Spin-orbit mediated anisotropic spin interaction in interacting electron systems

We investigate interactions between spins of strongly correlated electrons subject to the spin-orbit interaction. Our main finding is that of a novel, spin-orbit mediated anisotropic spin-spin coupling of the van der Waals type. Unlike the standard exchange, this interaction does not require the wave functions to overlap. We argue that this ferromagnetic interaction is important in the Wigner crystal state where the exchange processes are severely suppressed. We also comment on the anisotropy of the exchange between spins mediated by the spin-orbital coupling.