Magnetic charge pairing in CuO sheets: Classical and quantum studies

We consider a square lattice formed by quantum spin-12 particles interacting through a nearest-neighbor antiferromagnetic Heisenberg Hamiltonian. Each spin represents a Cu ion in CuO2 sheets of high-Tc superconductors. The O ions residing on the bonds of the lattice are normally doubly charged spinless particles O-2. The charged holes responsible for the supercurrent are supposed to be O-1 ions substituting O-2 in some bonds. As each O-1 ion is a spin-12 particle, the magnetic coupling between its two neighboring Cu is transformed into ferromagnetic instead of the normal Cu antiferromagnetic interaction. So, we consider some ferromagnetic bonds diluted in our antiferromagnetic host square lattice. For this system, we show that the bottom of the magnetic energy band presents a larger density of states when the holes come together than when they are distant from each other on the lattice. This behavior gives an effective attraction between holes that can be responsible for the charge pairing characteristic of superconductivity. As the dominant terms responsible for enhancing the density of states do not contain cross products between different spin components, a simplified Ising classical version of the model is used to perform Monte Carlo simulations.