Mean-field theories of the two-band model and the magnetism in high-Tcoxides

The antiferromagnetic ground state of a two-band model Hamiltonian which &) and O(2$p_{x\left(y\right)}$) orbitals within a ${\mathrm{CuO}}_2$ plane, a common structural unit of high-$T_c$ superconducting oxides (HTSO), is studied by using a Hartree-Fock approximation (HFA) and the Gutzwiller ansatz (GA). Using the GA, a weak-coupling effective Stoner theory is derived in the low hole density limit. Compared to HFA, the Stoner parameter is strongly reduced, showing that correlations tend to weaken the magnetic instability in this limit. In the localized limit both the HFA and the GA converge to the same solution, corresponding to a classical Heisenberg system with the correct superexchange. We point out that the local spin-density approximation has intrinsic difficulties for the present problem. For intermediate d-hole densities numerical results are obtained and the magnetism of the HTSO is discussed. We argue that, in spite of its qualitative success, the model cannot account at the same time for the known magnetic and electronic properties of the HTSO.