  We study the electronic transport through a noncollinear single-electron
spin-valve transistor. It consists of a small metallic island weakly coupled to
two ferromagnetic leads with noncollinear magnetization directions. The
electric current is influenced by Coulomb charging and by spin accumulation.
Furthermore, the interplay of Coulomb interaction and tunnel coupling to
spin-polarized leads yields a many-body exchange field, in which the
accumulated island spin precesses. We analyze the effects of this exchange
field in both the linear and nonlinear transport regime. In particular, we find
that the exchange field can give rise to a high sensitivity of the island's
spin orientation on the gate voltage.
