Ruderman-kittel-kasuya-yosida interaction near the surface of a semi-infinite rare-earth metal

We investigate the indirect exchange interaction of the magnetic moments localized near the surface of a semi-infinite rare-earth metal. The noninteracting- (conduction-) electron system in the semi-infinite metal is solved by the Greens-function technique. The interaction energy between the moments, mediated by the conduction electron, is then calculated by second-order perturbation. Our treatment allows the anisotropy nature of the interaction and the finite height of the surface barrier. We obtain analytical results for certain limiting cases although numerical integration is necessary in general. It is found that the interaction near the surface can be drastically different from the usual Ruderman-Kittel-Kasuya-Yosida interaction in the bulk. This vigorous variation indicates possible occurrence of the reconstruction of magnetic ordering near the surface.