Efficient spin injection in graphene using electron optics

We investigate theoretically spin injection efficiency from the ferromagnetic graphene to normal graphene (FG/NG) based on electron optics, where the magnetization in the FG is assumed from the magnetic proximity effect. Based on a graphene lattice model, we demonstrated that one spin-species electron flow from a point source could be nearly suppressed through the FG-NG interface, when the total internal reflection effect occurs with the help of an additional barrier masking the Klein tunneling, while the opposite spin-species electron flow could even be collimated due to the negative refraction under suitable parameters. Not only at the focusing point is the efficient spin injection achieved, but in the whole NG region the spin injection efficiency can also be maintained at a high level. It is also shown that the nonideal FG-NG interface could reduce the spin injection efficiency since the electron optics phenomena are weakened owing to the interfacial backscattering. Our findings may shed light on making graphene-based spin devices in the spintronics field.

Figure 1

(a) Plot of a schematic two-terminal graphene device. Gate voltage $V_{g1}$ and $V_{g2}$ can control the local potentials of FG and NG, respectively; a point source angularly spreads electrons while an extended drain collects those that refract around the tunnel barrier made from a lattice void. (b) Trajectories of the spin-up electrons (red solid-line arrows) that are collimated due to negative refraction and spin-down electrons (blue dotted-line arrows) that are totaly reflected with the help of a tunnel barrier.

Figure 2

Distribution of local particle density variation $\delta {\rho }_{\downarrow }\left(l\right)$ in an armchair FG/NG nanoribbon junction for $U_N=-0.1t$ in (a), $U_N=-0.07t$ in (b), and $U_N=-0.04t$ in (c) and (d). A tunnel barrier is considered in (d) with the barrier width $d=150b$ and length $l=20\times 3a$. Other parameters are the ribbon width $W=601b$, the source position is $(-250\times 3a,0)$, $h=0.1t$, and $U_F=-0.06t$.

Figure 3

Distribution of local particle density variation $\delta {\rho }_{\downarrow }\left(l\right)$ in an zigzag FG/NG nanoribbon junction. Parameters are exactly the same as the armchair ribbon case shown in Fig. 2.

Figure 4

Distribution of spin-up particle density variation $\delta {\rho }_{\uparrow }\left(l\right)$ in the FG/NG armchair-edge nanoribbon junction without a barrier (a) and with a barrier (b). Parameters are same as with those in Fig. 2.

Figure 5

Spin polarization $P$ in the armchair-edge FG/NG junction without a barrier in (a) and (c), and with a barrier in (b) and (d). A smooth FG-NG interface was considered in (c) and (d) instead of the sharp interface in (a) and (b). Parameters are the ribbon width $W=601b$, the source position at $(-250\times 3a,0)$, $h=0.1t$, and $U_F=-0.06t$, $U_N=-0.04t$, the barrier width $d=127b$, and length $l=20\times 3a$.

Figure 6

Spin polarization $P_1$ and $P_2$ in the armchair-edge FG/NG junction as a function of the barrier width $d$ in (a) and the local potential $U_N$. The lattice size is the width $W=601b$ and length $450\times 3a$ in the NG region. Parameters are $h=0.1t$, $U_F=-0.06t$, and $U_N=-0.04t$ in (a), $d=0$ in (b).