FLUX PHASE AND DOPING DEPENDENCE OF ANTIFERROMAGNETISM IN COPPER-OXIDE COMPOUNDS

The ground-state properties of copper oxide compounds are studied by using the fermion-spin transformation. At half-filling, there are many possible phases for the 2D Heisenberg model and the mean-field state with the lowest energy is the magnetized pi-flux state. It is shown that the mean-field ground state of the 2D XY model is a uniform pi-flux phase with no staggered antiferromagnetic long-range order, and a reasonable result is also obtained for the 2D anisotropic Heisenberg model. In the mean-field level, the quantum fluctuation and frustration of spins can be considered by introducing the next-nearest-neighbor magnetic exchange interaction J', the antiferromagnetic long-range order is destroyed at half-fitting within the J-J' model where the value of J' is larger than the critical value J'(c) = 0.24J. Away from half-filling, the antiferromagnetic long-range order is destroyed for a hole concentration less than approximately 4.3%-7% for reasonable values of the parameters J'/J = 0.05 and t/J = 3-5 within the t-J-J' model, which is in good agreement with the experiments on copper oxide superconductors.