We study the spin filtering and quantum phase transition (QPT) in double quantum dots attached to spin-polarized leads. For spin-independent leads, we observe a Kosterlitz-Thouless transition between the local triplet and doublet. For spin-polarized leads, the above QPT becomes first order, and Kondo splitting, gate-controlled spin reversal and a perfect spin filtering are observed. The breaking of spin-rotation SU(2) symmetry and the interdot transport mediated by the conduction electron are responsible for the fully spin-polarized conductance. Because spin-polarized leads suppress the Kondo effect, in order to obtain a large conductance with perfect spin filtering, one should choose leads with small spin polarization, such as Rashba spin-orbital coupling leads.
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