RUDERMAN-KITTEL-KASUYA-YOSIDA POLARIZATION IN SOME INHOMOGENEOUS SITUATIONS

Exact expressions for the spin polarization due to a point field have been obtained for various inhomogeneous situations. The presence of bo undaries or potentials modifies the nodes and amplitudes of the polari zation, which determines the coupling between ion spins or nuclear mag netic moments in metals. For the half-space both in three and one dime nsions, the analytic solution contains the usual Ruderman-Kittel-Kasuy a-Yosida polarization. around the source plus a polarization wave orig inating from the mirror point, although, with the same phase at the bo rder; there both are canceled by a third term. The case of a slab in t hree and one dimensions has been treated. A one-dimensional model with a reflectionless localized potential with one bound state proved to b e tractable. It is shown that the integrated polarization is given by the probability densities of the electron states at the position of th e field summed over the Fermi surface.