The occurrence of spin polarization in parallel configuration could be understood through an investigation of the space-resolved local density of states (LDOS) for 8-ZGNR with different spin orientations at the Fermi level. Fig. 4(a) and 4(b) show the spin-up and spin-down LDOS of 2-ZGNR in P configuration. While the spin-up and spin-down LDOS of 2-ZGNR in AP configuration are shown in Fig. 4(c) and 4(d). From the comparison of Fig. 4(a) and 4(b), we can see that the edge oxygen atoms play a critical role in the density of states distribution of electrons with different spin direction at central scatter region. As shown in Fig. 4(b), the π-orbital concentrate on carbon atoms under oxygen-terminated line. The overlap fully opens a channel for π electrons to go through easily. While in Fig. 4(a), the transmission channels are nearly absent for spin-up electrons. However, as shown in Fig. 4(c) and 4(d), LDOS conditions for two different spin-orientation electrons are nearly the same in AP configuration. Further investigations indicate that the transportation of electrons in AP configuration is dominated by band selection rule between the two hydrogen-terminated GNR electrodes. Fig. 5(a) and 5(b) show the band structure of the left lead and right lead under zero bias. A certain spin direction electron can only transport from π*(π) state at the left lead to the same spin direction π*(π) state at the right lead. In Fig. 5(a) and 4(b), the blue (green) overlap indicates transmission gap of the up (down) spin electrons. The existence of transmission gap consists with the Fig. 3(b).

Figure 4 (a)–(d) are Space-resolved local density of states (LDOS) for up/down spin orientations at the Fermi level. (a) Up-spin electrons LDOS of the P 2-ZGNR; (b) Down-spin electrons LDOS of the P 2-ZGNR; (c) Up-spin electrons LDOS of the P 2-ZGNR; (d) Down-spin electrons LDOS of the P 2-ZGNR. Full size image

Figure 5 (a) the band structure of the left lead; (b) the band structures of the right lead. Full size image

The spin current polarization can be calculated by the equation:

where I up (down) is up (down) spin current for the same spin orientation configuration. The obtained current is then used to calculate the magneto-resistance (MR) using the following equation:

where I P and I AP are the sum of spin up current and spin down current in the antiparallel and parallel configurations for the two electrodes.

As shown in Fig. 6, we investigate the spin current polarization and magnetoresistance (MR) as a function of the oxidation level of the scatter region. The inset in Fig. 6(a) and Fig. 6(b) are the spin polarization and MR of 8-ZGNR as a function of bias voltage. In our case, the oxidation level can be simply represented by N which is defined as the number of oxygen atoms along single side of the ZGNR (W = 6, L = 12). 0-ZGNR (12-ZGNR) means all edge carbon atoms are terminated by hydrogen (oxygen) atoms. 0-ZGNR device configuration has a large MR value (6.8 × 105%) under small bias but has no spin polarization effect. On the other hand, both spin polarization and MR value of the fully edge oxidized 12-ZGNR are small. For a large range of oxidization level between these two extreme conditions, the proposed devices could maintain their good spin-filter performance (80% to 99%) and have a stable magneto resistance value (104% to 105% under small bias). This allows us to fabricate a high performance spin-filter and spin-valve device without precise controlling of the oxidization level.

Figure 6 (a) spin polarization ratio and (b) MR as a function of oxidization level of the devices. The inset in (a) and (b) are spin polarization and MR of 8-ZGNR as a function of bias voltage. Full size image

In summary, we investigated the spin-dependent electron transport of a device configuration with an oxygen-terminated ZGNR central scatter region between two hydrogen-terminated ZGNR electrodes. The parallel (anti-parallel) spin configuration could be achieved by setting spin orientations in two leads same (opposite). The transportation of electrons through the device is blocked in AP configuration and for up spin direction in P configuration. This means the N-ZGNR is insulating under these conditions. However, the proposed devices can transform to the metallic behavior for down spin electrons in P configuration. As calculated, these devices show a high spin polarization ratio and a considerable large MR value in a broad range of oxidization level. Our study provides a way for fabricating a perfect spin filter and a spin valve with the combination of the hydrogenation and oxidization of ZGNR edge atom.