Model for the low-temperature magnetic phases observed in doped YBa2Cu3O6+x

A classical statistical model for the antiferromagnetic ordering of the Cu spins in the CuO₂ planes of reduced YBa₂Cu₃O_6+x-type materials is presented. The magnetic phases considered are the experimentally observed high-temperature antiferromagnetic (AFI) phase with ordering vector Q_I=(12120), and the low-temperature phases: antiferromagnetic (AFII) with Q_II=(121212) and intermediate Turn-Angle (TA) phases TAI, TAII, and TAIII with components of both ordering vectors. It is shown that the AFII and TA phases result from an effective ferromagnetic-type coupling mediated by free spins in the CuO_x basal plane. Good agreement with experimental data is obtained for realistic model parameters.