The Ruderman-Kittel-Kasuya-Yosida Interaction on Conduction Electrons Having the Brillouin Zone Boundary

The modified Ruderman-Kittel-Kasuya-Yosida exchange constant J ( Q ) of local magnetic moment interacting via the conduction electrons having energy gap at the Brillouin zone boundaries is expressed through the use of the state density and the susceptibility function of these electrons. The effects of the Brillouin zone boundary appear specially on J (0). A simple band model of conduction electrons with {100} boundaries is considered as an example. On this model, we show that the positive peak of the J (0) curve plotted against the conduction electron number n shifts, with the change of the energy gap at the boundary, to the value of n where the Fermi surface starts to fill outside the Brillouin zone boundary. We can understand on this model, for example, the change of sign of θ p observed in rare earth intermetallics with Mg having the CsCl structure by taking the suitable OPW potentials for these compounds.