  The spin up-down splitting of collective flows in intermediate-energy
heavy-ion collisions as a result of the nuclear spin-orbit interaction is
investigated within a spin- and isospin-dependent Boltzmann-Uehing-Uhlenbeck
transport model SIBUU12. Using a Skyrme-type spin-orbit coupling quadratic in
momentum, we found that the spin splittings of the directed flow and elliptic
flow are largest in peripheral Au+Au collisions at beam energies of about
100-200 MeV/nucleon, and the effect is considerable even in smaller systems
especially for nucleons with high transverse momenta. The collective flows of
light clusters of different spin states are also investigated using an improved
dynamical coalescence model with spin. Our study can be important in
understanding the properties of in-medium nuclear spin-orbit interactions once
the spin-dependent observables proposed in this work can be measured.
