Indirect exchange interaction in a thin film of rare-earth metals

The indirect exchange interaction between localized magnetic moments in a thin film of rare-earth metals is calculated by the second-order perturbation. The Greens function for the noninteracting conduction electron system is found by solving directly equations of motion set up for a slab. It is shown that the presence of surfaces, with or without surface potentials, severely changes the interaction energy near the surfaces. The peculiar behavior of surface magnetic interactions can be completely understood via the bulk-state local density of states as well as the surface-state local density of states, calculated directly from the imaginary part of the Greens function. The relation between our results and the surface enhancement of magnetic ordering is also briefly discussed.