  We have calculated the persistent spin current of an open ring induced by the
Aharonov-Casher phase. For unpolarized electrons there exist no persistent
charge currents, but persistent spin currents. We show that, in general, the
magnitude of the persistent spin current in a ring depends on the direction of
the direct current flow from one reservoir to another. The persistent spin
current is modulated by the cosine function of the spin precession angle. The
nonadiabatic Aharonov-Casher phase gives anomalous behaviors. The
Aharonov-Anandan phase is determined by the solid angle of spin precession.
When the nonadiabatic Aharonov-Anandan phase approaches a constant value with
the increase of the electric field, the periodic behavior of the spin
persistent current occurs in an adiabatic limit. In this limit the periodic
behavior of the persistent spin current could be understood by the effective
spin-dependent Aharonov-Bohm flux.
