk material

Experimental results concerning the temperature and polarization dependence of the one-magnon Raman light scattering in the canted antiferromagnet ${\text{NiF}}_{2}$ (N\'eel temperature ${T}_{N}=73\text{ }\text{K}$) are reported. The excitation frequencies, linewidths, and integrated intensities of the lower and upper magnon branches are obtained over the temperature range 5--65 K. A comparison between theory and experiment for the frequencies of the one-magnon branches shows good overall agreement for temperatures up to $0.3{T}_{N}$. A theoretical model that includes the effects of linear and quadratic magneto-optical coupling is used to account for the observed polarization characteristics of the Stokes and anti-Stokes peaks. The analysis takes account of the small canting angle of the spins which complicates the behavior of the lower magnon branch, in particular. The experimental data are indicative of a possible spin-reorientation transition at $\ensuremath{\sim}31\text{ }\text{K}$.

The structure of [(Si) m /(Ge) n ] p superlattice interfaces and the onset of relaxation and interdiffusion initiated by annealing have been investigated with the use of extended x-ray-absorption fine structure and Raman scattering. For the as-grown material, the Ge-Ge bond length (0.2409 nm) was equal to that calculated for a fully strained Ge layer (0.2412 nm) while the Si-Ge bond length was significantly shorter. The results show conclusively that substantial intermixing along with partial relaxation of the Ge-Ge bonds occurs even for the shortest anneal at 700°C

Ge K-edge extended x-ray-absorption fine-structure (EXAFS) spectra of a series of strained-layer [(Si${)}_{\mathit{m}}$/(Ge${)}_{\mathit{n}}$${]}_{\mathit{p}}$ superlattices grown by molecular-beam epitaxy on the 〈100〉 face of single-crystal Si have provided a determination of the degree of intermixing and the extent of relaxation as a function of the thickness of the Ge layer. The results are obtained with use of constrained simultaneous nonlinear least-squares curve fits to multiple data files from different samples. This procedure, along with associated analysis of the fit surface, has improved the reliability of the analysis. We discuss the general applicability of simultaneous analysis procedures to EXAFS analysis of a series of related samples, such as those spanning compositional variation or thermal processing.

The measurement of the strain coefficients for the three longitudinal-optical phonons in strained ${\mathrm{Si}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Ge}}_{\mathit{x}}$ (0x0.35) molecular-beam-epitaxy-grown epilayers on (100) Si is reported. Strain in the epilayers was varied by annealing metastable pseudomorphically grown epilayers at various temperatures and was measured by double-crystal x-ray diffractometry. The strain-shift coefficients for the phonons were obtained from Raman-scattering measurements of the annealed specimens. For all compositions it was found that the Si-Si phonon frequencies vary linearly with strain. The strain-shift coefficient, however, showed a small composition dependence, varying from about -750 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ at x=0.08 to about -950 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ at x=0.35, corresponding to a stress factor \ensuremath{\tau}\ensuremath{\approxeq}0.4+0.57x+0.13${\mathit{x}}^{2}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$/kbar for this vibration. The magnitude of the corresponding coefficients for the Si-Ge and Ge-Ge lines are slightly less than that of the Si-Si line, and vary in a similar way with x.

In three-dimensional cluster morphology multilayer Si/SiGe nanostructures, we find an anticorrelation between photoluminescence (PL) originating from SiGe clusters and the PL associated with electron-hole droplets (EHDs) localized within nanometer-thick Si separating layers. We show that Auger processes eject holes from SiGe clusters and facilitate the exciton/EHD phase transition in the Si layers. An unusual $N$-shaped SiGe cluster PL decay curve is attributed to the reverse EHD/electron-hole gas phase transition and carrier redistribution between Si spacer layers and SiGe clusters.

We report on the direct observation of polarons in $\mathrm{In}\mathrm{As}∕\mathrm{Ga}\mathrm{As}$ self-assembled quantum dots (QD) populated by few electrons. The polarons are strongly coupled modes of QD phonons and electron intersublevel transitions. The degree of coupling is varied in a systematic way with a set of samples having electron intersublevel spacing changing from larger to smaller than the longitudinal-optical-phonon energy. The signature of polarons is evidenced clearly by the observation of a large $(12\char21{}20\phantom{\rule{0.3em}{0ex}}\mathrm{meV})$ anticrossing for both InAs and GaAs-like QD phonons using resonant Raman spectroscopy.

Quantum squeezing of a collective spin-wave excitation or magnon using femtosecond optical pulses has been used to generate correlated pairs of spins with equal and opposite wave vectors in antiferromagnetic ${\mathrm{MnF}}_{2}$ and ${\mathrm{FeF}}_{2}$. In the squeezed state, the fluctuations of the magnetization of a crystallographic unit cell vary periodically in time and are reduced below that of the ground state quantum noise. The results obtained, including their temperature dependence for ${\mathrm{FeF}}_{2}$, are compared with earlier spontaneous Raman scattering measurements. The squeezing effect is observed to be at least one order of magnitude stronger in ${\mathrm{FeF}}_{2}$ than in ${\mathrm{MnF}}_{2}$.

Brillouin light scattering has been employed to study the magnetic-field dependence of the discrete spin waves in permalloy Ni80Fe20 nanowires. When a small magnetic field is applied transverse to the nanowire, the results reveal a low-frequency mode, which is absent in the longitudinal case. A Hamiltonian-based microscopic theory for nanowires with inhomogeneous magnetization shows that the appearance of this mode, along with its higher-field behavior, is a significant consequence of a small easy-plane single-ion anisotropy at the nanowire surface. The calculations provide a good description of experimental data for both the transverse and longitudinal cases.

A theoretical description of electronic Raman scattering from GaAs/AlxGa1 xAs artificial atoms under the influence of an external magnetic field is presented. Raman spectra with laser excitation energy in the interval Egap 30 meV to Egap are computed in the polarized and depolarized geometry. The polarization ratios for the collective and single-particle excitations indicate a breakdown of the Raman polarization selection rules once the magnetic field is switched on. A Raman intensity jump rule at the band gap is predicted in our calculations. This rule can be a useful tool for identifying the physical nature (charge or spin) of the electronic excitations in quantum dots in low magnetic fields. a few-electron CDEs in InGaAs self-assembled quantum dots by means of Raman spectroscopy. In this paper, we compute the near-resonance Raman spectrum of a medium-size disk-shaped quantum dot con- taining 42 electrons in an external magnetic field applied perpendicular to the plane of the dot. The method and approximations used to obtain the many-body wave func- tions and energies of the required states are explained in Ref. (7). Energies and wave-functions of the final ex- cited states are obtained by means of the random phase approximation 8 (RPA). The calculation of the monopole operator matrix elements between each final state and the ground state, allows the identification of the collec- tive modes (CDEs, SDEs) and the SPEs. By computing the Raman polarization ratios we evaluate the extent to which the magnetic field breaks down the polarization se- lection rules for both collective and SPEs. We report the first observation of what we term the Raman intensity jump-rule. This effect, more clearly seen for the collec- tive modes, can be enunciated as follows: a monotonic increase of a Raman peak intensity when the incident laser energy is increased from below up to the effective band-gap of the dot in the polarized (depolarized) geom- etry indicates that the excited state associated with that peak is a charge (spin) excitation. If we look at the same state in its opposite geometry, we find quite small values of the Raman intensities at any incident energy except at the effective band-gap, in which case a sudden jump of the Raman intensity should be detected. From theory 9 , we know that the Raman peak inten- sity is proportional to the transition amplitude squared, |Afi| 2 , where

A consistent semiquantitative theoretical analysis of electronic Raman scattering from many-electron quantum dots under resonance excitation conditions has been performed. The theory is based on random-phase-approximation-like wave functions, with the Coulomb interactions treated exactly, and hole valence-band mixing accounted for within the Kohn-Luttinger Hamiltonian framework. The widths of intermediate and final states in the scattering process, although treated phenomenologically, play a significant role in the calculations, particularly for well above band gap excitation. The calculated polarized and unpolarized Raman spectra reveal a great complexity of features and details when the incident light energy is swept from below, through, and above the quantum dot band gap. Incoming and outgoing resonances dramatically modify the Raman intensities of the single particle, charge density, and spin density excitations. The theoretical results are presented in detail and discussed with regard to experimental observations., Comment: Submitted to Phys. Rev. B

Polarized far infrared reflectance has been measured at oblique incidence for 11 ${\mathrm{In}}_{0.53}{\mathrm{Ga}}_{0.47}\mathrm{A}\mathrm{s}/\mathrm{I}\mathrm{n}\mathrm{P}$ superlattices grown lattice matched on InP(100) wafers by chemical beam epitaxy. Both the alloy layer thickness (0.25--20 nm) and number of periods (10--40) were varied. The spectra contained sharp reflectance peaks at the frequencies of the vertically propagating, zone-center, transverse optical (TO), and longitudinal (LO) optical phonons. The contributions of the individual phonon modes of the alloy layers were resolved using a generalized analysis procedure including GaAs-like, disorder induced, and InAs-like LO and TO phonons. A nonlinear variation of the alloy LO phonon frequencies with layer thickness was observed arising from phonon confinement in the alloy layers. From this result, the LO phonon in bulk InAs is predicted to exhibit anomalous dispersion. On both sides of the alloy layers we observed 0.6-nm-thick interface layers of significantly different alloy composition. Surprisingly for a lattice matched system, the InP layers exhibit a slight strain arising from the interface formation.

Raman spectroscopy has been used to investigate the lattice vibrations of ${\mathrm{Si}}_{1\ensuremath{-}x}{\mathrm{C}}_{x}$ $(0lxl0.02)$ epilayers grown on Si(100) by electron cyclotron resonance plasma-assisted molecular beam epitaxy. Spectral contributions due to first- and second-order longitudinal and transverse optic phonons together with disorder-induced features have been evaluated by a detailed polarization and C concentration dependence analysis. The band parameters exhibit generally a linear dependence on $x.$ A Raman line observed near $630{\mathrm{cm}}^{\ensuremath{-}1},$ which in past work has been associated with C ordering in the Si lattice, is found not to agree with this interpretation. It is associated with interstitial C. The optical absorption coefficient near 458 nm is deduced from the Raman intensity information, and is found to increase significantly with increasing $x.$

The electrical conductivity of single crystals of ${\mathrm{Na}}_{2}$${\mathrm{SO}}_{4}$ has been measured along the three principal crystallographic axes at temperatures in the range 160\char21{}400 \ifmmode^\circ\else\textdegree\fi{}C. The measurements reveal a hitherto unsuspected large anisotropy in the ${\mathrm{Na}}^{+}$ ion conduction in the stable room-temperature orthorhombic phase (V) of the as-grown crystals. The conductivity is restricted largely to the (010) crystallographic plane and is attributed to open tunnels in the [101] and [101\ifmmode\bar\else\textasciimacron\fi{}] directions that form an interconnected network facilitating ${\mathrm{Na}}^{+}$ ion diffusion. On heating, a pretransition region of sample-dependent conductivity occurs at 226 \ifmmode^\circ\else\textdegree\fi{}C followed by a sluggish but major structural transition at 241 \ifmmode^\circ\else\textdegree\fi{}C to a hexagonal phase (I). The microscopic details of this atypical irreversible transition are discussed. On cooling, further transitions to phase II (at 234 \ifmmode^\circ\else\textdegree\fi{}C) and phase III (at 229 \ifmmode^\circ\else\textdegree\fi{}C) occur, while on heating phase III transforms directly to phase I (at 249 \ifmmode^\circ\else\textdegree\fi{}C). The conductivity in phase I, II, and III is nearly isotropic and the activation energies are essentially independent of crystal orientation in each phase.

Inelastic neutron scattering from clusters of ${\mathrm{Co}}^{2+}$ ions in cubic KZn${\mathrm{F}}_{3}$ is reported. From measurements of the lowest pair mode at (1.676\ifmmode\pm\else\textpm\fi{}0.008) THz, we find that the exchange between ${\mathrm{Co}}^{2+}$ ions is surprisingly isotropic, with any bond anisotropy being less than 2.4%. An accurate value of the isotropic exchange parameter has been obtained [$J=(0.330\ifmmode\pm\else\textpm\fi{}0.005)$ THz] free of the many-body effects that complicate the interpretation of exchange coupling in concentrated crystals. Neutron scattering was also observed from triplet and quartet states at (2.47\ifmmode\pm\else\textpm\fi{}0.02) and (1.09\ifmmode\pm\else\textpm\fi{}0.05) THz, respectively, and a higher-frequency pair state at 8.8 THz. The results are interpreted in terms of an elementary theory of cluster spectra for ions with nonzero angular momentum.

Experiments are reported for the temperature dependence of phonon Raman scattering in Fe${\mathrm{F}}_{2}$. The ${B}_{1g}$ phonon exhibits anomalous frequency softening with decreasing temperature for temperatures in the range ${T}_{N}=78\ensuremath{-}340$ K. This softening is less marked for temperatures below ${T}_{N}$ because of spin-lattice effects resulting from the antiferromagnetic ordering. In the higher-temperature region the square of the ${B}_{1g}$-phonon frequency is proportional to temperature, which is suggestive of a virtual structural phase transition. However, consideration of other work on the pressure dependences of the Raman-active modes in similar compounds leads us to conclude that the mode softening results largely from the lattice thermal contraction. This contraction disproportionally influences the forces between nearest-neighbor fluorine ions in adjacent planes perpendicular to the $c$ axis.

The Raman spectrum of the mixed layered compound ${\mathrm{CdCl}}_{2(1\mathrm{\ensuremath{-}}\mathrm{x})}$${\mathrm{Br}}_{2\mathrm{x}}$ shows a complicated structure at frequencies between the corresponding ${A}_{1g}$ and ${E}_{g}$ phonon frequencies observed in isostructural ${\mathrm{CdCl}}_{2}$ and ${\mathrm{CdBr}}_{2}$. This Raman structure has a marked concentration dependence. General features of the results have been successfully described in terms of a simple model that predicts a ten-mode behavior for the Raman-active phonons in the mixed crystal. Particular features in the spectrum suggest that preferred clusters of ${\mathrm{Cl}}^{\mathrm{\ensuremath{-}}}$ or ${\mathrm{Br}}^{\mathrm{\ensuremath{-}}}$ ions occur in the mixed-crystal lattice, probably as a result of a difference in lattice constants of the two components.