Spintronic Faraday rotation spectroscopy and geometrical modulation of spin current in an Aharonov-Casher ring

We study the ballistic spin transmission through an AC ring between two ferromagnetic filter-electrodes in the presence of spin-orbit interaction, theoretically. It is shown that the spin precession of polarized electrons can be controlled via a cylindrically symmetric electric field, and the sequence of the polarized conductance depends on the relative orientation of magnetization between the left and right filters. The injected spin-polarized electrons can be blocked completely for the special values of electric field and angle of texture, which makes the magnetoresistance to be drastically enhanced. We also propose an interference scheme to detect the geometric phase.