Magnetic phase diagram of the one-band Hubbard Hamiltonian with application to high-Tcsuperconducting oxides

Using an extension of the Gutzwiller approximation and applying the Bethe-lattice method, we have studied the magnetic phase transition between various phases of one-band Hubbard Hamiltonian. We allow the magnetic moments to point in an up or down direction and determine self-consistently the local magnetic moment on each lattice site. We obtain that the paramagnetic state with local moments is energetically more favorable than the Pauli paramagnetic state. The phase transition from magnetically ordered to disordered states involves mainly a transition to a paramagnetic state with local moments. We calculated the magnetic phase diagram as function of on-site Coulomb repulsion U and dopant concentration δ. Results are discussed in connection with the phase diagram observed for high-${\mathit{T}}_{\mathit{c}}$ superconductors. In agreement with experiment, we obtain, for reasonably large values of U, a small critical dopant concentration of 3-5% for the destruction of antiferromagnetism 2 due to the occurrence of a paramagnetic state with local moments. We show that the Hartree-Fock approximation greatly exaggerates the stability of magnetic states. The validity of our results is discussed.