Showing papers in "Physical Review B in 1972"

Optical Constants of the Noble Metals

Abstract: The optical constants $n$ and $k$ were obtained for the noble metals (copper, silver, and gold) from reflection and transmission measurements on vacuum-evaporated thin films at room temperature, in the spectral range 0.5-6.5 eV. The film-thickness range was 185-500 \AA{}. Three optical measurements were inverted to obtain 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 0.02 over most of the spectral range. The results in the film-thickness range 250-500 \AA{} were independent of thickness, and were unchanged after vacuum annealing or aging in air. The free-electron optical effective masses and relaxation times derived from the results in the near infrared agree satisfactorily with previous values. The interband contribution to the imaginary part of the dielectric constant was obtained by subtracting the free-electron contribution. Some recent theoretical calculations are compared with the results for copper and gold. In addition, some other recent experiments are critically compared with our results.

High-Resolution X-Ray Photoemission Spectrum of the Valence Bands of Gold

Abstract: High-resolution gold-valence-band photoemission spectra were obtained by the use of monochromatized $\mathrm{Al} K\ensuremath{\alpha}$ radiation and a single-crystal specimen. After background and scattering corrections were made, the results were compared directly with broadened theoretical density-of-states functions. The following conclusions were drawn: (i) Relativistic band-structure calculations are required to fit the spectrum. (ii) Both the Korringa-Kohn-Rostoker calculation of Connolly and Johnson and the relativistic-augmented-plane-wave calculation by Christensen and Seraphin give density-of-states results that (after broadening) follow the experimental curve closely. (iii) Of the theoretical functions available to date, those with full Slater exchange agree best with experiment (perhaps because of a cancellation of errors). Fractional ($\frac{2}{3} or \frac{5}{6}$) exchange gives $d$ bands that are too wide. (iv) Eastman's 40.8-eV ultraviolet photoemission spectrum is similar to the x-ray spectrum, suggesting little dependence on photon energy above 40 eV. (v) Both (ii) and (iv) imply an absence of strong matrix-element modulation in the photoemission spectrum of gold.

Weak Absorption Tails in Amorphous Semiconductors

Abstract: Optical absorption measurements near the absorption edge are presented for three bulk semiconductor glasses: ${\mathrm{As}}_{2}$${\mathrm{S}}_{3}$, ${\mathrm{Ge}}_{33}$${\mathrm{As}}_{12}$${\mathrm{Se}}_{55}$, and ${\mathrm{Ge}}_{28}$${\mathrm{Sb}}_{12}$${\mathrm{Se}}_{60}$. The weak absorption tails observed below the exponential part of the edge also follow an exponential law, and they are not due to a light-scattering artifact. We associate them with localized states in the band gap. The results are interpreted in terms of a model in which optical transitions occur between localized states below the mobility edge and extended states of the opposite band.

Self-Consistent Results for n -Type Si Inversion Layers

Abstract: Self-consistent results for energy levels, populations, and charge distributions are given for $n$-type inversion layers on $p$-type silicon. Quantum effects are taken into account in the effective-mass approximation, and the envelope wave function is assumed to vanish at the surface. Approximate analytic results are given for some special cases. Numerical results are given for representative surface orientations, bulk acceptor concentrations, inversion-layer electron concentrations, and temperatures.

Optimization of the Statistical Exchange Parameter α for the Free Atoms H through Nb

Abstract: We have examined two criteria for determining the exchange parameter $\ensuremath{\alpha}$ which occurs in the $X\ensuremath{\alpha}$ local-statistical-exchange approximation, an approximation widely used in energy-band and molecular calculations. These criteria are (i) adjustment of the statistical total energy to the Hartree-Fock total energy, leading to ${\ensuremath{\alpha}}_{\mathrm{HF}}$, and (ii) satisfaction of the virial theorem, leading to ${\ensuremath{\alpha}}_{\mathrm{vt}}$. We have calculated the values of the parameter $\ensuremath{\alpha}$ corresponding to these two criteria for the neutral atoms H through Nb, and compared them with the values ${\ensuremath{\alpha}}_{min}$ corresponding to the Hartree-Fock total-energy minimization criterion employed earlier by Kmetko and Wood. While the last-mentioned criterion leads to $\ensuremath{\alpha}$ values which show large fluctuations across the periodic table as a function of $Z$, the $\ensuremath{\alpha}$ values obtained by either of the two criteria used in this paper show a systematic variation as a function of $Z$, reflecting the shell structure of the atoms, and varying linearly with $Z$ within the range of $Z$ for which a particular atomic subshell is being filled.

Corrections to scaling laws

Abstract: The effects of higher-order contributions to the linearized renormalization group equations in critical phenomena are discussed. This analysis leads to three quite different results: (i) An exact scaling law for redefined fields is obtained. These redefined fields are normally analytic functions of the physical fields. Corrections to the standard power laws are derived from this scaling law. (ii) The theory explains why logarithmic terms can exist in the free energy. (iii) The case in which the energy scales like the dimensionality is analyzed to show that quite anomalous results may be obtained in this special situation.

Stress-Induced Shifts of First-Order Raman Frequencies of Diamond- and Zinc-Blende-Type Semiconductors

Abstract: In this paper we report measurements of the effects of large static uniaxial stress along [001], [111], and [110] on the frequency of the $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}\ensuremath{\approx}0$ optical phonons in Ge, GaAs, GaSb, InAs, and ZnSe using first-order Raman scattering. In the absence of stress, the first-order Stokes-Raman spectrum of diamond-type materials exhibits a single peak which corresponds to the $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}\ensuremath{\approx}0$ triply degenerate optical phonons (${F}_{2g}$ or ${\ensuremath{\Gamma}}_{{25}^{\ensuremath{'}}}$) while the zinc-blende materials exhibit two peaks, corresponding to the $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}\ensuremath{\approx}0$ LO and TO phonons. The application of the uniaxial stress causes polarization-dependent splittings and/or shifts which are linear in the stress. From these observed splittings and shifts we have obtained experimental values for the phenomenological coefficients ($p, q, \mathcal{r}$) which describe the changes in the "spring constant" of these optical phonons with strain. Comparison of the experimental values is made with several theoretical considerations based on bond-stretching and bond-bending interactions between atoms. The shift due to the hydrostatic component of the strain yields a value for the mode-Gr\"uneisen parameter, which is compared with the results of hydrostatic-pressure measurements. For the zinc-blende-type materials, the doubly degenerate TO-phonon line exhibits both a splitting and shift with stress, while only a shift is observed for the singlet LO-phonon line. In the case of the III-V compounds, one of the split TO lines has a stress dependence equal to that of the LO-phonon line, while this is not the case for the group II-VI material (ZnSe) we have investigated. This latter result is interpreted in terms of the stress dependence of the effective charge.

Electron Correlations at Metallic Densities. V

Abstract: In this paper we present a modification of an earlier theory of Singwi et al of electron correlations at metallic densities The modification consists in allowing for the change of the pair correlation function in an external weak field via the density derivative of the equilibrium pair correlation function This results in a new expression for the local-field correction The present theory has the merit of satisfying almost exactly the compressibility sum rule and of giving a satisfactory pair correlation function Results of self-consistent numerical calculations for the static pair correlation function, correlation energy, compressibility, and plasmon dispersion relation for the electron liquid in the metallic-density range are presented For those interested in the application of the results of the present paper, numerical values of the local-field correction as a function of wave number have been tabulated in the density range ${r}_{s}=1\ensuremath{-}6$

Self-Consistent-Field X α Cluster Method for Polyatomic Molecules and Solids

Abstract: This paper describes a practical self-consistent-field (SCF) method of calculating electronic energy levels and eigenfunctions, adapted for polyatomic molecules and solids. The one-electron Schr\"odinger equation is set up for a so-called "muffin-tin" approximation to the true potential, spherically symmetrical within spheres surrounding the various nuclei, constant in the region between the spheres, spherically symmetrical outside a sphere surrounding the molecule. The method of solving this equation is a multiple-scattering method, equivalent to the Korringa-Kohn-Rostoker (KKR) method often used for crystals. Once the eigenfunctions and eigenvalues of this problem are determined, one assumes that the orbitals of lowest eigenvalue are occupied, up to a Fermi level. From the resulting charge densities, one can compute a total energy, using a statistical approximation for the exchange correlation. This approximation has an undetermined factor $\ensuremath{\alpha}$ (whence the name $X\ensuremath{\alpha}$ method). The spin orbitals and occupation numbers are varied to minimize this total energy, resulting in one-electron equations. The value of $\ensuremath{\alpha}$ for an isolated atom is determined by requiring that the total energy, using the statistical approximation, should equal the precise Hartree-Fock energy. This leads to very accurate spin orbitals. In a molecule or crystal, one uses the $\ensuremath{\alpha}'\mathrm{s}$ characteristic of the various atoms within the atomic spheres, and a suitable average in the region between. The computer programs for making these self-consistent calculations, for such radicals and polyatomic molecules as S${\mathrm{O}}_{4}^{\ensuremath{-}2}$, Cl${\mathrm{O}}_{4}^{\ensuremath{-}}$, Mn${\mathrm{O}}_{4}^{\ensuremath{-}}$, and S${\mathrm{F}}_{6}$ have been worked out and calculations made. They are more than 100 times as fast as comparable programs using the LCAO (linear-combination-of-atomic-orbitals) method, and the results appear to be in better agreement with experiment than such LCAO results. For calculating the frequencies of optical transitions, one must make a self-consistent calculation, not for the initial or final state, but for what we call the transition state, in which occupation numbers are halfway between the initial and final states. Then it can be proved that the differences of eigenvalues of the $X\ensuremath{\alpha}$ method are more accurate than Hartree-Fock energy values, in that they take account of the modification or relaxation of the orbitals in going from the initial to the final states. These transition states, for a crystal, involve a localized perturbation at the site of the excited atom. The multiple-scattering method is adapted to the use of such perturbed crystals, as well as to isolated molecules, and to perfect crystals. It results, in such problems as x-ray absorption, in the use of localized orbitals rather than bandlike functions. The method is adapted to the calculation of magnetic problems, by use of a spin-polarized version of the method. The method can also be used for calculations of cohesive energy of crystals, and has been used successfully for several types of metals. Unlike most other SCF methods, long-range correlation is automatically included, so that the energy of a system as a function of internuclear positions automatically reduces to the proper values at infinite internuclear distances.

ac Conductivity of Scandium Oxide and a New Hopping Model for Conductivity

Abstract: The ac conductivity of scandium-oxide thin films in the audio-frequency range at temperatures between 4 and 295 K has been measured. The frequency-dependent component of the conductivity was found to obey an equation of the form ${\ensuremath{\sigma}}_{1}(\ensuremath{\omega})=A{\ensuremath{\omega}}^{s}$, where $\ensuremath{\omega}$ is the circular frequency and $s$ is a temperature-dependent quantity whose value is close to, but less than, unity. Interpretation of the results in terms of a single-phonon hopping theory does not yield satisfactory agreement. To account for the data a new hopping model is proposed. The conductivity is calculated for classical hopping of carriers between localization sites over potential barriers with a height distribution caused by the random spatial distribution of these sites. This model yields the ${\ensuremath{\omega}}^{s}$ behavior at high frequencies with the quantity ($1\ensuremath{-}s$) increasing almost linearly with temperature. In addition, it is predicted that a thermally activated dielectric-loss peak should occur for very low frequencies. It is suggested that this model may find broad application in the interpretation of ac conductivity results in amorphous materials.

Toward a Unified Theory of Urbach's Rule and Exponential Absorption Edges

Abstract: Exponential absorption edges $\ensuremath{\alpha}=A{e}^{g(\ensuremath{\hbar}\ensuremath{\omega}\ensuremath{-}\ensuremath{\hbar}{\ensuremath{\omega}}_{0})}$ have been observed in both ionic (Urbach's rule: $g=\frac{\ensuremath{\sigma}}{{k}_{B}{T}^{*}}$ and covalent materials. Arguments are given to show that a unified theory of exponetial absorption edges must (i) rely on electric microfields as the cause, (ii) include exciton effects and the final-state interaction between the electron and the hole, and (iii) ascribe Urbach's rule to the relative, internal motion of the exciton. An approximate calculation has been made in which the nonuniform microfields are replaced by a statistical distribution of uniform microfields; this calculation is a generalization to physically relevant intermediate-strength fields of previous strong- and weak-field theories of Redfield and Dexter. In contrast with the other microfield models, which obtain the exponential spectral shape by averaging over microfield distributions, the present theory obtains a quantitatively exponential edge as an inherent feature. The temperature dependences of the edges in various materials follow qualitatively from the nature of the microfield sources. The specific temperature dependence of Urbach's rule in ionic crystals is obtained from this model, with supplementary arguments to account for nonuniformity of the fields.

Magnetic Ordering in Gold-Iron Alloys

Abstract: In an attempt to characterize the magnetic ordering in $\mathrm{Au}\mathrm{Fe}$ alloys, systematic studies were made of the temperature dependences of the thermoelectric power $S$ and the low-field magnetic susceptibility $\ensuremath{\chi}$ for Fe concentrations $C$ from 1 to 22 at.%. The concentration dependences of the magnitude and temperature of the maximum in $S(T)$ showed transitions clearly related to the magnetic ordering. Data analyses based on molecular field theories indicate the existence of small regions of short-range ferromagnetic order which undergo longrange interactions as the temperature is lowered. For $C\ensuremath{\gtrsim}12$ at.%, long-range ferromagnetism is dominant. Lower-concentration alloys ($C\ensuremath{\lesssim}12$ at.%) exhibit an antiferromagnetism with some properties similar to those of a magnetic spin-glass, but with well-defined ordering temperatures characterized by sharp cusps in $\ensuremath{\chi}(T)$, and with a negative Curie $\ensuremath{\theta}$ for $C=1 \mathrm{and} 2$ at.%. These properties indicate a more perfect antiferromagnetic order than that expected for a random alloy or a spin-glass, and this may be related to preferred local lattice arrangements in these alloys.

Lattice Dynamics of Pyrolytic Graphite

Abstract: The frequencies of certain normal modes of vibration of the graphite lattice have been studied on samples of high-quality pyrolytic graphite by coherent, inelastic-neutron-scattering techniques. Some of the data are not compatible with certain restrictions imposed by the valence-bond model as presented by Young and Koppel. Therefore, the data have been analyzed in terms of a simple axially symmetric, Born-von K\'arm\'an force-constant model. The results show that appreciable interactions exist between third nearest neighbors in the basal plane. The force model has been used to calculate a frequency distributio function and the lattice specific heat of graphite. These calculations are in excellent agreement with the specific heat measured for natural graphite in the temperature range 1.5-300\ifmmode^\circ\else\textdegree\fi{}K.

Transport Properties of Semiconducting Phosphate Glasses

Abstract: The temperature and frequency dependence of conductivity, dielectric properties, infrared absorption, and electron-paramagnetic-resonance data are presented for semiconducting phosphate glasses based on oxides of Ti, V, Mn, Fe, Co, Ni, Cu, Mo, and W. The vanadate system is examined in a range of compositions, most of the others in the composition 50 mol% oxide. A polaronic model is shown to be generally applicable, and the variation of activation energy for conduction with type of glass and transition-metal-ion (TMI) spacing is found to dominate the magnitude of the conductivity. In particular, a strong preexponential factor containing a term of the form ${e}^{\ensuremath{-}2\ensuremath{\alpha}a}$ arising from electron tunneling is not observed. The results suggest that the theory of small polaron hopping in the adiabatic approximation may be most appropriate for phosphate glasses. Measurements of the static dielectric constant show no effects of disorder at high temperatures. Characteristic differences are noted between the infrared spectra of glasses such as V, Mo, W, and Ti and Ni, Co, Cu, and Mn, respectively, which are attributed to different structures within the glass matrix. These differences are suggested to lead to larger phonon dispersion in the latter glasses. It is found that the dependence of the properties of vanadate glasses upon composition can be described only if effects of polaron interactions are considered leading to a hopping probability of the form $c{(1\ensuremath{-}c)}^{n+1}$, where $c$ is the proportion of TMIs in a reduced state and $n$ is the number of sites surrounding the polaron at which strong interactions occur. Reasonable agreement with experiment is obtained on this basis for the change in electrical properties with the value of $c$.

Envelope Modulation in Spin-Echo Experiments

Abstract: Expressions have been obtained for the envelope-modulation effect in spin-echo experiments of the two- and three-pulse type by partitioning the matrices which describe the evolution of the quantized system. The initial results are quite general and may be applied to a variety of systems. Simplified expressions are derived for the case of an electron spin transition split by small nuclear hyperfine interactions. The results are given in matrix product form. The problem of computing the envelope-modulation parameters in specific instances is discussed. Algebraic results are given for $S=\frac{1}{2}$, $I=\frac{1}{2}$ and $S=\frac{1}{2}$, $I=1$.

Electronic Structure of Amorphous Si from Photoemission and Optical Studies

Abstract: Photoemission from and optical studies of amorphous Si samples, carefully prepared to minimize the influence of defects, are reported. Photoemission yield and energy distribution curves were obtained from 5.5 to 11.7 eV and reflectance data were measured from 0.4 to 11.8 eV. Optical constants were determined by a Kramers-Kronig analysis. No evidence was found to indicate that the wave vector $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}$ provides a significant quantum number in amorphous Si.

Neutron spectroscopy of superconductors

Abstract: A complete understanding of the mechanism for superconductivity requires knowledge of the details of electrons, phonons, and their interactions, and can be summarized by the function ${\ensuremath{\alpha}}^{2}F(\ensuremath{\omega})$. This function is often very similar to the phonon density of states $F(\ensuremath{\omega})=\ensuremath{\Sigma}\ensuremath{\delta}(\ensuremath{\omega}\ensuremath{-}{\ensuremath{\omega}}_{Q})$, which can be derived from an analysis of neutron-scattering data. In this paper it is pointed out that the complete function ${\ensuremath{\alpha}}^{2}F(\ensuremath{\omega})$ is also (in principle) contained in neutron-scattering data if the intrinsic linewidth ${\ensuremath{\gamma}}_{Q}$ is measured as well as the dispersion relation ${\ensuremath{\omega}}_{Q}$. It is shown that ${\ensuremath{\alpha}}^{2}F$ differs from $F$ by having a weighting factor $\frac{2{\ensuremath{\gamma}}_{Q}}{\ensuremath{\pi}N{(0)}_{\ensuremath{\omega}}}$ inside the summation, where $N(0)$ is the electronic density of states at the Fermi surface for both spin orientations. The dimensionless coupling constant $\ensuremath{\lambda}$ can also be expressed in terms of $N(0)$, ${\ensuremath{\omega}}_{Q}$, and ${\ensuremath{\gamma}}_{Q}$. In practice, for most superconductors, the average widths ${\ensuremath{\gamma}}_{Q}$ are smaller than presently available resolution. However, for materials with a high density of states like $\ensuremath{\beta}\ensuremath{-}W$ superconductors, the widths ${\ensuremath{\gamma}}_{Q}$ may be measurable. Also, the question of whether superconductivity arises predominantly from coupling to certain groups of phonons can be answered experimentally by searching for anomalously large widths. Estimates of average phonon widths are given for a variety of metals.

Homogeneous Dynamical Conductivity of Simple Metals

Abstract: Within the jellium model the zero wave vector, frequency-dependent conductivity is expressed in terms of a regular memory function. This quantity is calculated in lowest order in the impurity concentration and the electron-phonon coupling, thus yielding a reasonable approximation for the conductivity valid in the complete frequency regime. The standard results for the static conductivity including vertex corrections are reproduced. Deviations from Drude's formula a because of spin-flip scattering in a magnetic field, because of resonance scattering, because of phonon creation at low temperatures, and because of breaking of the screening cloud attached to charged impurities are discussed.

Statistical mechanics of one-dimensional Ginzburg--Landau fields

Abstract: We have been studying the statistical mechanics of one-dimensional Ginzburg-Landau fields for real, complex, and phase-only fields. Here, results for the specific heat, the order-parameter-order-parameter, and energy-density-energy-density correlation functions, will be presented. Formally, these solutions are of interest because they describe the behavior of systems which are nearly ordered but do not undergo sharp phase transitions. Physically, the real-field results may have application in some organic chain systems, while the complex field and phase-only fields are associated with superconducting strips and linear arrays of coupled weak links, respectively.

Phase Transitions and Static Spin Correlations in Ising Models with Free Surfaces

Abstract: Phase transitions in Ising models with tree surfaces are studied from various points of view, including a phenomenological Landau theory, high-temperature series expansions, and a scaling theory for thermodynamic quantities and correlation functions. In the presence of a surface a number of new critical exponents must be defined. These arise because of the existence of "surface" terms in the thermodynamic functions, and because of the anisotropy of space and lack of translational symmetry introduced by the surface. The need for these new critical exponents already appears in the phenomenological theory, which is discussed in detail and related to the microscopic mean-field approximation. The essential new parameter appearing in this theory is an extrapolation length $\ensuremath{\lambda}$ which enters the boundary condition on the magnetization at the surface. For magnetic systems this length is of the order of the interaction range, in contrast to superconductors, where it is usually much larger. In order to go beyond the mean-field theory, high-temperature series expansions are carried out for the Ising half-space, to tenth order in two dimensions and to eighth order in three dimensions. A scaling theory is developed both for thermodynamic functions and for spin correlations near the surface, and relations are found among the exponents of the half-space. Both the scaling theory and the numerical calculations are compared with the exact solution of the Ising half-plane (two dimensions) by McCoy and Wu, and agreement is found wherever the theory is applicable. In analogy to the bulk situation, the scaling theory is found to agree with mean-field theory in four dimensions. The prediction of the present work which is most easily accessible to experiment is the temperature dependence of the magnetization at the surface, with critical exponent estimated to be ${\ensuremath{\beta}}_{1}=\frac{2}{3}$. The mean-field result, ${\ensuremath{\beta}}_{1}=1$, seems to agree more closely with presently available experiment, and more work is needed to clarify the situation.

Measurement of Spin-Wave Dispersion in NiO by Inelastic Neutron Scattering and Its Relation to Magnetic Properties

Abstract: Inelastic neutron scattering techniques have been used to measure the spin-wave dispersion relations at 78\ifmmode^\circ\else\textdegree\fi{}K in the fcc antiferromagnet NiO. The energy dispersion has a steep initial slope (\ensuremath{\sim}250 meV \AA{}) and a high maximum energy (\ensuremath{\sim}117 meV) and is further characterized by a relatively low zone boundary energy in certain directions. The exchange parameters defined by ${\mathcal{H}}^{1,2}={J}_{j}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{S}}}^{(1)}\ifmmode\cdot\else\textperiodcentered\fi{}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{S}}}^{(2)}$ were determined by fitting the theoretical expression for the spin-wave energies to the experimental data corrected for instrumental resolution effects. The predominant interaction is a large antiferromagnetic exchange ${J}_{2}=221\ifmmode^\circ\else\textdegree\fi{}$K (19.01 meV) between next-nearest neighbors, which are linked by a 180\ifmmode^\circ\else\textdegree\fi{} superexchange path. The interaction between nearest neighbors, linked by a 90\ifmmode^\circ\else\textdegree\fi{} ${\mathrm{Ni}}^{2+}$---${\mathrm{O}}^{2\ensuremath{-}}$---${\mathrm{Ni}}^{2+}$ configuration, is much smaller and ferromagnetic in sign, ${J}_{1}=\ensuremath{-}15.9\ifmmode^\circ\else\textdegree\fi{}$K (-1.37 meV). A consequence of the relatively small value of ${J}_{1}$ is that the spin waves from the four domains present in the sample can only be resolved in a limited region of reciprocal space. These values of exchange interactions are in accord with simple ideas of covalency and overlap, and the results emphasize the behavior of NiO as a weakly covalent insulator. The density of magnon states, estimates of the transition temperature, and several thermomagnetic properties of NiO have been calculated from the measured exchange parameters using molecular field and random-phase-approximation Green's-function formulas.

Spin-Dependent Recombination on Silicon Surface

Abstract: It is shown that, in pure silicon, the recombination time of photocreated excess carriers depends on the relative spin orientation of the carriers and of the recombination centers. This is evidenced by the observed decrease of the photoconductivity when the magnetization of the recombination centers is reduced. Several experiments show independently that the spin-dependent recombination mechanism involves surface states: (i) Reducing the magnetization of the recombination centers through spin resonance leads to a resonant change of the height of the surface potential barrier. (ii) The size of the effect on photoconductivity increases when surface recombination is favored with respect to bulk recombination. The change in photoconductivity when the magnetization of the surface recombination centers is saturated, provides a means to observe the spin resonance of these centers with a good signal-to-noise ratio, whereas the conventional electromagnetic detection does not yield any observable signal. One thus obtains an order of magnitude for the spin-lattice relaxation time of the centers ${T}_{1}\ensuremath{\approx}{10}^{\ensuremath{-}6}$ sec and an upper limit for their density ${N}_{t}\ensuremath{\lesssim}\frac{{10}^{12}}{{\mathrm{cm}}^{2}}$.

Intrinsic fluctuations in a superconducting ring closed with a josephson junction.

Abstract: The distribution in the external flux at which a superconducting ring closed with a weak link admits a quantum of flux is determined assuming that the weak link can be treated as a Josephson junction. We find that this transition occurs at an appreciable fraction of the flux quantum from the theoretical critical external flux. To a first approximation the width of the distribution is proportional to the inductance of the ring and varies as ${T}^{\frac{2}{3}}{i}_{c}^{\ensuremath{-}\frac{1}{3}}$, where $T$ is the temperature and ${i}_{c}$ the critical current.

Far-Ultraviolet Reflectance Spectra and the Electronic Structure of Ionic Crystals

Abstract: The use of synchrotron radiation as a light source has made possible the measurement of the normal-incidence reflectance spectra of a number of ionic crystals in the photon energy range $6 \mathrm{eV}l\ensuremath{\hbar}\ensuremath{\omega}l36 \mathrm{eV}$ for temperatures $90\ifmmode^\circ\else\textdegree\fi{}\mathrm{K}lTl400\ifmmode^\circ\else\textdegree\fi{}\mathrm{K}$. The crystals investigated include KCl, KBr, RbCl, CsCl, CsBr, Ca${\mathrm{F}}_{2}$, Sr${\mathrm{F}}_{2}$, and Ba${\mathrm{F}}_{2}$. The spectra are compared and analyzed with particular reference to their dependence on temperature, chemical composition, and crystal structure. Special attention is given to the region of the spectra dominated by electronic excitation of the $p$ core levels which form the outer shell of the + ions. Sharp peaks (width \ensuremath{\le}0.2 eV) characterize the lower-energy portion of this region. They are correlated with the identity of the + ion and are assigned to transitions in the Brillouin zone using their observed temperature dependence and separation. The evidence is analyzed and found to favor the interpretation of these peaks as core excitons. At higher energies, there appear broader structures (width g0.5 eV) considered to be caused by interband transitions of core electrons. Because the crystals studied here encompass three different crystal structures, it is possible to correlate the shape of the core interband spectra with not only the crystal structure, but in fact with the nearest-neighbor coordination of the + ions. The broadening of valence- and conduction-band energies by lattice vibrations at elevated temperatures produces strong temperature dependence of interband as well as excitonic structures throughout the spectral region. The inherent sharpness of the optical structures in ionic crystals, which allows the temperature broadening to be observed, is attributed to the strong ionic character and localization of the crystal eigenstates, because these properties produce fairly sharp interband densities of states as well as excitons.