▎ 摘　　要

We theoretically investigate spin-dependent Seebeck effects for a system consisting of a narrow graphene nanoribbon (GNR) contacted to square lattice ferromagnetic (FM) electrodes with noncollinear magnetic moments. Both zigzag-edge graphene nanoribbons (ZGNRs) and armchair-edge graphene nanoribbons (AGNRs) were considered. Compared with our previous work with two-dimensional honeycomb-lattice FM leads, a more realistic model of two-dimensional square-lattice FM electrodes is adopted here. Using the nonequilibrium Green's function method combining with the tight-binding Hamiltonian, it is demonstrated that both the charge Seebeck coefficient S-C and the spin-dependent Seebeck coefficient S-S strongly depend on the geometrical contact between the GNR and the leads. In our previous work, S-C for a semiconducting 15-AGNR system near the Dirac point is two orders of magnitude larger than that of a metallic 17-AGNR system. However, S-C is the same order of magnitude for both metallic 17-AGNR and semiconducting 15-AGNR systems in the present paper because of the lack of a transmission energy gap for the 15-AGNR system. Furthermore, the spin-dependent Seebeck coefficient S-S for the systems with 20-ZGNR, 17-AGNR, and 15-AGNR is of the same order of magnitude and its maximum absolute value can reach 8 mu VK. The spin-dependent Seebeck effects are not very pronounced because the transmission coefficient weakly depends on spin orientation. Moreover, the spin-dependent Seebeck coefficient is further suppressed with increasing angle between the relative alignments of magnetization directions of the two leads. Additionally, the spin-dependent Seebeck coefficient can be strongly suppressed for larger disorder strength. The results obtained here may provide valuable theoretical guidance in the experimental design of heat spintronic devices. (C) 2015 AIP Publishing LLC.