Ferromagnetic Spin Excitations in a Metallic Loop: The Case of Two Degenerate Bands

Abstract

We consider a system of $2N$ electrons in a periodic loop of $N$ lattice sites. These electrons are restricted to occupy the subspace of two degenerate bands. The interaction within a band is limited to nearest-neighbor and on-site Wannier integrals, but is otherwise arbitrary. The interaction between bands contains the complete set of intra-atomic terms but no nearest-neighbor term. The spectra of one-spin-flip excitations relative to the saturated ferromagnetic eigenstate are calculated exactly. The results show that it is necessary to have the intraband nearest-neighbor exchange coupling in order that the lowest spin-wave branch lie above the saturated ferromagnetic eignestate. Conditions for the local stability of the saturated ferromagnetic eigenstate are given. It is shown that the saturated ferromagnetic eigenstate can still be stable as a result of the nearest-neighbor exchange interaction $J$, even when the individual atoms would be non-magnetic when $J$ is turned off.