Nanostructured graphene for spintronics

Zigzag edges of the honeycomb structure of graphene exhibit magnetic polarization, making them attractive as building blocks for spintronic devices. Here, we show that devices with zigzag-edged triangular antidots perform essential spintronic functionalities, such as spatial spin splitting or spin filtering of unpolarized incoming currents. Near-perfect performance can be obtained with optimized structures. The device performance is robust against substantial disorder. The gate-voltage dependence of transverse resistance is qualitatively different for spin-polarized and spin-unpolarized devices, and can be used as a diagnostic tool. Importantly, the suggested devices are feasible within current technologies.

Figure 1

Device geometry (above) and infinite antidot lattice results (below). Spin up (down) is denoted red (blue) throughout. (a) Device geometry, with $W_{\mathrm{zz}}\approx 6\text{nm}, W_{\mathrm{ac}}\approx 4\text{nm}, L_{▵}\approx 1\text{nm}, L_{\mathrm{zz}}\approx L_{\mathrm{ac}}\approx 2\text{nm}$, and spin-splitting effect with color map displaying the local spin-dependent current magnitude for spin-unpolarized injection through the left electrode (L) $J_{\mathrm{L}}^{\mathrm{s}}$. (b) Same as (a) but with a ${180}^{\circ }$ rotated antidot. (c) Magnetic moment profile of the antidot lattice: Moments are represented by circles with radii $\propto |m_i|$. The inset illustrates magnetic moment profiles for, from left to right, $L_{▵}=1\text{nm}, L_{▵}=4\text{nm}$, rotated $L_{▵}=4\text{nm}$, and armchair-edged $L_{▵}=1\text{nm}$. (d) Spin-dependent transmissions ($T_{\sigma }$) and density of states (${\rho }_{\sigma }$) of the antidot lattice. The lattice geometry is shown in the inset and has a $\sim 6\times 6\text{nm}$ square unit cell (dotted box).

Figure 2

(a) Local current magnitude through a device with a single triangular antidot at $E=20\text{meV}$. (b) Spin polarization of currents in the same system (red: spin up; blue: spin down). Bottom: Spin-dependent transmissions left top [LT, (c)] and left bottom [LB, (d)].

Figure 3

(a) Schematic of the graphene cross device with a $5\times 4$ array of triangular antidots. All triangles are oriented in the same direction with same magnetic moment profile, i.e., as in Fig. 1 (red triangles). $W_{\mathrm{zz}}=60\sqrt{3}a\approx 26\text{nm}$ and $W_{\mathrm{ac}}=131a/2\approx 16\text{nm}$. (b) The splitting efficiency, as defined in main text, of the $5\times 4$ array (solid) and the single-antidot (dotted) devices. (c) The local charge currents and (d) spin polarization for injection from the left electrode for $E=20\text{meV}$ (red: spin up; blue: spin down).

Figure 4

(a), (b), (d) Transport splitting efficiency of $5\times 4$ antidot arrays with different disorder. The splitting efficiency of ten disordered device realizations is shown in gray, the configurational average for each type in black, and the pristine $5\times 4$ array in black dashed [reproduced from Fig. 3]. (a) Random flipping of antidots and reversal of spin polarization (see inset). An additional array realization with every second antidot flipped ($5\times 4_{\mathrm{R}}$) is shown by the black dotted curve. (b) Random variation of side length, as in the inset. (c) Realization of an antidot with removed atoms (black arrows) and the corresponding magnetic moment profile. The moment profile here and in Fig. 1 are scaled equally. (d) Splitting efficiencies for antidot edge atom disorder [see (c)].

Figure 5

Transverse resistance $R$ in units of $R_0=h/e^2$ for a single-antidot device and two $5\times 4$ array devices when injecting only $\uparrow$ electrons into the L lead (shown in red). The resistances of spin-unpolarized ($m_i=0$) and spin-polarized ($M=\sum m_i\ne 0$) antidot devices are shown in black and red, respectively. (a) Single-antidot device, with the inset showing a schematic of $\uparrow$-polarized electron injection. (b) $5\times 4$ array devices with aligned (solid) and the alternatingly flipped triangles (dotted). The inset shows the schematic of a $5\times 4$ array device with $\uparrow$-polarized electron injection).