Showing papers in "Physical Review B in 1977"

Special points for Brillouin-zone integrations

Abstract: The efficiency of two different methods for obtaining "special" points useful for Brillouin-zone integrations of periodic functions is compared. We find that for some Bravais lattices (such as body-centered cubic and hexagonal), the method suggested by Monkhorst and Pack leads to different and sometimes less efficient point sets than those previously obtained by Chadi and Cohen. For a two-dimensional oblique lattice, special points twice as efficient as those suggested by Cunningham are given.

"Special points for Brillouin-zone integrations"—a reply

Abstract: It is again emphasized that for all cubic lattices the method of Monkhorst and Pack generates not only point sets identical to those obtained by Chadi and Cohen, but also intermediate sets with the same properties. In addition, a comparison of these two methods for the hexagonal lattice reveals our method to be more flexible and efficient.

Infrared and Raman spectra of the silicon-hydrogen bonds in amorphous silicon prepared by glow discharge and sputtering

Abstract: We have studied the number and nature of the silicon-hydrogen bonds in amorphous silicon films prepared in plasmas either of silane or of hydrogen and argon. The films from silane glow discharges have qualitatively different Raman and infrared spectra which depend on deposition parameters such as substrate temperature and silane gas pressure. Three main groups of spectral bands are seen associated with the Si-H bonds: the Si-H bond stretch bands, the bands due to relative bending of two or three Si-H bonds with a common silicon atom, and the "wagging" bands of Si-H bonds with respect to the Si matrix. These bands are split in a way suggestive of the presence of SiH, Si${\mathrm{H}}_{2}$, and Si${\mathrm{H}}_{3}$ complexes: the bond-bending bands are absent when only SiH bonds are present. All three types of complexes are identified in films deposited from glow discharges of silane at pressures \ensuremath{\sim} 1 Torr and room temperature. Higher substrate temperatures and/or lower pressures reduce the Si${\mathrm{H}}_{2}$ and Si${\mathrm{H}}_{3}$ concentrations: films deposited at 250\ifmmode^\circ\else\textdegree\fi{}C and 0.1 Torr contain only SiH groups. From the strength of the corresponding absorption bands, H concentrations as high as 35 to 52 atomic percent are estimated. Films sputtered at 200\ifmmode^\circ\else\textdegree\fi{}C in a 10% ${\mathrm{H}}_{2}$-90% Ar mixture contain all three groupings observed in the silane-derived samples. Deuterated sputtered films are used to confirm the analysis. The first- and second-order Raman scattering spectra of the Si-Si bonds in pure and hydrogenated $a\ensuremath{-}\mathrm{S}\mathrm{i}$ are also discussed. The scattering efficiency of $a\ensuremath{-}\mathrm{S}\mathrm{i}$ is found to be as much as 10 times that of crystal Si. The depolarization ratio of the $a\ensuremath{-}\mathrm{S}\mathrm{i}$ Raman spectrum has been remeasured. Finally, a picture is presented of when it is appropriate to refer to heavily hydrogenated $a\ensuremath{-}\mathrm{S}\mathrm{i}$ as still being a material describable by $a\ensuremath{-}\mathrm{S}\mathrm{i}$ network models.

Renormalization, vortices, and symmetry-breaking perturbations in the two-dimensional planar model

Abstract: The classical planar Heisenberg model is studied at low temperatures by means of renormalization theory and a series of exact transformations. A numerical study of the Migdal recursion relation suggests that models with short-range isotropic interactions rapidly become equivalent to a simplified model system proposed by Villain. A series of exact transformations then allows us to treat the Villain model analytically at low temperatures. To lowest order in a parameter which becomes exponentially small with decreasing temperature, we reproduce results obtained previously by Kosterlitz. We also examine the effect of symmetry-breaking crystalline fields on the isotropic planar model. A numerical study of the Migdal recursion scheme suggests that these fields (which must occur in real quasi-two-dimensional crystals) are strongly relevant variables, leading to critical behavior distinct from that found for the planar model. However, a more exact low-temperature treatment of the Villain model shows that hexagonal crystalline fields eventually become irrelevant at temperatures below the ${T}_{c}$ of the isotropic model. Isotropic planar critical behavior should be experimentally accessible in this case. Nonuniversal behavior may result if cubic crystalline fields dominate the symmetry breaking. Interesting duality transformations, which aid in the analysis of symmetry-breaking fields are also discussed.

Nonradiative capture and recombination by multiphonon emission in GaAs and GaP

Abstract: Data are presented for 9 capture cross sections of deep levels in GaAs and 4 in GaP which can be interpreted as capture by multiphonon emission (MPE). At high temperatures the cross sections have the form $\ensuremath{\sigma}={\ensuremath{\sigma}}_{\ensuremath{\infty}}{e}^{\frac{\ensuremath{-}{E}_{\ensuremath{\infty}}}{\mathrm{kT}}}$ where ${\ensuremath{\sigma}}_{\ensuremath{\infty}}={10}^{\ensuremath{-}14}\ensuremath{-}{10}^{\ensuremath{-}15}$ ${\mathrm{cm}}^{2}$ and ${E}_{\ensuremath{\infty}}=0\ensuremath{-}0.56$ eV. A simple theory of MPE capture is presented in which vibrations of a single lattice coordinate modulate the depth of the potential well binding the carrier. In this model capture results from lattice vibrations causing the crossing of free- and bound-carrier levels. The breakdown of the adiabatic approximation near the crossing is discussed. The calculated cross sections have the form $\ensuremath{\sigma}=Af(0)$ where $f(h\ensuremath{ u})$ is the normalized line shape for radiative capture. The lattice relaxation properties of the center determine $f(0)$. The temperature dependence of $f(0)$ correctly accounts for the thermally activated behavior of the cross sections at high temperatures. Classical and quantum treatments of the lattice motion give the same expression for $\ensuremath{\sigma}$ at high temperature. A detailed calculation of $A$ is made for the capture of a carrier by an attractive neutral impurity in the case where both the free-carrier and bound-carrier wave functions are describable in a one-band effective-mass approximation. The theoretical value of $A$ leads to ${\ensuremath{\sigma}}_{\ensuremath{\infty}}\ensuremath{\approx}6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}$ ${\mathrm{cm}}^{2}$, the same order of magnitude as the experimental values. However, many of the experimental cross sections involve complexities not accounted for in this simple model such as charged impurities and transitions between free states and bound states of different symmetry. The lattice relaxation parameters are experimentally determined for the Zn-O and O centers in GaP. Lattice relaxation is found adequate to explain the large cross sections for electron capture by the Zn-O center and hole capture by the two-electron state of O. The studies of the O and Zn-O centers also provide evidence for nonlinear changes in the impurity energy level with lattice displacement which decrease the electron capture cross sections and greatly enhance the hole recombination cross sections. The source of this nonlinearity is discussed.

Exchange-correlation energy of a metallic surface: Wave-vector analysis

Abstract: The exchange-correlation energy of a jellium metal surface is analyzed in terms of the wavelength of the fluctuations that contribute to it, using a three-dimensional scheme different from that used by other authors. It is shown that with this scheme there exists an exact limiting form at long wavelengths which includes all many-body correlations and which is independent of the surface density profile. The local-density approximation is formulated as a function of wavelength, and it is shown to be exact at short wavelength. The interpolation scheme between these limits, which was discussed previously, is formulated and checked more completely and used to calculate surface energies.

Resonant Raman scattering in ZnO

Abstract: The resonance of the Raman scattering by ${E}_{2}, {A}_{1T}, {E}_{1L}$, and ${E}_{1T}$ phonons, and several second-order features, has been studied for ZnO for photon energies between 1.6 and 3 eV. The results are interpreted with a dielectric theory based on the first and second derivatives of the dielectric constant. By combining our results with absolute scattering cross sections previously determined by Arguello et al. at 2.41 eV absolute values of the deformation potentials of the band edge can be determined. The difference in strength between the longitudinal and the transverse modes provides the signs of these deformation potentials. The antiresonance around 1.6 eV suggested by the earlier work of Callender et al. and attributed to a cancellation of the deformation potential and electro-optical contributions to the Raman tensor is confirmed. The deformation potentials of the ${A}_{1}$ phonons at the band edge have been obtained from a pseudopotential calculation. While the sign of these deformation potentials agrees with the experimental determination, their magnitudes do not agree. This fact is attributed to difficulties with the pseudopotential of the ${\mathrm{O}}^{2\ensuremath{-}}$ ion. An estimate of the deformation potentials from the dependence of the band edges on uniaxial stress is also made.

Uniform susceptibilities of metallic elements

Abstract: The exchange-correlation enhanced spin susceptibilities of 32 metallic elements from Li through In have been calculated using the spin-polarized exchange-correlation functional of von Barth and Hedin. Since these 32 elements include both the 3d and 4d transition series, the calculations clearly exhibit both the normal trends with atomic number and the anomalies responsible for ferromagnetism. The susceptibilities were obtained by evaluating the Vosko-Perdew approximate formal solution of the linear-response problem for each element, using fully self-consistent nonmagnetic ground-state energy bands and wave functions. In addition, the accuracy of the Vosko-Perdew approximation itself was tested for Cr by performing a separate nonperturbative spin-polarized calculation of the response (for the same exchange-correlation functional) to an external magnetic field for this metal (the two susceptibilities agree to within 10%).

Multiphonon relaxation of rare-earth ions in oxide glasses

Abstract: Nonradiative decay of excited rare-earth ions by multiphonon emission has been investigated in a series of oxide glasses. Various rare-earth electronic levels were selectively excited by short-duration laser pulses and multiphonon relaxation rates were determined from measurements of fluorescence rise and decay times. Time resolution for fluorescence measurements was 3 nsec, so excited states were probed for which the decay was predominantly nonradiative. Excited states of ${\mathrm{Nd}}^{3+}$, ${\mathrm{Er}}^{3+}$, and ${\mathrm{Tm}}^{3+}$ with energy gaps to the next-lower $J$ state ranging from 1300 to 4700 ${\mathrm{cm}}^{\ensuremath{-}1}$ were studied. The multiphonon relaxation rates for each glass investigated exhibited an approximately exponential dependence on energy gap. Evidence of breakdown of this dependence was observed in the region of small energy gaps. The measured temperature dependences of the decay rates establish that the relaxation occurs predominantly by excitation of the highest-frequency vibrations associated with stretching modes of the glass network former. Borate, silicate, phosphate, germanate, and tellurite glasses were studied. From Raman spectra, the highest-frequency vibrations for these glasses ranged from 700 to 1400 ${\mathrm{cm}}^{\ensuremath{-}1}$. The corresponding multiphonon relaxation rates for a given energy gap differed by three orders of magnitude. The strength of the ion-phonon coupling was found to be approximately equal for all glasses.

Monte Carlo simulation of a many-fermion study

Abstract: The Metropolis Monte Carlo method is used to sample the square of an antisymmetric wave function composed of a product of a Jastrow wave function and a number of Slater determinants. We calculate variational energies for $^{3}\mathrm{He}$ and several models of neutron matter. The first-order Wu-Feenberg expansion is shown always to underestimate the energy, sometimes seriously. The phase diagram for ground-state Yukawa matter is determined. There is a class of Yukawa potentials which do not lead to a crystal phase at any density.

Adiabatic bond charge model for the phonons in diamond, Si, Ge, and α-Sn

Abstract: An adiabatic bond charge model (BCM) for the lattice dynamics of diamond-type crystals is developed. Our BCM unites elements of earlier models by Phillips and Martin, Keating, and Cochran. Four types of interactions are used: (a) central ion-ion forces, (b) Coulomb interactions of the ions and bond charges (BC's), (c) central ion-BC forces, and (d) bond-bending forces. These interactions represent the metal-like (a) and covalent (b)-(d) part of the crystal bonding. The phonon dispersion curves for Si, Ge, and $\ensuremath{\alpha}\ensuremath{-}\mathrm{Sn}$ are calculated using only four disposable parameters; for diamond, five parameters are employed. For all crystals, very good agreement with experiment is obtained. In particular, the typical flattening of the transverse acoustic phonons in the semiconducting materials is understood as a consequence of the adiabatic motion of the BC's, when the effective ion-BC coupling (b)+(c) is weak compared to the bond-bending forces (d). In an alternative representation of the BCM, the interactions (b) and (c) are replaced by central and noncentral ion-BC-ion potentials along one bond. The remaining long-range part of the Coulomb forces is unimportant; therefore, all essential interactions of the BCM are of very short range. Furthermore, the interaction parameters follow clear trends from diamond to $\ensuremath{\alpha}\ensuremath{-}\mathrm{Sn}$: type (a) increases, whereas types (b)-(d) decrease, especially the ion-BC coupling tends to vanish toward $\ensuremath{\alpha}\ensuremath{-}\mathrm{Sn}$.

Infrared and Raman spectra of the IV-VI compounds SnS and SnSe

Abstract: The results of Raman scattering and infrared reflectivity measurements on the IV-VI layer-type semiconductors SnS and SnSe are presented. The infrared-active TO, the associated LO-phonon frequencies, and the dielectric constants for all three principal polarizations have been determined from a Kramers-Kronig analysis of the reflectivity data. The symmetries of the zone-center phonons observed in the different polarization configurations are in agreement with the group-theoretical analysis of the ${D}_{2h}^{16}$ space group of these compounds. Despite the center of inversion symmetry in this structure, some infrared- and Raman-active modes are found to be nearly degenerate, suggesting the importance of the layerlike character in these compounds as in the isomorphic GeS and GeSe. A comparison of the phonon frequencies of the corresponding modes in the spectra of SnS and SnSe, or GeS and GeSe, indicates that the frequencies vary as a power (-2.2) of the lattice constant.

Structural phase transformation in K 2 Se O 4

Abstract: Successive phase transformations in ${\mathrm{K}}_{2}$Se${\mathrm{O}}_{4}$ at ${T}_{i}=130$ K and ${T}_{c}=93$ K were studied by the neutron-scattering technique. The superlattice reflections in the intermediate phase were found to be incommensurate with the lattice periodicity. The wave vector characterizing the reflections is ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}}_{\ensuremath{\delta}}=\frac{(1\ensuremath{-}\ensuremath{\delta}){\stackrel{\ensuremath{\rightarrow}}{\mathrm{a}}}^{*}}{3}$ with $\ensuremath{\delta}=0.07$ at 122.5 K. The deviation \ensuremath{\delta} decreases with decreasing temperature with an apparently discontinuous jump to zero at ${T}_{c}$. Below this temperature, the crystal remains commensurate and is known to be ferroelectric. The incommensurate-commensurate transition and the simultaneous occurrence of the commensurate phase and the spontaneous polarization are discussed using a Landau-type expansion of the free energy in which a term proportional to ${Q}^{3}({\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}}_{\ensuremath{\delta}}){P}_{z}({\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}}_{3\ensuremath{\delta}})$ plays an essential role in driving the incommensurate-commensurate phase transformation and in inducing the spontaneous polarization. Here, $Q({\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}}_{\ensuremath{\delta}})$ is the amplitude of the primary atomic displacements with wave vector ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}}_{\ensuremath{\delta}}$ and ${P}_{z}({\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}}_{3\ensuremath{\delta}})$ is the polarization wave with wave vector ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}}_{3\ensuremath{\delta}}=3\ensuremath{\delta}(\frac{{\stackrel{\ensuremath{\rightarrow}}{\mathrm{a}}}^{*}}{3})$ and becomes the macroscopic polarization below ${T}_{c}$. Above ${T}_{i}$, a ${\ensuremath{\Sigma}}_{2}$ optic-phonon branch along ($\ensuremath{\xi},0,0$) shows a striking softening and ${\ensuremath{\omega}}_{j}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}})$ for $\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}\ensuremath{\sim}(\frac{1}{3},0,0)$ tends to zero at ${T}_{i}$. The softening results from a temperature-dependent decrease of the interlayer forces with ranges $\frac{a}{2}$ and $a$ ($a$ is one unit-cell length along the $a$ axis) in the presence of strong and persisting forces with a range $\frac{3a}{2}$. The intensities of the soft phonon were measured about different reciprocal-lattice points and were used to determine the nature of the soft-phonon mode and suggest a coupled translation of potassium ions with rotational motion of Se${\mathrm{O}}_{4}$ groups to be the origin of the lattice instability.

New method for the calculation of atomic phase shifts: Application to extended x-ray absorption fine structure (EXAFS) in molecules and crystals

Abstract: The scattering of electrons of kinetic energy up to 1000 eV by an atom is of special interest in the understanding of extended x-ray absorption fine-structure (EXAFS) spectra. An important physical feature is the reduction of the exchange and correlation potential as the kinetic energy of the electron increases. This is taken into account by replacing the atom by an electron gas with spatially varying density and calculating the self-energy using the plasmon pole approximation. This results in a set of complex phase shifts which is then applied to the EXAFS problem. Comparison is made with phase shifts extracted from experimental EXAFS spectra and excellent agreement is obtained. Direct comparison of the theoretical and experimental spectra again shows excellent agreement in both the amplitude and the phase. We also analyze the EXAFS spectra by a Fourier-transform technique which first removes the amplitude and phase shift using the calculated result. The importance of a proper choice of zero of energy ${E}_{0}$ is emphasized. We choose ${E}_{0}$ by the requirement that the imaginary part and the absolute value of the Fourier transform should peak at the same distance, thus assuring that the absolute phase is given correctly. Using this procedure the nearest-neighbor distances in ${\mathrm{Br}}_{2}$, Ge${\mathrm{Cl}}_{4}$, and crystalline germanium are determined. In all cases the results are within 0.01 \AA{} of the known distances. Several shells in germanium are also determined, with accuracy of better than 1%. Application of our method to crystalline copper indicates that the outer shells are more seriously affected by multiple-scattering problems and our procedure permits us to discard peaks that are spurious or unreliable. The present determination of the nearest-neighbor distance in copper is found to be in error by 0.014 \AA{}. Results of the application of this method to the determination of the bond lengths of a variety of compounds are summarized.

Some static and dynamical properties of a two-dimensional Wigner crystal

Abstract: The static ground-state energy of a two-dimensional Wigner crystal has been obtained for each of the five two-dimensional Bravais lattices. At constant electron number density the hexagonal lattice has the lowest energy. Phonon dispersion curves have been calculated for wave vectors along the symmetry directions in the first Brillouin zone for the hexagonal lattice. In the long-wavelength limit one of the two branches of the dispersion relation vanishes with vanishing two-dimensional wave vector $\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}$ as $q$, the second as ${q}^{\frac{1}{2}}$. The coefficient of $q$ in the former branch is pure imaginary for certain directions of propagation in the square lattice, implying a dynamical instability of this lattice; the hexagonal lattice is stable. The vibrational zero-point energy and low-temperature thermodynamic functions have been obtained for the hexagonal lattice. The dielectric susceptibility tensor of a two-dimensional Wigner crystal ${\ensuremath{\chi}}_{\ensuremath{\alpha}\ensuremath{\beta}}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}})$ has been determined in the long-wavelength limit, in the presence of a static magnetic field perpendicular to the crystal, and the result has been used to obtain the dispersion relation for plasma oscillations in the electron crystal.

k → · p → perturbation theory in III-V compounds and alloys: a reexamination

Abstract: From the recent optical conduction-electron spin-resonance (CESR) measurements of the $g$ factors ${g}^{*}$ in III-V compounds and the known effective masses ${m}^{*}$, in the framework of the $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ensuremath{\rightarrow}}{\mathrm{p}}$ perturbation theory, we determine an experimental value of the interband matrix element ${P}^{2}=(\frac{2}{{m}_{0}}){|〈S|{p}_{x}|X〉|}^{2}$ coupling the conduction band and the upper valence bands. ${P}^{2}$ ranges from 21 \ifmmode\pm\else\textpm\fi{} 1.5 eV in InP to 29 \ifmmode\pm\else\textpm\fi{} 1 eV in GaAs. This unexpected strong variation can be justified by a crude tight-binding calculation, evidencing the combined influence of ionicity and cell dimension. We show that ${g}^{*}$ can be calculated with a precision of 10% in a three-band calculation, whereas a multiband approximation is required for ${m}^{*}$. The good agreement between our CESR measurements of the $g$ factors in ${\mathrm{Ga}}_{1\ensuremath{-}x}{\mathrm{In}}_{x}\mathrm{As}$ and ${\mathrm{Ga}}_{1\ensuremath{-}x}{\mathrm{Al}}_{x}\mathrm{As}$ and the calculated values by $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ensuremath{\rightarrow}}{\mathrm{p}}$ theory shows the correctness of this theory in alloys. Moreover, it is possible to obtain a satisfactory fit of the effective-mass data previously unexplained within simple $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ensuremath{\rightarrow}}{\mathrm{p}}$ theory by using a multiband model and correct values of ${P}^{2}$. The modifications to $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ensuremath{\rightarrow}}{\mathrm{p}}$ theory involving random potentials and strains are then not necessary at the precision of the experimental data available up to now.

Spin-orbit splitting in crystalline and compositionally disordered semiconductors

Abstract: The electronic structures of C, Si, Ge, $\ensuremath{\alpha}\ensuremath{-}\mathrm{Sn}$, GaP, GaAs, GaSb, InP, InAs, InSb, and ZnSe are studied using a tight-binding approach which includes spin-orbit interactions. The spin-orbit splittings ${\mathrm{\ensuremath{\Delta}}}_{0}$ and ${\mathrm{\ensuremath{\Delta}}}_{1}$ are related to atomic spin-orbit splittings and optical gaps. The variation of ${\mathrm{\ensuremath{\Delta}}}_{0}$ as a function of chemical composition is studied for a number of alloy systems. It is shown that the nonlinear dependence of ${\mathrm{\ensuremath{\Delta}}}_{0}$ on alloy composition is a disorder-induced effect. The bowing parameter is calculated in terms of tight-binding parameters and band gaps.

Low field electron-nuclear spin coupling in gallium arsenide under optical pumping conditions

Abstract: In a semiconductor, absorption of circularly polarized light (optical pumping) leads to spin-oriented photoelectrons. In this situation, the nuclei of the crystal are dynamically polarized through their hyperfine interaction with the electronic spins. Consequently the electrons experience a hyperfine magnetic field due to the oriented nuclei which may reach several kilogauss. When this large nuclear field is driven obliquely with respect to the direction of the exciting light, the precession of the electronic spins around the nuclear field leads to a decrease of the electronic polarization along the light excitation: it is a nuclear Hanle effect. This work is an experimental and theoretical study of these effects in weak external magnetic fields, of the order of the local field which characterizes the nuclear spin-spin interactions (a few gauss). Large nuclear fields are obtained at 77\ifmmode^\circ\else\textdegree\fi{}K in strongly doped and compensated $p$-type GaAs samples. We present a model which includes the different effects of the hyperfine coupling when there is a nuclear spin temperature among all the nuclei of the sample: Dynamic polarization, nuclear field, but also, existence of an electronic field acting on the nuclei. We show that a small external field is able to drive the large nuclear field acting on the electrons; consequently the electronic polarization is very sensitive to external fields which are too small to have a direct effect on the electronic spin motion. We study experimentally the variation of the electronic polarization with the direction and magnitude of a small external magnetic field, by measuring the circular polarization of the luminescence light. The experimental results are in quantitative agreement with the theoretical predictions. The usual Hanle Lorentzian depolarization curve is strongly modified in low fields and $W$-like singularities appear around zero field. The experimental values of the average electronic and nuclear fields are in reasonable agreement with theoretical evaluations. These nuclear effects may strongly alter the measurement of the Hanle linewidth in standard optical pumping experiments.

Electronic band structure of titanium dioxide

Abstract: The electronic band structure of titanium dioxide is calculated by a combined tight-binding and pseudopotential method in order to interpret the numerous experimental data. The gap anisotropy is clearly shown and the values of parallel and perpendicular gaps are in good agreement with the measured ones.

Neutron scattering study of the charge-density wave transitions in 2 H − Ta Se 2 and 2 H − Nb Se 2

Abstract: We have used the triple-axis neutron-scattering technique to study $2H\ensuremath{-}\mathrm{Ta}{\mathrm{Se}}_{2}$ and $2H\ensuremath{-}\mathrm{Nb}{\mathrm{Se}}_{2}$ which undergo charge-density wave transitions at ${T}_{0}=122.3$ K and ${T}_{0}=33.5$ K, respectively. The transitions in both compounds appear to be second-order and involve atomic displacements of ${\ensuremath{\Sigma}}_{1}$ symmetry. At inception, the superlattices in both compounds have nearly identical incommensurate wave vectors with magnitude ${q}_{\ensuremath{\delta}}=\frac{1}{3(1\ensuremath{-}\ensuremath{\delta}){a}^{*}}$, with $\ensuremath{\delta}\ensuremath{\sim}0.02$. The Nb${\mathrm{Se}}_{2}$ superlattice remains incommensurate to 5 K but Ta${\mathrm{Se}}_{2}$ undergoes a first-order lock-in transition where $\ensuremath{\delta}\ensuremath{\rightarrow}0$ at 90 K. The temperature dependence of the superlattice wave vector $\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}$ in the incommensurate phase and the lock-in transition are discussed using a free energy involving third-order "umklapp" terms and a secondary order parameter. The secondary lattice distortion which is predicted in this model is observed experimentally. Most phonon branches having energies less than 10 meV with propagation vectors in the [$\ensuremath{\zeta}00$] and [$00\ensuremath{\zeta}$] directions have been measured at 300 K. Strong anomalies are found in the ${\ensuremath{\Sigma}}_{1}[\ensuremath{\zeta}00]$ phonon branches in both materials near the wave vector ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}}_{c}=(\frac{1}{3},0,0)$ characteristic of the low-temperature superlattices. Substantial softening of this phonon is observed as the transition is approached. In addition, the spectral profile exhibits a central peak which is not measurably inelastic.

Optical absorption of Co 2 + in ZnO

Abstract: Polarized-optical-absorption spectra of ${\mathrm{Co}}^{2+}$ in ZnO are reported. The crystal-field transitions from the $^{4}A_{2}$ ground state to the $^{4}T_{2} (F)$, $^{4}T_{1} (F)$, and $^{2}E (G)$ multiplets are analyzed in detail. These bands consist of sharp zero-phonon lines and their vibronic sidebands, where coupling to 528-${\mathrm{cm}}^{\ensuremath{-}1}$ optical phonons and 100-${\mathrm{cm}}^{\ensuremath{-}1}$ acoustical phonons from the $M$ point of the ZnO Brillouin zone is shown to be dominant. In order to explain the level scheme derived from the spectra the Hamiltonian describing cubic and trigonal crystal field, Coulomb and spin-orbit interaction has been diagonalized within the full ${d}^{7}$ configuration. With $Dq=400$, $v=120$, ${v}^{\ensuremath{'}}=320$, $B=760$, $C=3500$, and $\ensuremath{\zeta}=430$ ${\mathrm{cm}}^{\ensuremath{-}1}$ both the band positions and the electronic-fine-structure splittings are satisfactorily accounted for. In addition the $g$ factors of the ${\mathrm{Co}}^{2+}$ ground state, ${g}_{\ensuremath{\parallel}}$ and ${g}_{\ensuremath{\perp}}$, are correctly predicted.

Theory for the dynamics of "clusters." II. Critical diffusion in binary systems and the kinetics of phase separation

Abstract: A semiphenomenological cluster theory is developed for the dynamics of systems with a conserved (one component) order parameter, which is not limited to small deviations from equilibrium. Concentration fluctuations of the binary system are parametrized in terms of clusters of various "sizes" $l$; these fluctuations decay by cluster reactions and cluster diffusion. The cluster diffusivity ${D}_{l}$ is estimated using the master equation for atomic exchange processes, and is confirmed by recent computer simulations of Rao et al. Close to equilibrium the nonlinear set of kinetic equations is reduced to a Fokker-Planck equation for the concentration of large clusters, which contains an effective chemical potential produced by the small clusters. Due to the conservation law this potential slowly varies with time. From this equation, we obtain as special cases the critical behavior of the diffusion constant both in solid and liquid binary systems close to ${T}_{c}$, and the Lifshitz-Slyozov theory of grain growth (below ${T}_{c}$). Additional terms describing the coagulation of large clusters have to be included in the latter case, however. At intermediate times the Lifshitz-Slyozov mechanism may even be neglected. A dynamic scaling solution of the coagulation equation predicts that the typical linear dimension should increase $\ensuremath{\propto}{t}^{\frac{1}{(3+d)}}$ in $d$ dimensions, in agreement with our previous heuristic arguments. The results are compared to computer simulations and to experiments on real systems. For the nonlinear relaxation above ${T}_{c}$ both scaling analysis and cluster dynamics give identical predictions. We also compare our approach to other theories of spinodal decomposition, deriving them in a unified way by factorization approximations of a rigorous kinetic equation, and thus elucidate their validity.

Critical exponents for the conductivity of random resistor lattices

Abstract: This paper presents three results concerning the critical exponents which characterize the conduction threshold of a resistor lattice (a) There are no rigorous inequalities similar to those for the phase-transition critical exponents (b) There is a dual transformation in two dimensions which relates the critical exponents: in particular $s=t$, $u=\frac{1}{2}$ for the two-dimensional bond problem (c) The exponents for the two- and three-dimensional bond and site problems are estimated by numerically solving for the voltage distributions of large finite disordered lattices The results are in agreement with the "scaling" exponent relationship

Lmm auger-spectra of cu, zn, ga, and ge .1. transition-probabilities, term splittings, and effective coulomb interaction

Abstract: The $\mathrm{LMM}$ Auger spectra of Cu, Zn, Ga, and Ge are presented and discussed. Transition probability calculations are described and with these a clear assignment of the peaks can be made. It is further shown that from the ${L}_{3}{M}_{45}{M}_{45}$ Auger lines the term splittings and the effective on-site electron-electron interaction can be determined. The latter is shown to be strongly reduced from the free-atom value. This has important consequences for the description of the band structure using one-electron theories. The satellite structure for Cu and Zn in the ${L}_{3}{M}_{45}{M}_{45}$ region of the spectrum is shown to be a result of strong Coster-Kronig processes involving the ${L}_{2}$ and ${L}_{3}$ core levels.

Theory of one-dimensional hopping conductivity and diffusion

Abstract: Hopping motion is considered in a linear chain containing an arbitrary density of particles that are not allowed to hop to occupied sites. The general case of two inequivalent lattice sites $A$ and $B$ is treated. Transition-rate equations are solved by Monte Carlo simulation and, where possible, by analytic techniques. Only for the case of equivalent sites do the results here agree with those recently obtained by Huber from nonlinear differential equations for site occupancy which neglect certain correlations. The conductivity is mean-field-like for equivalent sites, but shows sizeable departure for inequivalent sites, having an activation energy increased over the mean-field value. Here "mean-field" behavior is one where the only effect of forbidden hops to occupied sites is to reduce effective transition rates by a factor $1\ensuremath{-}n$, where $n$ is the average occupation number of the site to which a jump occurs. The velocity correlation function is shown to consist of a $\ensuremath{\delta}$-function part which reproduces the mean-field conductivity and a function $\ensuremath{\beta}(t)$ which is negative for times $tg0$. This is qualitatively quite different from the picture given by Huber's equations. Motion of a single distinguishable particle shows an anomalous ${x}^{2}\ensuremath{\propto}{t}^{\frac{1}{2}}$ dependence of the mean square displacement upon time $t$, but the displacement $X$ of all the particles does obey a diffusion relation ${X}^{2}\ensuremath{\propto}t$. This difference is explained in terms of the number of particles which have to be pushed aside in order for a particle to move a distance $x$, and in terms of the ensuing density fluctuation. Differences between time dependences and attempt fequencies as measured by bulk conductivity and microscopic probes such as NMR are noted and discussed in light of data on the one-dimensional superionic conductor $\ensuremath{\beta}$ eucryptite (LiAlSi${\mathrm{O}}_{4}$). Reinterpretation of NMR relaxation data on some of the organic charge-transfer salts is also suggested.

Spectral diffusion, phonon echoes, and saturation recovery in glasses at low temperatures

Abstract: Many features of glasses below 1 K are explicable in terms of localized tunneling levels, for which a spin-$\frac{1}{2}$ analogy exists. Here we show that spectral diffusion, resulting from fluctuations in resonant frequency, is essential to our understanding of recent ultrasonic experiments. Our model involves a coupling among the levels of the form ${J}_{\mathrm{ij}}{S}_{z}^{i}{S}_{z}^{j}$, which acquires a time dependence when a spin-flipping rate ${T}_{1}^{\ensuremath{-}1}$ is introduced. For two- and three-pulse phonon-echo experiments near $T=20$ mK, we predict phase-memory times which agree qualitatively with the experimental results of Golding and Graebner. For saturation recovery, we predict a linewidth whose time dependence should be observable near $T=100$ mK. Estimates of tunneling-model parameters and comparison with specific-heat experiments suggest that glasses may contain two types of tunneling levels.