  We obtain a microscopic description of the interaction between electron spins
in bulk semiconductors and in pairs of semiconductor quantum dots. Treating the
k.p band mixing and the Coulomb interaction on the same footing, we obtain in
the third order an asymmetric contribution to the exchange interaction arising
from the coupling between the spin of one electron and the relative orbital
motion of the other. This contribution does not depend on the inversion
asymmetry of the crystal. We find that it is ~0.001 of the isotropic exchange,
which is of interest in quantum information. Detailed evaluations are given for
several quantum dot systems.
