Momentum-Dependent Charge Correlations in ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6+\delta }$ Superconductors Probed by Resonant X-Ray Scattering: Evidence for Three Competing Phases

We use resonant x-ray scattering to determine the momentum-dependent charge correlations in ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6.55}$ samples with highly ordered chain arrays of oxygen acceptors (ortho-II structure). The results reveal nearly critical, biaxial charge density wave (CDW) correlations at in-plane wave vectors (0.315, 0) and (0, 0.325). The corresponding scattering intensity exhibits a strong uniaxial anisotropy. The CDW amplitude and correlation length are enhanced as superconductivity is weakened by an external magnetic field. Analogous experiments are carried out on a ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6.6}$ crystal with a dilute concentration of spinless (Zn) impurities, which had earlier been shown to nucleate incommensurate magnetic order. Compared to pristine crystals with the same doping level, the CDW amplitude and correlation length are found to be strongly reduced. These results indicate a three-phase competition between spin-modulated, charge-modulated, and superconducting states in underdoped ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6+\delta }$.