Effective Hamiltonian for FeAs-based superconductors

The recently discovered FeAs-based superconductors show intriguing behavior and unusual dynamics of electrons and holes which occupy the Fe d orbitals and As 4s and $4p$ orbitals. Starting from the atomic limit, we carry out a strong-coupling expansion to derive an effective Hamiltonian that describes the electron and hole behaviors. The hopping and the hybridization parameters between the Fe d and As s and p orbitals are obtained by fitting the results of our density-functional-theory calculations to a tight-binding model with nearest-neighbor interactions and a minimal orbital basis. We find that the effective Hamiltonian, in the strong on-site Coulomb-repulsion limit, operates on three distinct subspaces coupled through Hund's rule. The three subspaces describe different components (or subsystems): (a) one spanned by the d_x²-y² Fe orbital, (b) one spanned by the degenerate atomic Fe orbitals dxz and dyz, and (c) one spanned by the atomic Fe orbitals dxy and d_z². Each of these Hamiltonians is an extended t-t^'-J-J^' model and is characterized by different coupling constants and filling factors. For the case of the undoped material the second subspace alone prefers a ground state characterized by a spin-density-wave order similar to that observed in recent experimental studies, while the other two subspaces prefer an antiferromagnetic order. We argue that the observed spin-density-wave order minimizes the ground-state energy of the total Hamiltonian.