The Onsager-reaction-field correction to Hartree-Fock theory recently derived by Georges and Yedidia [Phys. Rev. B 43, 3475 (1991)] is evaluated analytically for the half-filled positive-U Hubbard model on a d-dimensional hypercubic lattice. It is shown that the Onsager correction is for all d≥3 irrelevant in the weak-coupling limit, while for d=1 and d=2 it strongly renormalizes the Hartree-Fock result, although it does note completely destabilize the spin-density wave. We examine the perturbation theory for the energy change induced by a small staggered magnetization m to all orders in U, and show that one obtains an infinite series in powers of (U/t)ln[${\mathit{m}}^{\mathrm{-}1}$ln(${\mathit{m}}^{\mathrm{-}1}$)] for d=1, and in powers of (U/t)${\ln }^2$[${\mathit{m}}^{\mathrm{-}1}$${\ln }^2$(${\mathit{m}}^{\mathrm{-}1}$)] for d=1. The close similarity between d=1 and d=2 is interpreted as evidence that antiferromagnetism in the weak coupling regime is not stable in d=2.

Within the framework of the ‘‘brick-wall’’ model, we review in detail how various physical mechanisms could act to limit the critical current in high-${\mathit{T}}_{\mathit{c}}$ superconducting tapes. The brick-wall model attempts to mimic in a simplified manner the complicated tape microstructure. We generalized it to take into account a distribution of grains sizes and possible different strengths of weak links between the grains and the existence of weak links associated with intergrain boundaries perpendicular to the plane of the tape. We discuss what experiments can distinguish between a situation where weak links limit the critical current, and another plausible scenario where intragranular pinning is the limiting factor. Our conclusion is that according to the available experimental data only a small, well-connected fraction of the high-${\mathit{J}}_{\mathit{c}}$ tapes is effective in providing high critical current densities. For this fraction of the tape, pinning turns out to be the limiting mechanism. Finally, several possibilities for increasing the critical current of the high-${\mathit{T}}_{\mathit{c}}$ superconducting tapes are discussed.

Both the static and dynamic properties of the antiferromagnetic state in ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{6.15}$ have been reinvestigated by neutron scattering. The crystal studied exhibited a Néel temperature of 410±3 K, with a continuous transition below 15 K to a magnetic structure with a doubled unit cell along the c axis. The Cu magnetic form factor has been extracted from magnetic Bragg peak intensities measured at 15 K, and it is shown to have the large anisotropy expected for a Cu 3${\mathit{d}}_{\mathit{x}}^2$-${\mathit{y}}^2$ state. The form-factor anisotropy can explain much of the Q dependence of the inelastic magnetic cross section that has been observed in superconducting ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{6+\mathit{x}}$. A search for the optical spin-wave modes at excitation energies up to 60 meV was unsuccessful. Analysis of acoustic spin-wave measurements yields an intralayer superexchange energy ${\mathit{J}}_{\mathrm{\parallel }}$ of 120±20 meV (without correction for quantum renormalization) with an anisotropy ${\mathrm{\alpha }}_{\mathit{x}\mathit{y}}$=(7±1)×${10}^{\mathrm{-}4}$, and an effective next-nearest-layer exchange ${\mathit{J}}_{\mathrm{\perp }2}$ of 0.04±0.01 meV. A lower limit for the intrabilayer exchange, ${\mathit{J}}_{\mathrm{\perp }1}$, of 8 meV is established. Use of theoretical and experimental results for Q-integrated spin-wave intensities in the antiferromagnet, together with a crystal volume normalization based on phonon measurements, allows us to put previous measurements of spin fluctuations in superconducting ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{6.6}$ on an absolute scale. The results for the superconductor are shown to be consistent with the relaxation rates determined by nuclear magnetic resonance.

We study the dynamical spin susceptibility of a two-dimensional antiferromagnet that is weakly doped with mobile holes. The motion of the holes leads to a renormalization of the velocity v and of the linewidth of spin-wave excitations. In agreement with inelastic-neutron-scattering experiments for high-${\mathit{T}}_{\mathit{c}}$ superconductors v vanishes at a critical hole concentration ${\mathrm{\delta }}_{\mathit{c}}$ of a few percent. This behavior is mainly due to the low energy or so-called coherent part of the hole motion and not to its incoherent part as was claimed recently. Therefore spin and hole excitations have the same energy scale and adiabiatic approximations are not allowed. Moreover, the system undergoes a magnetic phase transition at a critical hole-concentration value ${\mathrm{\delta }}_{\mathit{c}}$. At ${\mathrm{\delta }}_{\mathit{c}}$ the transverse staggered susceptibility diverges for all wave vectors for which the spin-wave excitations ${\mathrm{\omega }}_{\mathbf{q}}$ are approximately linear in q.

We present an explicit solution of the problem of two coupled spin-1/2 impurities, interacting with a band of conduction electrons. We obtain an exact effective bosonized Hamiltonian, which is then treated by two different methods (low-energy theory and mean-field approach). Scale invariance is explicitly shown at the quantum critical point. The staggered susceptibility behaves like ln(${\mathit{T}}_{\mathit{K}}$/T) at low T, whereas the magnetic susceptibility and 〈${\mathbf{S}}_1$⋅${\mathbf{S}}_2$〉 are well behaved at the transition. The divergence of C(T)/T when approaching the transition point is also studied. The non-Fermi-liquid (actually marginal-Fermi-liquid) critical point is shown to arise because of the existence of anomalous correlations, which lead to degeneracies between bosonic and fermionic states of the system. The methods developed in this paper are of interest for studying more physically relevant models, for instance, for high-${\mathit{T}}_{\mathit{c}}$ cuprates.

Magnetic relaxation in a ${\mathrm{Pr}}_{1.85}$${\mathrm{Ce}}_{0.15}$${\mathrm{CuO}}_{4\mathrm{-}\mathit{y}}$ single crystal has been studied as a function of field and temperature. Two different regimes are evident in the relaxation process. The usual logarithmic decay of the magnetization is observed at low fields. A crossover from logarithmic to exponential relaxation takes place at higher fields. The magnetization decay becomes exponential as H approaches ${\mathit{H}}_{\mathrm{irr}}$(T), and eventually any trace of relaxation disappears. The logarithmic decays have been used to estimate the field dependences of the critical currents and the relevant activation energies at high driving currents. The functional dependence U(J) has been evaluated by using Maley’s method. The extracted values for U(J,T,B) are discussed in terms of the available models for flux motion; we conclude that the observed behavior might be a signature of a crossover in the nature of the thermally activated process, from jumps of elastically correlated flux volumes to plastic flux motion.

A full account is given of an NMR investigation of planar oxygen in the normal state (T>${\mathit{T}}_{\mathit{c}}$) of two characteristic superconducting Y-Ba-Cu-O single crystals: ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{6.52}$ representing the underdoped ‘‘60-K phase,’’ and ${\mathrm{YBa}}_{1.92}$${\mathrm{Sr}}_{0.08}$${\mathrm{Cu}}_3$${\mathrm{O}}_7$ representing the overdoped ‘‘90-K phase.’’ (We argue that Sr impurities in the latter crystal do not significantly change the behavior of the system.) Data are analyzed within the framework of the Mila-Rice spin Hamiltonian and using inelastic-neutron-scattering results, in order to obtain detailed and consistent information on the antiferromagnetic fluctuations (AFF) in this system. Within the model, the filtering of the AFF at the oxygen site is always found to be imperfect, even for the AFF that are localized to a maximum degree in the q space around ${\mathbf{Q}}_{\mathrm{AF}}$. In our overdoped sample this is also confirmed experimentally, in contradiction to other published data. Any shape of χ’’(q-${\mathbf{Q}}_{\mathrm{AF}}$) that falls off slower than Gaussian is found to be incompatible with experimental data. In the underdoped regime, the observed temperature dependence of the ${\mathit{T}}_1$ anisotropy is in clear contradiction with any single-component model. A possible explanation could involve an extra contribution to relaxation coming from spinless quasiparticles.

We report a detailed study of the temperature and magnetic-field dependence of free energy, magnetization, and specific heat of superconducting ${\mathrm{Bi}}_2$${\mathrm{Sr}}_2$${\mathrm{Ca}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{10}$ in the critical fluctuation region near ${\mathit{H}}_{\mathit{c}2}$(T) line. Our approach is to apply the recently developed nonperturbative scaling theory (Tešanović et al.) in high fields to describe the reversible magnetization data taken on a c-axis-oriented superconducting ${\mathrm{Bi}}_2$${\mathrm{Sr}}_2$${\mathrm{Ca}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{10}$ thin tape. We find good agreement on some of the superconducting parameters obtained in the present study with those derived by applying the Ginzburg-Landau theory to our reversible magnetization data taken outside the critical fluctuation region.

Simple analytical expressions are derived for the harmonic susceptibilities in type-II superconductors, using a critical-state model with a general dependence of the critical current upon magnetic field. It is shown that the harmonic susceptibilities are determined by a single parameter, δ, which is a function of the full penetration field of the sample and the applied alternating field. This implies that measurements of harmonic susceptibilities as a function of any experimental variable, in any irreversible type-II superconductor, can be reduced to universal curves that describe the harmonic susceptibilities versus δ. In particular, the maximum values that can be attained by the harmonic susceptibilities are universal constants for irreversible type-II superconductors. Fitting of experimental data to the universal curves provides models for the dependence of the critical current density upon field and temperature. This is demonstrated using data of the third-harmonic response measured in a sintered ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ sample.

We study an extended Hubbard model in the limit of infinite dimensions and its zero-dimensional counterpart, a generalized asymmetric Anderson model. In the impurity model we find three kinds of mixed valence states: (a) the usual strong-coupling state in which a resonance forms at the Fermi level; (b) a weak-coupling state in which neither the impurity spin nor the impurity charge degrees of freedom are quenched; and (c) an intermediate-coupling state where the spin but not the charge degree of freedom is quenched. The corresponding phases of the extended Hubbard model in infinite dimensions are (a) a Fermi liquid; (b) a non-Fermi-liquid state with incoherent charge and spin excitations; and (c) a non-Fermi-liquid state with incoherent charge but coherent spin excitations. The non-Fermi-liquid phases are incoherent metallic states with vanishing quasiparticle residue, self-similar local correlation functions, and asymptotically decoupled charge and spin excitations. The non-Fermi-liquid phases occur for a wide range of parameters.

The conductance curves of point-contact tunnel junctions between Ag and ${\mathrm{Ba}}_{1\mathrm{-}\mathit{x}}$${\mathrm{K}}_{\mathit{x}}$${\mathrm{BiO}}_3$ (x≃0.4) reveal a BCS behavior with low leakage current at zero voltage and some broadening of the superconducting-gap structure. In the energy range above the superconducting energy gap, the structure in the voltage dependence of the second derivative ${\mathit{d}}^2$V/${\mathit{dI}}^2$ of the voltage with respect to the current of the tunnel junction has been investigated in detail in magnetic fields up to 10 T. While part of this structure is rapidly changing in a magnetic field, three reproducible peaks in ${\mathit{d}}^2$V/${\mathit{dI}}^2$(V) remain stable up to the transition temperature from the superconducting to the normal state with only additional broadening in the applied magnetic field. An analysis of this structure in terms of strong-coupling effects yields the spectral function ${\mathrm{\alpha }}^2$F for the electron-phonon interaction. The obtained spectral weight in the energy region 20–70 meV points to the importance of the oxygen optical modes in the electron-phonon coupling for the superconductivity of ${\mathrm{Ba}}_{1\mathrm{-}\mathit{x}}$${\mathrm{K}}_{\mathit{x}}$${\mathrm{BiO}}_3$.

Magnetic properties of epitaxial thin films of ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$ have been studied in the superconducting state in fields perpendicular to the sample, along the c crystallographic axis. In the low-temperature state, susceptibility, hysteresis loop, and remanent magnetization (trapped flux) studies show that a critical state is established in very low applied fields. The flux penetration process and the related thickness properties are well accounted for by simple electromagnetic models for the critical current. It is shown that the evaluation of the critical current ${\mathit{J}}_{\mathit{c}}$ by the classical Bean formula is roughly valid, in spite of the curvature of the vortices. A decrease in the low-temperature value of ${\mathit{J}}_{\mathit{c}}$ with increasing thickness is found above 100 nm. In the temperature range close to ${\mathit{T}}_{\mathit{c}}$, the irreversibility line moves towards higher field with increasing thickness according to a ${\mathit{d}}^{1/2}$ law. This is discussed in relation with the theories of vortex-lattice and vortex-glass melting.

Magnetic hysteresis, flux pinning, and flux creep in melt-powder-melt-growth processed ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$ (Y 1:2:3) containing nominal 0, 25, and 40 mol % concentration of ${\mathrm{Y}}_2$${\mathrm{BaCuO}}_5$ (Y 2:1:1) inclusions were investigated. The strong pinning due to 2:1:1-phase precipitates in these samples allows for characterization of the hysteretic response as a function of pinning-site concentration over a large portion of magnetic-field–temperature space. We have found the following: (i) The curves of effective pinning energy ${\mathit{U}}_{\mathrm{eff}}$ versus current density J reveal a diverging behavior of ${\mathit{U}}_{\mathrm{eff}}$(J) in the low-J regime. This supports the existence of a vortex-glass state, and is a signature of a vanishing resistance as the current density approaches zero. (ii) Both the ${\mathit{U}}_{\mathrm{eff}}$ and the J values obtained from magnetic hysteresis loops were observed to increase with Y 2:1:1 concentration. The appearance of the butterfly-shaped (or ‘‘fishtail’’) hysteresis loops indicates a ${\mathit{J}}_{\mathit{c}}$ that is an increasing function of H (or B). Moreover, it has been demonstrated that the additional pinning leads to an increase in ${\mathit{U}}_{\mathrm{eff}}$ in an H-T region in which the butterfly is developed.

The derived effective pinning energy is fit, from the instantaneous experimental relaxation data, to the relation, ${\mathit{U}}_{\mathrm{eff}}$(J,T,H)=${\mathit{U}}_{\mathit{i}}$[G(T)/${\mathit{H}}^{\mathit{n}}$](${\mathit{J}}_{\mathit{i}}$/J${)}^{\mathrm{\mu }}$, where ${\mathit{U}}_{\mathit{i}}$ is the scale of the activation energy, G(T) =[1-(T/${\mathit{T}}_{\mathit{x}}$${)}^2$${]}^{\mathit{m}}$, and ${\mathit{T}}_{\mathit{x}}$ is close in value to ${\mathit{T}}_{\mathrm{irr}}$(H) (the irreversibility line of the material). This description breaks down in the vicinity of the ‘‘butterfly’’ peak. We observed two power-law regimes of J dependence of ${\mathit{U}}_{\mathrm{eff}}$ which have μ values that agree qualitatively with the theoretical predictions (=7/9 and 3/2) for a three-dimensional flux-line lattice.

The specific heat of several Zn- and Co-doped ${\mathrm{Bi}}_{1.8}$${\mathrm{Pb}}_{0.2}$${\mathrm{Sr}}_2$Ca(${\mathrm{Cu}}_{1\mathrm{-}\mathit{x}}$${\mathit{M}}_{\mathit{x}}$${)}_2$${\mathrm{O}}_{\mathit{y}}$ superconductors was investigated. Co substitution is paramagnetic, and introduces a linear term in ${\mathit{C}}_{\mathit{p}}$ at low temperatures, without reduction in the specific-heat discontinuity Δ${\mathit{C}}_{\mathit{p}}$/${\mathit{T}}_{\mathit{c}}$ at ${\mathit{T}}_{\mathit{c}}$. The results can be understood as gapless superconductivity in a highly anisotropic s-wave or d-wave superconductor. Zn substitution is nonmagnetic and does not lead to these phenomena.

The presence of phase intergrowth in Bi-Sr-Ca-Cu-O thin films, in situ grown using a laser-ablation technique, has been investigated. A simple intergrowth model has been used to analyze the experimental x-ray-diffraction patterns of the films and has allowed us to measure the stacking-fault proportion in the films. Rutherford-backscattering spectrometry (RBS) has also been used in order to determine the cationic composition. The Bi/Cu ratio obtained by x-ray-diffraction analysis is in very good agreement with the results of RBS analysis. The intergrowth phenomenon allows one to change the structure continuously from one pure phase to another one, a fact that is experimentally observed when the oxygen pressure during deposition is changed.

Antiferromagnetic spin fluctuations and charge-transfer correlation are studied in an extended Hubbard model of cuprate superconductors. We have carried out finite-temperature Monte Carlo and variational Monte Carlo simulations of ${\mathrm{CuO}}_2$ lattices described by a three-band Hubbard model. Using parameters derived by local-density-functional theory, our results appear to be consistent with experimental data. At half-filling, we find strong antiferromagnetic correlation with large local moment on copper sites and evidence of a charge-transfer gap. Upon doping, the antiferromagnetic correlations decrease; the excess holes primarily go onto the oxygen sites, while additional electrons prefer the copper sites. Equal-time pairing correlation functions suggest that extended s-wave and d-wave pairing are possible in this model.

Using electronic states and phonon states from first-principles calculations on ${\mathrm{K}}_3$${\mathrm{C}}_{60}$ to evaluate the quantities in the McMillan equation, we examine the effects of both electron-phonon dynamic charge coupling (Q) and Jahn-Teller coupling (JT) on various superconducting properties, including ${\mathit{T}}_{\mathit{c}}$, Δ${\mathit{T}}_{\mathit{c}}$ (the shift of ${\mathit{T}}_{\mathit{c}}$ for 1 GPa pressure), ${\mathrm{\alpha }}_{\mathrm{C}}$ (the isotope exponent for ${}_{}{}^{12}{}_{}{}^{}\to _{}^{13}{}_{}{}^{}$C), and ${\mathrm{\alpha }}_{\mathrm{K}}$ (the isotope exponent for ${}_{}{}^{39}{}_{}{}^{}\to _{}^{41}{}_{}{}^{}$K). All quantities including electron-phonon coupling are evaluated (without modification) directly from theory, except for the screening length between conducting electrons and ions, ${\mathit{R}}_{\mathrm{sc}}$. With ${\mathit{R}}_{\mathrm{sc}}$=0.8–1.0 Å, we find that the calculated properties, ${\mathit{T}}_{\mathit{c}}$, Δ${\mathit{T}}_{\mathit{c}}$, and ${\mathrm{\alpha }}_{\mathrm{C}}$, are all in good agreement with experimental measurements. We find that the superconducting properties depend critically upon the synergy between Q and JT coupling.

This article calculates the Fourier transform of a quasicrystalline solid, the pinwheel tiling, proposed by Conway and Radin. The solid is isotropic, but the Fourier transform has large fluctuations as a consequence of correlations.

The coupling between a quantum dynamical system and a two-level-system reservoir is analyzed within the framework of the Feynman-Vernon theory. We stress the differences between this reservoir and the well-known bath of oscillators and show that, in order to obtain the Langevin equation for the system of interest in the high-temperature regime, we have to choose a spectral distribution function J(ω) that is finite for ω=0.

An important theoretical concept in the ‘‘droplet’’ model of spin glasses is the existence of an overlap length. Experimentally this concept was verified by dc-magnetization measurements. However, recent ac-susceptibility measurements by Lefloch et al. [Europhys. Lett. 18, 647 (1992)] have been interpreted to contradict this result. In this paper, ac-susceptibility and dc-magnetization measurements on a Cu (2% Mn) spin glass are reported. The results of the ac-susceptibility measurements are consistent with dc measurements and provide evidence for the existence of an overlap length in 3d spin glasses at low temperatures.