Spiral spin state in high-temperature copper-oxide superconductors: evidence from neutron scattering measurements

An effective spiral spin phase ground state provides a new paradigm for the high-temperature superconducting cuprates. It accounts for the recent neutron scattering observations of spin excitations regarding both the energy dispersion and the intensities, including the "universal" rotation by 45 degrees around the resonance energy . The intensity has a 2D character even in a single twin crystal. The value of is related to the nesting properties of the Fermi surface. The excitations above are shown to be due to in-plane spin fluctuations, a testable difference from the stripe model. The form of the exchange interaction function reveals the effects of the Fermi surface, and the unique shape predicts large quantum spin fluctuations in the ground state.     

Anisotropic scattering rates and antiferromagnetic precursor effects in the t-t'-U Hubbard model

We have investigated the evolution of the electronic properties of the t-t'-U Hubbard model with hole doping and temperature. Due to the shape of the Fermi surface, scattering from short wavelength spin fluctuations leads to strongly anisotropic quasi-particle scattering rates at low temperatures near half-filling. As a consequence, significant variations with momenta near the Fermi surface emerge for the spectral functions and the corresponding ARPES signals. At low doping the inverse lifetime of quasiparticles on the Fermi surface is of order varying linearly in temperature from energies of order t down to a very low energy scale set by the spin fluctuation frequency while at intermediate doping a sub-linear T-dependence is observed. This behavior is possibly relevant for the interpretation of photoemission spectra in cuprate superconductors at different hole doping levels. Received 31 July 2000     

A criterion for the existence of spin waves in polarized gases in a wide temperature range

We derive a kinetic equation for a polarized paramagnetic gas that is exact in the Boltzmann (binary) approximation. The equation is written in a compact form and applies to both Fermi and Bose gases in a wide temperature range as long as the Boltzmann approximation remains applicable. The derived equation is used to analyze the conditions for the propagation of spin waves in polarized Fermi and Bose gases. We deduce a universal criterion for the propagation of weakly damped spin waves in a wide temperature range. The criterion is reduced to the condition that the real parts of the particle zero-angle scattering amplitudes (or T matrices) be much larger than their imaginary parts. We derive dispersion equations for spin waves at high and low gas temperatures and show that spin waves can propagate in both these limiting cases.     

Wilson's renormalization group applied to 2D lattice electrons in the presence of van Hove singularities

The weak coupling instabilities of a two dimensional Fermi system are investigated for the case of a square lattice using a Wilson renormalization group scheme to one loop order. We focus on a situation where the Fermi surface passes through two saddle points of the single particle dispersion. In the case of perfect nesting, the dominant instability is a spin density wave but d-wave superconductivity as well as charge or spin flux phases are also obtained in certain regions in the space of coupling parameters. The low energy regime in the vicinity of these instabilities can be studied analytically. Although saddle points play a major role (through their large contribution to the single particle density of states), the presence of low energy excitations along the Fermi surface rather than at isolated points is crucial and leads to an asymptotic decoupling of the various instabilities. This suggests a more mean-field like picture of these instabilities, than the one recently established by numerical studies using discretized Fermi surfaces. Received 11 April 2001 and Received in final form 6 September 2001     

Non-Abelian bosonization and topological aspects of BCS systems

It is shown that many features of the low energy behaviour of weak coupling BCS systems are topological in character. This is done by writing the BCS action as a Fermi surface sum of (1 + 1)-dimentional non-Abelian actions, each one of which can be bosonized à la Witten. This process leads to the correct current generating parts (as found by Cross) in the effective action for the gap function, and in addition a Wess-Zumino term. The mass and spin currents are calculated for the three-dimensional theory, and it is shown that upon averaging over all directions on the Fermi surface, the contribution from the Wess-Zumino term vanishes for a pure spin singlet or pure spin triplet gap, but not otherwise.     

NMR Anomalies in Quasi-2D Organic Superconductors: Effects of Spin Fluctuations in a Fermi Liquid Approach

The -(BEDT-TTF)₂X organic superconductors are described by a two parameter 2D Fermi surface model, in which bandwidth and departure from perfect nesting can be varied. We have studied the spin fluctuations effect on the normal state properties in a Fermi liquid approach using the RPA approximation. The calculated NMR relaxation rate exhibits a peak in 1/(T ₁ T), which strongly decreases when the departure from perfect nesting of the Fermi surface and the bandwidth increase. These results are in good agreement with NMR experiments done in -(ET)₂X at least qualitatively. In conclusion, we have shown that, in the normal state and with a Fermi liquid approach, the spin fluctuations, which are present in the system due to an imperfect nesting property of the Fermi surface, can induce anomalies of the magnetic properties. Besides, we can restore the usual behaviour like the Korringa law by increasing the bandwidth or by considering a more imperfect nesting. Our calculation reproduces qualitatively the applied pressure relaxation rate experiment done in -(ET)₂X salt.     

Spin-polarized Dirac-cone-like surface state with d character at W(110)

The surface of W(110) exhibits a Dirac-cone-like state with d character within a spin-orbit-induced symmetry gap. As a function of the wave vector parallel to the surface, it shows a nearly massless energy dispersion and a pronounced spin polarization, which is antisymmetric with respect to the Brillouin zone center. In addition, the observed constant energy contours are strongly anisotropic for all energies. This discovery opens new pathways to the study of surface spin-density waves arising from a strong Fermi surface nesting as well as d-electron-based topological properties.     

Noncoplanar magnetic ordering driven by itinerant electrons on the pyrochlore lattice

Exchange interaction tends to favor collinear or coplanar magnetic orders in rotationally invariant spin systems. Indeed, such magnetic structures are usually selected by thermal or quantum fluctuations in highly frustrated magnets. Here we show that a complex noncoplanar magnetic order with a quadrupled unit cell is stabilized by itinerant electrons on the pyrochlore lattice. Specifically, we consider a Kondo-lattice model with classical localized moments at quarter filling. The electron Fermi "surface" at this filling factor is topologically equivalent to three intersecting Fermi circles. Perfect nesting of the Fermi lines leads to magnetic ordering with multiple wave vectors and a definite handedness. The chiral order might persist without magnetic order in a chiral spin liquid at finite temperatures.     

Charge and spin dynamics of interacting fermions in a one-dimensional harmonic trap

We study an atomic Fermi gas interacting through repulsive contact forces in a one-dimensional harmonic trap. Bethe-ansatz solutions lead to an inhomogeneous Tomonaga-Luttinger model for the low energy excitations. The equations of motion for charge and spin density waves are analyzed both near the trap center and near the trap edges. While the center shows conventional spin-charge separation, the edges cause a giant increase of the separation between these modes.     

Reconstruction of the Fermi surface in the pseudogap state of cuprates

Reconstruction of the Fermi surface of high-temperature superconducting cuprates in the pseudogap state is analyzed within a nearly exactly solvable model of the pseudogap state, induced by short-range order fluctuations of the antiferromagnetic (AFM), spin-density wave (SDW), or a similar charge-density wave (CDW) order parameter, competing with the superconductivity. We explicitly demonstrate the evolution from “Fermi arcs” (on the “large” Fermi surface) observed in the ARPES experiments at relatively high temperatures (when both the amplitude and phase of the density waves fluctuate randomly) towards the formation of typical “small” electron and hole “pockets,” which are apparently observed in the de Haas-van Alphen and Hall resistance oscillation experiments at low temperatures (when only the phase of the density waves fluctuate and the correlation length of the short-range order is large enough). A qualitative criterion for the quantum oscillations in high magnetic fields to be observable in the pseudogap state is formulated in terms of the cyclotron frequency, the correlation length of fluctuations, and the Fermi velocity. The text was submitted by the authors in English.     

Pseudogap-state superconductivity in a “hot-point” model: Gor’kov equations

The specific features of the superconducting state (with s and d pairing) are considered in terms of a pseudogap state caused by short-range order fluctuations of the “dielectric” type, namely, antiferromagnetic (spin density wave) or charge density wave fluctuations, in a model of the Fermi surface with “hot points.” A set of recurrent Gor’kov equations is derived with inclusion of all Feynman diagrams of a perturbation expansion in the interaction between an electron and short-range order fluctuations causing strong scattering near hot points. The influence of nonmagnetic impurities on superconductivity in such a pseudogap state is analyzed. The critical temperature for the superconducting transition is determined, and the effect of the effective pseudogap width, correlation length of short-range-order fluctuations, and impurity scattering frequency on the temperature dependence of the energy gap is investigated.     

Thermal fluctuations in d-wave layered superconductors

We study the thermal fluctuations of anisotropic order parameters (OP) in layered superconductors. In particular, for copper oxides and a d-wave OP, we present some experimental consequences of fluctuations in the direction normal to the layers. It is shown that the c-axis penetration depth λ_c can have a “disorder-like” quadratic temperature dependence at low temperature. The fluctuations are analyzed in the framework of a Lawrence-Doniach model with an isotropic Fermi surface. Anisotropies pin the orientation of the OP to the crystallographic axes of the lattice. Then we study an extended t-J model that fits Fermi surface data of bilayers YBCO and BSCCO. This leads to a d-wave OP with two possible orientations and, including the thermal fluctuations, yields the announced temperature dependence of λ_c. Furthermore a reservoir layer is introduced. It implies a finite density of states at the Fermi energy which is successfully compared to conductance and specific heat measurements.     

Destruction of the Fermi surface due to pseudogap fluctuations in strongly correlated systems

We generalize the dynamical-mean field theory (DMFT) by including into the DMFT equations dependence on the correlation length of the pseudogap fluctuations via the additional (momentum dependent) self-energy Σ_k. This self-energy describes nonlocal dynamical correlations induced by short-ranged collective SDW-like antiferromagnetic spin (or CDW-like charge) fluctuations. At high enough temperatures, these fluctuations can be viewed as a quenched Gaussian random field with finite correlation length. This generalized DMFT + Σ_k approach is used for the numerical solution of the weakly doped one-band Hubbard model with repulsive Coulomb interaction on a square lattice with nearest and next nearest neighbor hopping. The effective single impurity problem is solved by using a numerical renormalization group (NRG). Both types of strongly correlated metals, namely, (i) doped Mott insulator and (ii) the case of the bandwidth W ? U (U-value of local Coulomb interaction) are considered. By calculating profiles of the spectral densities for different parameters of the model, we demonstrate the qualitative picture of Fermi surface destruction and formation of Fermi arcs due to pseudogap fluctuations in qualitative agreement with the ARPES experiments. Blurring of the Fermi surface is enhanced with the growth of the Coulomb interaction.     

d-wave superconductivity and pomeranchuk instability in the two-dimensional hubbard model

We present a systematic stability analysis for the two-dimensional Hubbard model, which is based on a new renormalization group method for interacting Fermi systems. The flow of effective interactions and susceptibilities confirms the expected existence of a d-wave pairing instability driven by antiferromagnetic spin fluctuations. More unexpectedly, we find that strong forward scattering interactions develop which may lead to a Pomeranchuk instability breaking the tetragonal symmetry of the Fermi surface.     

Electron spectrum in high-temperature cuprate superconductors

A microscopic theory for the electron spectrum of the CuO₂ plane within an effective p-d Hubbard model is proposed. The Dyson equation for the single-electron Green’s function in terms of the Hubbard operators is derived and solved self-consistently for the self-energy evaluated in the noncrossing approximation. Electron scattering on spin fluctuations induced by the kinematic interaction is described by a dynamical spin susceptibility with a continuous spectrum. The doping and temperature dependence of electron dispersions, spectral functions, the Fermi surface, and the coupling constant λ are studied in the hole-doped case. At low doping, an arc-type Fermi surface and a pseudogap in the spectral function close to the Brillouin zone boundary are observed. The text was submitted by the authors in English.     

Surface and interface magnons: Magnetic structures near the surface

After a short review of the recent experimental data in the study of static and dynamic properties of magnetism in finite samples with attention to the surface effect, a theoretical treatment of the surface effect is presented. Different experiments are concerned: magnetization measurements, Mössbauer analysis, spin polarized photoemission, low energy electron diffraction, spin wave resonance and Brillouin scattering of spin waves. The choice of a typical Hamiltonian consistent with the experimental results is carefully made, with either a quite local surface perturbation leading to a discrete treatment or a quasi-continuous surface perturbation leading to a continuum treatment. Then the ground state of this spin Hamiltonian is derived in both cases with evidence for a surface of interface magnetic rearrangement with standard conditions. The first excited states, i.e. the one-magnon eigenstates are then derived in a quite general way, which allows non-uniformities in the sample. Several simple cases are completely treated, with, for instance, the study of the magnetic decoupling of the different parts of coupled thin films. These results enable us to discuss the temperature effects, and by means of a Tyablikov-Bogoliubov renormalization technique, high temperatures are correctly studied, including the Curie transitions. Now a careful investigation of the experimental situation compared to these theoretical results is given, with attention to new effects such as spin wave polarization and to a surface classification with evidence for “hard” and “soft” surface different behavior.     

Itinerant-localized duality description of the spin fluctuations in the normal state of high-Tc cuprates. An explanation of neutron scattering experiments

On the basis of the itinerant-localized duality theory of spin fluctuations, the puzzling aspects of the neutron scattering experiments in the normal state of high-T_c cuprates are clarified from a global point of view. The dynamical spin structure factor exhibits two different aspects depending on the energy transfer ω. At lower energies, ω < ω_c, where ω_c is the fermion coherence energy, the spectrum is coherent so that the characteristic scales for wavevector and energy are temperature dependent, while at higher energies, ω > ω_c, the spectrum is incoherent so that those characteristic scales are temperature independent. The integrated weight of the coherent part of the spectrum exhibits the so-called “spin gap” behavior when the Fermi surface of the itinerant fermion is technically nested, even though there is no excitation gap in the spectrum at all.     

Spin-wave spectroscopy and application of its methods to heterostructures of silicon dioxide with Co nanoparticles on a GaAs substrate

A method has been developed for determining magnetic and electrical characteristics of film nanostructures containing magnetic nanoparticles from dispersion curves of surface spin waves propagating in these nanostructures. The dispersion curves of spin waves are determined by the dynamics of the spin component described by the generalized Landau-Lifshitz equations and an alternating electromagnetic field induced by a spin wave. Since spin waves are very sensitive to inhomogeneity of magnetic parameters, spin disorder, and conductivity of an object near or inside which these waves propagate, they can be used for determining magnetic and electrical characteristics of the objects under investigation. The developed calculation method, which can be employed both in spin-wave spectroscopy and in analysis of dispersion curves obtained by other methods, has been used for determining parameters of heterostructures consisting of a SiO₂ film with Co nanoparticles on a GaAs substrate. It has been found from the shape of dispersion curves of the surface spin waves that, in the film near the interface, spins of the nanoparticles are close to a ferromagnetic ordering, whereas near the free surface, the spin orientation of nanoparticles is more chaotic. It has been revealed that a conducting layer is formed in GaAs, and the SiO₂(Co) film near the interface has an increased conductivity.     

On a new approach to the theory of the Heisenberg ferromagnet

Summing up the infinite classes of the Feynman diagrams for the spin operators with increasing power of the high density parameter we obtained the formulas both for the magnetization and the free energy. These formulas include the gaussian fluctuations of self-consistent field as well as scattering of spin waves on these fluctuations.     

Interplay among superconductivity,charge density waves,and magnetism in EuMo6S8

In a one-dimensional metal, the energy of the electrons can always be lowered by opening an energy gap around the Fermi energy (the Peierls instability): all occupied states are then in the lower-energy band, while the higher-energy band is empty. The opening of such a gap requires a structural distortion, resulting in the formation of a charge density wave. In a three-dimensional system, the gapping takes place in the region where the Fermi surface is nested (i.e., large parallel areas of the Fermi surface are spanned by a certain wave vector), giving rise to partial gapping of the Fermi surface, accompanied by a structural distortion. In this case, a charge density wave can coexist with superconductivity. Both charge-density-wave and superconducting transitions involve the formation of an energy gap at the Fermi energy. A charge-density-wave gap is formed at a region of the Fermi surface where there is a high density of electronic states. In such a material, there is also a strong electronphonon interaction. A region with high density of states and a high electron-phonon interaction is just the portion of the Fermi surface that will enhance the superconducting transition temperature, according to the BCS (Bardeen-Cooper-Schrieffer) theory. When a charge-density-wave gap opens up at the Fermi surface these electronic states are no longer available to form Cooper pairs and to enhance the superconducting transition temperature. The opposite is also true; if a superconducting gap opens, the states involved in forming this gap are no longer available to take part in a charge-density-wave transition. It appears that charge density waves and superconductivity compete for the same portion of the Fermi surface and thus inhibit each other. In this paper, we will review a unique situation with respect to the competition between these two ground states and will also discuss how this competition affects the anomalous behavior of critical field in EuMo6S, at high pressure.