The nature of transverse vibrational eigenmodes of a regular Vicsek fractal with hierarchical nearest-neighbor interactions has been analyzed using a real-space renormalization-group approach. Different types of spatial scaling behavior for the nondegenerate transverse vibrational modes are obtained depending on a positive hierarchical parameter R: for R>${\mathit{R}}_{\mathit{c}}$, the nondegenerate modes are all extended in nature, while for R<${\mathit{R}}_{\mathit{c}}$, they exhibit a type of power-law behavior, with the exponent of power depending explicitly on R.

We report ${}_{}{}^{59}{}_{}{}^{}\mathrm{Co}$ NMR measurements on three MBE-grown Co/Cu(111) multilayer films that show a progression of saturation magnetoresistance from ΔR/R=4% to ΔR/R=40%. Our results demonstrate unambiguously that the increase in magnetoresistance is correlated with an improvement in the quality of the interfaces in these MBE-grown materials.

Magnetic multilayers [Fe(20 Å)/Pd(x Å)${]}_{25}$ grown by electron-beam evaporation in high vacuum were studied by x-ray-diffraction, superconducting quantum interference device, vibrating-sample-magnetometer, magnetoresistance, and conversion-electron-Mössbauer-spectra measurements. From x-ray-diffraction measurements a structure transition of Fe layers from bcc to fcc was observed if the thickness of Pd layers was over 36 Å. An oscillatory behavior of saturation magnetization per unit Fe volume was found with increment of thickness of Pd layer in the range of 6 to 60 Å. Conversion-electron-Mössbauer-spectra measurements proved that the moment of Fe atoms in Fe/Pd multilayers is almost the same as for a single Fe film and the oscillatory magnetization is caused by the magnetic-polarization effect of the Pd layers. An antiferromagnetic coupling between the polarization moments in the Pd layer could clearly be observed in a special Pd thickness range, and it might make the magnetization oscillate with the Pd layer thickness. No antiferromagnetic coupling between two Fe layers and the giant magnetoresistance effect were observed. The relationship among structure, interlayer coupling, and the magnetic-polarization effect of Pd layers was discussed.

${\mathrm{CuFeS}}_{2\mathrm{-}\mathit{x}}$${\mathrm{Se}}_{\mathit{x}}$ has been studied by Mössbauer spectroscopy and x-ray diffraction. The crystal is found to have a tetragonal structure and the lattice constants ${\mathit{a}}_0$ and ${\mathit{c}}_0$ increase linearly with increasing selenium concentration. It is noteworthy that the replacement of S by Se in the chalcopyrite decreases the strength of both the superexchange interaction and the interatomic binding. As the interatomic distance increases by 1%, the magnetic hyperfine field and the Debye temperature decrease by 0.8 and 6 %, respectively. The iron ions are found to be in ferric states.

A modified spin-wave theory is applied to the one- and two-dimensional quantum Heisenberg model with long-range ferromagnetic interactions proportional to ${\mathit{r}}^{\mathrm{-}\mathit{p}}$[scrH=-1/2${\mathit{tsum}}_{\mathit{i}\mathrm{\ne }\mathit{j}}$ (${\mathit{J}}_0$/${\mathit{r}}_{\mathit{i}\mathit{j}}^{\mathit{p}}$)${\mathbf{S}}_{\mathit{i}}$⋅${\mathbf{S}}_{\mathit{j}}$]. It is shown that for d<p<2d there exists a phase transition at finite temperatures; the critical temperature is estimated. The susceptibility and the specific heat are obtained at low temperatures. Our results for d=1, p=2, and S=1/2 agree with the exact solution of the Haldane-Shastry model. For d=1, we find a scaling relation α+1=${\gamma }^{\mathrm{-}1}$ when 2<p<3.

We have studied the electric structure of an icosahedral (${\mathit{I}}_{\mathit{h}}$) 13-atom cobalt (${\mathrm{Co}}_{13}$) cluster, which is the smallest cluster in the icosahedral structure, using the discrete variational Xα cluster method. We have found that two electric states in the ${\mathit{I}}_{\mathit{h}}$ ${\mathrm{Co}}_{13}$ cluster—a low-spin state and a high-spin state—exist with the interatomic distance of equilibrium geometry. The average magnetic moment of the low-spin state of the cluster is 1.77${\mathrm{\mu }}_{\mathit{B}}$, while that of the high-spin state is 2.23${\mathrm{\mu }}_{\mathit{B}}$. It seems that the magnetic moments extrapolating these results are in agreement with the magnetic doublets of the ${\mathrm{Co}}_{55}$ cluster Bucher et al. observed. The magnetic doublets of the ${\mathrm{Co}}_{55}$ cluster may be due to those of the ${\mathit{I}}_{\mathit{h}}$ ${\mathrm{Co}}_{55}$ cluster.

We consider a two-dimensional Hubbard model within a conserving spin-fluctuation exchange approximation and determine the change in the ${\mathit{d}}_{\mathit{x}}^2$-${\mathit{y}}^2$ superconducting transition temperature ${\mathit{T}}_{\mathit{c}}$ produced by variations in the spin-fluctuation spectral weight. We find that ${\mathit{T}}_{\mathit{c}}$ is increased when spectral weight is shifted to large momentum transfers and frequencies greater than ${\mathit{T}}_{\mathit{c}}$ with an optimal frequency for ${\mathit{T}}_{\mathit{c}}$ enhancement of order 10${\mathit{T}}_{\mathit{c}}$.

The magnetization curves of a slablike uniform Josephson-junction array with resistive shunts are calculated from the dc and ac Josephson equations and the gauge-invariant phase difference. The parameters are chosen in accord with actual values for high-${\mathit{T}}_{\mathit{c}}$ superconductors (HTSC’s). With decreasing sweep rate of the applied field, the result changes from a complete shielding to one approaching the envelope of the static magnetization curve, which is oscillatory and amplitude modulated. At certain intermediate sweeping rates the curves are critical-state-like. However, since these rates are a few orders of magnitude higher than those used in conventional experiments, the intergranular critical state shown in HTSC’s cannot be modeled by such a uniform array.

The anion doping effect on the superconducting transition temperature (${\mathit{T}}_{\mathit{c}}$) of ${\mathrm{HgBa}}_2$${\mathrm{CuO}}_{4+\mathrm{\delta }}$ has been determined with a wide ${\mathit{T}}_{\mathit{c}}$ variation. We found a parabolic variation of ${\mathit{T}}_{\mathit{c}}$ with δ over the entire range of superconductivity. Remarkably, the dependence of ${\mathit{T}}_{\mathit{c}}$ on p (the number of holes per ${\mathrm{CuO}}_2$) has richer features: for δ≤0.28, ${\mathit{T}}_{\mathit{c}}$ is parabolic in p, but with an unusual prefactor and p=0.72δ, giving significantly less than two holes per oxygen; and for δ>0.28, a drastic departure from the parabolic ${\mathit{T}}_{\mathit{c}}$(p) occurs. Implications for the occurrence of superconductivity in this material are discussed.

To interpret the metal-insulator transition and the depression of ${\mathit{T}}_{\mathit{c}}$ induced by Pr doping for the ${\mathrm{Y}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Pr}}_{\mathit{x}}$${\mathrm{Ba}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$ system, we propose a model following the Hamiltonian of Fehrenbacher and Rice for the ${\mathrm{CuO}}_2$-Pr-${\mathrm{CuO}}_2$ subcell. In our model, the role of the reservoir hole is particularly emphasized and a scenario for the Pr-doping-dependent hole distribution is proposed. As a natural consequence, most of the experimental results on ${\mathrm{Y}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Pr}}_{\mathit{x}}$${\mathrm{Ba}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$, including the metal-insulator transition, the depression of ${\mathit{T}}_{\mathit{c}}$, the valence states deduced from magnetic and spectroscopic measurements, and so on, can be explained. The critical doping density of Pr takes the value of ${\mathit{x}}_{\mathit{c}}$≊0.5.

Specular scattering of x rays by electrons in a material becomes large at grazing angles below the critical angle for external reflection. In contrast, we observe specular scattering by resonant nuclei to peak at the critical angle and decrease at smaller angles. This is the result of the influence of the electronic scattering on the nuclear response of the system and is explained using an optical model. A distorted-wave Born approximation shows the specular nuclear signal should be large at angles where the electronic reflectivity varies rapidly with angle.

The hcp-to-bcc pressure-induced transformation in Mg is simulated at finite temperatures using a recently developed ab initio molecular-dynamics algorithm with variable cell shape. The process is induced in both directions by preparing the parent phase within the thermodynamical stability field of the daughter phase and allowing it to evolve. In both cases, the structural dynamical evolution proceeds according to the Burgers mechanism for this transition.

An ab initio variable-cell-shape molecular-dynamics algorithm is used to investigate the stability of three carbon nitrides with composition ${\mathrm{C}}_3$${\mathrm{N}}_4$. The hexagonal β-${\mathrm{C}}_3$${\mathrm{N}}_4$ structure, which has been the subject of earlier investigations, is refined and its metastability is verified. Two other metastable structures are identified: a structure resembling zinc-blende CN with one C vacancy per cubic cell and a structure resembling graphitic CN with one C vacancy per four N sites. Both the refined β phase and the cubic phase have compressibilities comparable to that of diamond. The graphitic and the β phases lie very close in energy and are slightly favored over the cubic phase.

A three-dimensional covalent network of N atoms possessing a fraction (${\mathit{n}}_{\mathit{r}}$/N) of r-fold-coordinated atoms will, in general, display percolation of rigidity at an average coordination number 〈r〉=2.4-0.4(${\mathit{n}}_1$/N), where ${\mathit{n}}_1$/N represents the fraction of onefold-coordinated atoms. As an example, we show how these ideas can elucidate the glass-forming region in the Ge-S-I ternary system.

We observed fast nonexponential luminescence decay from a molecular dye in a suspension of dyed polystyrene spheres when both the interparticle distance and the sphere size is comparable to the wavelength of the emission. This nonexponential lifetime depends on the square root of the time, suggesting a resonance dipole-dipole interaction associated with the Mie resonances. This phenomenon is interpreted in terms of resonance energy transfer between molecules leading to the formation of a photonic band mode.

We have used the vibrating-reed technique to investigate the magnetoelastic properties of ${\mathrm{NbSe}}_3$ in an attempt to detect any contribution to stiffness from magnetic-field-assisted normal-to-charge-density-wave (CDW) carrier conversion below the material’s lower CDW transition. For a magnetic-field transverse to the reed, we find the resonant frequency to decrease quadratically with field strength. However, the magnitude of this change is too large to be associated with carrier conversion. We can attribute the effect to the interaction between the field and the material’s anisotropic magnetic susceptibility. This phenomenon is large enough to obscure attempts to detect stiffness contribution from carrier conversion. However, there exists the possibility of exploiting this effect to study the CDW through its influence on the magnetic susceptibility.

The first-principles spin-polarized, relativistic linear muffin-tin orbital method has been applied to calculate electronic and magneto-optical properties of Co in both fcc and hcp structures. In particular, the magneto-optical properties have been calculated for several magnetization directions in order to study their magnetization orientation dependences. A pronounced anisotropy in the polar Kerr effect is found for hcp Co while the magneto-optical properties of fcc Co are predicted to be insensitive to the magnetization direction. Moreover, this magneto-optical anisotropy in hcp Co is found to be correlated with the presence of a large anisotropy in the orbital magnetic moment and orbital hyperfine field. Changing the structure from fcc to hcp gives rise to even greater changes in the magneto-optical properties of Co. Calculated Kerr angles and ellipticities are in reasonable agreement with the latest experiment.

Static, nonmagnetic impurities are shown to give rise to gap states in a doped Mott-Hubbard antiferromagnet. The spectral and spatial features of these gap states are discussed and it is argued that these gap states are responsible for the observed local-moment behavior in zinc-doped cuprates. The magnetic dynamics in doped antiferromagnets is discussed with reference to the Néel-temperature variation with static-impurity concentration.

An expansion in inverse spin anisotropy, which enables us to study the behavior of discrete spin models as the spins soften, is developed. In particular we focus on models, such as the chiral clock model and the p-state clock model with competing first- and second-neighbor interactions, where there are special multiphase points at zero temperature at which an infinite number of ground states are degenerate. The expansion allows calculation of the ground state phase diagram near these points as the spin anisotropy, which constrains the spin to take discrete values, is reduced from infinity. Several different behaviors are found, from a single first-order phase boundary to infinite series of commensurate phases.

The ‘‘glassy’’ superconducting transition at high magnetic fields can be induced by columnar disorder. A model is proposed in which the thermodynamics of Bose condensation of Cooper pairs into the lowest Landau-level eigenstate of the random potential can be solved exactly. The solution reflects a peculiar character of the high-field limit: for example, the effective dimensionality of the transition is shown to be a function of magnetic field.