Numerical micromagnetic calculations rigorously describe the correlation between the microstructure and the magnetic properties of nanocrystalline permanent magnets. In isotropic nanocrystalline permanent magnets exchange interactions override the anisotropy of the individual grains. Therefore the spontaneous magnetic polarization deviates from the easy axes in a region along the grain boundaries. For a fine grain structure with a mean grain size d<20 nm the remanence is considerably enhanced, since the volume fraction of the boundary regions where the spontaneous magnetic polarization points towards the direction of the applied field becomes significantly high. The inhomogeneous ground state, however, favors the nucleation of reversed domains leading to a reduction of the coercive field with decreasing grain size. A uniform grain structure with a very small range in grain size avoids large demagnetizing fields and thus preserves a high coercivity. For a grain size of 10 nm isotropic two-phase permanent magnets based on ${\mathrm{Fe}}_{14}$${\mathrm{Nd}}_2$B and α-Fe show remarkable high-energy products, because the volume fraction of the magnetically soft phase can be increased up to 50% without a significant loss of coercivity.

In a unified description of superconductor–normal-metal–superconductor (SNS) and superconductor-semiconductor-superconductor (SSmS) junctions with mean free paths exceeding the N- or Sm-layer thickness it is shown how off-diagonal (Andreev) scattering from spatial variations of the pair potential in competition with diagonal scattering from interface potentials, mismatches of Fermi energies, and effective masses determines the quasiparticle states and Josephson current densities. The bound states with subgap energies provide the main channels for Cooper pair transfer via Andreev scattering. Scattering states only contribute to the net Cooper pair transfer in narrow ‘‘resonance’’ windows just above the gap at energies which are a continuation of the bound-states spectrum. The corresponding part of the Josephson current density flows in or against the direction of the bias current, depending upon the phase difference and thickness of the nonsuperconducting layer. The current contributions from the bound and scattering states oscillate opposite to each other as functions of this thickness. The weakening of phase coherence by increases of temperature and interface potentials and the corresponding approach to the sinusoidal current-phase relationship are discussed. Perturbation theory and comparison with the exact calculations show that the Bardeen-Johnson current density is exact in the limit of thin-film SNS junctions and a good approximation in junctions with cross-sectional dimensions of the S-banks much larger than the London penetration depth, if the N-layer thickness 2a exceeds considerably the BCS coherence length ${\xi }_0$. The possibility of Josephson-Bloch oscillations in SSmS junctions is discussed.

We have calculated the effect of impurity scattering on the temperature dependence of the nuclear-spin-lattice-relaxation rate and Knight shift for a two-dimensional superconductor with ${\mathit{d}}_{\mathit{x}}^2$-${\mathit{y}}^2$ symmetry. Lowest-order Born scattering as well as T-matrix scattering in the unitary limit is considered. Strong scattering profoundly changes the low-temperature dependences of both quantities giving rise to a constant contribution. Strong-coupling effects, which are never large, are included approximately in our simplified Eliashberg formulation of the problem.

We present the exact solution via Bethe’s ansatz to an integrable model consisting of two parabolic bands of electrons of equal mass with a local δ-function exchange interaction. The interaction is attractive or repulsive depending on whether the interacting particles are in a spin-singlet or spin-triplet state. The structure of the Bethe ansatz and the classification of states is similar to the one of the two-channel Kondo problem. The interest in two-band models arises from the possibility that both the 3${\mathit{d}}_{\mathit{x}}^2$-${\mathit{y}}^2$ and 3${\mathit{d}}_{\mathit{z}}^2$ orbitals may play a role in high-${\mathit{T}}_{\mathit{c}}$ cuprates. Some low-temperature properties of this model are discussed as a function of the interaction strength, a magnetic field, and the (crystalline field) splitting between the bands. The attractive interaction leads to Cooper-pair-like bound states, which exist at every temperature. There is no long-range order and no condensation of the Cooper pairs. A threshold magnetic field is required to overcome the binding energy of the Cooper pairs and there is no response to fields smaller than the critical one. The low-temperature specific heat is proportional to T, except at critical points (van Hove singularities of the bands) where C∝${\mathit{T}}^{1/2}$. The spectrum of elemental excitations is approximately parabolic.

We have calculated, for a d-wave superconductor, the strong-coupling corrections to the Bardeen-Cooper-Schrieffer (BCS) ratios: ΔC(${\mathit{T}}_{\mathit{c}}$)/γ${\mathit{T}}_{\mathit{c}}$,2${\mathrm{\Delta }}_0$/${\mathit{T}}_{\mathit{c}}$,γ${\mathit{T}}_{\mathit{c}}^2$/${\mathit{H}}_{\mathit{c}}^2$(0), ${\mathit{h}}_{\mathit{c}}$(0) as well as the ratios for the normalized slope in the specific-heat jump at ${\mathit{T}}_{\mathit{c}}$ and London penetration depth. We have used a step-function approximation for the gap function and considered an Einstein spectral density for the bosons. We have obtained terms up to O(${\mathit{T}}_{\mathit{c}}^4$/${\mathrm{\omega }}_{\mathit{E}}^4$) (here ${\mathit{T}}_{\mathit{c}}$/${\mathrm{\omega }}_{\mathit{E}}$ is the strong-coupling parameter and ${\mathrm{\omega }}_{\mathit{E}}$ is the Einstein energy). While our results are approximate for the strong-coupling cases, the weak-coupling results are exact. These weak-coupling ratios are no longer universal and depend on the d-wave considered. Our formulas are also applicable for some extended s-wave superconductors which have a basis function with a zero average over the Fermi surface.

The dynamical response of a superconducting array, modeled by the two-dimensional classical XY model, is studied by using equations of motion for vortices and spin waves. The vortex conductivity ${\mathrm{\sigma }}_{\mathit{v}}$ is evaluated in the framework of Mori’s formalism. ${\mathrm{\sigma }}_{\mathit{v}}$ has a finite zero-frequency limit in the case of a spin dynamics corresponding to the resistively shunted junction model, but it goes to zero logarithmically with frequency for a Landau-Ginzburg dynamics. The latter behavior has been observed in recent experiments and computer simulations.

We study a gauge-invariant theory of the response of a superconductor to the static magnetic field using the negative-U Hubbard Hamiltonian and the random phase approximation (RPA). We extend the usual condition of the gauge invariance to the case of the tight-binding model of the superconductor and find it to be fulfilled by our RPA theory for all wave vectors in the Brillouin zone. At the same time the transverse part of the response kernel is modified by the collective effects, contrary to the continuum model. We find that the response kernel shows substantial anisotropy in the long-wavelength limit in both weak- and strong-coupling regimes. With the numerical results for the square lattice, we examine evolution of the kernel with the change of the coupling strength and band filling.

The thermodynamics of a two-dimensional vortex plasma in thin-film superconductors is described in the framework of a cycle approximation. The equations for density of free vortices are obtained from the virial expansion. These equations provide a unified approach to describe both the Kosterlitz-Thouless-like behavior in the vicinity of the characteristic transition temperature ${\mathit{T}}_{\mathrm{KT}}$ (smooth, but very rapid crossover from the state with lower free vortex density to the state with larger vortex density) and the resistive tail at low temperatures. It is shown that in an applied magnetic field ${\mathit{H}}_0$ the discontinuous vortex-unbinding transition occurs before the Kosterlitz-Thouless-like transition when an external field exceeds some critical value. The dependence of the Kosterlitz-Thouless-like transition on the vortex core radius ${\mathit{r}}_0$ connected to the vortex core energy is discussed. It is suggested that for ${\mathit{r}}_0$ less than some critical value ${\mathit{r}}_0^{\mathit{c}}$ there is the discontinuous vortex-unbinding transition while for ${\mathit{r}}_0$>${\mathit{r}}_0^{\mathit{c}}$ the transition has the usual Kosterlitz-Thouless-like form.

We study the dynamical response of triangular Josephson-junction arrays, modeled as a network of resistively and capacitively shunted junctions. A flux-flow regime is found to extend between a lower vortex-depinning current and a higher critical current, in agreement with previous calculations for square arrays. The upper current corresponds either to row-switching events accompanied by steplike jumps in the array resistance, or to a depinning of the entire array. In the flux-flow regime, the dynamical response to the bias current is roughly Ohmic, and the time-dependent voltage can be well understood in terms of vortex degrees of freedom. The vortex friction coefficient η depends strongly on the McCumber-Stewart parameter β, and at large β is approximately independent of the shunt resistance R. To account for this, we generalize a model of Geigenmüller et al. to treat energy loss from moving vortices to the phase analog of optical spin waves in a triangular lattice. The value of η at all values of β agrees quite well with this model in the low-density limit. The vortex depinning current is estimated as 0.042${\mathit{I}}_{\mathit{c}}$, independent of the direction of applied current, in agreement with static calculations by Lobb et al. A simple argument suggests that quantum effects in vortex motion may become important when the flux-flow resistivity is of order h/(2e${)}^2$ per unit frustration.

We measure the transmission of THz pulses through thin films of ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ at temperatures between 10 and 300 K. The pulses possess a usable bandwidth extending from ∼0.1 to 1.5 THz (3.3–50 ${\mathrm{cm}}^{\mathrm{-}1}$). Below ${\mathit{T}}_{\mathit{c}}$ we observe pulse reshaping caused by the kinetic inductance of the superconducting charge carriers. From transmission data, we extract values of the London penetration depth, as a function of temperature, and find that they agree well with a functional form (λ(0)/λ(T)${)}^2$=1-(T/${\mathit{T}}_{\mathit{c}}$${)}^{\mathrm{\alpha }}$, where λ(0)=148 nm and α=2.

We consider a pointlike vortex in a layered superconductor with linear defects in the superconducting layers. We treat these defects as Josephson junctions with high critical current density. We consider the electrodynamics of these junctions within the framework of nonlocal Josephson electrodynamics. We show that Josephson current through a linear defect in a superconducting layer results in a pointlike vortex with a superconducting core residing in this layer (Josephson pancake). We find the mobility of a Josephson pancake. We consider a small amplitude wave in a Josephson junction with nonlocal electrodynamics. We treat a bending wave for an infinite stack of Josephson pancakes. We find the dispersion relation for these waves. We show that their velocities tend to a certain finite limit when the wavelength tends to infinity.

We have measured the energy gap of highly c-axis-oriented ${\mathrm{Bi}}_2$${\mathrm{Sr}}_2$${\mathrm{Ca}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{10\mathrm{-}\mathit{x}}$ (2:2:2:3) polycrystals along the ab plane with a low-temperature scanning tunneling microscope. Our best tunneling conductance curve showed that the ${\mathrm{\Delta }}_{\mathit{a}\mathit{b}}$ of 2:2:2:3 should be close to, but not larger than 39 meV. Both 2:2:2:3-to-normal-metal, and 2:2:2:3-to-2:2:2:3 tunneling show similar energy-gap values.

Using a variational approach we calculate the hole-hole contact interaction on the quantum Néel background. Explicit analytical expressions for the vertex function of the interaction are obtained. Solution of the Bethe-Salpeter equation with this interaction gives bound states in d and p waves with binding energies close to those obtained recently by numerical methods. At t/J≥2–3 the bound state disappears.

Using anisotropic London theory we obtain the intrinsic magnetic torque for extreme type-II uniaxial superconductors for any value of the magnetic induction. We consider the vortex lines straight and take into account the contribution of the supercurrents flowing inside the vortex core within the London theory. We show that the interline and intraline free energies give opposite torque contributions; the first drives the magnetic induction parallel to the superconductor’s axis of symmetry and the second orthogonal to it. At high magnetic induction our torque expression generalizes Kogan’s formula, since it has no free parameters other than the anisotropy γ=${\mathit{m}}_1$/${\mathit{m}}_3$ and the Ginzburg-Landau parameter κ. At low magnetic induction, we propose a way to observe vortex chain effects in the total torque based on the fact that London theory is linear and the energy to make a single vortex line in space is independent of the magnetic induction.

Dynamics of a hole introduced into the antiferromagnetic states of the honeycomb, simple cubic, body-centered-cubic lattices, and a layered structure in which each layer forms the square lattice have been studied. A variational method which restricts the Hilbert space is applied to the t-J model. The energy dispersion of the hole as a quasiparticle can be expressed by effective hoppings on the same sublattice irrespective of the dimensionality and lattices, but the momentum of the hole of the ground state depends on the lattice structures. In the layered structure, the momentum changes discontinuously as the magnitude of the interlayer coupling is varied. It is shown that the exchange interaction within the layers suppresses the interlayer hopping of the hole. Mobility of the hole is shown to be determined by the number of bonds of the nearest-neighbor exchange interaction. By applying the present method to four- and five-dimensional hypercubic lattices, it is found that the bandwidth of the coherent state of the hole can be normalized by scaling the hopping and exchange parameters t and J by 1/ √d and 1/d, respectively, where d denotes the dimensionality of the lattices.

The chain oxygen dynamics of ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathit{x}}$ have been investigated using a Monte Carlo simulation of the asymmetric next-nearest-neighbor Ising model for the oxygen atoms in the basal plane. The effect of an externally applied electric field is shown to change the basal plane coordination of Cu ions, resulting in a change in the carrier doping of the ${\mathrm{CuO}}_2$ planes. Good quantitative agreement is obtained with the asymmetry observed in field effect experiments. We present results under different applied external fields, study the long-term ordering dynamics and investigate the effect of oxygen content on the phenomenon. We discuss the relevance of our results to studies of point-contact spectroscopy, tunneling, electromigration, and the enhancement of superconductivity by photoexcitation. We also present a historical perspective in terms of the Verwey transition in ${\mathrm{Fe}}_3$${\mathrm{O}}_4$, which involves a similar mechanism.

The superconducting transition temperature ${\mathit{T}}_{\mathit{c}}$ has been measured in the multilayered system Nb/CuX, where CuX represents Cu, ${\mathrm{Cu}}_{1\mathrm{-}\mathit{y}}$${\mathrm{Mn}}_{\mathit{y}}$, or ${\mathrm{Cu}}_{0.95}$${\mathrm{Ge}}_{0.05}$. The advantage of this system is that the superconductor layer thickness, normal-metal layer thickness, normal-metal magnetic concentration, and normal-metal bulk resistivity can be independently varied. Our data show that the variation of ${\mathit{T}}_{\mathit{c}}$ with changing superconductor-layer thickness ${\mathit{d}}_{\mathit{s}}$ exhibits scaling consistent with the equation (${\mathit{T}}_{\mathit{c}}^{\mathit{b}}$-${\mathit{T}}_{\mathit{c}}$)/${\mathit{T}}_{\mathit{c}}^{\mathit{b}}$=(${\mathit{d}}_{\mathit{s}}$/${\mathit{d}}_0$${)}^{\mathrm{-}\mathit{p}}$, where ${\mathit{d}}_0$ is a fitting parameter and ${\mathit{T}}_{\mathit{c}}^{\mathit{b}}$ is ${\mathit{T}}_{\mathit{c}}$ for bulk Nb. We find the exponent p to increase systematically with increasing normal-metal layer thickness, and magnetic impurity concentration, with 1≤p<2, consistent with the limiting forms of two theoretical models.

Tunneling measurements have been made on a series of high-quality ${\mathrm{Bi}}_2$${\mathrm{Sr}}_2$${\mathrm{CaCu}}_2$${\mathrm{O}}_{8+\mathrm{\delta }}$ (BSCCO) single crystals with transition temperatures (${\mathit{T}}_{\mathit{c}}$) ranging from 79 to 92 K. From these systematic studies it has been possible to delineate the intrinsic features of the low-energy electronic spectrum in the BSCCO materials. These results demonstrate that the magnitude of 2Δ at 4.2 K is nearly constant in the different ${\mathit{T}}_{\mathit{c}}$ samples, and thus, that 2Δ/${\mathit{kT}}_{\mathit{c}}$ increases as ${\mathit{T}}_{\mathit{c}}$ decreases. In addition, intrinsic quasiparticle excitations are detected within the gap irrespective of the sample ${\mathit{T}}_{\mathit{c}}$’s. Analyses of these electronic spectra using a variety of pairing models suggest that gap functions having a large anisotropy can provide a good fit to the experimental data.

The miscibility gap of ${\mathrm{La}}_2$${\mathrm{CuO}}_{4+\mathrm{\delta }}$ was investigated by studying three electrochemically oxygenated samples with different oxygen contents, using variable-temperature neutron powder diffraction. The low-temperature lattice parameters of the two coexisting orthorhombic phases (antiferromagnetic, Bmab and superconducting, Fmmm) were found to be in good agreement with those determined for high-pressure annealed samples, indicating that the two techniques yield essentially identical samples, at least in this concentration range. A sample with δ≊0.032 remained phase separated up to 415 K and, above this temperature, was found to be single-phase tetragonal (F4/mmm). The phase separation temperature and the orthorhombic-to-tetragonal phase transition temperature were obtained for all samples, allowing the shape of the miscibility gap to be determined.

Polarized electroreflectance spectra are reported for single-crystal ${\mathrm{La}}_2$${\mathrm{CuO}}_{4+\mathit{y}}$. Depending on the electrode structure, the primary effect of modulating the electrode potential is addition of charge carriers or variation of the electric field in the space-charge region. By adding charge carriers we observe changes in the optical spectra similar to those caused by chemical doping. For modulation of the electric field the perturbed absorption spectrum is very different, corresponding to electric-field-induced crystal-field transitions. Bands near 1.4 and 1.6 eV respond to the electric field in ways consistent with ${\mathit{d}}_{\mathit{x}}^2$-${\mathit{y}}^2$→${\mathit{d}}_{\mathit{x}\mathit{y}}$ and ${\mathit{d}}_{\mathit{x}}^2$-${\mathit{y}}^2$→${\mathit{d}}_{\mathit{z}\mathit{x}}$,${\mathit{d}}_{\mathit{y}\mathit{z}}$ transitions, respectively. Our observations are consistent with Perkins et al. [Phys. Rev. Lett. 71, 1621 (1993)] who ascribe transitions near 0.4 and 1.5 eV to the ${\mathit{d}}_{\mathit{x}}^2$-${\mathit{y}}^2$→${\mathit{d}}_{3\mathit{z}}^2$-${\mathit{r}}^2$ and ${\mathit{d}}_{\mathit{x}}^2$-${\mathit{y}}^2$→${\mathit{d}}_{\mathit{x}\mathit{y}}$ excitons.