RESUMO
We investigate the effect of the electric field on the spin-dependent thermoelectric properties of graphene nanoribbons with asymmetric zigzag edge extensions. The Hubbard Hamiltonian predicts spin-semiconducting behavior with localized band structures due to the magnetic properties of the zigzag edge extensions. Applying a temperature gradient induces thermal spin-dependent currents, pure spin currents, and large spin-Seebeck coefficients, which are similar to other graphene-based structures. Considering the effect of the electric field sensitively reduces the spin gap and finally the threshold temperature. Moreover, the electric field slightly widens the localized band structures around the Fermi energy and could induce ten times more spin current in these nanoribbons.