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 ${\mathrm{\varepsilon }}_{\mathit{f}}$ is deep enough: ${\mathrm{\varepsilon }}_{\mathit{f}}$${\mathrm{\varepsilon }}_{\mathit{f}\mathit{c}}$, where ${\mathrm{\varepsilon }}_{\mathit{f}\mathit{c}}$ is of the order of the bandwidth. Rigorous arguments show that if ${\mathrm{\varepsilon }}_{\mathit{f}}$${\mathrm{\varepsilon }}_{\mathit{f}\mathit{c}}$, the ground state has the total spin S=(N-1)/2 for ${\mathit{N}}_{\mathit{e}}$=N+1, where N is the number of lattice sites and ${\mathit{N}}_{\mathit{e}}$ is that of electrons. This indicates that a transition to a (incompletely) magnetically ordered ground state will occur for a value of ${\mathrm{\varepsilon }}_{\mathit{f}}$ less than ${\mathrm{\varepsilon }}_{\mathit{f}\mathit{c}}$. We observe this transition for finite U if -${\mathrm{\varepsilon }}_{\mathit{f}}$ is sufficiently large. An extension to more generalized models is discussed. The exact diagonalization technique is applied to a cluster cut out of the ${\mathrm{CuO}}_2$ 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.