Phonons and magnetic excitations were studied as a function of temperature in the spin-Peierls phase of an inorganic material ${\mathrm{CuGeO}}_3$ by Raman scattering. All of the phonon Raman peaks observed at room temperature can be assigned on condition that the crystal symmetry is ${\mathit{D}}_{2\mathit{h}}^5$(Pbmm). Five peaks intrinsic to the spin-Peierls state were observed at 30, 105, 228, 370, and 818 ${\mathrm{cm}}^{\mathrm{-}1}$ in the spin-Peierls phase. The temperature dependence of the frequency of the 30-${\mathrm{cm}}^{\mathrm{-}1}$ peak agrees approximately with 2Δ(T), where Δ(T) is the spin-Peierls gap. The Raman spectrum between 0 and 300 ${\mathrm{cm}}^{\mathrm{-}1}$ was compared with the density of states of the magnetic excitons. The 105- and 228-${\mathrm{cm}}^{\mathrm{-}1}$ peaks were assigned to two-magnetic-exciton Raman scattering. The peaks at 370 and 818 ${\mathrm{cm}}^{\mathrm{-}1}$ were assigned to one-phonon Raman scattering of the folded ${\mathit{A}}_{\mathit{g}}$ modes, which occurs due to the formation of a dimerization in the spin-Peierls phase.

Interesting compounds of the ${\mathit{ABX}}_3$ family can be modeled by antiferromagnetic chains arranged according to a triangular pattern, where each spin is coupled with six nearest neighbors via a weak interchain antiferromagnetic interaction. The behavior of this model in an external magnetic field perpendicular to the c axis has been studied when a sufficiently strong anisotropy forces the spins in the c plane in order to explain the low-temperature transition occurring in ${\mathrm{CsMnBr}}_3$. We find that interesting phenomena occur in the opposite limit of weak anisotropy. Indeed an umbrella configuration intervenes between the low-field distorted-helix configuration and the high-field fan configuration. We evaluate the elastic-neutron-scattering cross section and suggest ${\mathrm{CsVCl}}_3$, ${\mathrm{CsVBr}}_3$, and ${\mathrm{CsVI}}_3$ as good candidates to test our theoretical prevision.

A classical continuum model of an effectively one-dimensional ferromagnet will exchange and anisotropies of hard and easy-axis type is considered. In the presence of an external magnetic field along the easy axis, the lowest-lying topological excitations are shown to be untwisted or twisted pairs of π-domain walls. The fluctuations around these structures are investigated. It is shown that the fluctuations around the twisted and untwisted domain-wall pair are governed by the same set of operators. The untwisted domain-wall pair has exactly one unstable mode and thus represents a critical nucleus for magnetization reversal in effectively one-dimensional systems. The twisted domain-wall pair is stable for small external fields but becomes unstable for large magnetic fields. The former effect is related to thermally induced coercivity reduction in elongated particles while the latter effect is related to ‘‘chopping’’ of twisted Bloch wall pairs in thin films. In view of a statistical mechanical theory of magnetization reversal which will be presented in a separate article, the scattering phase shifts of spin waves around these structures are calculated. The applicability of the present theory to magnetic thin films is discussed. Finally, it is noted that the static properties of the present model are equivalent to those of a nonlinear σ model with anisotropies and an external field.

Thermally activated magnetization reversal in elongated particles is studied within a model that allows for spatially nonuniform magnetization configurations along the particle. An external field antiparallel to the existing magnetization is shown to given rise to an energy barrier which represents a spatially localized deviation from the initial uniform magnetization configuration. For sufficiently elongated particles, thermal fluctuations thus substantially lower the coercivity compared to the previous theories by Néel and Brown which assume a spatially uniform magnetization. The magnetization reversal rate is calculated using a functional Fokker-Planck description of the stochastic magnetization dynamics. Analytical results are obtained in the limits of small fields and fields close to the anisotropy field. In the former case the hard-axis anisotropy becomes effectively strong and the magnetization reversal rate is shown to reduce to the nucleation rate of kink-antikink pairs in the overdamped sine-Gordon model. The present theory therefore includes the nucleation theory of the double sine-Gordon chain as a special case.

In the superconductor ${\mathrm{Lu}}_2$${\mathrm{Fe}}_3$${\mathrm{Si}}_5$ (${\mathit{T}}_{\mathit{c}}$=6.25 K) lutetium can be replaced by uranium up to a maximum of 40% [(${\mathrm{Lu}}_{0.6}$${\mathrm{U}}_{0.4}$${)}_2$${\mathrm{Fe}}_3$${\mathrm{Si}}_5$], maintaining the original P4/mnc structure. When the uranium content in (${\mathrm{Lu}}_{1\mathrm{-}\mathit{x}}$${\mathrm{U}}_{\mathit{x}}$${)}_2$${\mathrm{Fe}}_2$${\mathrm{Si}}_5$ is increased the superconductivity vanishes and a heavy-fermion state is built up. Already for small amounts of uranium there is a strong suppression of superconductivity (${\mathit{T}}_{\mathit{c}}$=1.8 K for x=0.01). According to the Abrikosov-Gorkov theory this suppression can be described by a strong exchange coupling between the uranium 5f electrons and the conduction electrons. In agreement with this high exchange coupling we detect drastically reduced magnetic (uranium) moments. For low dopings (x<0.1) there is no significant change of the Sommerfeld parameter γ. When the U content exceeds x>0.1 there is a strong γ increase. The enhanced specific heat remains unchanged when the sample is exposed to a magnetic field of 13 T. This field-independent specific heat, the screened magnetic moments, and the Wilson ratio χ/γ corroborate that the increase in γ is indeed indicative of an enhanced effective mass and not a result of magnetic entropy.

Just like in other U-based systems (e.g., ${\mathrm{UPt}}_3$ and ${\mathrm{UBe}}_{13}$) the evolution of the heavy-fermion state in (${\mathrm{U}}_{\mathit{x}}$${\mathrm{Lu}}_{1\mathrm{-}\mathit{x}}$${)}_2$${\mathrm{Fe}}_3$${\mathrm{Si}}_5$ cannot merely be explained by a pure single-ion Kondo effect. The fact that the γ enhancement begins only after the U content exceeds x>0.1 points out that collective phenomena (i.e., interaction between the U ions) play a decisive role for the evolution of the heavy-fermion state in this system. Cerium-doped samples (${\mathrm{Lu}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Ce}}_{\mathit{x}}$${)}_2$${\mathrm{Fe}}_3$${\mathrm{Si}}_5$ revealed a distinctly weaker ${\mathit{T}}_{\mathit{c}}$ suppression (${\mathit{T}}_{\mathit{c}}$=1.9 K for x=0.1), less reduced magnetic moments, and no significant γ enhancement.

The structure’s of the flux-line lattice and of individual vortices on the surface of a uniaxial anisotropic superconductor 2H-${\mathrm{NbSe}}_2$ are studied for arbitrary magnetic fields using the scanning tunneling microscope. The basis vectors show a distortion consistent with bulk anisotropic London theory, however, their angular orientation with respect to the tilt direction differs by about 30° from that predicted. Various lattice-buckling instabilities are observed when the field is inclined more than 80° away from the c axis. The star-shaped structure of the core distorts into a spiky comet shape as the field is tilted into the plane. If the field is along the surface (perpendicular to the c axis), evenly spaced parallel streaks reveal the subsurface vortex spacing.

One of the first reported oxide superconductors lithium titanate ${\mathrm{Li}}_{1+\mathit{x}}$${\mathrm{Ti}}_{2\mathrm{-}\mathit{x}}$${\mathrm{O}}_4$ (${\mathit{T}}_{\mathit{c}}$∼12 K for 0<x<0.10) is studied here by nuclear magnetic resonance of the titanium nucleus ${(}^{49}$Ti and ${}_{}{}^{47}{}_{}{}^{}\mathrm{Ti}$) in the temperature range 160–330 K. The study encompasses the temperature variation of the Knight-shift components and the quadrupole interaction for ${\mathrm{LiTi}}_2$${\mathrm{O}}_4$ (the x=0 end member), the variation of the spectrum at room temperature as a function of x in the range 0<x<0.10, and some preliminary measurements of the nuclear spin-lattice relaxation time. The samples have been well characterized by a combination of x-ray and neutron diffraction, and magnetic-susceptibility (superconducting quantum interference device ac inductance) measurements. A feature of the present samples is the very low density of localized moments in the metallic regime, as compared to previous studies of the same system. The results show strong broadening of the Ti spectrum induced by lithium substitution and fast relaxation. The isotropic and axial Knight-shift components and the quadrupole interaction in ${\mathrm{LiTi}}_2$${\mathrm{O}}_4$ exhibit a strong temperature dependence. The isotropic Knight-shift component is linked to a temperature variation of the electron spin susceptibility χ, leading to an estimate of the average orbital susceptibility in the x=0 compound of 30×${10}^{\mathrm{-}6}$ emu/mole, a value corroborated by theoretical calculations. The axial component of the shift indicates that both the orbital and the spin susceptibilities in the x=0 compound are highly anisotropic. The values of isotropic shift and χ indicate that the electronic system at x=0 is a narrow d-band metal with significant electron-electron interaction.

Results of high-resolution measurements of the inelastic scattering of neutrons from normal and superfluid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ are presented. A complicated structure of peaks corresponding to phonon-maxon-roton excitations is observed. At T<${\mathit{T}}_{\lambda }$, the scattering can be described by a narrow peak plus a wide component. The relative intensity of the narrow and wide components in the maxon-roton region follows the temperature dependence of density of the Bose condensate. Above ${\mathit{T}}_{\lambda }$, for the wave vectors q>0.65 A${\mathrm{̊}}^{\mathrm{-}1}$, only the wide component exists. In the long-wave region (q<0.65 A${\mathrm{̊}}^{\mathrm{-}1}$), a considerable transformation of peaks with changing temperature occurs as well, although the two-component structure persists in the normal phase.

We report an ultrahigh-resolution photoemission study of ${\mathrm{Rb}}_3$${\mathrm{C}}_{60}$ single crystals (${\mathit{T}}_{\mathit{c}}$=30.5 K) and the measurement of the superconducting energy gap. The crystals were cleaved at 13 K to expose the (111) plane. They show a sharp Fermi cutoff above ${\mathit{T}}_{\mathit{c}}$ and a superconducting gap opening below ${\mathit{T}}_{\mathit{c}}$ (2Δ/${\mathit{k}}_{\mathit{B}}$${\mathit{T}}_{\mathit{c}}$∼4.1 at 13 K). The valence band shows a ∼0.15-eV-wide band near ${\mathit{E}}_{\mathit{F}}$ that is consistent with calculations, and a broad band at 0.15–1.3 eV, possibly contributed by the surface ${\mathrm{C}}_{60}$ layer.

Magnetic-field gradients in the mixed state of a type-II superconductor are studied using ${}_{}{}^{205}{}_{}{}^{}\mathrm{Tl}$ nuclear magnetic resonance (NMR) on ${\mathrm{Tl}}_2$${\mathrm{Ba}}_2$${\mathrm{Ca}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{10+\mathrm{\delta }}$. An anomalous peak was observed in the temperature dependence of the transverse relaxation rate at T/${\mathit{T}}_{\mathit{c}}$≊0.25. We attribute this behavior to magnetic-field flucutations from vortex dynamics. We interpret this behavior as a crossover of the principal time scale for vortex dynamics with that of the NMR experiment, approximately 100 μs. The temperature dependence of this time scale is discussed.

We consider a charged quantum particle in a two-dimensional disordered system subject to a spatially and temporally fluctuating magnetic field. The fluctuations are assumed to be Gaussian, with correlations typical for a metal in the anomalous-skin-effect regime. We derive a scaling form for the quantum correction to the conductivity in terms of a scaled temperature, elastic mean free path, and magnetic field. The weak localization correction to the conductivity is calculated for the case of rapid magnetic-field fluctuations. We express the result in terms of a phenomenological phase relaxation rate 1/${\mathrm{\tau }}_{\mathrm{\phi }}^{\mathrm{*}}$, which is found to scale with temperature as ${\mathit{T}}^{1/3}$, provided the potential disorder is sufficiently strong and the temperature is above a critical value. In all other cases, including the normal-skin-effect regime and the case of quasistatic field fluctuations, 1/${\mathrm{\tau }}_{\mathrm{\phi }}$ is found to be proportional to T, albeit with unusual prefactors.

Collective depinning transitions in Coulomb solid-on-a-lattice systems are investigated in the low-charge-density limit. It is argued that depinning occurs at an inverted, continuous, dislocation unbinding transition of the Halperin-Nelson type. The depinning transition temperature is shown to be linear in the charge density, with a slope which is in good agreement with recent Monte Carlo simulations.

We give a general thermodynamic analysis of the behavior of the chemical potential of electrons in metals at a second-order phase transition, including in our analysis the effect of long-range Coulomb forces. It is shown that this chemical potential can have a kink at ${\mathit{T}}_{\mathit{c}}$, both for fixed sample volume and fixed external pressure. The Coulomb term transfers the changes in chemical potential of the electrons into an experimentally observable shift of the surface potential if the sample is electrically connected to a ground potential.

We report on a Raman study that compares the behavior of phonons in several a-axis- and c-axis-oriented superlattices of (${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$${)}_{\mathit{m}}$(${\mathrm{PrBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$${)}_{\mathit{n}}$. The number of individual layers within a superlattice period varied between 1≤m,n≤15. The dependence of the phonon frequencies on m and n shows a significant softening of the vibration associated with the apical oxygen atom [O(4)] in ${\mathrm{PrBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$ with reductions in the Pr layer thickness (${\mathit{d}}_{\mathrm{Pr}}$). The modifications to the self-energy of this phonon for both superlattice orientations only occur when ${\mathit{d}}_{\mathrm{Pr}}$≲25 Å and therefore establishes the primary importance of the Pr layer thickness in affecting the observed softening. These phonon renormalizations are consistent with charge redistribution in the immediate vicinity (∼10 Å) of the interface arising from the unequal Fermi energies associated with the alternating layers. Our study also establishes that the significant differences in the dependence of the superconducting transition temperatures on layer thickness in a- and c-axis-oriented multilayers are not attributable to enhanced interdiffusion between Y and Pr sites or greater loss of oxygen in the a-axis structures. We also find no evidence of a Raman excitation proposed to be a combination ${\mathit{B}}_{1\mathit{u}\mathrm{-}}$${\mathit{B}}_{1\mathit{g}}$-type vibration recently reported in a c-axis oriented (${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$${)}_2$(${\mathrm{PrBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$${)}_1$ superlattice.

We investigate the relevance to the physics of underdoped ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{6+\mathit{x}}$ and ${\mathrm{YBa}}_2$${\mathrm{Cu}}_4$${\mathrm{O}}_8$ of the quantum critical point which occurs in a model of two antiferromagnetically coupled planes of antiferromagnetically correlated spins. We use a Schwinger boson mean-field theory and a scaling analysis to obtain the phase diagram of the model and the temperature and frequency dependence of various susceptibilities and relaxation rates. We distinguish between a low ω,T coupled-planes regime in which the optic spin excitations are frozen out and a high ω,T decoupled-planes regime in which the two planes fluctuate independently. In the coupled-planes regime the yttrium nuclear relaxation rate at low temperatures is larger relative to the copper and oxygen rates than would be naively expected in a model of uncorrelated planes. Available data suggest that in ${\mathrm{YBa}}_2$${\mathrm{Cu}}_4$${\mathrm{O}}_8$ the crossover from the coupled to the decoupled planes regime occurs at T>700 K or T∼200 K. The predicted correlation length is of order six lattice constants at T=200 K. Experimental data related to the antiferromagnetic susceptibility of ${\mathrm{YBa}}_2$${\mathrm{Cu}}_4$${\mathrm{O}}_8$ may be made consistent with the theory, but available data for the uniform susceptibility are inconsistent with the theory.

On the basis of the phenomenological tight-binding model with the intersite pairing interaction, the collective modes of the anisotropic narrow-band superconductors consisting of Bloch electrons are investigated within the ladder-diagram approximation with the vacuum-polarization correction. For the extended s- and d-wave states on a two-dimensional square lattice, the velocity of the sound mode for the artificial neutral system and the energy of the plasma mode for the charged system are calculated as functions of hole density at T=0. Both of them depend on hole and electron densities symmetrically, and are almost unaffected by the anisotropy of the order parameter. The main term in the sound-velocity expression is shown to have the generalized form of the standard hydrodynamic expression. The plasma-energy expression almost coincides with that for the normal-state Bloch electrons. Possible additional approximations are examined.

Cu K-edge x-ray-absorption spectra for the chemically well-defined ${\mathrm{Cu}}^{\mathrm{III}}$-containing oxides, ${\mathrm{La}}_2$${\mathrm{Li}}_{0.5}$${\mathrm{Cu}}_{0.5}$${\mathrm{O}}_4$ and ${\mathrm{LaCuO}}_3$, have been carefully studied in order to correlate the complex spectral features with the copper valence, the local symmetry, and the bonding nature. According to the extended x-ray-absorption fine structure spectra, it was found that the (Cu-O) bond distances for both compounds agree well with the x-ray crystallographic data, but in x-ray absorption near-edge structure (XANES) spectra, a clear higher-energy shift of the Cu K-edge position was observed for both trivalent copper oxides compared to divalent ones of ${\mathrm{Nd}}_2$${\mathrm{CuO}}_4$ and ${\mathrm{La}}_2$${\mathrm{CuO}}_4$. When the site symmetry of trivalent copper is lowered from ${\mathit{O}}_{\mathit{h}}$ to ${\mathit{D}}_{4\mathit{h}}$ as in ${\mathrm{La}}_2$${\mathrm{Li}}_{0.5}$${\mathrm{Cu}}_{0.5}$${\mathrm{O}}_4$, the feature by the shakedown process was observed to be split to A and A’, corresponding to transitions to the ‖1${\mathit{s}}^1$3${\mathit{d}}^{\mathit{n}+1\mathrm{}}$${\mathit{L}}^{\mathrm{-}1}$4${\mathit{p}}_{\mathrm{\pi }}^1$〉 final state and ‖1${\mathit{s}}^1$3${\mathit{d}}^{\mathit{n}+1\mathrm{}}$${\mathit{L}}^{\mathrm{-}1}$4${\mathit{p}}_{\mathrm{\sigma }}^1$〉 one, respectively. Therefore, it is proposed that Cu K-edge XANES spectral fine features below the main edge should be interpreted with the molecular-orbital concept, mainly depending upon the copper valence and the crystal-field effect by the local symmetry on the copper site. This work also reveals that a spectral separation (∼2.7 eV) between ${\mathrm{Cu}}^{\mathrm{II}}$ and ${\mathrm{Cu}}^{\mathrm{III}}$ compounds is smaller than the theoretically expected one (∼4 eV), and the XANES spectrum of metallic compound shows a tendency of a lower energy shift compared to that of insulating or semiconducting one. Thus these facts should be taken into account when determining the presence of trivalent copper from Cu K-edge XANES spectra of copper-based superconductors.

The NQR spectra of Cu in the ${\mathrm{Sm}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Pr}}_{\mathit{x}}$${\mathrm{Ba}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathit{y}}$ system at room temperature have been measured and analyzed. When Pr is substituted for Sm in ${\mathrm{Sm}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Pr}}_{\mathit{x}}$${\mathrm{Ba}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$, there are no significant structural changes. However, the electric charge distributions in the vicinity of both the Cu(2) and Cu(1) sites are quite different due to the influence of Pr atoms, which modify the quadrupole interaction. This work provides information on the normal-state properties of high-${\mathit{T}}_{\mathit{c}}$ superconductors.

Anisotropic irreversibility lines due to thermal fluctuation for quasi-two-dimensional high-${\mathit{T}}_{\mathit{c}}$ superconductors (HTS’s) were observed in c-axis-aligned powders of the ${\mathrm{HgBa}}_2$${\mathrm{Ca}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{8+\mathrm{\delta }}$ compound with ${\mathit{T}}_{\mathit{c}}$=131±0.5 K. The anisotropic ratio ${\mathit{H}}_{\mathrm{irr}}$(⊥c)/${\mathit{H}}_{\mathrm{irr}}$(∥c) below 2 was observed in all temperature regions. The simple three-dimensional-like power law ${\mathit{H}}_{\mathrm{irr}}$=a(1-T/${\mathit{T}}_{\mathit{c}}$${)}^{\mathit{n}}$ was observed only in the low-field region (≤2000 G) with n=1.40±0.1 for H⊥c and n=1.63±0.1 for H∥c. In the higher field region up to 5 T, the temperature dependence of ${\mathit{H}}_{\mathrm{irr}}$(T) lines changes into a two-dimensional-like exponential function ${\mathit{H}}_{\mathrm{irr}}$=a exp(-T/${\mathit{T}}_0$) due to the breakdown of the interlayer coupling of the conduction channel, which consists of three Cu-O planes, with ${\mathit{T}}_0$=16.0±1.3 K for H⊥c and ${\mathit{T}}_0$=16.6±1.1 K for H∥c. The exponent n is independent of the pinning strength or anisotropy related to interlayer coupling between ${\mathrm{CuO}}_2$ planes. The characteristic crossover field giving deviation from the power function depends strongly on the anisotropic nature of materials; e.g., ≥5 T for Y HTS’s, ∼0.2 T for Hg HTS’s, ∼0.02 T for Bi HTS’s, and ∼0.01 T for Tl HTS’s; this means that flux dynamics depend strongly on coupling strength between ${\mathrm{CuO}}_2$ blocks in the HTS.

A contribution to superexchange coming from empty oxygen orbitals is pointed out. We also estimate the small anisotropy of the in-plane superexchange, as well as the superexchange between two adjacent layers in the specific ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_6$ compound. In doped compounds, we improve the description of the transport properties of Zhang-Rice singlets over the simple t-J model. Particularly important for the bandwidth is the role of what we call ${\mathrm{t}}_{\mathrm{unequal}\mathrm{}\mathrm{spins}}^{\prime }$ and ${\mathrm{t}}_{\mathrm{unequal}\mathrm{}\mathrm{spins}}^{\mathrm{″}}$. When more than one doped hole is present in the system, the interaction between holes becomes rapidly non-negligible: two Zhang-Rice singlets placed on neighboring cells highly repel each other. Some aspects of oxygen spin dynamics are discussed, in connection with NMR experiments.