▎ 摘　　要

We study the behavior of charge and spin transport properties in the presence of magnetic field and Rashba spin-orbit interaction in a six-terminal graphene nanoribbon using the multi-terminal Landauer-Buttiker formula and Green's function approach. We find that the Rashba spin-orbit coupling have detrimental effect on the quantum Hall plateaus in the sense that the width of the plateaus have drastically reduced in presence of the spin-orbit term. To assess whether presence of magnetic fields will have effects on the spintronic applications, we study the spin Hall conductance in presence of magnetic field. The spin Hall conductance features are also affected by the presence of a magnetic field where the antisymmetric nature with respect to zero of the Fermi energy, a prominent signature of the electron-hole symmetry, is destroyed. The local density of states data provides strong evidence of the above results.