Temperature dependence of noncollinear interlayer coupling

Abstract

Based on the Anderson s-d mixing model in the presence of spin-orbit coupling, the noncollinear interlayer coupling in metallic magnetic layered structures is studied theoretically. After transforming the Anderson s-d mixing model into the s-d exchange model, both the isotropic and anisotropic Dzyaloshinsky-Moriya (DM) scattering potentials between the conduction electrons and localized moments are obtained. This anisotropic DM scattering potential can lead to a noncollinear interlayer coupling in magnetic metallic layered structures. At finite temperature, the anisotropic interlayer exchange coupling has the same spacer layer thickness dependence as the usual isotropic Ruderman-Kittel-Kasuya-Yosida (RKKY) interlayer coupling and consists of two terms. One term has the same temperature dependence as the isotropic coupling, but its oscillation with spacer layer thickness has a phase shift of π 2 . The other term has a different temperature dependence and no phase shift. Their relevance to the experimental results is also discussed.