Symmetry-dependent spin-charge transport and thermopower through a ZSiNR-based FM/normal/FM junction

We investigate the spin-dependent transport and spin thermopower for a zigzag silicene nanoribbon (ZSiNR) with two ends covered by ferromagnets (FMs) under the modulation of a perpendicular electric field, where we take the 6- and 7-ZSiNR to exemplify the effect of the even- and odd-N ZSiNRs, respectively. By using the nonequilibrium Green's function approach, it is demonstrated that a ZSiNR-based FM/normal/FM junction still shows an interesting symmetry-dependent property although the σ mirror plane is absent for any ZSiNR due to the buckled structure of silicene. The junction with even- or odd-N ZSiNR has very different transport and thermopower behavior, which is attributed to the different parity of π and ${\pi }^{\ast }$ band wavefunctions under the c ₂ symmetry operation with respect to the centre axis between two edges, and is linked to the unique symmetry of the band structure for the ribbon. As a result, the magnetoresistance (MR) for the 6-ZSiNR junction with a 100% plateau around zero electron energy is observed, but the plateau is absent for the 7-ZSiNR one. In addition, the spin thermopower also displays the even–odd behaviour. The 6-ZSiNR junction is found to possess superior thermospin performance compared with the 7-ZSiNR one, and its spin thermopower can be improved by one order of magnitude in the absence of an electric field. As the strength of the field increases, the spin thermopower for the 6-ZSiNR junction dramatically decreases, while it notably enhances for the 7-ZSiNR one. Interestingly, the spin thermopower for both junctions is strongly dependent on the strength of magnetisation in FM, and it can be very pronounced with a maximum absolute value of 200 μV K⁻¹by the optimisation of the parameters. However, with the increase in temperature, the spin thermopower for the 6-ZSiNR junction decreases, but the situation for the 7-ZSiNR one is opposite. Finally, the spin figure of merit for the 6-ZSiNR junction is found to be four orders of magnitude larger than that for the 7-ZSiNR one. This even–odd effect is common for N-SiNR, and the result can be regarded as an advance in the understanding of the characteristics of silicene and may be valuable for experimentally designing spin valve and heat spintronic devices based on silicene. (paper)