In-plane anisotropy of spin excitations in the normal and
  superconducting states of underdoped YBa$_2$Cu$_3$O$_{6+x}$

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Abstract

A detailed inelastic neutron scattering study of the in-plane anisotropy of magnetic excitations in twin-free YBa$_2$Cu$_3$O$_{6.6}$ ($T_c =$ 61 K) reveals that the spin excitation spectra in the superconducting and normal states are qualitatively different. Below $T_c$, the spectrum consists of upward- and downward-dispersing branches with modest in-plane anisotropy merging at an energy $E_{res} =$ 37.5 meV. In the normal state, the singularity at $E_{res}$ disappears, and the spectrum exhibits a steep dispersion with a strongly anisotropic in-plane geometry. These data have important implications for models based on static or dynamic "stripe" order of spins and charges.

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Two-Dimensional Geometry of Spin Excitations in the High Temperature Superconductor YBa2Cu3O6+x

A. Kulakov, B. Keimer, C. Bernhard … (2004)

The fundamental building block of the copper oxide superconductors is a Cu4O4 square plaquette. In most of these materials, the plaquettes are slightly distorted and form a rectangular lattice. An influential theory predicts that high-temperature superconductivity is nucleated in "stripes" aligned along one of the axes of this lattice. This theory had received strong support from experiments that appeared to indicate a one-dimensional character of the magnetic excitations in the high temperature superconductor YBa2Cu3O6.6. Here we report neutron scattering data on "untwinned" YBa2Cu3O6+x crystals, in which the orientation of the rectangular lattice is maintained throughout the entire volume. Contrary to the earlier claim, we demonstrate that the geometry of the magnetic fluctuations is two-dimensional. Rigid stripe arrays therefore appear to be ruled out over a wide range of doping levels in YBa2Cu3O6+x, but the data may be consistent with liquid-crystalline stripe order.

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The Spin Excitation Spectrum in Superconducting ${\bf YBa_2Cu_3O_{6.85}}$

B. Keimer, A. Ivanov, J Bossy … (2000)

A comprehensive inelastic neutron scattering study of magnetic excitations in the near-optimally doped high-temperature superconductor ${\rm YBa_{2}Cu_{3}O_{6.85}}$ is presented. The spin correlations in the normal state are commensurate with the crystal lattice, and the intensity is peaked around the wave vector characterizing the antiferromagnetic state of the insulating precursor ${\rm YBa_{2}Cu_{3}O_{6}}$. Profound modifications of the spin excitation spectrum appear abruptly below the superconducting transition temperature, $\rm T_C$, where a commensurate resonant mode and a set of weaker incommensurate peaks develop. The data are consistent with models based on an underlying two-dimensional Fermi surface that predict a continuous, downward dispersion relation connecting the resonant mode and the incommensurate excitations. The magnetic incommensurability in the ${\rm YBa_{2}Cu_{3}O_{6+x}}$ system is thus not simply related to that of another high temperature superconductor, ${\rm La_{2-x}Sr_xCuO_{4}}$, where incommensurate peaks persist well above $\rm T_C$. The temperature dependent incommensurability is difficult to reconcile with interpretations based on charge stripe formation in ${\rm YBa_{2}Cu_{3}O_{6+x}}$ near optimum doping.