Electron Spin Pairing and the Phase Diagram of High-T_c Superconductors

The origin of the instability of the normal state of electrons in the superconducting copper oxides is shown by the K-J model, in which the superexchange (K) between local moments and the Kondo exchange (J) between electron and local moment are considered. The suppression of superexchange via impurity doping may induce effective spin coupling between electrons and triplet pairing ( S = 1, S_z = 0 ). The spin pairing theory explains the phase diagram of the high-T_c superconductors, especially the superconducting transition temperature T_c, the pseudogap temperature T^* and the magnetic crossover temperature T_n as a function of the doped hole concentration. The universal expression for the empirical law of the superconducting transition temperature is derived from the theory.