Superconducting Phase Diagram of the Yttrium, Barium, and YBa-core in YBa₂Cu₃O_7–δ by an Ising Model

We investigate the temperature dependent of magnetizations, hysteresis properties and present the superconducting phase diagrams of the YBa₂Cu₃O_7–δ (YBCO) by an Ising model within the effective-field theory. We obtain the magnetizations of the YBCO and its components (Cu1, Cu2, O1, O2, O3, O4, Ba, Y, CuO-shell, YBa-core, and total YBCO) versus the reduced temperature and external magnetic field. We find that the copper atoms have two different magnetizations (Cu1 and Cu2) and oxygen atoms have four different magnetizations (O1, O2, O3, O4) but yttrium and barium has one magnetization. The differences in the magnetizations of the copper and oxygen atoms result from the lattice location of them on the YBCO lattice. The magnetization of the Cu1 atoms is the lowest and the yttrium is highest than those of the others; hence magnetizations of the YBCO increase from the corner to inner of the orthorhombic YBCO lattice. We also find that the YBa-core, yttrium and barium atoms of the YBCO exhibit superconductivity behaviors. Therefore, Y–Ba core, yttrium and barium atoms have the superconducting phase diagram and it has Meissner, vortex, and normal states. It is also found that the upper critical coercive field (H_c2) and the critical vortex temperature (T_v) of the Ba are high than those of the Y and YBa-core.