Itinerant ferromagnetism in strongly correlated electron systems

We exactly show that the ground state of the Anderson lattice with U={∞} is ferromagnetic at quarter filling if the level of localized electrons εf is deep enough: εf{{{ε}}}fc$, where ${{{ε}}}fc$ is of the order of the bandwidth. Rigorous arguments show that if ${{{ε}}}fεfc, the ground state has the total spin S=(N-1)/2 for Nₑ=N+1, where N is the number of lattice sites and Nₑ is that of electrons. This indicates that a transition to a (incompletely) magnetically ordered ground state will occur for a value of εf less than εfc. We observe this transition for finite U if -εf is sufficiently large. An extension to more generalized models is discussed. The exact diagonalization technique is applied to a cluster cut out of the CuO₂ plane. Our analysis shows that the system with one-hole doping has a ferromagnetic phase in the ground state, indicating that a doped hole in the O p orbital is moving around in the ferromagnetic background of Cu spins.