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We theoretically investigate the spin-dependent transport through a graphene sheet between two ferromagnetic (FM) leads with arbitrary polarization directions at low temperatures, where a magnetic insulator is deposited on the graphene to induce an exchange splitting between spin-up and spin-down carriers. By using standard nonequilibrium Green's function (NGF) techniques, it is demonstrated that the density of states (DOS) decreases for spin-up and increases for spin-down when the polarization strength of the two leads in parallel alignment increases. For the electron energy around the exchange splitting, the DOS for both spin-up and spin-down channels is independent of the polarization. In contrast, the conductance increases for spin-up but decreases for spin-down with an increase of the polarization. Interestingly, the magnitude of tunneling magnetoresistance (TMR) can be dramatically suppressed with the increase of the exchange splitting in graphene. Furthermore, the current-induced spin transfer torque (STT) dependence on the relative angle. between the magnetic moments of the two leads shows a sine-like behavior and is enhanced with an increase of the polarization and/or the bias voltage. We attribute these spin-resolved effects to the breaking of the insulator-type properties of graphene with an exchange splitting between spin-up and spin-down carriers.

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