  We theoretically investigate the spin-dependent transport for the system of
an armchair-edge graphene nanoribbon (AGNR) between two ferromagnetic (FM)
leads with arbitrary polarization directions at low temperatures, where a
magnetic insulator is deposited on the AGNR to induce an exchange splitting
between spin-up and -down carriers. By using the standard nonequilibrium
Green's function (NGF) technique, it is demonstrated that, the spin-resolved
transport property for the system depends sensitively on both the width of AGNR
and the polarization strength of FM leads. The tunneling magnetoresistance
(TMR) around zero bias voltage possesses a pronounced plateau structure for
system with semiconducting 7-AGNR or metallic 8-AGNR in the absence of exchange
splitting, but this plateau structure for 8-AGNR system is remarkably broader
than that for 7-AGNR one. Interestingly, the increase of exchange splitting
$\Delta$ suppresses the amplitude of the structure for 7-AGNR system. However,
the TMR is enhanced much for 8-AGNR system under the bias amplitude comparable
to splitting strength. Further, the current-induced spin transfer torque (STT)
for 7-AGNR system is systematically larger than that for 8-AGNR one. The
findings here suggest the design of GNR-based spintronic devices by using a
metallic AGNR, but it is more favorable to fabricate a current-controlled
magnetic memory element by using a semiconducting AGNR.
