  We extend the classical phase-space distribution function to include the spin
and electromagnetic fields coupling and derive the modified constitutive
relations for charge current, energy-momentum tensor, and spin tensor. Because
of the coupling, the new tensors receive corrections to their perfect fluid
counterparts and make the background and spin fluid equations of motion
communicate with each other. We investigate special cases which are relevant in
high-energy heavy-ion collisions, including baryon free matter and large mass
limit. Using Bjorken symmetries, we find that spin polarization increases with
increasing magnetic field for an initially positive baryon chemical potential.
The corrections derived in this framework may help to explain the splitting
observed in Lambda hyperons spin polarization measurements.
