Decoherence of localized spins interacting via RKKY interaction

We theoretically study decoherence of two localized spins interacting via the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction in one-, two-, and three-dimensional electron gas. We derive the kinetic equation for the reduced density matrix of the localized spins and show that energy relaxation caused by singlet-triplet transition is suppressed when the RKKY interaction is ferromagnetic. We also estimate the decoherence time of the system consisting of two quantum dots embedded in a two-dimensional electron gas.