Showing papers on "Brillouin zone published in 1976"

Special points for brillouin-zone integrations

Abstract: A method is given for generating sets of special points in the Brillouin zone which provides an efficient means of integrating periodic functions of the wave vector. The integration can be over the entire Brillouin zone or over specified portions thereof. This method also has applications in spectral and density-of-state calculations. The relationships to the Chadi-Cohen and Gilat-Raubenheimer methods are indicated.

Introduction to solid state physics

Abstract: Mathematical Introduction Acoustic Phonons Plasmons, Optical Phonons, and Polarization Waves Magnons Fermion Fields and the Hartree-Fock Approximation Many-body Techniques and the Electron Gas Polarons and the Electron-phonon Interaction Superconductivity Bloch Functions - General Properties Brillouin Zones and Crystal Symmetry Dynamics of Electrons in a Magnetic Field: de Haas-van Alphen Effect and Cyclotron Resonance Magnetoresistance Calculation of Energy Bands and Fermi Surfaces Semiconductor Crystals I: Energy Bands, Cyclotron Resonance, and Impurity States Semiconductor Crystals II: Optical Absorption and Excitons Electrodynamics of Metals Acoustic Attenuation in Metals Theory of Alloys Correlation Functions and Neutron Diffraction by Crystals Recoilless Emission Green's Functions - Application to Solid State Physics Appendix: Perturbation Theory and the Electron Gas Index.

Temperature dependence of the optical properties of Au, Ag and Cu

Abstract: The optical properties of Au and Ag are measured between 0.5 and 5.4 eV for temperatures ranging from 40 to 840K. The analysis of these spectra-also extended to the case of Cu-permits the assessment of energy separations associated with interconduction-band transitions in the vicinity of L over a wide temperature range. Notably the L4- to L4+ (nonrelativistic: L2' to L1) energy gap at 295K is found to be 4.81 eV for Cu, 4.11 eV for Ag and 4.20 eV for Au. The temperature dependence of this gap (around 295K) typically is -6.5*10-4 eV K-1 for all noble metals, i.e., considerably larger than predicted on the basis of band calculations. The present analysis also shows the interband absorption edge of Ag to arise from transitions in extended regions of the Brillouin zone. A comparison of experimental and theoretical spectra suggests lattice expansion to be the major source of temperature dependence of the band structure. It also yields information regarding the influence of dipole matrix elements on the epsilon 2 spectra.

cw Brillouin laser

Abstract: The observation of efficient continuous‐wave Brillouin laser action in an optical‐fiber ring resonator is reported. Internal laser conversion efficiencies of 50% and a Brillouin‐shifted output of 20 mW have been achieved.

Spin Waves in Heusler Alloys Pd2MnSn and Ni2MnSn

Abstract: The magnetic interactions in Heusler alloys Pd 2 MnSn and Ni 2 MnSn have been investigated using neutron spin wave scattering. The spin wave dispersion relations along the [00ζ], [ζζ0] and [ζζζ] directions have been observed across the whole magnetic Brillouin zone. The results have been analyzed using a Heisenberg Hamiltonian where only Mn atoms have a localized moment. It has been found that the interactions between more than 6th neighbors should be taken into account to reproduce the observation. The exchange constants at large distances have an oscillatory character which can be interpreted by the s - d type interactions based on the nearly free electron model. However, the n . n . and n . n . n . interactions have signs opposite to those expected from the simple s - d model. The n . n . and n . n . n . exchange constants in Ni 2 MnSn ( T C =344 K) are larger than those in Pd 2 MnSn ( T C =189 K), although the oscillatory parts have nearly the same values for both alloys.

cw generation of multiple Stokes and anti‐Stokes Brillouin‐shifted frequencies

Abstract: Continuous‐wave laser action in multiply Brillouin‐shifted spectral lines in a novel Fabry‐Perot optical‐fiber resonator is reported. Oscillation has been observed over a 200‐GHz bandwidth and a total of 14 Brillouin‐shifted lines have been detected. This Brillouin laser configuration is potentially a source of mode‐locked picosecond pulses.

De Haas-van alphen effect and the Fermi surface of LaB6

Abstract: Extremal cross-sectional areas and effective masses of the Fermi surface of LaB6 in the (100) and (110) planes have been measured using the de Haas-van Alphen (dHvA) effect. In addition, measurements of the field dependence of the magnetoresistance in the (100) plane have also been performed which show the existence of open orbits in certain directions and suggest the presence of magnetic breakdown. Much of the dHvA data are consistent with a set of nearly spherical ellipsoids located at the points X of the Brillouin zone and connected by necks which intersect the M line; magnetic breakdown across the necks must be postulated to explain the remaining data. The proposed Fermi surface is consistent with the discrete variational band-structure calculations of Walch et al. © 1976 The American Physical Society.

The Origin of Mechanical Twins in (NH4)2SO4

Abstract: We have found that, if in (NH 4 ) 2 SO 4 a hexagonal phase happened to exist somewhere on higher temperature side, we can explain group-theoretically various experimental results of mechanical twins observed in (NH 4 ) 2 SO 4 crystals as straightforward consequences of a hypothetical hexagonal-orthorhombic phase transition. The transition occurs through an instability at the M point of the Brillouin zone. The microscopic picture of the transition may be the ordering in the orientations of the tetrahedral SO 4 - ions.

Light scattering from shear modes in liquid salol

Abstract: Depolarized spectra of liquid salol have been observed and analyzed over a range of temperature, from 122 to −22 °C, with the viscosity varying from ∼2 to more than 104 cP. At the lowest temperatures, the spectra exhibit a central line and well‐separated Brillouin components, characteristic of light scattering by oscillatory shear waves. As the temperature is raised, the Brillouin components merge with the central line. At the highest temperatures, broad depolarized doublets with intensity minima at the exciting frequency appear, and are ascribed to light scattering from highly damped shear modes. The spectra observed over the entire temperature range are shown to be in good agreement with the ’’two variable’’ theory of Andersen and Pecora.

Interatomic forces and lattice dynamics of α-quartz

Abstract: The axially symmetric force-constant model of Elcombe (1966-7) for alpha -quartz is developed to take account of (i) forces between SiO4 tetrahedra and (ii) rotational invariance. For a non-ionic model without rotational invariance, stiffening the Si-O-Si angles with an Si-Si interaction leads to rather better agreement with experimental phonon frequencies and much better agreement with elastic constants. However, subsequent imposition of the conditions for rotational invariance reduces some of the calculated frequencies, especially that of the lowest acoustic mode at the A-point on the Brillouin zone boundary; this indicates that further weak intertetrahedral forces are required. Ionic (rigid-ion) models are also investigated, but give little improvement. The observed variation with temperature of certain phonon frequencies as the alpha - beta transition is approached can be qualitatively explained by the change in lattice geometry.

Optical spectra of orientationally disordered crystals. VI. The Raman spectrum of the translational lattice vibrations of ice Ih

Abstract: The Raman spectrum of the translational vibrations of polycrystalline ice Ih has been investigated in the range 350–20 cm−1. All the vibrations are Raman active, and there is much fine structure, presumably due to particular points in the Brillouin zone. Tentative assignments are suggested for some of the features. The theory of the Raman scattering by the translational vibrations of orientationally disordered crystals has been discussed and it is shown that the origin of the Raman intensity lies mainly in the disorder in the location of the hydrogen atoms surrounding an O–H⋅⋅⋅O bond. The intensity of scattering below ∼200 cm−1 is much weaker than that above ∼240 cm−1, which suggests that while the vibrations below ∼200 cm−1 are disorder allowed, those above ∼240 cm−1 might be connected with the order‐allowed A1g, E1g, and E2g vibrations of the hypothetical crystal with real hexagonal symmetry. The strong Raman scattering near 310 cm−1 is not caused by a splitting of the transverse and longitudinal optic vibrations, such as occurs in ionic crystals, but by significant electrostatic interactions, particularly of the transition moments of neighboring hydrogen bonds. They cause the hydrogen‐bond stretching constant to depend on the relative orientation of the two water molecules, and the coupling constant for the stretching of neighboring hydrogen bonds to differ for the symmetric, O–H⋅⋅⋅O⋅⋅⋅H–O and O⋅⋅⋅H–O–H⋅⋅⋅O, and asymmetric, O–H⋅⋅⋅O–H⋅⋅⋅O, configurations. The differing coupling constants cause significant differences in the forces restricting the motion of molecules parallel and perpendicular to their polar axes, and probably causes the peaks in the spectrum at ∼310 and 228 cm−1.

Brillouin Scattering Studies of the Uniaxial Ferroelectric Phase Transition in TGS and TGSe

Abstract: The Brillouin spectra of the ferroelectric triglycine sulfate (TGS) and its isomorphous selenate (TGSe) crystals have been observed in three cases of orientations of the longitudinal or quasi-longitudinal phonon vector q ; (1) q // c -axis, (2) q // b -axis and (3) q deviates 5° from b -axis in the (100) plane. The temperature dependence of both the frequency shift and the spectral width shows a remarkable anisotropy near T c . In the case (1) the temperature at which the width becomes maximum shifts to the lower temperature than T c which has simultaneously been determined by an accompanied measurement of dielectric constant. The polarization relaxation time is determined from this temperature shift using the phenomenological relation. In the case (2) and the case (3), the decrease in the anomaly is explained as the depolarization field effect of the long range dipole-dipole interaction which is characteristic in the ferroelectric phase transition.

Brillouin scattering from isotropic metals

Abstract: Brillouin scattering from isotropic metals is investigated experimentally and theoretically. The observation of highly asymmetric Brillouin spectra from liquid mercury and liquid gallium is reported. A comparison is made between theory and experiment; the theory includes the damping of the acoustic phonons. It is found that the present state of the theory only qualitatively describes the Brillouin scattering of light from highly opaque materials. The velocities of sound of mercury and gallium deduced from the measurements are found to be 38% larger than the corresponding values determined by ultrasonic techniques. The observed intensity is at least an order of magnitude larger than the theory predicts, and the line shape, especially in the case of liquid gallium, differs appreciably from the theoretical line shape. The major origin of the discrepancy between theory and experiment is believed to be the simple model employed for the description of the dynamics of the density fluctuations near the surface. The spectra observed may therefore contribute to further understanding of the surface physics of liquid metals.

Determination of magnetic and elastic properties of FeBO3 by light scattering

Abstract: Brillouin back-scattering measurements on the weak ferromagnet FeBO3 (TN=348K) are reported in the temperature range 77-350K in magnetic field up to 6 kG for an incident wavelength of 514.5 nm. From the magnetic field and directional dependence of the magnon frequency, the Dzialoshinski-Moriya field HDM (1958, 1960) was obtained over the whole temperature range, and precise values were found for the three dominant exchange contributions. The full set of elastic constants is reported.

Rayleigh-Brillouin spectra in molecular nitrogen

Abstract: Rayleigh-Brillouin spectra of gaseous ${\mathrm{N}}_{2}$ is measured for light scattered at 15\ifmmode^\circ\else\textdegree\fi{} over a pressure range from 1 to 661 Torr. Spectral profiles are analyzed by means of an appropriate kinetic model. A least-${\ensuremath{\chi}}^{2}$ method determines the optimum values of the theory parameters: total collision frequency and rotational relaxation number. These parameters are compared with values obtained by other methods. Information provided by light-scattering measurements concerning rotational relaxation in dilute systems is discussed.

The central mode in the critical scattering of X-rays by SrTiO3

Abstract: The dynamics of the phase transition in SrTiO3 (Tc approximately 105K) is complicated by the presence of a central mode in the scattering at the R point of the cubic Brillouin zone in addition to the expected soft-mode scattering. Experiments using Mossbauer gamma rays are reported in which 'elastic' scattering with an energy change of less than 1.5*10-8 eV is detected at the R-point for temperatures as high as 170K. Furthermore, by using X-rays of different incident energy, it is shown that above Tc the scattering power of the crystal at the R point is depth-dependent. The intensity of the scattering above Tc can be altered by annealing the crystal. The results are interpreted in terms of a depth-dependent transition temperature; the crystal begins to transform to the lower-temperature phase first at the surface, and as Tc is approached from above the transformed surface region extends further into the bulk.

Theory of the Brillouin scattering lineshape in an opaque material

Abstract: Derives an expression for the lineshape of the Brillouin spectrum of an acoustic phonon in an absorbing material taking account of phonon reflection at the sample boundary. The shape is asymmetric and differs appreciably from that previously used to interpret experimental spectra.

Observation of stimulated Brillouin backscattering from an underdense plasma

Abstract: Observations of stimulated Brillouin scattering from an underdense plasma in a magnetic field are reported. The observed shifts correspond to those expected from a plasma with the measured temperature. Scattering with twice the Brillouin shift was observed when the fundamental Brillouin reflectivity approached 5%.

Directional uv photoemission from (100) and (110) molybdenum surfaces

Abstract: A study of the (100) and (110) molybdenum surfaces by directional photoemission spectroscopy is presented. Energy distribution spectra formed by photoelectrons emitted normal to the surfaces have been measured for photon energies between 10.2 and 21.2 eV. The results are discussed in terms of calculated band structure within the framework of the ${K}_{\ensuremath{\parallel}}$-conservation assumption. A good agreement is found between the main features of the experimental spectra and the emission expected from the band structure along the corresponding symmetry line in the Brillouin zone, assuming essentially direct-transition and surface-emission processes. Two extra structures are interpreted in terms of surface states or resonances: on the (100) surface, 0.5 eV below ${E}_{F}$; on the (110) surface, 4.5 eV below ${E}_{F}$ in the $s$-$d$ hybridization gap.

Surface states on the (001) surface of Nb

Abstract: The electronic structure of the (001) ideal surface of niobium is calculated using a self-consistent pseudopotential method. Surface states are identified and analyzed throughout the two-dimensional Brillouin zone. Charge densities and the local density of states near the surface are presented and discussed. Our calculations predict strong surface features in the density of states in the range 0--2 eV above the Fermi energy. Occupied surface states are also discussed. (AIP)

Structural aspects of phase transitions

Abstract: Two kinds of phase transitions are considered in the perovskite structure which involve instabilities located either at the Brillouin zone center (ferroelectric transition) or at the zone corners (antiferrodistortive transition). X-ray diffuse scattering and neutron inelastic scattering results are discussed. The steep narrowing of the energy spectrum recently observed in the cubic phase of NaNbO3 close to the transition temperature is related to the cross-over between the 2d and 3d fluctuation regimes.

Detection of Brillouin Backscattering in Underdense Plasmas

Abstract: Two new results are reported: (1) verification of the finite-interaction- length threshold for stimulated Brillouin scattering in a plasma with no critical layers, and (2) use of the time-dependent Stark effect to detect ion-frequency electric fields in a plasma. (AIP)

Energy bands of a (110) iron thin film

Abstract: We have performed a tight-binding calculation of the energy bands of a 29-layer (110) ferromagnetic iron thin film. The matrix parameters were obtained by fitting a bulk calculation of Tawil and Callaway with the diagonal surface matrix elements shifted by a constant amount to obtain surface charge neutrality. The energy bands were calculated at 117 points in the irreducible (one fourth) two-dimensional Brillouin zone. The planar and total densities of states are also reported and compared to previous results. A discussion of the surface states and energy bands is given and the structure of the energy bands is correlated to structure seen in the planar density of states and the effects of $s\ensuremath{-}d$ hybridization.

Lattice-dynamical applications to crystallographic problems: consideration of the Brillouin zone sampling

Abstract: In lattice-dynamical calculations, especially of crystallographic temperature factors and thermodynamic functions, a considerable saving of computing time can be obtained by a suitable choice and sampling of the first Brillouin zone To this purpose, an uneven sampling is proposed and examples of its advantages are given For a convenient use of this sampling, 'unconventional' Brillouin zones are adopted: in most cases, simplifications due to crystal symmetry can be made

Second-Order Raman Spectra of Thorium Dioxide

Abstract: The second-order Raman spectra of the thorium dioxide crystal have been investigated. The results are interpreted in terms of the phonon energies near the Brillouin zone boundaries and the zone center, which have been calculated by using Born-von Karman force model. A nearly complete interpretation of the spectra is given. The observed polarization of Raman spectra is in good agreement with the calculated selection rules for the second-order Raman process at the symmetric points \(\varGamma\), M and L.