A Comparison of the High-Frequency Magnetic Fluctuations in Insulating and Superconducting La2-xSrxCuO4

Inelastic neutron scattering performed at a spallation source is used to make absolute measurements of the dynamic susceptibility of insulating La2CuO4 and superconducting La2-xSrxCuO4 over the energy range 15<EN<350 meV. The effect of Sr doping on the magnetic excitations is to cause a large broadening in wavevector and a substantial change in the spectrum of the local spin fluctuations. Comparison of the two compositions reveals a new energy scale of 22 meV in La1.86Sr0.14CuO4.Comment: RevTex, 7 Pages, 4 postscript figure

High-Frequency Spin Waves in YBa2Cu3O6.15

Pulsed neutron spectroscopy is used to make absolute measurements of the dynamic magnetic susceptibility of insulating YBa2Cu3O6.15. Acoustic and optical modes, derived from in- and out-of-phase oscillation of spins in adjacent CuO2 planes, dominate the spectra and are observed up to 250 meV. The optical modes appear first at 74 meV. Linear-spin-wave theory gives an excellent description of the data and yields intra- and inter-layer exchange constants of J_parallel =125 meV and J_perp = 11 meV respectively and a spin-wave intensity renormalization Z_chi = 0.4.Comment: postscript, 11 pages, 4 figures, Fig.2 fixe

Superconducting Gap Modulation in Weak Stripe States

The superconducting gap modulation is investigated in the presence of a weak stripe structure, using the Bogoliubov-de Gennes theory on the two-dimensional Hubbard model with nearest-neighbor site pairing interaction. We calculate the local density of states and discuss the recently observed scanning tunneling spectroscopy spectra with four lattice periodicity on Bi_2 Sr_2 Ca Cu_2 O_{8+delta} We also consider the spectral weight in the reciprocal space, where the Fermi surface and the superconducting gap are modulated by the band folding effect of the stripe structure.Comment: 4 pages, 4 figures, to be published in J. Phys. Soc. Jp

Spacetime Embedding Diagrams for Black Holes

We show that the 1+1 dimensional reduction (i.e., the radial plane) of the Kruskal black hole can be embedded in 2+1 Minkowski spacetime and discuss how features of this spacetime can be seen from the embedding diagram. The purpose of this work is educational: The associated embedding diagrams may be useful for explaining aspects of black holes to students who are familiar with special relativity, but not general relativity.Comment: 22 pages, 21 figures, RevTex. To be submitted to the American Journal of Physics. Experts will wish only to skim appendix A and to look at the pictures. Suggested Maple code is now compatible with MapleV4r

Magnetic Order in YBa2_2Cu3_3O6+x_{6+x} Superconductors

Polarized and unpolarized neutron diffraction has been used to search for magnetic order in YBa$_2$Cu$_3$O$_{6+x}$ superconductors. Most of the measurements were made on a high quality crystal of YBa$_2$Cu$_3$O$_{6.6}$. It is shown that this crystal has highly ordered ortho-II chain order, and a sharp superconducting transition. Inelastic scattering measurements display a very clean spin-gap and pseudogap with any intensity at 10 meV being 50 times smaller than the resonance intensity. The crystal shows a complicated magnetic order that appears to have three components. A magnetic phase is found at high temperatures that seems to stem from an impurity with a moment that is in the $a$-$b$ plane, but disordered on the crystal lattice. A second ordering occurs near the pseudogap temperature that has a shorter correlation length than the high temperature phase and a moment direction that is at least partly along the c-axis of the crystal. Its moment direction, temperature dependence, and Bragg intensities suggest that it may stem from orbital ordering of the $d$-density wave (DDW) type. An additional intensity increase occurs below the superconducting transition. The magnetic intensity in these phases does not change noticeably in a 7 Tesla magnetic field aligned approximately along the c-axis. Searches for magnetic order in YBa$_2$Cu$_3$O$_{7}$ show no signal while a small magnetic intensity is found in YBa$_2$Cu$_3$O$_{6.45}$ that is consistent with c-axis directed magnetic order. The results are contrasted with other recent neutron measurements.Comment: 11 pages with 10 figure

Incommensurate Magnetic Fluctuations in YBa2Cu3O6.6

We use inelastic neutron scattering to demonstrate that at low temperatures, the low frequency magnetic fluctuations in YBa_2Cu_3O_{6.6} ($T_c=62.7$ K) are incommensurate, being found at positions displaced by $\pm\delta$ ($0.057\pm 0.006$ r.l.u.) along the $[\pi,\pi]$ direction from the wave vector $(\pi,\pi)$ associated with the antiferromagnetic order of the parent insulator, YBa_2Cu_3O_{6}. The dynamical susceptibility $\chi''(q,\omega)$ at the incommensurate positions increases on cooling below $T_c$, accompanied by a suppression of magnetic fluctuations at the commensurate points.Comment: 11 pages, Latex, 4 figure

X-Ray-Diffraction Study of Charge-Density-Waves and Oxygen-Ordering in YBa2Cu3O6+x Superconductor

We report a temperature-dependent increase below 300 K of diffuse superlattice peaks corresponding to q_0 =(~2/5,0,0) in an under-doped YBa_2Cu_3O_6+x superconductor (x~0.63). These peaks reveal strong c-axis correlations involving the CuO_2 bilayers, show a non-uniform increase below \~220 K with a plateau for ~100-160 K, and appear to saturate in the superconducting phase. We interpret this unconventional T-dependence of the ``oxygen-ordering'' peaks as a manifestation of a charge density wave in the CuO_2 planes coupled to the oxygen-vacancy ordering.Comment: 4 pages, 4 figure

Translational Symmetry Breaking in the Superconducting State of the Cuprates: Analysis of the Quasiparticle Density of States

Motivated by the recent STM experiments of J.E. Hoffman et.al. and C. Howald et.al., we study the effects of weak translational symmetry breaking on the quasiparticle spectrum of a d-wave superconductor. We develop a general formalism to discuss periodic charge order, as well as quasiparticle scattering off localized defects. We argue that the STM experiments in $Bi_2Sr_2CaCu_2O_{8+\delta}$ cannot be explained using a simple charge density wave order parameter, but are consistent with the presence of a periodic modulation in the electron hopping or pairing amplitude. We review the effects of randomness and pinning of the charge order and compare it to the impurity scattering of quasiparticles. We also discuss implications of weak translational symmetry breaking for ARPES experiments.Comment: 12 pages, 9 figs; (v2) minor corrections to formalism, discussions of dispersion, structure factors and sum rules added; (v3) discussion of space-dependent normalization added. To be published in PR

Spin and charge excitations in incommensurate spin density waves

Collective excitations both for spin- and charge-channels are investigated in incommensurate spin density wave (or stripe) states on two-dimensional Hubbard model. By random phase approximation, the dynamical susceptibility \chi(q,\omega) is calculated for full range of (q,\omega) with including all higher harmonics components. An intricate landscape of the spectra in \chi(q,\omega) is obtained. We discuss the anisotropy of the dispersion cones for spin wave excitations, and for the phason excitation related to the motion of the stripe line. Inelastic neutron experiments on Cr and its alloys and stripe states of underdoped cuprates are proposed