Spin-orbit induced spin-spin coupling between electrons in coupled quantum dots

We investigate spin-spin interaction between electrons localized in spatially separated quantum dots. We show that in the presence of single electron spin-orbit interaction (of Rashba type) in the dots and Coulomb interactions between electrons, a new anisotropic coupling of the van der Waals type between spins emerges. Unlike the standard exchange this coupling does not require overlap of the wavefunctions, and as a result becomes dominant for large distance between the dots.This ferromagnetic interaction is important in the Wigner crystal state where the exchange processes are severely suppressed.