The role of the boundary condition on the transverse vibrations of an nth-stage Vicsek fractal as n→∞ was studied using nearest-neighbor interactions. Our findings indicate that, although the interplay among the local symmetry, the self-similarity, and the structure is the underlying reason for the unusual properties of the Vicsek fractal, the boundary condition has definitely left its imprint on almost every feature of the dynamics of the system.

We have measured steady-state photoabsorption spectra of a soluble trans-polyacetylene. We have found that photoexcitation of the soluble polyacetylene transforms only into neutral solitons in the temperature range 85–300 K, with photoabsorption signals associated with charged solitons not observed. We consider the features of soliton excitations in comparison with other known types of polyacetylene.

We investigate the dielectric response of the lowest-energy TO phonon of ${\mathrm{A}}_1$ symmetry of ${\mathrm{LiNbO}}_3$ via the impulsive excitation and heterodyne detection of THz phonon polaritons. We find that the low-frequency polariton dispersion of ${\mathrm{LiNbO}}_3$ is strongly influenced by four resonances at 1.3, 2.4, 3.4, and 4.1 THz. These resonances lead to avoided crossings in the polariton dispersion and to polariton beats. The presence of these resonances provides strong evidence that the microscopic potential of this phonon is extremely anharmonic and consists of three walls.

The sign-reversal phenomenon of the quantized Hall conductance as a function of an external magnetic field (H) observed in (TMTSF${)}_2$X is investigated theoretically. After giving a general Hall-conductance formula written in terms of order parameters of the field-induced spin-density wave (FISDW), we have done extensive mean-field calculations for a simplified standard model. It is shown that the many competing order parameters ${\mathrm{\Delta }}_{\mathit{n}}$ (n=0,±1,±2, . . .) which coexist in a FISDW state can make the sign of the Hall constant change particularly near the subphase boundary of the FISDW and that numbering of the integer subphases (N=0,1,2, . . . stabilized in this order from high fields) does not necessarily coincide with the Hall number L defined by L=${\mathrm{\sigma }}_{\mathit{x}\mathit{y}}$/(${\mathit{e}}^2$/h). We have found that the jumps of the Hall constant are accompanied by the spin-density wave gap closing when a FISDW is continuously evolving as H varies. In order for the sign reversal to occur a FISDW must contain many order parameters ${\mathrm{\Delta }}_{\mathit{n}}$ with n being both signs.

Transport, as well as scattering, mean free paths are calculated within the weak-scattering approximation and within a recently developed extension of the well-known coherent-potential approximation for a random arrangement of dielectric spheres. The different theoretical results of the mean free paths are compared with experiments on scattering from dielectric spheres.

We examine the interaction between a tunneling atom moving in a double potential well and the conduction electrons when the electron-assisted hopping to the excited states of the tunneling particle is taken into account. Using the renormalization-group transformation we show that virtual electron assisted hoppings to the excited states play a determining role in the low-temperature dynamics of the tunneling center, which scales to the two-channel Kondo problem at low temperature. The Kondo temperature ${\mathit{T}}_{\mathit{K}}$ separating the high temperature and the strongly correlated regime can be either increased or decreased due to the virtual hoppings to the excited states depending on the actual value of the bare couplings. However, carrying out a model calculation we find that for the physically relevant model parameters ${\mathit{T}}_{\mathit{K}}$ is always increased by one or two orders of magnitude even if the direct assisted tunneling between the potential minima is ignored. Thus this model can resolve the long-standing problem that the ${\mathit{T}}_{\mathit{K}}$ estimated earlier has always been somewhat small.

We present linearized augmented-plane-wave calculations for FeCu fcc and bcc metastable phases using the local-density approximation (LDA) as well as the local-spin-density approximation (LSDA). The nonpolarized density of states calculated within the framework of LDA together with the reformulated Stoner theory provide results in excellent agreement with those obtained from LSDA calculations. The magnetization is calculated for several alloy compositions—the magnetic moment per Fe atom is almost constant over a wide range of Fe content—in good agreement with recent experiments.

In this paper, the perturbation formulas for the zero-field splitting (ZFS) parameters of 3${\mathit{d}}^4$ and 3${\mathit{d}}^6$ ions in tetragonal symmetry are derived taking into account all the excited spin-triplet states ${}_{}{}^3{}_{}{}^{}$L (L=P,D,F,G,H), in the strong-field scheme. The contribution of the spin triplets to the ZFS and the validity of the ${}_{}{}^5{}_{}{}^{}$D approximation for 3${\mathit{d}}^4$ ions at tetragonal sites are investigated. The results show that the spin-triplet contribution to the ZFS is not negligible, and the validity of ${}_{}{}^5{}_{}{}^{}$D approxmation is highly limited in general, although a great deal of early studies of the ZFS for 3${\mathit{d}}^4$ and 3${\mathit{d}}^6$ ions in crystals were based on the ${}_{}{}^5{}_{}{}^{}$D approximation. Applications are made to ${\mathrm{Fe}}^{4+}$ ions in ${\mathrm{CdSiP}}_4$ and ${\mathrm{Cr}}^{2+}$ ions in ${\mathrm{Rb}}_2$${\mathrm{CrCl}}_{\mathit{r}}$, and the obtained results are in good agreement with the experimental data. The contribution of spin triplets is found to be either comparable to or larger than that of ${}_{}{}^5{}_{}{}^{}$D state in these crystals.

The coupled and discretized XY-Ising models describing frustrated XY and Josephson-junction systems are studied by the discretized Migdal-Kadanoff renormalization-group approach. Both uniform and disordered systems are considered. The phase diagram of the uniform two-dimensional (2D) model generally agrees with the previous studies but existence of a new antiferromagnetic phase is predicted. The random-gauge XY-Ising model is introduced to describe two-dimensional disordered systems with a half-integer number of the average flux per plaquette. Finite-temperature reentrancy from the paramagnetic to ferromagnetic Ising phases is predicted for the 2D random-gauge systems. At T=0, the gauge glass and Ising spin-glass phases can coexist provided the coupling to the Ising degrees of freedom is less than a critical value. In the 3D case, the finite-temperature gauge glass phase can exist only provided the Ising subsystem is also ordered, either in the ferromagnetic or the spin-glass fashion. The chaotic behavior of two mixed phases (one of them is of gauge glass and Ising spin glass and the other one is of gauge glass and Ising ferromagnet) is studied at T=0. Within the discretization scheme the Lyapunov exponents are found to be different for these phases.

The model Hamiltonian describing the partially delocalized $f$-electron system has been generalized to include both hybridization and band-$f$ exchange Coulomb interaction. A method has been developed to calculate the parameters appearing in such a model Hamiltonian from first principles. This enables us to calculate $f$-electron-based electronic and magnetic phenomena of pertinent materials on a quantitative basis. Calculations have been done for cerium monopnictides and monochalcogenides. Results are in agreement with experiment on various unusual behaviors of these materials, such as anomalous crystalfield splitting and anisotropic magnetic ordering, all of which are caused by the interactions between $f$ electrons and band electrons. In contrast to the earlier version of this theory that included only hybridization effects and produced range parameters (two-ion "exchange" coupling) that failed by an order of magnitude in matching the phenomenologically determined parameters which provide agreement with experiment, the present first-principles theory calculations which also include band-$f$ Coulomb exchange provide excellent agreement with the phenomenologically required magnitude.

Neutron-diffraction experiments and polarization analysis techniques reveal that the metal-insulator transition in the orthorhombic perovskites ${\mathrm{PrNiO}}_3$ and ${\mathrm{NdNiO}}_3$ is accompanied by a sudden three-dimensional magnetic ordering of the Ni sites (${\mathrm{\mu }}_{\mathrm{Ni}}$≊0.9${\mathrm{\mu }}_{\mathit{B}}$). The electronic localization is followed by a magnetic ground state consisting of an unusual antiferromagnetic structure, with k=(1/2,0,1/2) relative to the orthorhombic crystal cell. This propagation vector implies the symmetrical coexistence of ferro- and antiferromagnetic couplings along the three pseudocubic axes. This suggests the existence of a nonuniform orbital distribution of the single ${\mathit{e}}_{\mathit{g}}$ electron. The orbital superlattice may result from the breakdown of the degeneracy of the ${\mathrm{Ni}}^{\mathrm{III}}$(${\mathit{t}}_{2\mathit{g}}^6$${\mathit{e}}_{\mathit{g}}^1$) state due to electronic correlation. This type of spin arrangement has not been observed in other perovskite oxides. These findings are confirmed by the magnetic behavior of the single crystallographic Nd site: half of these ions become ordered and the other half remain disordered as in a simple paramagnet. This can be explained by the combination of polarization effects due to the exchange field from nickel moments and the breaking down of point symmetry at Ni site.

Aluminum–transition-metal compounds, at the aluminum end of their phase diagrams, form a fascinating variety of complex structures. We present a microscopic theory of the chemical trends in the phase stability of these complex structures based on a remarkably strong and long-range interaction between the transition-metal atoms in an aluminum host. The mechanism described here provides satisfactory explanation of the observed chemical trends. We also treat the effects of Cu on the transition-metal interactions.

On the basis of extended recursion-scheme calculations and general analysis we show that the instabilities and oscillations of the magnetic anisotropy energy (MAE) curve result from numerical inaccuracies. We explain how to obtain quickly convergent results within the tight-binding recursion method. For an Fe(001) monolayer we find a negligible MAE, for a Co(111) monolayer the in-plane anisotropy is preferred whereas for a Co(111) bilayer the result is sensitive to the choice of parameters. Crystal-field effects are also discussed.

The theory of surface spin waves in a pure exchange ferromagnet in a weak nonlinear approximation has been considered. The nonlinear dispersion equation for these waves is derived. The nonlinear Schrödinger equation is derived for the envelope amplitude of magnetization in the wave. Conditions for the existence of a solitonic solution are discussed.

We report systematic calculations of the residual resistivity and the low-field Hall coefficient of Al-based dilute alloys with 3d and 4sp impurities, by self-consistently solving the linearized Boltzmann equation. We employ the on-Fermi-sphere approximation, which allows us to combine the full anisotropy of the aluminum Fermi surface, obtained by the four-orthogonal-plane-wave method, with the phase shifts associated with isotropic impurity scattering, evaluated by self-consistent local-density-functional impurity-in-jellium calculations. Our results show that the anisotropic scattering increases the residual resistivity, thus obtaining better agreement with the experiment. Moreover, a consistent interpretation of the observed trends of the low-field Hall coefficient is presented.

The electron covalency contributions to the polarizability in oxide dielectric compounds are studied in the electron-lattice coupling model by means of the exact diagonalization technique. These contributions originate from the charge transfer between the anion and the cation sites which produces an electric dipole moment extended over the anion-cation bond distance. When a strong on-site Coulomb repulsion between electrons is included, the electronic system is found to undergo a transition between the ionic and Mott insulating phases, and the covalency contributions to the polarizability are largely enhanced near the phase boundary. It is suggested that the present results may explain the high indices of refraction observed in the titanium oxides and the birefringence in the ferroelectric compounds.

A Hubbard model is solved exactly to characterize confined, intermediate-dimensional excitons for the full range of electron and hole hopping and interaction strengths. Finite systems with periodic boundary conditions model unconfined excitons. Finite systems with terminated ends model confined excitons. Exciton energies, oscillator strengths, and electron and hole distributions are determined. Oscillator strengths and electron-hole distributions of confined intermediate-dimensional excitons exhibit anomalous, nonmonotonic, nonuniversal dependences on the electron-hole interaction strength and hopping that are counter to the conventional behavior for quantum-confined excitons and free excitons. Perturbation theory is used to clarify the weak and large interaction limits. In the large-interaction limit, an exciton dead layer occurs near the boundary of the system because electron-hole correlation is suppressed near the boundary. Second-order perturbation theory determines the surface potential barrier caused by the suppression of pair correlation near the surface and determines the hopping rate for tunneling into this barrier. In the weak-interaction limit, on-site correlation of a confined electron-hole pair is suppressed by asymmetry in the electron and hole hopping. For large asymmetry in the electron and hole hopping, the oscillation strength of the confined intermediate-dimensional exciton can be less than the oscillator strength of an uncorrelated, noninteracting pair.

We report x-ray photoemission, UV photoemission, and bremsstrahlung isochromat spectra of TiO with ordered vacancies in both Ti and O sublattices and of the series ${\mathrm{TiO}}_{\mathit{x}}$ (0.8<x<1.3) containing disordered Ti and O vacancies. The details of the electronic structure are discussed in comparsion to band-structure calculations for the ordered structures performed in this work as well as to density of states obtained for the disordered systems within different approximate methods reported earlier in the literature. Our results in the valence-band regions indicate the need for a better theoretical approach to describe the effect of disordered vacancies on the electronic structure than has been attempted to date. Ti 2p core-level spectra indicate the existence of vacancy-induced local environments with the formal charge on the Ti atom ranging from 2+ to 4+.

We report an experimental study of the electronic structure of the alloy system ${\mathrm{Au}}_{\mathit{x}}$${\mathrm{Pd}}_{1\mathrm{-}\mathit{x}}$. Valence-band photoemission spectra were recorded using synchrotron radiation, exploiting the different photoionization cross sections of the Au and Pd d bands to identify the spectral features. We find that recent electronic-structure calculations using the Korringa-Kohn-Rostoker method with the coherent-potential approximation (KKR-CPA) give good agreement with our results, whereas earlier calculations using other methods show serious discrepancies. In addition we measured the Au ${\mathit{N}}_{6,7}$VV and Pd ${\mathit{M}}_{4,5}$VV Auger line shapes. We find that one-electron calculations using the KKR-CPA results give reasonable qualitative agreement for the Au line shapes across the alloy series. Similar agreement is found for the Pd Auger line shapes at high Pd concentrations, but this breaks down for low Pd concentrations. We suggest that this disagreement results from a neglect of many-body interactions rather than a problem with the KKR-CPA calculations.

In small samples of o-${\mathrm{TaS}}_3$ detailed spectra of broadband noise provide characteristic patterns identifying clusters of metastable configurations. The dependences of the characteristic frequencies of features in these spectra on temperature and current bias provide an indication of how the free-energy landscape changes as a function of these variables. These dependences are found to be very strong and of apparently random sign. The results are reminiscent of theoretical predictions for thermal chaos in spin glasses.