  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.
