Showing papers in "Physical Review B in 1974"

Optical constants of transition metals: Ti, V, Cr, Mn, Fe, Co, Ni, and Pd

Abstract: The optical constants $n$ and $k$ were determined for some transition metals (Ti, V, Cr, Mn, Fe, Co, Ni, Pd) from reflection and transmission measurements on vacuum-evaporated polycrystalline thin films at room temperature, in the spectral range 0.5-6.5 eV. Three optical measurements were inverted to determine the film thickness $d$ as well as $n$ and $k$. The estimated error in $d$ was \ifmmode\pm\else\textpm\fi{}2 \AA{} and that in $n$, $k$ was less than \ifmmode\pm\else\textpm\fi{}2% over most of the spectral range. Transmission measurements were made on films in the thickness range 200-500 \AA{}. Many transition metals oxidize rapidly in the air and so measurements on those samples were performed in a nitrogen atmosphere. A detailed analysis of the effect of oxidation on the measured quantities indicates that it is small. The effects on the optical constants of the film thickness and the evaporation rate are discussed. Some recent theoretical calculations of the interband optical conductivity are compared with the results for V, Cr, and Ni. In addition, some other recent experiments are compared with our results.

Computer simulation of atomic-displacement cascades in solids in the binary-collision approximation

Abstract: A comprehensive computer program has been developed for the simulation of atomic-displacement cascades in a variety of crystalline solids, using the binary-collision approximation to contruct the projectile trajectories. The atomic scattering is governed by the Moli\'ere potential.Impact-parameter-dependent inelastic losses are included using Firsov's theory. Thermal vibrations of the target atoms and crystal surfaces may be included. Permanent displacement of lattice atoms may be based on either an energy-threshold criterion or a Frenkel-pair-separation criterion. An extensive series of calculations has been made for cascades in the simple metals Cu, Fe, and Au, to test the effects on the results of many of the model parameters. When a displacement-threshold energy is used, the number of Frenkel pairs is found to be a linear function of that part of the primary recoil energy which remains as the kinetic energy of atoms. This result is independent of target temperature, of the presence or absence of inelastic energy losses, and of various details of the model. In contrast, when a separation criterion is used, the number of defects increases less rapidly than linearly. This effect is caused by increased recombination in the highly disturbed tracks of the energetic recoils. Agreement between theoretical and experimental estimates of the radiation damage produced by neutron irradiation of Cu is substantially improved in the latter model.

Percolation and conductivity: A computer study. I

Abstract: In this paper we present a large number of computer solutions of various types of resistor networks. Some of these are analogous to physical problems such as impurity conduction in lightly compensated semiconductors and variable-range hopping in amorphous semiconductors. A significant extension of the standard relaxation techniques was required to implement these solutions. The results of these calculations are compared to percolation-model predictions based on concepts developed in the first paper of this series. A simple criterion is found for the applicability of the critical-percolation-path analysis to problems of this type and this is used to formulate an accurate prediction for the impurity-conduction case. Arguments based on percolation models are also given to show that the ${T}^{\ensuremath{-}\frac{1}{4}}$ and ${T}^{\ensuremath{-}\frac{1}{3}}$ dependence of ${log}_{10}\ensuremath{\sigma}$ often predicted for three-dimensional and two-dimensional variable-range hopping are indeed expected to be observed, and results on resistivity networks analogous to these problems are shown to be consistent with these arguments. Accurate empirical formulas are deduced from these computer calculations and we use them to analyze some recent data on films of $a$-Ge. Employing the results of the preceding paper, several experimental studies, and our computer models we have also examined the utility of the critical-volume-fraction rule of Sher and Zallen in solving various types of mixture conduction problems. We find that application of this rule is appropriate only in rather limited circumstances, and that in general a knowledge of the topological properties of these problems must be employed in finding the percolation threshold.

Fundamental energy gap of GaN from photoluminescence excitation spectra

Abstract: In the absence of samples suitable for transmission measurements, photoluminescence excitation spectra (PLE) have been found useful in the evaluation of detailed information about the lowest direct-absorption edge of GaN. In this work the results of PLE measurements are combined with data on reflection and luminescence in the intrinsic region to determine the positions of $A\ensuremath{-}$, $B\ensuremath{-}$, and $C$-exciton ground-state transition energies and the lowest band gap. Neglecting polariton effects, the value of the $A$-exciton ground-state transition energy is determined as being ${E}_{A}^{x}=3.4751\ifmmode\pm\else\textpm\fi{}0.0005$ eV at 1.6 K from combined PLE and emission spectra. The corresponding values for $B$ and $C$ exciton transitions are found to be ${E}_{B}^{x}=3.4815\ifmmode\pm\else\textpm\fi{}0.001$ eV and ${E}_{C}^{x}=3.493\ifmmode\pm\else\textpm\fi{}0.005$ eV from PLE spectra. The lowest band gap is determined to be ${E}_{g}^{A}={3.503}_{\ensuremath{-}0.002}^{+0.005}$ eV at 1.6 K, which fixes the ground-state $A$-exciton binding energy as ${E}_{B}(A)={28}_{\ensuremath{-}3}^{+6}$ meV, in good agreement with the effective-mass value. The temperature dependence of the band gap could also be accurately measured in PLE spectra and can be described by an expression ${E}_{g}^{A}=[3.503+\frac{(5.08\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}{T}^{2})}{(T\ensuremath{-}996)}]$ eV for $Tl295$ K, with an estimated relative uncertainty of \ifmmode\pm\else\textpm\fi{} 0.002 eV.

The Toda lattice. II. Existence of integrals

Abstract: Following recent computer studies which suggested that the equations of motion of Toda's exponential lattice should be completely H\'enon discovered analytical expressions for the constants of the motion. In the present paper, the existence of integrals is proved by a different method. Our approach shows the Toda lattice to be a finite-dimensional analog of the Korteweg-de Vries partial differential equation. Certain integrals of the Toda equations are the counterparts of the conserved quantities of the Korteweg-de Vries equation, and the theory initiated here has been used elsewhere to obtain solutions of the infinite lattice by inverse-scattering methods.

Theory of the extended x-ray-absorption fine structure

Abstract: A general theory of the fine structure observed on the high-energy side of the $K$-absorption edge (EXAFS) is presented. The form of the theory presented is useful when the excited atom is not too highly ionized and the potential is approximately spherically symmetric. A critical analysis is made of long-range-order theories of EXAFS and it is shown that the coherent effects of the periodic potential are not the dominant mechanism as assumed previously. The dominant mechanism is the scattering in the vicinity of the absorbing atom, and can most naturally be calculated by considering only the immediate environment surrounding the absorbing atom. Fourier-transforming EXAFS data determines the spatial dependence of a scattering matrix. This scattering matrix is expected to peak at the location of surrounding atoms, locating them, and can give information on the type of surrounding atoms and possibly the surrounding valence electron density. Because the $K$ edges of different atoms are separated, such information can be obtained around each atom type separately, making EXAFS a potentially powerful tool for determining the microscopic structure of condensed matter.

Total valence-band densities of states of III-V and II-VI compounds from x-ray photoemission spectroscopy

Abstract: A comprehensive survey of the total valence-band x-ray-photoemission spectra of 14 semiconductors is reported: cubic GaP, GaAs, GaSb, InP, InAs, InSb, ZnS, ZnSe, ZnTe, CdTe, and HgTe, hexagonal ZnO, CdS, and CdSe. The binding energies of the outermost d shells were determined relative both to the top of the valence bands (E;sup V;sub B;) and to the Fermi level of a thin layer of gold that was vapor deposited after each run (E;sup F;sub B;). The Fermi level fell near the center of the gap for six samples, near the top for two, and near the bottom for three. Evidence for an apparent increase in core d-level spin-orbit slitting over free-atom values was interpreted as a possible spreading of a ..gamma../sub 7/ and a ..gamma../sub 8/ level from the upper (d /sub 3///sub 2/) ..gamma../sub 8/ level by a tetrahedral crystal field. The s, p valence-band spectra showed three main peaks, wth considerable structure on the ''least-bound'' peak. Characteristic binding energies of spectral features in I'(E) are tabulated. The energies of the characteristic symmetry points L/sub 3/, X/sub 5/, W/sub 2/ ..sigma..;sup min 1;, W/sub 1/, X/sub 3/(L/sub 1/), X/sub 1/, L/sub 1/, and ..gamma../sub 1/ for the 11 cubicmore » compounds are compared with UPS and theoretical band-structure results. The energies calculated using the relativistic-orthogonalized-plane-wave approach with X;sub infinityBETA; exchange agree very well with experiment, on the whole. The desities of states calculated using the empirical-psuedopotenital method provided a useful basis for relating features in I'(E) to energies of the characteristic symmetry points. 21 tables, 16 figures« less

Calculation of multiplet structure of core p -vacancy levels. II

Abstract: The multiplet splittings of core $p$-vacancy levels have recently been observed in various transition-metal complexes and in some rare-earth as well as actinide complexes. This paper presents the calculation of the multiplet structure of core $p$-vacancy levels in the Hartree-Fock free-ion approximation. The spin-orbit and crystal-field effects have been included. The cases studied are ${\mathrm{Mn}}^{2+}$ in Mn${\mathrm{F}}_{2}$ and the free ion ${\mathrm{Fe}}^{3+}$. For $3p$ vacancies these effects appear to be unimportant from the point of view of photoelectron spectroscopy owing to the limited resolution of the technique. For $2p$ vacancies the spin-orbit interaction is comparable to the electrostatic interaction between the electrons and both the interactions must be considered simultaneously. The conclusion is that the x-ray photoelectron spectra of inner-core electrons are more suitable for chemical analysis than those of outer electrons which, in addition, contain large correlation and many-body effects.

Single-particle states, Kohn anomaly, and pairing fluctuations in one dimension

Abstract: We compute the single-particle spectral density, susceptibility near the Kohn anomaly, and pair propagator for a one-dimensional interacting-electron gas. With an attractive interaction, the pair propagator is divergent in the zero-temperature limit and the Kohn singularity is removed. For repulsive interactions, the Kohn singularity is stronger than the free-particle case and the pair propagator is finite. The low-temperature behavior of the interacting system is not consistent with the usual Ginzburg-Landau functional because the frequency, temperature, and momentum dependences are characterized by power-law behavior with the exponent dependent on the interaction strength. Similarly, the enrgy dependence of the single-particle spectral density obeys a power law whose exponent depends on the interaction and exhibits no quasiparticle character. Our calculations are exact for the Luttinger or Tomonage model of the one-dimensional interacting system.

X-ray photoemission studies of diamond, graphite, and glassy carbon valence bands

Abstract: The high-resolution x-ray photoemission spectra (XPS) of the total valence bands of atomically clean diamond, graphite, and glassy carbon, obtained with monochromatized Al K ..cap alpha.. radiation, are reported and discussed. By comparing valence-band and carbon-1s photoelectron kinetic energies, the XPS valence-band spectra I'E) of diamond and graphite were rigorously affixed to the same energy scale as earlier K x-ray emission spectra i(E). The two spectra - I'(E) and i(E) - have very different energy dependencies of intensity because selection rules and cross-section ratios render i(E) sensitive only to 2p character and I'(E) far more sensitive to 2s character. Taken together, I'(E) and i(E) show that the fractional p character in the diamond valence band increases from approx. 16% at the bottom of the band to approx. 92% at the top, with an average hybridization of approx. s/sup 1/ /sup 2/p/sup 2/ /sup 8/. The spectra agree well with the density of states of Painter et al, but indicate a valence-band width of 24.2(10) eV rather than their 20.8 eV. The C(1s) binding energy of 284.68(20) eV in graphite agrees well with a recent theoretical estimate of 284.4(3) eV by Davis and Shirley. Analysis of I'(E) i(E) for graphite resolvesmore » the valence bands cleanly into sigma and ..pi.. bands, with the spectrum I'(E) of the former resembling that of diamond, but with a stronger 2s admixture (sp/sup 2/ vs sp/sup 3/). The XPS cross section of the (p/sub z/)..pi.. bands was very low, as expected by symmetry. The bandwidth of 24(1) eV somewhat exceeded Painter and Ellis's calculated value of 19.3 eV. Glassy carbon showed an I'(E) between that of diamond and graphite, consistent with an amorphous lattice containing both trigonal and tetrahedral bonds. 8 figures, 3 tables.« less

Surface effects on magnetic phase transitions

Abstract: The surface scaling theory previously presented by the authors is developed further, and derived heuristically from a cluster model. Monte Carlo calculations are carried out to obtain the spatial and temperature dependence of the magnetization in Ising and Heisenberg systems with free surfaces. The exponent ${\ensuremath{\beta}}_{1}$ of the (surface) layer magnetization is shown to agree with the scaling value (${\ensuremath{\beta}}_{1}\ensuremath{\approx}\frac{2}{3}$) previously derived. In the Heisenberg system, the results at low temperature agree with a spin-wave calculation by Mills and Maradudin. Ising models with modified exchange ${J}_{s}=J(1+\ensuremath{\Delta})\ensuremath{ e}J$ on the surface are considered, both in mean-field theory and by means of high-temperature-series expansions. The critical value ${\ensuremath{\Delta}}_{c}$ for surface ordering is found from the series to be 0.6, compared to the mean-field value of 0.25. For $\ensuremath{\Delta}g{\ensuremath{\Delta}}_{c}$ there is a temperature region in which the surface behaves like a bulk two-dimensional Ising model near its phase transition. The critical exponents experience a crossover at $\ensuremath{\Delta}={\ensuremath{\Delta}}_{c}$, which is reflected in poorly behaved series, and effective exponents differing from the true ones for $\ensuremath{\Delta}\ensuremath{\lesssim}{\ensuremath{\Delta}}_{c}$. In the case of weakened surface exchange ($0l{J}_{s}lJ$), the layer magnetization is shown to fit a linear temperature dependence over a large temperature range below ${T}_{c}$, thus providing a possible explanation for previous experiments. For sufficiently strong negative ${J}_{s}$, mean-field theory predicts that the surface will order antiferromagnetically while the bulk is ferromagnetic.

Structural interpretation of the infrared and Raman spectra of glasses in the alloy system Ge 1-x S x

Abstract: We report a study of the infrared and Raman spectra of bulk glasses in the binary alloy system ${\mathrm{Ge}}_{1\ensuremath{-}x}{\mathrm{S}}_{x}$ ($0.90\ensuremath{\ge}x\ensuremath{\le}0.55$). The spectra are interpreted in terms of models based on covalent bonding in which the $8\ensuremath{-}N$ rule is satisfied; i.e., models in which the Ge atoms are fourfold coordinated and the S atoms are twofold coordinated. For the compound composition Ge${\mathrm{S}}_{2}$, $x=0.67$, the spectra are interpreted in terms of a chemically ordered network in which the element of local order is a tetrahedral arrangement of S atoms about a central Ge atom. For the S-rich alloys, $0.90\ensuremath{\ge}xg0.67$, the data support a generalized chain-crossing model (CCM) rather than a random-covalent-network model (RCNM). The generalized CCM allows for a second species of ${\mathrm{S}}_{8}$ rings to be in solution with a Ge-S network. The ${\mathrm{S}}_{8}$ ring fraction shows a sharp increase in concentration for $xg0.80$ indicating that on the average only one to two S atoms are incorporated between the Ge Sites of the network component. For Ge-rich alloys the more limited experimental data support a restricted network model of Philipp which allows Ge-Ge and Ge-S bonds, but not S-S bonds, rather that a RCNM.

Photoemission spectroscopy-Correspondence between quantum theory and experimental phenomenology

Abstract: We describe the relation between the observed behavior of photoemission energy distributions vs frequency, angle, etc., and the quantum theory of photoemission as recently set forth formally by Caroli et al. We derive a Fermi's Golden-Rule formula for the angle- and energy-resolved photocurrent from an independent electron solid, and show in detail the approximations which render this formula equivalent to that of the familiar three-step model of bulk photoemission. In terms of the Golden-Rule formula, we account for the direct-transition band-structure regime generally observed at low photon energies (hν≲20−30 eV) and the "photoemission density of states", or x-ray-photoemission-spectroscopy regime, observed at higher energies. We also propose an explanation of Feuerbacher et al.'s observation of "direct photoemission into the vacuum" from single-crystal tungsten surfaces. Finally, we discuss the criteria which determine the relative magnitudes of photocurrents from a surface adsorbate layer and an underlying substrate.

Renormalization-group methods for critical dynamics: I. Recursion relations and effects of energy conservation

Abstract: The renormalization-group method for studying critical phenomena is generalized to a class of dynamical systems---the time-dependent Ginzburg-Landau models. The effects of conservation laws on the critical dynamics are investigated through the study of models with different conservation properties for the energy and the space integral of the order parameter. Dynamic critical exponents near four dimensions ($d\ensuremath{\approx}4$) are obtained from recursion relations, analogous to those of Wilson and Fisher. The physical significance of the time-dependent Ginzburg-Landau models is explored and the applicability of the results to experiments on the NMR linewidth of Fe${\mathrm{F}}_{2}$ is discussed.

Stimulated-emission cross section and fluorescent quantum efficiency of Nd 3+ in yttrium aluminum garnet at room temperature

Abstract: The stimulated-emission cross sections and fluorescence branching ratios for the principal fluorescence transitions of YAG:Nd emanating from the $^{4}F_{\frac{3}{2}}$ state have been measured at room temperature. The peak cross section of the well-known 1064.2-nm laser line is here found to have a value of 4.6\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}19}$ ${\mathrm{cm}}^{2}$. Since the cross sections reported here are inconsistent with the generally accepted value of near unity for the radiative quantum efficiency $\ensuremath{\eta}$ of the $^{4}F_{\frac{3}{2}}$ state the quantity $\ensuremath{\eta}$ has been measured directly. A value of 0.56\ifmmode\pm\else\textpm\fi{}0.11 is found for $\ensuremath{\eta}$ which is consistent with the observed fluorescence lifetime of the $^{4}F_{\frac{3}{2}}$ state and the measured cross sections.

Superparamagnetism and relaxation effects in granular Ni-Si O 2 and Ni- Al 2 O 3 films

Abstract: The susceptibility of an array of fine nickel particles was measured as a function of temperature from 1.5 to 300 \ifmmode^\circ\else\textdegree\fi{}K at a frequency of 5 kHz. The particles were formed by cosputtering nickel with Si${\mathrm{O}}_{2}$ or ${\mathrm{Al}}_{2}$${\mathrm{O}}_{3}$ and varied in diameter between 10 and 100 \AA{}. With increasing temperature, the susceptibility increased from its initial value to a maximum at a temperature ${T}_{B}$ followed by a hyberbolic decrease. A theory based on the relaxation time for single-domain particles $\ensuremath{\tau}={\ensuremath{\tau}}_{0}{e}^{\frac{KV}{kT}}$ ($K$ is the anisotropy energy, $V$ is the particle volume) quantitatively explains the data. At $T=0$ all the particles are blocked by the anisotropy barriers. As the temperature is increased the susceptibility increases because particles for which $\ensuremath{\omega}\ensuremath{\tau}l1$ ($\ensuremath{\omega}$ is the angular frequency) are no longer blocked. Above ${T}_{B}$ all the particles are unblocked and the susceptibility is characteristic of superparamagnetism. Analysis of the data yields information about the particle volume distribution function and a value for the effective anisotropy energy.

Band structure of nickel: Spin-orbit coupling, the Fermi surface, and the optical conductivity

Abstract: A previous self-consistent calculation of energy bands in ferromagnetic nickel using the tight-binding method has been extended to include spin-orbit coupling. Exchange was incorporated using the $X\ensuremath{\alpha}$ method with $\ensuremath{\alpha}=\frac{2}{3}$. Energy levels were obtained at 1357 points in 1/16th of the Brillouin zone. The direction of spin alignment was taken to be [001]. The density of states was computed by a hybrid method. Cross sections of the Fermi surface were determined, and effective masses were obtained. The interband contribution to the conductivity tensor was calculated using matrix elements computed from wave functions including spin-orbit coupling. Results were obtained for both the diagonal and the off-diagonal elements of the conductivity tensor.

Special points in the two-dimensional Brillouin zone

Abstract: Using the method of Chadi and Cohen, we present, for each of the two-dimensional lattice types, the mean-value point, the set of generating wave vectors, and the sets of special points in the two-dimensional Brillouin zone which are the most efficient in finding accurate averages of a periodic function over the Brillouin zone.

Peierls instability in Heisenberg chains

Abstract: Dimerization phase transitions for $S=\frac{1}{2}$ linear antiferromagnetic chains is investigated by analogy with Peirels transitions in linear conducting chains. This analogy is very close when the fermion representation is used to describe the spin system, and the fermion interactions are treated in the Hartree-Fock approximation. Since the Fermi wave vector can be varied continuously by a magnetic field, the linear antiferromagnetic chain may be a convenient system for studying questions concerning. the commensurability of the Fermi wave vector with the underlying lattice which have arisen in connection with the conventional Peierls transition.

Electronic structure of silicon

Abstract: It is shown that a purely local-pseudopotential calculation is able to accurately reproduce the major optical gaps and cyclotron masses. However, deviations from the experimental results become manifest in photoemission and x-ray charge-density results as we extend our calculations to the lower valence bands. These deviations indicate the necessity of an energy-dependent nonlocal $s$-well potential, a conclusion which is also supported by an analysis of the Heine-Abarenkov pseudopotential scheme. A detailed comparison is made between experimental results obtained from optical, photoemission, x-ray, and cyclotron-resonance measurements, and the results of both the local calculation and an energy-dependent nonlocal calculation. Yang and Coppens's recent determination of the valence charge density in silicon makes it possible to assess the accuracy of the pseudocharge densities for the first time.

Dispersion of the nonlinear optical susceptibility tensor in centrosymmetric media

Abstract: The production of light at the combination frequency $2{\ensuremath{\omega}}_{1}\ensuremath{-}{\ensuremath{\omega}}_{2}$ in centrosymmetric media has been observed as a function of the frequencies ${\ensuremath{\omega}}_{1}$ and ${\ensuremath{\omega}}_{2}$ and the polarization directions of two incident dye-laser beams. The interference of the Raman resonance with the complex electronic contribution to ${\ensuremath{\chi}}^{(3)}$ has been observed. In diamond and in benzene all of the components of the third-order nonlinear susceptibility have been measured and calibrated with respect to known cross sections for spontaneous Raman emission. Contributions to the cubic nonlinearity have also been measured in the fluoride series Ca${\mathrm{F}}_{2}$, Sr${\mathrm{F}}_{2}$, Cd${\mathrm{F}}_{2}$, Ba${\mathrm{F}}_{2}$, and in calcite.

Generalized-master-equation theory of excitation transfer

Abstract: A theory of the time dependence of resonance transfer of excitation energy between molecules is developed in terms of memory functions appearing in the transition rates of a generalized master equation (GME). The memory can be computed explicitly and, due to the coarse-graining operation incorporated in our derivation of the GME, the accuracy of the memory function depends only on the amount of detailed information one has, or wishes to include, about the spectrum and dynamics of the system. The formalism yields a unified description of coherent motion at short times and diffusive transport at long times, and for the case of transfer between and among identical molecules provides a generalized approach to the theory of exciton transport. Memory functions for transfer between anthracene molecules are obtained as an illustration of the theory. The connection between the new formalism and existing exciton-transport theories is indicated and its relation to the theory of non-Markoffian random walks is presented.

Cubic contributions to the spherical model of shallow acceptor states

Abstract: In a previous paper the effective-mass Hamiltonian for shallow acceptor states was separated into a spherical term and a cubic contribution. Neglecting the latter term, a spherical model was formulated which explained the main features of the experimental acceptor spectra. Here the effects of the cubic term are studied using perturbation theory, and all the details of the observed spectra are reproduced. As in the case of the spherical model, the eigenvalue problem is reduced to simple radial Hamiltonians which are explicitly given for the most important acceptor states. These Hamiltonians are solved numerically and the resulting eigenvalues are tabulated as functions of the relevant parameters. The predicted spectra are in good agreement with available experimental data for acceptors in Ge, InSb, and GaAs, but not for acceptors in Si, where the unusual strength of the cubic term makes the present analysis unsatisfactory.

Dimerization of a linear Heisenberg chain in the insulating phases of V 1-x Cr x O 2

Abstract: The nuclear magnetic resonance (NMR) of ${\mathrm{V}}^{51}$ has been studied in the series of compounds ${\mathrm{V}}_{1\ensuremath{-}x}{\mathrm{Cr}}_{x}{\mathrm{O}}_{2}$ between 100 and 350 K. Three insulating phases are clearly distinguished. In the low-temperature ${M}_{1}$ phase only one V site is seen with a positive Knight shift and electric-field gradient identical to the insulating phase of pure V${\mathrm{O}}_{2}$. At temperatures just below the metal-insulator transition a second phase ${M}_{2}$ is stable in which two sites are resolved. One site has a small positive Knight-shift characteristic of a paired ${\mathrm{V}}^{4+}$ site while the other has a negative Knight shift showing a localized ${\mathrm{V}}^{4+}$ site. These two sites are identified as the V atoms on the paired chains and the equispaced chains in $\frac{C2}{m}$ structure of Marezio et al. At intermediate temperatures a transitional phase $T$ is stable in which two sites can be resolved by their electric-field gradients. The two sites are progressively differentiated by increasing temperature and Cr concentration and are interpreted as arising from two sets of inequivalent paired chains, one of which is depairing with increasing temperature and Cr concentration. These results are inconsistent with the monoclinic symmetry and a disordered bond model proposed previously for the transitional phase. Triclinic splittings were observed recently by Villeneuve et al. and additional crystallographic evidence supporting this result is presented. The magnetic properties are interpreted as a set of noninteracting linear Heisenberg chains and the ${M}_{2}\ensuremath{-}T$ transition as a dimerization of the linear Heisenberg chain. The results demonstrate a breakdown of the band model in the insulating phases.

Surface polaritons in a circularly cylindrical interface: Surface plasmons

Abstract: A theoretical investigation of surface polaritons in the circularly cylindrical geometry is presented. The complete set of Maxwell's equations (retardation effects are not neglected) is solved with the simple dielectric function, $\ensuremath{\epsilon}(\ensuremath{\omega})=1\ensuremath{-}\frac{{\ensuremath{\omega}}_{p}^{2}}{{\ensuremath{\omega}}^{2}}$, where ${\ensuremath{\omega}}_{p}$ is the bulk plasma frequency. The resulting transcendental equation for the eigenfrequencies is solved via numerical methods for three representative values of the cylindricality constant, $\ensuremath{\alpha}=\frac{{\ensuremath{\omega}}_{p}a}{c}$, where $a$ is the cylinder radius and $c$ the velocity of light. In addition to the real nonradiative surface plasmons, various virtual radiative surface plasmons exist with properties depending rather strongly on $\ensuremath{\alpha}$. The results are compared with existing experimental data. Further experiments are proposed in order to reveal the most interesting features of the surface plasma modes.

Temperature dependence of transverse- and longitudinal-optic modes in Ti O 2 (rutile)

Abstract: The temperature dependence of the infrared reflectivity of rutile, Ti${\mathrm{O}}_{2}$, is reported in the range 275-900 ${\mathrm{cm}}_{\ensuremath{-}1}$ and from room temperature up to 1500 K, for both the ${A}_{2u}$- and ${E}_{u}$-type mode spectra. Reflectivity spectra are fitted with the aid of a four-parameter dispersion model based on the factorized form of the dielectric function. The equivalence between the classical dielectric response function and the phonon propagator provides a correlation between adjusted frequencies and damping and their quantum counterparts in terms of the phonon self-energy. The temperature dependence of the anharmonic frequency shift for the ferroelectric (FE) ${A}_{2u}(\mathrm{TO})$ mode which has been shown to be linear in the vicinity of room temperature looks more rapid at high temperature. This may indicate the occurrence of an anharmonic coupling that involves the sixth-order Hamiltonian, which acts as a quadratic function of temperature to stabilize the FE mode together with quartic anharmonicity. The behavior of TO and LO phonon damping with increasing temperature shows that the phonon lifetimes in rutile are limited by anharmonic three-phonon coupling. Phonon lifetimes are found shorter than in other oxide crystals. Moreover, the ratio of the damping function evaluated at the harmonic frequency on the frequency of the ${A}_{2u}(\mathrm{TO})$ mode is six times higher than the same ratio averaged on all other modes. Thus rather large anharmonicities are revealed in rutile that are correctly described by lowest-order terms in the phonon self-energy.

Pressure-volume relationship and pressure-induced electronic and structural transformations in Eu and Yb monochalcogenides

Abstract: The pressure-volume relationships for EuSe, EuS, YbSe, and YbS have been obtained from high-pressure x-ray-diffraction studies to nearly 300 kbar. Like EuTe, EuSe and EuS exhibit normal compression and undergo the NaCl-to-CsCl-type transition at about 145 and 215 kbar. The compression curves of YbSe and YbS are anomalous in the 150-200-kbar region, which we believe is because of a change in the valence state of Yb from ${2}^{+}$ towards the ${3}^{+}$ state. Among the Eu monochalcogenides EuO is the only substance that shows a valence transformation (\ensuremath{\sim}300 kbar) followed by a NaCl-to-CsCl-type transition (\ensuremath{\sim}400 kbar). However, all the Yb monochalcogenides undergo the valence transformation continuously with pressure. The bulk moduli evaluated from the experimental $P\ensuremath{-}V$ data and the measured pressure coefficients of the energy gap between the $4f$ level and the conduction-band edge from optical-absorption studies of divalent rare-earth monochalcogenides are compared. These data are used to rationalize the occurrence or nonoccurrence of the valence transitions in this series of compounds.