The photopyroelectric technique has been used to study the critical behavior of thermal diffusivity and thermal conductivity of ${\mathrm{Cr}}_2$${\mathrm{O}}_3$ at the antiferromagnetic-paramagnetic phase transition. Deviation from the conventional Van Hove theory has been observed and the results have been explained in terms of a uniaxial model (n=1) with energy conservation and a nonconserved order parameter. A sharp dip, due to critical slowing down, is present in the thermal diffusivity while the thermal conductivity shows no anomaly in the critical region. A power-law fit with a background contribution and a term to correct for the thermal-diffusivity anomaly gives a critical exponent b=-0.09±0.02 and a critical amplitude ratio of ${\mathit{U}}^{+}$/${\mathit{U}}^{\mathrm{-}}$=0.51.

An exact expression for the Hamiltonian H of the t-J model in terms of local spin (${\mathbf{S}}_{\mathit{i}}$) and fermionic holon (${\mathit{e}}_{\mathit{i}}$) operators is derived which requires no constraint between these operators. The result for the Hamiltonian H is H=-t t${sum}_{\mathit{i}\mathit{j}}$${\mathit{e}}_{\mathit{i}}$${\mathit{e}}_{\mathit{j}}^{\mathrm{°}}$(1/2+2${\mathbf{S}}_{\mathit{i}}$⋅${\mathbf{S}}_{\mathit{j}}$)+(J/2)t ${\mathrm{sm}}_{\mathrm{ij}}$(1-${\mathit{e}}_{\mathit{i}}^{\mathrm{°}}$${\mathit{e}}_{\mathit{i}}$)(${\mathbf{S}}_{\mathit{i}}$⋅${\mathbf{S}}_{\mathit{j}}$-1/4)(1-${\mathit{e}}_{\mathit{j}}^{\mathrm{°}}$e The number of electrons at site i is given by ${\mathit{n}}_{\mathit{i}}$=1-${\mathit{e}}_{\mathit{i}}^{\mathrm{°}}$${\mathit{e}}_{\mathit{i}}$, and the true spin operator S${\mathrm{̃}}_{\mathit{i}}$, is related to the local spin operator by S${\mathrm{̃}}_{\mathit{i}}$=(1-${\mathit{e}}_{\mathit{i}}^{\mathrm{°}}$${\mathit{e}}_{\mathit{i}}$)${\mathbf{S}}_{\mathit{i}}$. The expression correctly produces the Nagaoka theorem in the limit J→0, and preserves the time-reversal symmetry of the original model. For a bipartite lattice, H describes a competition between ferromagnetism, favored by the hopping term, and antiferromagnetism, favored by the Heisenberg term.

We report the study of magnetic properties of a molecular-based alternating-spin chain: metallocenium electron-transfer salt decamethylchromocenium tetracyanoethanide, [${\mathrm{CrCp}}_2^{\mathrm{*}}$] [TCNE]. We give a modified spin-wave theory for the Heisenberg alternating-spin chains. The low-field susceptibility and magnetization data agree with the theoretical results indicating that one-dimensional linear magnon excitations dominate the magnetic behavior above the three-dimensional ordering temperature. Strong ferromagnetic intrachain coupling, J≃9 K, is found. Unusual critical phenomena associated with lattice dimensional crossover are discussed.

Starting from the ${\mathit{CP}}^{\mathit{N}\mathrm{-}1}$ model description of the thermally disordered phase of the D=2 quantum antiferromagnet, we examine the interaction of the Schwinger-boson spin-1/2 mean-field excitations with the generated gauge (chirality) fluctuations in the framework of the 1/N expansion. This interaction dramatically suppresses the one-particle motion, but enhances the staggered static susceptibility. This means that the actual excitations in the system are represented by the collective spin-1 excitations, whereas the one-particle excitations disappear from the problem. We also show that massive fluctuations of the constraint field are significant for the susceptibility calculations. A connection with the problem of a particle in random magnetic field is discussed.

Electronic Raman scattering has been investigated for metallic ${\mathrm{Sr}}_{1\mathrm{-}\mathit{x}}$${\mathrm{La}}_{\mathit{x}}$${\mathrm{TiO}}_3$ in which the 3d band filling (x) can be systematically changed from x=0 (a band insulator) to x=1 (a Mott-Hubbard insulator). The symmetry dependence of the scattering intensity can be accounted for in terms of the neutral carrier density fluctuation model. However, a systematic change of the spectral shape with the carrier density (≃x) is observed. All the spectra can be reproduced by a relaxational function with an ω-dependent scattering rate (Γ). The ω dependence of Γ gets stronger with x, which is in accord with the x-dependent enhancement of the effective mass, due to the electron correaltion effect.

ac-magnetic-susceptibility ${\mathrm{\chi }}_{\mathrm{ac}}$(T) measurements as a function of frequency f and excitation field ${\mathit{h}}_{\mathrm{ac}}$ have been performed on a single crystal of the heavy-fermion superconductor ${\mathrm{URu}}_2$${\mathrm{Si}}_2$ in magnetic fields H up to 30 kOe applied along the c axis. The apparent superconducting transition temperature ${\mathit{T}}_{\mathit{c}}$ shows an unexpected and approximately logarithmic increase (decrease) with f (${\mathit{h}}_{\mathrm{ac}}$) that is enhanced with H, which suggests the existence of an irreversibility line below the upper critical field ${\mathit{H}}_{\mathit{c}2}$(T) in ${\mathrm{URu}}_2$${\mathrm{Si}}_2$. Isothermal ${\mathrm{\chi }}_{\mathrm{ac}}$ vs H sweeps were used to define ${\mathit{H}}_{\mathit{c}2}$(T) which was independent of f and ${\mathit{h}}_{\mathrm{ac}}$.

With a bolometric technique, we have measured, in intense fields, the low-temperature surface resistance of both 90- and 60-K ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ single crystals. In the former, the observed vortex viscosity ${\mathrm{\eta }}_{\mathrm{eff}}$=5×${10}^{\mathrm{-}5}$ N s/${\mathrm{m}}^2$ exceeds by 2 orders of magnitude the viscosity in conventional superconductors. This corresponds to a normal-state resistivity of 0.4 μΩ cm, and a quasiparticle lifetime τ∼6 ps. (The corresponding numbers for the 60-K crystal are ${\mathrm{\eta }}_{\mathrm{eff}}$=2.5×${10}^{\mathrm{-}6}$ N s/${\mathrm{m}}^2$ and τ=1.9 ps at 3 K.) These lifetimes place ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ firmly in the superclean regime where the lifetime broadening of core energy levels is much less than the energy spacing. We discuss how a very large Hall angle in this regime affects the analysis of surface resistance.

A demonstration of critical scaling of the magnetic susceptibility in a ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$ single crystal is performed for 350 frequencies (f) from 1 kHz to 2 MHz. Near the vortex-glass melting temperature ${\mathit{T}}_{\mathit{M}}$(H) and in the linear-response limit, the susceptibility χ≡‖χ‖${\mathit{e}}_{\mathrm{\chi }}^{\mathit{i}(\mathrm{\pi }\mathrm{-}\mathrm{\phi }}$) follows the scaling relations ‖χ‖∼‖1-(T/${\mathit{T}}_{\mathit{M}}$)${\mathrm{\Vert }}^{\nu /2\mathrm{}}$ for f→0, ‖χ‖∼${\mathit{f}}^{1/\left(2\mathit{z}\right)}$ and ${\mathrm{\phi }}_{\mathrm{\chi }}$=π/4z for T→${\mathit{T}}_{\mathit{M}}$. The static and dynamic exponents (ν≊2/3 and z≊3) as well as ${\mathit{T}}_{\mathit{M}}$(H) are found to be in excellent agreement with our previous dc and ac transport measurements, lending strong support for a second-order phase transition.

A theoretical model for the elastic softening observed in ${\mathrm{La}}_{2\mathrm{-}\mathit{x}}$${\mathrm{Sr}}_{\mathit{x}}$${\mathrm{CuO}}_4$ is presented. It is shown that the electronic redistribution mechanisms between the strain-split itinerant p bands and also between the strain-shifted energy pockets can satisfactorily account for the elastic softening of ${\mathit{c}}_{66}$ and (${\mathit{c}}_{11}$-${\mathit{c}}_{12}$)/2. The result suggests that the Fermi level shifts from the M point to the Γ point as a consequence of the tetragonal-to-orthorhombic structural transition. Implications of the present result on the superconducting mechanism are discussed.

Crystal-field transitions within the ${}_{}{}^3{}_{}{}^{}$${\mathit{H}}_4$ multiplet of ${\mathrm{Pr}}^{3+}$ in ${\mathrm{Pr}}_2$${\mathrm{CuO}}_4$ were studied by Raman scattering as a function of temperature. We observed three crystal-field excitations at 156, 540, and 675 ${\mathrm{cm}}^{\mathrm{-}1}$. The peak at 156 ${\mathrm{cm}}^{\mathrm{-}1}$, assigned by other authors to the lowest ${\mathit{E}}_{\mathit{g}}$ phonon mode, shows a thermal broadening of the linewidth, which is the signature for acoustical-phonon-relaxation processes between crystal-field levels. Our results are in excellent agreement with recent inelastic neutron scattering experiments in ${\mathrm{Pr}}_2$${\mathrm{CuO}}_4$.

Considering Hubbard models with infinite U, the leading terms of the electronic self-energy due to an on-site electron-phonon interaction are calculated within a 1/N expansion. In particular, the modifications of the Eliashberg function ${\mathrm{\alpha }}^2$F(ω) due to strong correlations are described and calculated for a simple square lattice as a function of doping. We find that the on-site electron-phonon coupling is in general slightly enhanced in forward scattering but dramatically suppressed for scattering with large momentum transfers by correlations. This implies at least in the single-band case that the electron-phonon coupling is greatly reduced in transport quantities and to a much smaller degree in ${\mathrm{\alpha }}^2$F because of electronic correlations.

We have investigated c-axis transport in the normal and mixed states of ${\mathrm{Bi}}_2$${\mathrm{Sr}}_2$${\mathrm{CaCu}}_2$${\mathrm{O}}_8$ single crystals. The temperature dependence of the normal-state resistivity along the c axis is significantly affected by thermal annealing, but all data are well described by the relation ρ=${\mathrm{\rho }}_0$T exp(E/${\mathit{k}}_{\mathit{B}}$T), suggesting a thermally activated hopping motion. In the mixed state, the behavior of ${\mathrm{\rho }}_{\mathit{c}}$(T,H) and ${\mathit{J}}_{\mathit{c}}$(H) is observed to be closely related to the behavior of ${\mathrm{\rho }}_{\mathit{c}\mathit{N}}$(T). Some implications of these results are discussed.

We measured the peak effect in the magnetic hysteresis loop of an untwinned ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ crystal in the vicinity of the critical temperature and studied its temperature, time, and angular dependence. The location of the peak is determined by the component of the field along the c direction. The pinning force density ${\mathit{F}}_{\mathit{p}}$(B) is scaled into a single curve for all measured isotherms (75–87 K) and time scales (4–1500 sec), and its functional form reflects the observed peak effect. The scaling field is related to the irreversibility field of oxygen-deficient regimes. The results indicate that pinning in this system is due to inhomogeneity of the oxygen deficiency and that the peak is related to the formation of a percolationlike network of reversible regimes.

Low-energy excited states of a neutral ${\mathrm{C}}_{60}$ molecule are studied in detail. The system is described by a Su-Schrieffer-Heeger Hubbard-type Hamiltonian which is solved perturbatively in the electron-electron interactions. The optical-absorption spectrum is computed including both the direct and one-phonon-induced processes. Electronic-correlation effects are qualitatively important and, if and only if the electron-electron interaction is taken to be large enough, good agreement with experiments is achieved. Furthermore, it is shown that, in this model, the lowest-energy spin-triplet state is stable against decay due to a large Coulomb binding. Also, the theory predicts a triplet-triplet band about at 0.45 eV which, to my knowledge, has not yet been observed experimentally.

Ground-state properties of the one-dimensional Kondo lattice model are investigated using the quantum Monte Carlo (QMC) simulation method. To reduce the difficulty of the negative sign problem, we employ the variationally optimized singlet wave function. Since the improvement of Monte Carlo sampling efficiency is achieved in the half-filling case, we can perform the simulations on large systems (up to 26-site system). The QMC data on the local spin correlations are closely compared with those of the variational Monte Carlo (VMC) calculations as well as with the exact diagonalization data of the Ruderman-Kittel-Kasuya-Yoshida (RKKY) lattice model. We find that the local spin correlation decays exponentially with the correlation length ${\xi }_{\mathit{f}\mathit{f}}$∼2.54 in the QMC data, while ${\xi }_{\mathit{f}\mathit{f}}$∼1.08 in the VMC results (J/t=1). This implies the absence of the long-range order (the existence of the spin gap) and the importance of intersite correlation effects which are not taken into account in the VMC results. On the other hand, the system size dependence is almost absent in the Kondo lattice model results, which contrasts the behavior in the RKKY data.

The electronic structures of trivalent and divalent rare-earth hexaborides R${\mathrm{B}}_6$ are calculated by using the modified orthogonalized-plane-wave method within the framework of the muffin-tin-potential approximation based on the self-consistent-field atomic-structure calculations. By regarding the 4f state as a partially filled corelike state and for the transition between 4f and 5d states, and adopting the transition state introduced by Slater which includes the effect of the screening of 4f states by 5d electrons, an attempt is made to understand the x-ray-photoemission spectroscopy (XPS) experiments and bremsstrahlung isochromat spectra (BIS). It is shown that the calculated results of the 4f levels relative to the Fermi level generally agree with the experimental ones obtained from the XPS for ${\mathrm{CeB}}_6$, ${\mathrm{PrB}}_6$, ${\mathrm{NdB}}_6$, ${\mathrm{SmB}}_6$, ${\mathrm{GdB}}_6$, and ${\mathrm{YbB}}_6$ and the BIS for ${\mathrm{GdB}}_6$, ${\mathrm{TbB}}_6$, and ${\mathrm{DyB}}_6$, but there is a considerable difference between the calculations and experiments for the XPS for ${\mathrm{TbB}}_6$, ${\mathrm{DyB}}_6$, and ${\mathrm{HoB}}_6$ and the BIS for ${\mathrm{LaB}}_6$, ${\mathrm{CeB}}_6$, and ${\mathrm{PrB}}_6$. The reason for this disagreement is mainly attributed to the effect of 4f multiplets which is not taken into account in the present study.

In this work we present a method of fitting augmented-plane-wave energy bands and total-energy results for the fcc and bcc structures to a nonorthogonal tight-binding Hamiltonian from which the sum of the eigenvalues is derived, and to a simple pair potential that is designed to account for all the other terms of the total-energy expression. We have applied this method to calculate the elastic constants of the metals Rh, Pd, Ta, Ir, and Au, avoiding the expensive first-principles calculations of the distorted structures. We obtained very good agreement with both first-principles local-density-functional-theory calculations and experiment.

The electronic structure of ${\mathrm{NaCuO}}_2$ has been calculated within the local-density approximation, using an extended general-potential linearized-augmented-plane-wave method. These calculations reveal that (i) ${\mathrm{NaCuO}}_2$ is a conventional insulator with a band gap arising from simple covalent effects and (ii) Cu is far from trivalent in this material.

Momentum- and frequency-dependent self-consistent field theories provide a potentially powerful tool for analyzing condensed-matter models for interacting electrons. Such theories generally require the solution of multidimensional integral equations. Solutions are limited by demands on computational time and storage, which increase rapidly for calculation of low-temperature properties. A renormalization-group technique which allows the sequential elimination of regions of high frequency and momentum is presented in detail, and is then applied to the solution of the fluctuation exchange approximation for the two-dimensional Hubbard model. Effective meshes with as many as ${10}^4$ frequencies and ${512}^2$ k points can be analyzed on a vector supercomputer using this approach. As a sample application, it is demonstrated that the fluctuation exchange approximation exhibits non-Fermi liquid behavior near half filling for sufficiently large interaction strengths.

A relation between the thermodynamic potential and certain spectral-weight functions in mixed singlet-triplet states of a Fermi fluid with weakly attractive interaction is established. The entire thermodynamics of the system can be derived using this relation. A similar relation is also established for an assembly of spinless, interacting bosons in the ordered phase. The latter corresponds to the Kadanoff-Baym relation for the normal phase when the necessary conditions are fulfilled. Crossover scaling forms for the susceptibility and the deviation of pressure from its critical value for the Bose system are calculated using the established relation. These forms are in general agreement with those obtained earlier by renormalization-group approaches to the problem.