RudermanKittelKasuyaYosida

The Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction is an indirect exchange interaction between localized magnetic moments in a metal, mediated by conduction electrons. When a localized spin couples to itinerant electrons, those electrons become spin-polarized and interact with another localized spin, producing an effective coupling between the two moments. This interaction can be described as an indirect, distance-dependent exchange between spins, with a characteristic oscillatory form.

Historically, Ruderman and Kittel proposed the mechanism in 1954, Kasuya expanded the theory in 1956, and Yosida completed the formal framework in 1957. The combined term is named after these three researchers. The interaction arises from the static spin susceptibility of the conduction-electron sea and is often expressed as an effective Heisenberg exchange J(r) S1·S2 between two localized spins separated by distance r.

In three dimensions, J(r) decays roughly as cos(2kF r)/r^3 at large distances, where kF is the Fermi wavevector. The cosine factor causes the coupling to oscillate in sign, yielding ferromagnetic or antiferromagnetic alignment depending on the separation. In lower dimensions, the decay is slower (roughly 1/r^2 in 2D, 1/r in 1D) and the precise form depends on geometry and electronic structure. The strength of the interaction depends on the s–d exchange coupling and the conduction-electron density of states, and finite temperature or scattering introduces damping.

Applications and relevance include magnetic ordering in alloys and dilute magnetic systems, Kondo lattice models, spin glasses, and the design of layered magnetic structures where conduction electrons mediate interlayer coupling. The RKKY interaction is a cornerstone of understanding long-range magnetic coupling in metals.