Voltage-driven spintronic logic gates in graphene nanoribbons

Abstract

Electronic devices lose efficacy due to quantum effect when the line-width of gate decreases to sub-10 nm. Spintronics overcome this bottleneck and logic gates are building blocks of integrated circuits. Thus, it is essential to control electronic transport of opposite spins for designing a spintronic logic gate, and spin-selective semiconductors are natural candidates such as zigzag graphene nanoribbons (ZGNR) whose edges are ferromagnetically ordered and antiferromagnetically coupled with each other. Moreover, it is necessary to sandwich ZGNR between two ferromagnetic electrodes for making a spintronic logic gate and also necessary to apply magnetic field to change the spin orientation for modulating the spin transport. By first principle calculations, we propose a method to manipulate the spin transport in graphene nanoribbons with electric field only, instead of magnetic field. We find that metal gates with specific bias nearby edges of ZGNR build up an in-plane inhomogeneous electric field which modulates the spin transport by localizing the spin density in device. The specific manipulation of spin transport we have proposed doesn't need spin-charge conversion for output and suggests a possible base for designing spintronic integrated circuit in atomic scale.

Figure 1. Spintronic logic gate of ZGNR.

Diagram of the spintronic logic gate and electronic structure of a molecule analogous to the central device of the logic gate. (a), The 4ZGNR logic gate consists of four metal Gates_(1,2,3,4) (yellow) and two dielectric regions (red) beside the edges of the ribbon that has three parts: left electrode, device and right electrode. Because electrodes are semi-infinite long, only one primitive cell (green) is shown for each electrode in this figure. The width for metal gates and dielectric regions is 4 Å. Distance between Gate₁ and Gate₂ is 12 Å. a is the lattice constant of ZGNR, and 2.46 Å is used in this letter. (b), The spin density is plotted for the molecule of central device saturated by hydrogen atoms. The isovalue of the spin density is set to 0.0358 μ_B/ų (μ_B is Bohr magneton). α and β spins are shown in blue and red, respectively. (c), In electric field of 0.0 V/Å, 0.5 V/Å and 1.0 V/Å, energy levels of the molecule is plotted. Highest Occupied Molecular Orbital (HOMO) and Lowest Unoccupied Molecular Orbital (LUMO) are denoted by red and green dash lines. The energy gap between HOMO and LUMO is marked by black arrows. The energy gap of 0.5 V/Å is the smallest (60 meV) while the energy gaps of 0.0 V/Å and 1.0 V/Å are around 0.37 eV.

Figure 2. Transport properties of the spintronic logic gate.

Columns from left to right refer to spin-polarized transmission spectra in unit of e²/h, external potential of metal gates, transmission pathway and spin density. In the first column, transmission of α and β spins are denoted as grey up-triangle and dark down-triangle, respectively. In the second column, the bias of metal gates are displayed and color map shows the corresponding electrostatic potential with respect to the color legend from 0 V to 12 V. In the third column, blue arrows denote forward transmission from left electrode to right electrode, whereas red arrows denote backscattering. In the fourth column, density of α and β spins are displayed in blue and red, respectively. Rows from a to e refer to the seven irreducible combinations of bias on metal gates.