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We have used resonant x-ray scattering to determine the momentum dependentcharge correlations in YBa$_2$Cu$_3$O$_{6.55}$ samples with highly orderedchain arrays of oxygen acceptors (ortho-II structure). The results revealnearly critical, biaxial charge density wave (CDW) correlations at in-planewave vectors (0.315, 0) and (0, 0.325). The corresponding scattering intensityexhibits a strong uniaxial anisotropy. The CDW amplitude and correlation lengthare enhanced as superconductivity is weakened by an external magnetic field.Analogous experiments were carried out on a YBa$_2$Cu$_3$O$_{6.6}$ crystal witha dilute concentration of spinless (Zn) impurities, which had earlier beenshown to nucleate incommensurate magnetic order. Compared to pristine crystalswith the same doping level, the CDW amplitude and correlation length were foundto be strongly reduced. These results indicate a three-phase competitionbetween spin-modulated, charge-modulated, and superconducting states inunderdoped YBa$_2$Cu$_3$O$_{6+\delta}$.

physical review letters

Momentum-dependent charge correlations in YBa$_2$Cu$_3$O$_{6+\delta}$  superconductors probed by resonant x-ray scattering: Evidence for three  competing phases