  We propose a general scattering matrix formalism that guarantees the charge
conservation at junctions between conducting arms with arbitrary spin
interactions. By using our formalism, we find that the spin-flip scattering can
happen even at nonmagnetic junctions if the spin eigenstates in arms are not
orthogonal. We apply our formalism to the Aharonov-Bohm interferometer
consisting of $n$-type semiconductor ring with both the Rashba spin-orbit
coupling and the Zeeman splitting. We discuss the characteristics of the
interferometer as conditional/unconditional spin switch in the
weak/strong-coupling limit, respectively.
