  The effect of the spin-orbit coupling in heavy ion collisions is investigated
based on an updated version of the ultra-relativistic quantum molecular
dynamics (UrQMD) model, in which the Skyrme potential energy density functional
is employed. And in special, the spin-orbit coupling effects on the directed
and elliptic flows of free nucleons emitted from $^{197}$Au+$^{197}$Au
collisions as functions of both the beam energy and the impact parameter are
studied. Our results show that the net contribution of the spin-orbit term to
flows of nucleons is negligible, whereas a directed flow splitting between
spin-up and spin-down nucleons is visible especially at large impact parameters
and a peak of the splitting is found at the beam energy around 150
MeV$/$nucleon. We also found that the directed flow splitting between spin-up
and spin-down neutrons is comparable with the neutron directed flow difference
calculated by a soft and a stiff symmetry energy, indicating that the directed
flow of neutrons cannot be used to pin down the stiffness of symmetry energy
any more without considering the spin degree of freedom in models in case of
spin polarization.
