  Spin properties of single electron states in laterally coupled quantum dots
in the presence of a perpendicular magnetic field are studied by exact
numerical diagonalization. Dresselhaus (linear and cubic) and Bychkov-Rashba
spin-orbit couplings are included in a realistic model of confined dots based
on GaAs. Group theoretical classification of quantum states with and without
spin orbit coupling is provided. Spin-orbit effects on the g-factor are rather
weak. It is shown that the frequency of coherent oscillations (tunneling
amplitude) in coupled dots is largely unaffected by spin-orbit effects due to
symmetry requirements. The leading contributions to the frequency involves the
cubic term of the Dresselhaus coupling. Spin-orbit coupling in the presence of
magnetic field leads to a spin-dependent tunneling amplitude, and thus to the
possibility of spin to charge conversion, namely spatial separation of spin by
coherent oscillations in a uniform magnetic field. It is also shown that spin
hot spots exist in coupled GaAs dots already at moderate magnetic fields, and
that spin hot spots at zero magnetic field are due to the cubic Dresselhaus
term only.
