Spin-Orbit Mediated Anisotropic Spin-Spin Coupling

We study 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 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.