# Showing papers in "Physical Review B in 1975"

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TL;DR: In this article, the authors proposed a method to improve our understanding of the behavior of real solids by using calculations of the electronic structure of real molecules and solids in order to improve the search for new and better materials.

Abstract: We would like to improve our understanding of the behaviour of real solids. Why do atoms combine into molecules and solids in the way they do and what is the response of these aggregates of atoms to external fields, stress, temperature, etc. ? Answers to such questions would, for instance, be a useful guide in our, so far mostly empirical, search for new and better materials Stronger materials, materials which corrode less, better catalysts, better magnets, better semi- or superconductors, and, materials with properties unknown today. I expect that future advances in this field will be aided by insight obtained from calculations of the electronic structure.

4,733 citations

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TL;DR: In this paper, the authors developed a stochastic transport model for the transient photocurrent, which describes the dynamics of a carrier packet executing a time-dependent random walk in the presence of a field-dependent spatial bias and an absorbing barrier at the sample surface.

Abstract: Measurements of the transient photocurrent $I(t)$ in an increasing number of inorganic and organic amorphous materials display anomalous transport properties. The long tail of $I(t)$ indicates a dispersion of carrier transit times. However, the shape invariance of $I(t)$ to electric field and sample thickness (designated as universality for the classes of materials here considered) is incompatible with traditional concepts of statistical spreading, i.e., a Gaussian carrier packet. We have developed a stochastic transport model for $I(t)$ which describes the dynamics of a carrier packet executing a time-dependent random walk in the presence of a field-dependent spatial bias and an absorbing barrier at the sample surface. The time dependence of the random walk is governed by hopping time distribution $\ensuremath{\Psi}(t)$. A packet, generated with a $\ensuremath{\Psi}(t)$ characteristic of hopping in a disordered system [e.g., $\ensuremath{\Psi}(t)\ensuremath{\sim}{t}^{\ensuremath{-}(1+\ensuremath{\alpha})}$, $0l\ensuremath{\alpha}l1$], is shown to propagate with a number of anomalous non-Gaussian properties. The calculated $I(t)$ associated with this packet not only obeys the property of universality but can account quantitatively for a large variety of experiments. The new method of data analysis advanced by the theory allows one to directly extract the transit time even for a featureless current trace. In particular, we shall analyze both an inorganic ($a\ensuremath{-}{\mathrm{As}}_{2}{\mathrm{Se}}_{3}$) and an organic (trinitrofluorenone-polyvinylcarbazole) system. Our function $\ensuremath{\Psi}(t)$ is related to a first-principles calculation. It is to be emphasized that these $\ensuremath{\Psi}(t)$'s characterize a realization of a non-Markoffian transport process. Moreover, the theory shows the limitations of the concept of a mobility in this dispersive type of transport.

2,610 citations

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TL;DR: In this article, a through analysis of the dependence of the superconducting transition temperature on material properties is made, based on a combination of analytic and numerical solutions of the Eliashberg equations, and a comparison with tunneling data.

Abstract: A through analysis is made of the dependence of the superconducting transition temperature ${T}_{c}$ on material properties ($\ensuremath{\lambda}$, ${\ensuremath{\mu}}^{*}$, phonon spectrum) as contained in Eliashberg theory. The most striking new feature of the analysis is in the asymptotic regime of very large $\ensuremath{\lambda}$ where ${T}_{c}$ is found to equal $0.15 {(\ensuremath{\lambda}〈{\ensuremath{\omega}}^{2}〉)}^{\frac{1}{2}}$ (assuming ${\ensuremath{\mu}}^{*}=0.1$). This result implies the surprising conclusion that within Eliashberg theory ${T}_{c}$ is not limited by the phonon frequencies, and also shows that McMillan's "$\ensuremath{\lambda}=2$ limit" is spurious. The McMillan equation (with a prefactor altered from $\frac{{\ensuremath{\Theta}}_{D}}{1.45}$ to $\frac{{\ensuremath{\omega}}_{log}}{1.2}$) is found to be highly accurate for all known materials with $\ensuremath{\lambda}l1.5$ but in error for large values of $\ensuremath{\lambda}$. Correction factors to McMillan's equation are found in terms of $\ensuremath{\lambda}$, ${\ensuremath{\mu}}^{*}$, and one additional parameter, $\frac{{(〈{\ensuremath{\omega}}^{2}〉)}^{\frac{1}{2}}}{{\ensuremath{\omega}}_{log}}$. The frequency ${\ensuremath{\omega}}_{log}$ is defined as $\mathrm{exp} 〈\mathrm{ln}\ensuremath{\omega}〉$ where the averages $〈\mathrm{ln}\ensuremath{\omega}〉$ and $〈{\ensuremath{\omega}}^{2}〉$ are defined using $(\frac{2}{\ensuremath{\lambda}\ensuremath{\omega}}){\ensuremath{\alpha}}^{2}F(\ensuremath{\omega})$ as a weight factor. These conclusions are based on a combination of analytic and numerical solutions of the Eliashberg equations, and are supported by a comparison with tunneling data. Especially strong support comes from a new experimental result for amorphous ${\mathrm{Pb}}_{0.45}$${\mathrm{Bi}}_{0.55}$ reported herein. This material has parameters $\ensuremath{\lambda}=2.59$ and $\frac{{T}_{c}}{{\ensuremath{\omega}}_{log}}=0.284$, in serious disagreement with McMillan's formula but in good agreement when the correction factors are included. The McMillan-Hopfield parameter $\ensuremath{\eta}$ [or $N(0) 〈{I}^{2}〉$] is extracted from tunneling measurements or from a combination of empirical values of $\ensuremath{\lambda}$ and neutron-scattering measurements of phonon dispersion. It is proposed that $\ensuremath{\eta}$ (which is now known not to be accurately constant) is the most significant single parameter in understanding the origin of high ${T}_{c}$ and the limitation of ${T}_{c}$ by colvalent instabilities.

2,234 citations

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TL;DR: In this paper, the basic physical parameters which govern the metal-insulator transition in vanadium dioxide are determined through a review of the properties of this material, and the major importance of the Hubbard intra-atomic correlation energy in determining the insulating phase, which was already evidenced by studies of the magnetic properties of alloys, is further demonstrated from an analysis of their electrical properties.

Abstract: The basic physical parameters which govern the metal-insulator transition in vanadium dioxide are determined through a review of the properties of this material. The major importance of the Hubbard intra-atomic correlation energy in determining the insulating phase, which was already evidenced by studies of the magnetic properties of ${\mathrm{V}}_{1\ensuremath{-}x}{\mathrm{Cr}}_{x}{\mathrm{O}}_{2}$ alloys, is further demonstrated from an analysis of their electrical properties. An analysis of the magnetic susceptibility of niobium-doped V${\mathrm{O}}_{2}$ yields a picture for the current carrier in the low-temperature phase in which it is accompanied by a spin cloud (owing to Hund's-rule coupling), and has therefore an enhanced mass ($m\ensuremath{\simeq}60{m}_{0}$). Semiconducting vanadium dioxide turns out to be a borderline case for a classical band-transport description; in the alloys at high doping levels, Anderson localization with hopping transport can take place. Whereas it is shown that the insulating phase cannot be described correctly without taking into account the Hubbard correlation energy, we find that the properties of the metallic phase are mainly determined by the band structure. Metallic V${\mathrm{O}}_{2}$ is, in our view, similar to transition metals like Pt or Pd: electrons in a comparatively wide band screening out the interaction between the electrons in a narrow overlapping band. The magnetic susceptibility is described as exchange enhanced. The large density of states at the Fermi level yields a substantial contribution of the entropy of the metallic electrons to the latent heat. The crystalline distortion removes the band degeneracy so that the correlation energy becomes comparable with the band width and a metal-insulator transition takes place.

883 citations

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TL;DR: In this article, a theory of the absorption fine structure starting from theoretically obtained electron-atom scattering phase shifts is presented, where the electron scattering is treated using a spherical wave expansion which takes into account the finite size of the atoms.

Abstract: The extended x-ray absorption fine structure is a consequence of the modification of the photoelectron final state due to scattering by the surrounding atoms. We present a theory of the absorption fine structure starting from theoretically obtained electron-atom scattering phase shifts. The electron scattering is treated using a spherical wave expansion which takes into account the finite size of the atoms. Multiple-scattering effects are included by classifying multiple-scattering paths by their total path lengths. Their effects are quite large but appear to make quantitative but not qualitative changes on the single-scattering contribution. The exceptional case is the fourth shell in fcc or bcc structure, where it is shadowed by the first-shell atom and is profoundly affected by forward scattering due to the first shell. This may account for the anomaly observed experimentally at the fourth-shell radius in metals. A detailed numerical calculation is carried out for copper and is shown to agree quite well with experiment.

808 citations

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TL;DR: In this paper, the authors generalize Lai's model to higher-spin systems and a lattice of SU(3) triplets, making application to various systems such as dilute Heisenberg magnets.

Abstract: In a recent paper, Lai introduced a lattice-gas model. In this paper we generalize Lai's model, making application to various systems such as dilute Heisenberg magnets, higher-spin systems, and a lattice of SU(3) triplets. By a careful consideration of general thermodynamic stability, and by variational arguments, we demonstrate Lai's solution to be incorrect, and in turn produce the correct solution in this case and in other cases including higher-dimensional models. The remaining cases we treat in one dimension by Bethe's ansatz, reducing the problem to coupled integral equations. We locate the singularities of the ground-state energy in the phase plane; and we explicitly calculate the absolute-ground-state energy, excitations above the absolute ground state, and the first correction to the absolute ground state for small concentrations of impurities.

760 citations

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TL;DR: In this article, the authors studied thermodynamic and some dynamic properties of a one-dimensional model system whose displacement field Hamiltonian is strongly anharmonic, and is representative of those used to study displacive phase transitions.

Abstract: We have studied thermodynamic and some dynamic properties of a one-dimensional-model system whose displacement field Hamiltonian is strongly anharmonic, and is representative of those used to study displacive phase transitions. By studying the classical equations of motion, we find important solutions (domain walls) which cannot be represented effectively by the usual phonon perturbation expansions. The thermodynamic properties of this system can be calculated exactly by functional integral methods. No Hartree or decoupling approximations are made nor is a temperature dependence of the Hamiltonian introduced artificially. At low temperature, the thermodynamic behavior agrees with that found from a phenomenological model in which both phonons and domain walls are included as elementary excitations. We then show that equal-time correlation functions calculated by both functional-integral and phenomenological methods agree, and that the dynamic correlation functions (calculated only phenomenologically) exhibit a spectrum with both phonon peaks and a central peak due to domain-wall motion.

685 citations

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TL;DR: In this paper, the orientation of domain walls in full ferroelastic materials has been investigated based on the same criterion of spontaneous strain compatibility defined by Fousek and Janovec for ferroelectric crystals.

Abstract: The orientations of domain walls in ferroelastic materials are theoretically investigated. The procedure followed is based on the same criterion of spontaneous strain compatibility defined by Fousek and Janovec for ferroelectric crystals. Two given domains in a ferroelastic are found to be separated by a planar wall whose orientation belongs to a set of two mutually perpendicular orientations. Domain walls are not always crystallographically prominent planes of fixed indices ($W$ planes) and can instead be determined by the relative magnitude of the components of the second-rank tensor representing the spontaneous strain (${W}^{\ensuremath{'}}$ walls). In the latter case the orientation is expected to be temperature dependent. It is also shown that symmetry considerations are sufficient to find all $W$ planes. According to the considered ferroelastic species the pair of permissible walls between two domains can be two $W$ planes, or a $W$ plane and a ${W}^{\ensuremath{'}}$ plane, or two ${W}^{\ensuremath{'}}$ planes. The situation where no permissible walls are expected is of particular interest and is examined in known crystals. The predicted orientations of walls are given for the 94 species of full ferroelastics. Available experimental data of the literature are all consistent with our results.

674 citations

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642 citations

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TL;DR: In this article, a detailed description of the analysis of EXAFS data is presented including details of the Fourier transform of the data and the extraction of structural and other physical parameters from these transforms.

Abstract: Fourier transforms of extended x-ray-absorption fine structure (EXAFS) give structural information in the vicinity of each kind of atom, separately, in a wide variety of gaseous, liquid, and solid systems. A detailed description of the analysis of EXAFS data is presented including details of the Fourier transform of the data and the extraction of structural and other physical parameters from these transforms. Included in this description are the measurement of interatomic distances, coordination numbers, disorder effects (thermal and structural), energy-dependent electron scattering amplitudes, inelastic mean free paths, and phase shifts. EXAFS spectra of Ge, Cu, and Ge${\mathrm{O}}_{2}$ are analyzed in detail. Multiple-scattering effects between atoms are generally found to be small. There are no multiple-scattering effects in the first shell of the Fourier transform. The phase shifts introduced by both the absorbing and surrounding atoms empirically appear to be characteristic of the particular atoms and independent of the surroundings for a given class of material. This is of great practical importance because it indicates that EXAFS can be calibrated by measuring known structures and then used to determine unknown ones.

634 citations

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TL;DR: In this paper, a relationship between the Baxter model in two dimensions and the Luttinger model in one was constructed, and the relationship was used to calculate critical exponents for the Baxter models from appropriate Lutteringer-model correlation functions.

Abstract: We construct a relationship between the Baxter model in two dimensions and the Luttinger model in one, and use it to calculate critical exponents for the Baxter model from appropriate Luttinger-model correlation functions. An important part of this work involves the generalization of the Jordan-Wigner transformation to provide a representation for continuum spin operators. With this generalization, we are also able to calculate spin correlation functions for a continuum generalization of the spin-\textonehalf{} Heisenberg-Ising chain. We discuss the difference between the continuum and discrete lattice models, and with the help of a new scaling law, use previous results for the Baxter model to calculate new exponents for the Baxter and Heisenberg-Ising model on a lattice.

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TL;DR: In this paper, a technique for obtaining extended x-ray-absorption fine structure (EXAFS) using a conventional, horizontal, xray diffractometer is presented.

Abstract: A technique is presented for obtaining extended x-ray-absorption fine structure (EXAFS) using a conventional, horizontal, x-ray diffractometer. Preparation of monochromator crystals, spectrometer alignment, counting techniques, evaluation of the energy scale and data normalization techniques are discussed. EXAFS spectra from a wide variety of materials are then presented to show the variability of the effect and interplay between various parameters of the theory. A final section illustrates a simple graphical scheme to obtain a first-neighbor distance from EXAFS data.

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TL;DR: In this article, an effective medium approximation for the conductivity tensor of a randomly inhomogeneous medium is generalized to treat, in principle, materials consisting of crystallites of arbitrary shape and conductivities tensors of arbitrary symmetry.

Abstract: An old effective-medium approximation for the conductivity tensor of a randomly inhomogeneous medium is generalized to treat, in principle, materials consisting of crystallites of arbitrary shape and conductivity tensors of arbitrary symmetry. The effective-medium approximation is roughly analogous to the coherent-potential approximation (CPA) of alloy theory. The analog of the average-$t$-matrix approximation (ATA) is also formulated in a general way. The method is fully tractable analytically for ellipsoidal crystallites. Several applications are discussed. The effective conductivity of a polycrystal consisting of randomly oriented uniaxial crystallites is calculated as a function of the anisotropy of the grains. For a model polycrystal in an intense magnetic field, the CPA and ATA are compared, the former giving more accurate results.

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TL;DR: In this article, the upper critical field in layered superconductors is calculated from a microscopic theory in which the electrons are assumed to propagate freely within the individual layers subject to scattering off impurities and to propagate via tunneling between the layers.

Abstract: The upper critical field ${H}_{c2}$ in layered superconductors is calculated from a microscopic theory in which the electrons are assumed to propagate freely within the individual layers subject to scattering off impurities and to propagate via tunneling between the layers. For the magnetic field parallel to the layers, there is a temperature ${T}^{*}l{T}_{c}$ below which the normal cores of the vortices fit between the metallic layers, removing the orbital effects as a mechanism for the quenching of superconductivity in the individual layers. In this temperature regime, ${H}_{c2\ensuremath{\parallel}}$ is thus determined by the combined effects of Pauli paramagnetism and spin-orbit scattering, and for sufficiently strong spin-orbit scattering rates, ${H}_{c2\ensuremath{\parallel}}(T=0)$ can greatly exceed the Chandrasekhar-Clogston Pauli limiting field ${H}_{P}$. This unusual behavior is found to be most pronounced in the dirty limit for the electron propagation within the layers and when the electrons scatter many times in a given layer before tunneling to an adjacent layer. Our results are also discussed in light of the available experimental data.

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TL;DR: In this paper, the experimental results for electrons obtained with the time-of-flight technique are presented for temperatures between 8 and 300 and fields ranging between 1.5 and 5 \ifmmode\times\else\texttimes\fi{} ${10}^{4}$ V ${\mathrm{cm}}^{\ensuremath{-}1} 1}$ oriented along crystallographic directions.

Abstract: Experimental results for electrons obtained with the time-of-flight technique are presented for temperatures between 8 and 300\ifmmode^\circ\else\textdegree\fi{}K and fields ranging between 1.5 and 5 \ifmmode\times\else\texttimes\fi{} ${10}^{4}$ V ${\mathrm{cm}}^{\ensuremath{-}1}$ oriented along $〈111〉$, $〈110〉$, and $〈100〉$ crystallographic directions. At 8\ifmmode^\circ\else\textdegree\fi{}K the dependence of the transit time upon sample thickness has allowed a measurement of the valley repopulation time when the electric field is $〈100〉$ oriented. These experimental results have been interpreted with Monte Carlo calculations in the same ranges of temperature and field. The theoretical model includes the many-valley structure of the Si conduction band, acoustic intravalley scattering with correct momentum and energy relaxation and correct equilibrium phonon population, several intervalley scatterings, and ionized impurity scattering.

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Xerox

^{1}TL;DR: The Onsager theory of dissociation has been used to explain the electric field, excitation wavelength, and temperature dependence of photogeneration in amorphous selenium.

Abstract: The Onsager theory of dissociation has been used to explain the electric field, excitation wavelength, and temperature dependence of photogeneration in amorphous selenium. The Onsager theory was formulated to explain the departure from Ohmic behavior in either weak electrolytes or solid dielectrics, and the analysis of charge separation was carried out using the theory of Brownian motion of one particle under the action of Coulomb attraction and the collecting field. Both the absolute magnitude and functional dependence on electric field of the photogeneration efficiency in amorphous selenium at any excitation wavelength can be unambiguously explained using a single parameter which is the initial separation between thermalized electron-hole pairs. This initial separation varies from 7.0 nm at 400-nm excitation to 0.84 nm at 620-nm excitation. The application of the theory to the measured photogeneration data also leads to the important conclusion that each absorbed photon creates a pair of thermalized carriers bound by their mutual Coulomb attraction. The low quantum efficiency measured for long-wavelength excitation is due to the smaller initial separation between oppositely charged thermalized pairs of carriers resulting in smaller dissociation efficiency. Good agreement is also obtained between the measured temperature dependence of the photogeneration efficiency and that predicted by the theory.

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TL;DR: In this paper, a theoretical description of the scattering and absorption of electromagnetic radiation induced by roughness on the surface of a semi-infinite medium is presented, where the authors use scattering theory applied to the classical Maxwell equations.

Abstract: In this paper, we present a theoretical description of the scattering and absorption of electromagnetic radiation induced by roughness on the surface of a semi-infinite medium. We approach the problem by the use of scattering theory applied to the classical Maxwell equations. We obtain formulas for the roughness-induced scattering from the surface of an isotropic dielectric for both $s$- and $p$-polarized waves incident on the surface at a general angle of incidence. When the real part of the dielectric constant of the material is negative and its imaginary part small (as in a simple nearly-free-electron metal), we extract from the expressions for the total absorption rate that portion which describes roughness-induced absorption by surface polaritons (surface plasmons). We compare our results with those recently published by Ritchie and collaborators for the case of normal incidence, and we present a series of numerical studies of the roughness-induced scattering and absorption rates in aluminum.

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TL;DR: In this paper, a theory for optical properties of particles of arbitrary shape, composed of a homogeneous isotropic material with a dielectric constant, was developed for the optical properties.

Abstract: A theory is developed for the optical properties of particles of arbitrary shape, composed of a homogeneous isotropic material with a dielectric constant $\ensuremath{\epsilon}(\ensuremath{\omega})$. The particles are so small that retardation can be neglected. An expression is obtained for the average dielectric constant of a medium containing a small fractional volume of particles. Calculations for a cube show that six resonances contribute to the optical absorption. They span a frequency range such that ${\ensuremath{\epsilon}}^{\ensuremath{'}}(\ensuremath{\omega})$, the real part of the dielectric constant, lies between -3.68 and -0.42, as contrasted with the single resonance for a sphere at ${\ensuremath{\epsilon}}^{\ensuremath{'}}(\ensuremath{\omega})=\ensuremath{-}2$. A comparison of the theory with experiments on the optical absorption of NaCl and MgO cubes shows that the width of the absorption peak can be explained by the frequency range of the cube resonances. Previous theories which assumed spherical particles required an unphysically high damping in $\ensuremath{\epsilon}(\ensuremath{\omega})$ to account for the width.

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TL;DR: In this article, a Landau theory is proposed for charge-density waves (CDW) in transition-metal dichalcogenides with the charge density as an order parameter, which predicts the sequence of phases, normal-state, commensurate-CDW, with decreasing temperature, separated by first-order phase transitions.

Abstract: A Landau theory is proposed for charge-density waves (CDW) in transition-metal dichalcogenides with the charge density as an order parameter. The theory predicts the sequence of phases, normal-state---incommensurate-CDW---commensurate-CDW with decreasing temperature, separated by first-order phase transitions. The peaks in charge density lie at "lattice sites" of a hexagonal crystal and for the incommensurate case the theory predicts phononlike distortions of the CDW "lattice" as well as dislocations. Impurities pin the charge density wave, broaden the phase transitions, and stabilize the incommensurate state relative to the commensurate state.

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TL;DR: In this paper, the Brillouin spectrum of diamond excited with either the arXiv:1708.1640$ or He-Ne laser radiation was measured with a triple-passed piezoelectrically scanned Fabry-Perot interferometer.

Abstract: The Brillouin spectrum of diamond excited with either the ${\mathrm{Ar}}^{+}$ or He-Ne laser radiation is measured with a triple-passed piezoelectrically scanned Fabry-Perot interferometer. The polarization features and the selection rules have been verified for a number of scattering geometries. From the measured frequency shifts of the Brillouin components, the following values are obtained for the elastic moduli: ${c}_{11}=10.764\ifmmode\pm\else\textpm\fi{}0.002$, ${c}_{12}=1.252\ifmmode\pm\else\textpm\fi{}0.023$, and ${c}_{44}=5.774\ifmmode\pm\else\textpm\fi{}0.014$ in units of ${10}^{12}$ dyn/${\mathrm{cm}}^{2}$. The relative intensities of the observed Brillouin components for a variety of scattering geometries are consistent with the following elasto-optic contants: ${p}_{44}=\ensuremath{-}0.172$ and ${p}_{11}\ensuremath{-}{p}_{12}=\ensuremath{-}0.292$ determined by Denning et al. and ${p}_{11}+2{p}_{12}=\ensuremath{-}0.1640$ obtained by Schneider. From a comparison of the Brillouin spectrum and the Raman spectrum associated with the zone-center optical phonon, observed under identical conditions, we obtain a value for the single independent component characterizing the Raman tensor per unit cell, viz., $|a|=4.4\ifmmode\pm\else\textpm\fi{}0.3$ ${\mathrm{\AA{}}}^{2}$.

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TL;DR: A detailed study of the generalized susceptibility of Sc metal determined from an accurate augmented-plane-wave method calculation of its energy-band structure is presented in this article, which yields simple analytic expressions for the integral inside a tetrahedral microzone of the Brillouin zone which depends only on the volume of the tetrahedron and the differences of the energies at its corners.

Abstract: A detailed study of the generalized susceptibility $\ensuremath{\chi}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}})$ of Sc metal determined from an accurate augmented-plane-wave method calculation of its energy-band structure is presented. The calculations were done by means of a computational scheme for $\ensuremath{\chi}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}})$ derived as an extension of the work of Jepsen and Andersen and Lehmann and Taut on the density-of-states problem. The procedure yields simple analytic expressions for the $\ensuremath{\chi}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}})$ integral inside a tetrahedral microzone of the Brillouin zone which depends only on the volume of the tetrahedron and the differences of the energies at its corners. Constant-matrix-element results have been obtained for Sc which show very good agreement with the results of Liu, Gupta, and Sinha (but with one less peak) and exhibit a first maximum in $\ensuremath{\chi}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}})$ at $(0, 0, 0.31)\frac{2\ensuremath{\pi}}{c}$ [vs $(0, 0, 0.35)\frac{2\ensuremath{\pi}}{c}$ obtained by Liu et al.] which relates very well to dilute rare-earth alloy magnetic ordering at ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}}_{m}=(0, 0, 0.28)\frac{2\ensuremath{\pi}}{c}$ and to the kink in the LA-phonon dispersion curve at $(0, 0, 0.27)\frac{2\ensuremath{\pi}}{c}$.

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TL;DR: In this paper, a generalized Ginzburg-Landau theory is proposed to describe the phase transition of an array of weakly coupled pseudo-one-dimensional chains, which is based on a mean-field approximation.

Abstract: A generalized Ginzburg-Landau theory is suggested to describe the phase transition of an array of weakly coupled pseudo-one-dimensional chains. Using a mean-field approximation, the coupled-chain problem is reduced to that of a single chain in an effective field. The finite-range correlations which develop along the chain are treated using exact one-dimensional solutions. The results obtained are then used to construct a generalized Ginzburg-Landau theory. We argue that this approach provides a means of treating the remaining slowly varying long-range fluctuations. Results are given for a variety of arrays consisting of Ising, classical Heisenberg, real and complex ${\ensuremath{\psi}}^{4}$ chains.

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Philips

^{1}TL;DR: In this article, optical and magneto-optical measurements have been performed at room temperature on both polycrystalline samples and thin single-crystal films of bismuth-substituted iron garnets.

Abstract: Optical and magneto-optical measurements have been performed at room temperature on both polycrystalline samples and thin single-crystal films of bismuth-substituted iron garnets. Kerr rotation, ellipticity, and reflectivity are given for polycrystalline samples of composition ${\mathrm{Y}}_{3\ensuremath{-}x}{\mathrm{Bi}}_{x}{\mathrm{Fe}}_{5}{\mathrm{O}}_{12}$ ($0lx\ensuremath{\le}1$) between 2.0 and 5.2 eV (wavelengths between 0.6 and 0.24 \ensuremath{\mu}m). The absorption and the Faraday rotation and ellipticity of epitaxial films with $0lxl0.5$ were measured up to 3.5 eV. The experimental results have been used to calculate the diagonal and off-diagonal elements of the dielectric tensor at optical frequencies. Strong magneto-optic active transitions have been found at 2.8, 3.3, 4.1, and 4.9 eV, apart from the weaker crystal-field transitions. The bands at 2.8 and 3.3 have been studied in more detail: The oscillator strengths and splittings due to spin-orbit coupling were calculated, both increase with bismuth substitution. The large splitting of the band at 3.3 eV for the bismuth-substituted compounds is concluded to be the origin of the anomalous Faraday rotation of these compounds. The assignment of these bands in terms of an energy level scheme is discussed.

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TL;DR: In this paper, the authors present nonlinear self-consistent calculations of the charge density induced by isolated ions when placed in an electron gas of the appropriate metallic density and show that in the first four metals nonlinear effects in the response of the conduction electrons to the ionic perturbations play an important role in determining charge density and the interionic potential.

Abstract: We present nonlinear self-consistent calculations of the charge density induced by isolated ${\mathrm{Li}}^{+}$, ${\mathrm{K}}^{+}$, ${\mathrm{Mg}}^{++}$, ${\mathrm{Al}}^{+++}$, and ${\mathrm{Ca}}^{++}$ ions when placed in an electron gas of the appropriate metallic density. By comparison with linear-response theory we show that in the first four metals nonlinear effects in the response of the conduction electrons to the ionic perturbations play an important role in determining the charge density and the interionic potential. However as in the case of Na studied in the previous paper these nonlinear effects can be simulated by using a suitably adjusted model potential. The calculated phonon dispersion curves for Li, K, and Al agree very well with experiment. Nonlinear effects are also very likely to be important in Ca but further work is necessary before conclusions can be drawn.

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IBM

^{1}TL;DR: In this article, Kohn and Sham showed that the cohesive energy, lattice constant, and bulk modulus of Li, Be, Na, Al, Ar, K, Ca, and Cu can be computed using the local density scheme of Kohn, to within \ensuremath{\sim}20% and \ensuresuremath{sim}03 Bohr radii, and ≤ 1.10% respectively, of experimental values.

Abstract: We show that the cohesive energy, lattice constant, and bulk modulus of Li, Be, Na, Al, Ar, K, Ca, and Cu can be calculated using the local-density scheme of Kohn and Sham, to within \ensuremath{\sim}20%, \ensuremath{\sim}03 Bohr radii, and \ensuremath{\sim}10%, respectively, of experimental values These calculations are truly a priori in that the only inputs are the atomic number $Z$ and the zero-point lattice properties Self-consistent crystal calculations were performed using the muffin-tin approximation, and atomic calculations were performed using the spin-polarized exchange-correlation functional constructed by von Barth and Hedin The results show that these approximations are adequate for computing the equilibrium properties of crystals (errors in the computed pressure-volume relations are less than \ensuremath{\sim} 10 kbar), but errors occur in the atomic calculations for atoms with more than one electron outside a closed shell, and possibly in the muffin-tin approximation for transition-element crystals

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TL;DR: In this paper, the Stoner model was applied to calculate the magneto-optical absorption spectrum of ferromagnetic nickel using an approach similar to the component state density method that has been successfully used in obtaining valence-band emission and absorption x-ray spectra of metals.

Abstract: The ${M}_{23}$ magneto-optical absorption spectrum of ferromagnetic nickel is calculated using an approach similar to the component state-density method that has been successfully used in obtaining valence-band emission and absorption x-ray spectra of metals. The ${M}_{23}$ magneto-optical effects result predominantly from spin-orbit splitting of the $3p$ core state in conjunction with the final $d$-state spin polarization. The calculated spectrum exhibits features that are directly related to electronic structure parameters including the $3p$ core spin-orbit splitting, and the unfilled $d$-band spin polarization. Temperature variations in the magneto-optical structure can be used to determine separately the exchange-splitting variation and spin-wave excitation contributions to the decrease in the magnetization. Experimental verification of these predictions should provide insight into the applicability of the Stoner model to ferromagnetic nickel and may be helpful in resolving some of the apparently conflicting results of other experimental probes of the spin polarization near the Fermi level in nickel.

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TL;DR: In this article, a self-consistent pseudopotential method was used to calculate the electronic structure of several Si (111) surface models, including Haneman's (2\ifmmode\times\else\texttimes\fi{}1) reconstructed surface model.

Abstract: A recently developed method involving self-consistent pseudopotentials has been used to calculate the electronic structure of several Si (111) surface models. The results for (1\ifmmode\times\else\texttimes\fi{}1) unreconstructed, relaxed and unrelaxed surfaces are compared with earlier calculations and discussed in terms of density-of-states curves and charge-density distributions. A fully self-consistent calculation has been carried out for Haneman's (2\ifmmode\times\else\texttimes\fi{}1) reconstructed surface model. It is found that the important experimental results can be understood using this model, and changes in the electronic structure occurring after reconstruction are rationalized on chemical grounds. In particular infrared-absorption measurements, photoemission measurements, and recent angular-dependent photoemission measurements find consistent explanations.