Strong spin-dependent negative differential resistance in composite graphene superlattices

We find clear signatures of spin-dependent negative differential resistance in compound systems comprising a graphene nanoribbon and a set of ferromagnetic insulator strips deposited on top of it. The periodic array of ferromagnetic strips induces a proximity exchange splitting of the electronic states in graphene, resulting in the appearance of a superlattice with a spin-dependent energy spectrum. The electric current through the device can be highly polarized and both the current and its polarization manifest nonmonotonic dependence on the bias voltage. The device operates therefore as an Esaki spin diode, which opens possibilities to design new spintronic circuits.

Figure 1

The upper panel shows the GNR connected to source (S) and drain (D) leads, with $N=5$ perpendicular strips of a ferromagnetic insulator (green bars) on top of it. The model potential profiles for spin-up (dashed red lines) and spin-down (dotted blue lines) electrons in the unbiased and biased device are shown in the middle and lower panels, respectively.

Figure 2

(a) Scheme of a GNR of width $W=8a_0$. The boundary conditions for wave functions can be obtained by adding two rows of atoms (plotted in gray) at $y=0$ and $W+a_0$ and setting the wave function to 0 in those points. (b) Transmission across a series of $M$ potential steps. The incident plane wave with amplitude $A_0$ splits into a reflected and a transmitted component with amplitudes $B_0$ and $A_{M+1}$, respectively.

Figure 3

(a) Transmission probabilities $T_{\pm }$ as functions of energy for spin-up (red) and spin-down (blue) electrons. There is a very good agreement between the Dirac approximation (solid lines) and the tight-binding calculation (dotted lines). Horizontal bars in the lower part of the figure indicate the energy bands of the infinite superlattice, obtained from (10). (b) Transmission polarization $P_T$ as a function of energy for different numbers $N$ of ferromagnetic strips.

Figure 4

Panels (a) and (b) show that the transmission bands for both spins at finite bias $V_{\mathrm{SD}}$ are shifted, quenched and distorted compared to the unbiased case [Fig. 3a]. Panels (c) and (d) display the spin-polarized currents $I_{\pm }$ as functions of the bias $V_{\mathrm{SD}}$, for $T=4\mathrm{K}$ and different values of the chemical potential: $\mu -E_0=0\mathrm{meV}$ (dashed), $0.5\mathrm{meV}$ (dotted), and $1.0\mathrm{meV}$ (dash-dotted) lines. Finally, panels (e) and (f) show the total current $I=I_{+}+I_{-}$ and the current polarization $P=(I_{+}-I_{-})/I$ for the same parameters. All the intensity graphs use the same arbitrary scale.

Figure 5

Transmissions $T_{\pm }$ for both spins at finite bias $V_{\mathrm{SD}}=2\mathrm{mV}$, assuming that the voltage drop occurs at the edges of the EuO strips (solid) or linearly along the sample (dashed). Here, we use the tight-binding model, which can be compared with the Dirac approximation on Fig. 4b.