FERROMAGNETISM IN NARROW NON-DEGENERATE ENERGY BANDS - A VARIATIONAL PRINCIPLE

We consider conduction electrons moving in a narrow non-degenerate energy band and subject to a strong repulsive potential which acts between two electrons of opposite spin when they occupy the same atomic site. We restrict our analysis to cases where the density of electrons per atom c<1 and formulate a trial wave function for that state for which all the electron spins except one are aligned. This odd electron we assume to be localized around a particular lattice site whilst the remaining electrons adjust their motion adiabatically to the presence of this single electron. The variational energy associated with this particular choice of trial wave function can be calculated exactly and we expect it to be a good approximation to the true energy in the high density and extremely strong interaction limit. Since the energy of the ferromagnetic state, for which all the electron spins are aligned, can also be deduced exactly we can then formulate a sufficient criterion for the instability of the ferromagnetic state. We conclude quite generally that when the repulsive potential is sufficiently large and the density of electrons is sufficiently high, or 1-c<<1, the ferromagnetic state is never the stable ground state of the model.