We identify theoretically the geometric phases of the electrons spin that can be detected in measurements of charge and spin transport through Aharonov-Bohm interferometers threaded by a magnetic flux $Phi$ (in units of the flux quantum) in which both the Rashba spin-orbit and Zeeman interactions are active. We show that the combined effect of these two interactions is to produce a $sin(Phi)$ [in addition to the usual $cos(Phi)$] dependence of the magnetoconductance, whose amplitude is proportional to the Zeeman field. Therefore the magnetoconductance, though an even function of the magnetic field is not a periodic function of it, and the widely-used concept of a phase shift in the Aharonov-Bohm oscillations, as indicated in previous work, is not applicable. We find the directions of the spin-polarizations in the system, and show that in general the spin currents are not conserved, implying the generation of magnetization in the terminals attached to the interferometer.
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