  We report a novel relation between rotation and magnetic field in a charged
fluid system: there is naturally a magnetic field along the direction of fluid
vorticity due to the currents associated with the swirling charges. This
general connection is demonstrated using a fluid vortex. Applying the idea to
heavy ion collisions we propose a new mechanism for generating in-medium
magnetic field with a relatively long lifetime. We estimate the magnitude of
this new magnetic field in the Au-Au colliding systems across a wide span of
collisional beam energy. Such a magnetic field is found to increase rapidly
toward lower beam energy and could account for a significant amount of the
experimentally observed global polarization difference between hyperons and
anti-hyperons.
