Spintronics devices from bilayer graphene in contact to ferromagnetic insulators

Graphene-based materials show promise for spintronic applications due to their potentially large spin coherence length. On the other hand, because of their small intrinsic spin-orbit interaction, an external magnetic source is desirable in order to perform spin manipulation. Because of the flat nature of graphene, the proximity interaction with a ferromagnetic insulator (FI) surface seems a natural way to introduce magnetic properties into graphene. Exploiting the peculiar electronic properties of bilayer graphene coupled with FIs, we show that it is possible to devise very efficient gate-tunable spin rotators and spin filters in a parameter regime of experimental feasibility. We also analyze the composition of the two spintronic building blocks in a spin-field-effect transistor.

Figure 1

(a) Setup of the double gate BG with FI used as a spacer between the $U$ layer and the top gate. (b) Dispersion curve of biased BG, showing the typical Mexican hat behavior, subject to EPI. A gate bias $\Delta =-150$ meV is imposed between the BG layers. The full blue lines are $\nearrow$-spin-polarized bands (concord to the FI magnetization axis), while the dashed red lines are $\swarrow$-spin polarized. The dotted lines represent the normal nonmagnetic BG dispersion, as used for the LS and RS leads.

Figure 2

Conductance of spin up and spin down carriers as a function of chemical potential $\mu$ for a BG device acting as a SF calculated for increasing values of $L_C$. A FI is in contact to the $U$ layer of the BG, giving rise to an EPI with $E_z=8$ meV. The gate bias is $\Delta =-150$ meV and a potential shift of $U_0=5$ meV is applied in the $C$ region. In the inset, we show the spin-resolved conductance of the SF with $L_C=400a_0$ calculated for different temperatures.

Figure 3

Conductance with transmission into spin up $G_{\uparrow \uparrow }$ and spin down $G_{\downarrow \uparrow }$ carriers for a BG device acting as a SR in ON state, feeded by $\uparrow$-polarized electrons. In the inset the spin-flip conductance fraction $\chi =G_{\downarrow \uparrow }/(G_{\downarrow \uparrow }+G_{\uparrow \uparrow })$ is shown for ON ($\Delta <0$) and OFF ($\Delta >0$) state of the SR for $L_C=175a_0$. The dashed curves, data set (a), are calculated with $\left|\Delta \right|=40$ meV for $L_C=200a_0$.

Figure 4

In (a)–(c), we present the $\chi$ factor calculated for a SR with different values of the $E_z$ parameter for $L_C$ varying from 150 to $300a_0$. For comparison we show in (d)–(f) the corresponding first conduction-band dispersion: in a dotted curve that of the leads, while in full and dashed lines the $\nearrow$- and $\swarrow$-spin-splitted bands in the $C$ region of the SR, corresponding to the ON state.

Figure 5

Hybrid devices combining the SF and SR blocks described in Figs. 2 and 3, respectively. The full lines represent the total conductance for a series of two SFs in “open” or “closed” configuration. The dashed and dotted lines are for the total conductance of combined system made by the series of a SF($\uparrow$), a SR(ON/OFF), and a SF($\downarrow$). The calculation has been performed for a gate bias of $\left|\Delta \right|=150$ meV, with $L_C=400a_0$ for the SFs and $L_C=175a_0$ for the SR.

Figure 6

Spinor projection on the $U$ BG plane for the eigenstate corresponding to $k_{\min }$ of the first conduction (full line) and valence band (dashed line), as a function of the layer potential bias $\Delta$.

Figure 7

Projection of the eigenstates of the first conduction band on the $U$ BG plane, with (dashed line) and without (full line) trigonal warping corrections, for an applied bias of $\Delta =40$ meV; (a) is along the $X$ axis and (b) along the $Y$ axis.