Dual spin filter effect in a zigzag graphene nanoribbon

By first principle calculations, a dual spin filter effect under finite bias voltages is demonstrated in an antiferromagnetic junction of symmetric zigzag graphene nanoribbon (ZGNR). Unlike conventional spin filter devices using half metallic materials, the up and down-spin electrons are unidirectionally filtered in the counter direction of the bias voltage, making the junction a dual spin filter. On the contrary, asymmetric ZGNRs do not exhibit such a spin filter effect. By analyzing Wannier functions and a tight-binding model, we clarify that an interplay between the spin polarized band structure of $\pi$ and ${\pi }^{\ast }$ states near the Fermi level and decoupling of the interband hopping of the two states, arising from the symmetry of the wave functions, plays a crucial role in the effect.

Figure 1

(Color online) (a) 8-ZGNR, terminated by hydrogen atoms, with an AFM junction together with the spatial distribution of the spin density at $V_{\text{bias}}=0\text{V}$, where the red and blue colors stands for positive and negative signs, and $L$, $R$, and $C$ means the left and right leads, and the central scattering region of which lengths are 4.88, 4.88, and $9.76\text{Å}$, respectively, and width is $17.78\text{Å}$. $I\text{−}{V}_{\text{bias}}$ curves for (b) the up-spin and (c) the down-spin states of seven and 8-ZGNRs with the AFM junction.

Figure 2

(Color online) Conductance of 8-ZGNR with the AFM junction with $V_{\text{bias}}$ of (a) 0.0, (b) $-0.4$, and (c) $-1.0\text{V}$. The inset in (a) shows the conductance gap near the chemical potentials.

Figure 3

(Color online) (a)–(c) Band structures of 8-ZGNR with a FM coupling corresponding to the left lead region in Fig. 1a. Band structures shifted with (d) 0.0, (e) $-0.4$, and (f) $-1.0\text{eV}$ of 8-ZGNR with a FM coupling corresponding to the right lead region in Fig. 1a, where the roles of the up and down-spin states are reversed because of the opposite spin direction in the right lead. The blue and red shades show the conductance gap for the up and down-spin electrons, respectively. The horizontal dot line indicates the chemical potential, being position dependent, of 8-ZGNR shown in Fig. 1a.

Figure 4

(Color online) Wannier functions for (a) the $\pi$ and (b) ${\pi }^{\ast }$ states of the nonspin polarized 8-ZGNR. (c) $I\text{−}{V}_{\text{bias}}$ curves of the up-spin state calculated by the simple TB model with the AFM junction for a series of the gate voltage $V_{\text{gate}}$.