We perform time-dependent simulations of spin exchange for an electron pair
in laterally coupled quantum dots. The calculation is based on configuration
interaction scheme accounting for spin-orbit (SO) coupling and
electron-electron interaction in a numerically exact way. Noninteracting
electrons exchange orientations of their spins in a manner that can be
understood by interdot tunneling associated with spin precession in an
effective SO magnetic field that results in anisotropy of the spin swap. The
Coulomb interaction blocks the electron transfer between the dots but the spin
transfer and spin precession due to SO coupling is still observed. The
electron-electron interaction additionally induces an appearance of spin
components in the direction of the effective SO magnetic field which are
opposite in both dots. Simulations indicate that the isotropy of the spin swap
is restored for equal Dresselhaus and Rashba constants and properly oriented
dots