Calculated effects of charge fluctuations on the phonon dispersion of YBa2Cu3O6 and YBa2Cu3O7. II. Results

Using the model presented in the preceding paper we investigate the effects of charge fluctuations (CF) on the phonon dispersion of YBa₂Cu₃O₆ (O₆) and YBa₂Cu₃O₇ (O₇). Starting from an ab-initio rigid-ion model as a reference system, CF are allowed for at the copper- and oxygen ions. The CF are treated as adiabatic electronic degrees of freedom. Within the rigid-ion model (RIM) the structural parameters are calculated by minimization of the energy. The results agree reasonably well with the experiment, indicating the suitability of the ionic model as a starting point and the importance of ionic forces for the properties of the high-temperature superconductors (HTSC) in general. Next, the phonon dispersion is calculated in the RIM as well as including CF additionally and the renormalization of the individual modes is discussed. By restricting the CF optionally to the planes, effects arising specifically from CF in the planes on the one hand and from CF in the chain as well as at the axial bridging oxygens (O4) on the other hand can be separated. We find the oxygen axial modes at the γ- and Z point (A_1g/A_2μ in O₆, A_g/B_1μ in O₇) particularly interesting. Most of these modes show considerable renormalizations. Moreover, the γ/Z-axial modes are characterized by the possibility of having CF of the same sign in the whole CuO planes what distinguishes them from the modes at other symmetry points. In particular, the Z-point axial modes are singular in having CF of alternating sign in consecutive structural units in c direction. Such a “c-direction-charge-transfer” has been shown previously to be an effective screening mechanism in La₂CuO₄. Indeed, we find a drastic renormalization of the plane-oxygen A_g mode at the Z point (A_g(O23;Z)) in O₇ (oxygen ions in neighboring planes vibrating in-phase), at least in the adiabatic approximation used here. In the insulating phase this mode exhibits, on the other hand, very large changes of the potential at the ion sites, whereas its renormalization is moderate only. The reason for this behaviour is that in the insulating phase in case of a two-dimensional electronic structure the charge transfer (screening) is restricted locally in the structural unit and long-range charge transfer is not possible as in the metal. However, a strong suppression of screening for this mode can also be expected for the metallic phase in O₇ in case non-adiabatic electron-phonon coupling would be important. The A_g (O23;Z)-mode thus seems to be by far the most interesting mode in O₇. These features are directly related to the layered structure of the HTSC compounds considered here. The O4-axial-breathing modes show significant renormalizations too, and are characterized by plane-chain charge transfer. Moreover, besides the O23- and O4-modes, the yttrium modes appear to be important too. In addition to the phonon-dispersion curves, we present values for the CF amplitudes and screened site-potential changes at the copper-and oxygen ions. Finally, we give transverse effective charges and dielectric constants for the insulating phase (O₆) as calculated within our formalism.     

Antiferromagnetic fluctuations in water-intercalated YBa2Cu3O6.8

Raman scattering by phononic and electronic excitations, as well as the magnetic susceptibility of water-intercalated YBa₂Cu₃O_6.8, has been studied. Direct evidence of the incorporation of OH^?-groups into the structure of the crystal has been obtained. The observed changes in the phonon spectrum and the appearance of the spectrum of antiferromagnetic fluctuations with an increased exchange coupling constant imply the localization of carriers and suppression of superconductivity. Change in the resonance behavior of the two-magnon scattering of light indicates the transformation of the electronic structure in crystallites absorbing water.     

In-plane polarized collective modes in detwinned YBa2Cu3O6.95 observed by spectral ellipsometry

The in-plane dielectric response of detwinned YBa₂Cu₃O_6.95 has been studied by far-infared ellipsometry. A surprisingly large number of in-plane polarized modes are observed. Some of them correspond to pure phonon modes. Others possess a large electronic contribution which strongly increases in the superconducting state. The free carrier response and the collective modes exhibit a pronounced a–b anisotropy. We discuss our results in terms of a charge density wave state in the 1-D CuO chains and induced charge density fluctuations within the 2-D CuO₂ planes.     

Ac-Josephson effect in YBa2Cu3O7/YBa2Cu3O7 point contact junctions

The ac-Josephson effect could be demonstrated up to dc voltages of 20 mV on the I–V characteristic of adjustable YBa₂Cu₃O₇/YBa₂Cu₃O₇ point contacts at 4.2 K. A detailed analysis of the rf power dependence of the size of microwave-induced constant voltage steps is given for microwave frequencies of 70 and 90 GHz. The results prove that electron pairing is responsible for the superconductivity in YBa₂Cu₃O₇.     

Dielectric function of YBa2Cu3O7-δ between 50 meV and 50 eV

Electronic excitations with polarization parallel to the CuO₂-planes in single-crystalline YBa₂Cu₃O₇ and YBa₂Cu₃O₆ have been investigated by optical reflectance and by highenergy electron energy-loss spectroscopy in transmission in the energy ranges from 50 meV to 6 eV and 0.2 eV to 150 eV, respectively. From a combination of these experimental data the dielectric function, the reflectivity and the optical conductivity have been obtained in a wide energy range. The observed spectra are interpreted in terms of optical phonons, free-carrier absorption, transitions across the charge-transfer gap, further interband transitions, low-lying core-level excitations, excitonic transitions and valence conservingd-d transitions within the Cu 3d shell combined with O 2p intraband transitions. The charge carrier plasmon and the 4 eV-excitation in YBa₂Cu₃O₆ show quadratic dispersions in momentum transfer. From the dispersion constant of the plasmon a mean value of the Fermi velocity of the charge carriers parallel to the CuO₂ planes has been derived.     

Interface and grain boundary structures in YBa2Cu3O7-x and YBa2Cu4O8 materials

Y₂BaCuO₅YBa₂Cu₃O_7-x (Y211/Y123) interfaces in melt-processed YBa₂Cu₃O_7-x were studied by high-resolution transmission electron microscopy and energy dispersive X-ray spectroscopy. Yttrium enrichment and barium depletion were observed locally at the Y211/Y123 interfaces where Y123 (001) facets were present. This effect may be interpreted as the result of lattice substitution of Ba by Y near these interfaces. Cation nonstoichiometry was found near Y211/Y123 interfaces where liquid phases (Cu-Ba-O) were present. This chemical disorder introduces numerous point defects in the Y123, and these defects may act as additional pinning sites alongwith stacking faults. A comparison of grain boundary (GB) chemical composition in polycrystalline YBa₂Cu₃O_7-x and YBa₂Cu₄O₈(Y124), studied using nanoprobe parallel-detection electron energy-loss spectroscopy (EELS), is presented. The studies of Y124 show that stoichiometric grain boundaries can also form weak links between superconducting grains. It is suggested that weak-link behavior is determined largely by misorientation at grain boundaries.     

63Cu and17O NMR studies on the magnetic and superconducting properties of YBa2Cu3O7−y

Results of⁶³Cu and¹⁷O NMR experiments in YBa₂Cu₃O₇ and YBa₂Cu₃O_6.63 are reviewed. The normal state data revealed two important aspects of the magnetic properties of these materials, namely, the temperature dependent antiferromagnetic Cu spin correlations and the spin gap behavior, the latter being observed in the reduced oxygen material. These features appear to be the general properties of many high-T _c cuprates. Anomalous temperature dependence of the anisotropy of the Cu relaxation rate was found in the superconducting state of YBa₂Cu₃O₇, which can be explained by a d-wave pairing model.     

Theory of high temperature superconductivity in YBa2Cu3O7_δ

A theory of high temperature superconductivity in YBa₂Cu₃O₇__δ compound has been developed on the basis of the momentum pairing of electrons through the relativistic Darwin interaction. The transport behaviour of electrons is explained in terms of a mechanism of correlated electron transfer arising from the electron-phonon coupling. A model Hamiltonian has been developed to describe the superconducting properties of the system. This gives an energy gap which is higher than the BCS value. Attempts have been made to explain the absence of isotope effect, the linear dependence of specific heat, the presence of larger temperature-independent paramagnetism in the normal phase and the softening of some of the optic phonon modes observed in this system.     

Dynamics of optically excited quasiparticles in YBa2Cu3O7

We present a detailed investigation of the dynamics of laser-excited quasiparticles in YBa₂Cu₃O₇ thin films below the critical temperature. Reflectivity transients at low temperature trace the generation and recombination behavior of quasiparticles. The quasiparticle cascading and recombination rates are determined by comparison with a detailed nonlinear model of the quasiparticle dynamics based on extended Rothwarf-Taylor equations.     

Superconductivity induced phonon anomalies in the Raman spectra of Zn and Ni doped YBa2Cu3O7

Here we present Raman spectra of YBa₂(Cu_1–x Zn _x )₃O₇ and YBa₂(Cu_1–x Ni _x )₃O₇ as a function of temperature and Zn or Ni content. The temperature dependence of two modes at 340 and 440 cm^–1 is analyzed. Similarly to the infrared measurements it is found that Zn substantially suppresses the superconductivity induced phonon softening whereas, Ni does not affect much that effect. Moreover, the superconductivity induced phonon stiffening of the 440 cm^–1 mode completely disappeared with the Zn doping. We find this behaviour might support the model where Zn acts effectively as a magnetic pair breaker.     

Electronic properties of YBa2Cu4O8 and Y2Ba4Cu7O15 as probed by NMR/NQR

Nuclear Magnetic Resonance (NMR) and Nuclear Quadrupole Resonance (NQR) allow the investigation of electronic properties at the atomic level. We will report on such studies in typical members of the Y-Ba-Cu-O family of high-temperature superconductors, namely YBa₂Cu₄O₈ and Y₂Ba₄Cu₇O₁₅. We will deal with temperature and orientational dependences of Cu and O Knight shifts and spin-lattice relaxation. Topics to be discussed are: (1) Existence of a common electronic spin-susceptibility (a single-spin fluid) in the planes and in the chains of YBa₂Cu₄O₈. (2) Evidence for the existence of a pseudo spin-gap in the anti-ferromagnetic fluctuations in YBa₂Cu₄O₈ and Y₂Ba₄Cu₇O₁₅. (3) Evidence for non-s symmetry of the pair wave function in YBa₂Cu₄O₈. (4) First NQR observation of a strong coupling of inequivalent Cu-O planes in Y₂Ba₄Cu₇O₁₅. (5) Alternative explanations of relaxation and Knight shift.     

Positive muon sites and possibility of anyons in the YBa2Cu3O x system

Possible positive muon sites in YBa₂Cu₃O _x were determined from the observedμ ⁺ hyperfine fields in antiferromagnetically ordered YBa₂Cu₃O _x and GdBa₂Cu₃O₇. After determining theμ ⁺ sites, the possibility of anyons or chiral spin ordering in the superconducting YBa₂Cu₃O₇ is discussed. Positive muon implanted in YBa₂Cu₃O₇ feel static magnetic fields of average 1.4G, which are explicable in terms of nuclear magnetic dipolar fields. Non observation of static local magnetic fields of electronic origin (the upper limit is the order of 0.1 G) means that anyons or chiral spin ordering might not exist in superconducting YBa₂Cu₃O₇.     

Site of the positive muon in YBa2Cu3O7

A combination of μSR and¹⁷O nuclear quadrupolar μLCR has been used to obtain detailed information on the muon site in YBa₂Cu₃O₇. The rms magnitude of the nuclear dipolar fields in YBa₂Cu₃O₇ enriched with 38%¹⁷O is about twice that in the natural¹⁶O sample. In addition the¹⁷O μLCR spectrum shows that the electric field gradient tensor at the oxygen closest to the muon is almost equal to that measured by NMR for the CuO₂ plane sites O(2,3). These results suggest that the muon in fully oxygenated YBa₂Cu₃O₇ is located at a single site 1.0 Å from an oxygen ion, probably O(2,3).     

Volume dependence of the A1g phonons in YBa2Cu3O7

By employing first-principles frozen-phonon calculations we have determined the force-free geometry and the dynamical matrix for the five Raman-active A1g modes in a volume-reduced YBa₂Cu₃O₇ crystal. By this mean we investigate the relation between the effect of overbinding caused by the local density approximation and the vibronic properties of this material. This procedure reveals noticeably improved phonon frequencies in comparison to the theoretical results obtained for the measured lattice constants.     

Shape of the Cu(2) NQR spectra in YBa2Cu3O7, TmBa2Cu3O7 and TmBa2Cu4O8

We present a study of shape of the Cu(2) NQR spectra in YBa₂Cu₃O₇, TmBa₂Cum₃O₇, and TmBa₂Cu₄O₈ compounds at temperatures of 4.2–300 K. The results of the quantitative analysis lead us to conclude that the shape of the Cu(2) NQR spectra in all the samples studied can be described in the framework of the “motional narrowing” model, which implies that the Cu(2) nucleus possesses two different NQR frequencies between which it can rapidly jump. The difference in frequencies seems to be related to the charge-stripe correlations in CuO₂ planes resulting in a dynamical modulation of the electric field gradients at the Cu(2) nuclei. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 9, 594–598 (10 November 1997)     

Cu nuclear spin-spin relaxation in YBa2Cu3O6.98 and YBa2Cu4O8

We have measured the temperature (T) dependence of the transverse relaxation rate (T _G ^–1 ) of the Cu(1) nuclear spin in YBa₂Cu₃O_6.98 (T _c=92 K) and YBa₂Cu₄O₈ (T _c=82 K). From the scaling ratio ofT _G ^–2 (Cu1) toT _G ^–2 (Cu2), we have estimated the strength of a covalent bonding between the CuO₂ plane and the CuO chain to be B0.38×A _zz. The experimentalT _G ^–1 (Cu1) in YBa₂Cu₄O₈ was of the same order of magnitude as the estimated one fromT _G ^–1 (Cu2). These results appear to indicate that the electrons in the CuO₂ plane fairly spread out of the plane in both compounds.     

Microstructural investigations of melt grown YBa2Cu3O7

The results of microstructural investigations on bulk YBa₂Cu₃O₇ prepared by melt growth process are reported.     

Magnetic phase present in YBa2(Cu1−x Fe x )3O6+δ oxides

The Mössbauer study of⁵⁷Fe: YBa₂Cu₃O_6+δ oxides was very important to establish the preferential occupation of Cu(1) site by Fe at very low concentrations. Recent determination of antiferromagnetic ordering for Cu moments in Cu(2) sites (T≈450 K) and our early observation of a small proportion of a magnetic phase at room temperature for Fe:YBa₂Cu₃O₆ lead us to perform systematic studies of YBa₂(Cu_1?x Fe _x )₃O₆ withx=0.005, 0.03, 0.05, 0.10 and 0.15 in order to obtain information about the iron occupation of Cu(2) sites.     

Anomalies of the electronic spin-lattice relaxation of Gd3+ in YBa2Cu4O8 and YBa2Cu3O6+x near 200 K

A sharp kink in the temperature dependence of the electronic spin-lattice relaxation rate near 200 K was found in the high-temperature superconductors YBa₂Cu₄O₈ and YBa₂Cu₃O_6+x . The effect is correlated with opening of a spin gap and microscopic phase separation. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 8, 567–572 (25 April 1999)     

Structure of grain boundaries in YBa2Cu3O7 thin-film step-edge junctions

The atomic structure of 90° [100] (or [010]) tilt grain boundaries in YBa₂Cu₃O₇ thin-film step-edge junctions and, for comparison, in the interface between a-axis and c-axis oriented YBa₂Cu₃O₇ grains is investigated by means of high-resolution transmission electron microscopy. For (100)(001)-type boundaries two different structures are found. In the first a (001) CuO₂ plane of one grain faces a (100) Y–Ba–O plane of the other grain, in the second a (001) BaO plane faces a (100) Cu–O plane. In the former structure an incomplete unit cell of YBa₂Cu₃O₇ terminates at the boundary and a smaller strain in the adjacent CuO₂ planes is detected in comparison with the latter. It is found that a combination of a partial dislocation with a 124 stacking fault is a way to accommodate the lattice mismatch between c and 3a of YBa₂Cu₃O₇ in the boundary. For a symmetric (103)(103)-type boundary a displacement of the Cu-atoms of the CuO₂ planes is found near the boundary plane. From this a redistribution of the oxygen atoms around the Y-atoms located right in the boundary plane is inferred. The possible effect of the boundary structure on the superconducting properties of YBa₂Cu₃O₇ films is discussed.