Magnetic and metal-insulator transitions in coupled spin-fermion systems

We use quantum Monte Carlo to determine the magnetic and transport properties of coupled square lattice spin and fermionic planes as a model for a metal-insulator interface. Specifically, layers of Ising spins with an intra-layer exchange constant $J$ interact with the electronic spins of several adjoining metallic sheets via a coupling $J_H$. When the chemical potential cuts across the band center, that is, at half-filling, the N\'eel temperature of antiferromagnetic ($J>0$) Ising spins is enhanced by the coupling to the metal, while in the ferromagnetic case ($J<0$) the metallic degrees of freedom reduce the ordering temperature. In the former case, a gap opens in the fermionic spectrum, driving insulating behavior, and the electron spins also order. This induced antiferromagnetism penetrates more weakly as the distance from the interface increases, and also exhibits a non-monotonic dependence on $J_H$. For doped lattices an interesting charge disproportionation occurs where electrons move to the interface layer to maintain half-filling there.