High-Tc superconductivity in copper oxides emerges from antiferromagnetic (AF) Mott-insulating parent compounds upon doping. In the YBa2Cu3O6+x system, short-range incommensurate (IC) magnetic order is observed for x ≲ 0.5, below a critical hole-doping level for static magnetism, pc ~ 0.09. Although magnetic Bragg peaks are absent for p > pc , IC spin fluctuations persist and develop a low-energy gap below Tc. A deeper understanding of these IC spin correlations could clarify how hole doping suppresses AF order and provide new insight into the superconducting pairing mechanism.

We present a detailed neutron scattering study of the evolution of static magnetic correlations with hole doping. Our results reveal progressively weakening three-dimensional spin correlations up to pc. We find that YBa2Cu3O6.4 (p = 0.07, Tc = 20 K) exhibits both commensurate and incommensurate magnetic reflections that are closely related, consistent with a three-dimensionally correlated state characterized by a single temperature dependence. Polarization analysis indicates that the magnetism has a dominant unidirectional component, which can be understood in terms of an amplitude-modulated structure.

We discuss how the inferred spin correlations in YBa2Cu3O6+x might be related to the stripe ordering phenomenon observed in other cuprates such as La2-xBaxCuO4.