On the possibility of saturated ferromagnetism

Abstract

This paper is concerned with the possible degree of spin alignment in the ground state of a system of spin-½ fermions whose Hamiltonian (spin independent) consists of the usual kinetic-energy term plus a coordinate-dependent potential energy. It is shown that by suitable choice of the one- and two-body potentials one can rigorously insure that the ground state of a finite system of this sort is one of maximum multiplicity. This result contradicts a contention by Izuyama that when certain very general postulates are fulfilled, a crystal having complete spin alignment in its ground state in the thermodynamic limit will have to have a vanishing or negative spin-wave stiffness. It is shown that there is in fact no conflict with any of Izuyama's several correct expressions for the spin-wave stiffness, provided that in each case the last step in the evaluation is carried out with sufficient care.