Spin transport properties of a quantum dot coupled to ferromagnetic leads with noncollinear magnetizations

A correct general formula for the spin current through an interacting quantum dot coupled to ferromagnetic leads with magnetization at an arbitrary angle $\theta$ is derived within the framework of the Keldysh formalism. Under asymmetric conditions, the spin current component J_{z} may change sign for $0<\theta<\pi$. It is shown that the spin current and spin tunneling magnetoresistance exhibit different angle dependence in the free and Coulomb blockade regimes. In the latter case, the competition of spin precession and the spin-valve effect could lead to an anomaly in the angle dependence of the spin current.