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 behavior. 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 sub-spaces coupled through Hund's rule. The three sub-spaces describe different components (or subsystems): (a) one spanned by the $d_{x^2-y^2}$ Fe orbital; (b) one spanned by the degenerate atomic Fe orbitals $d_{xz}$ and $d_{yz}$; and (c) one spanned by the atomic Fe orbitals $d_{xy}$ and $d_{z^2}$. 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.