Improved all-carbon spintronic device design

Abstract

The discovery of magnetism in carbon structures containing zigzag edges has stimulated new directions in the development and design of spintronic devices. However, many of the proposed structures are designed without incorporating a key phenomenon known as topological frustration, which leads to localized non-bonding states (free radicals), increasing chemical reactivity and instability. By applying graph theory, we demonstrate that topological frustrations can be avoided while simultaneously preserving spin ordering, thus providing alternative spintronic designs. Using tight-binding calculations, we show that all original functionality is not only maintained but also enhanced, resulting in the theoretically highest performing devices in the literature today. Furthermore, it is shown that eliminating armchair regions between zigzag edges significantly improves spintronic properties such as magnetic coupling.

Figure 1

(a) Kekulé structure of a triangular zigzag graphene nanoflake (TZGNF). No matter how the double bonds are arranged, at least two atoms will always be lacking a double bond, leading to the creation of free radicals (or topological frustrations, in this case two). This phenomenon can be quantified with a concept borrowed from graph theory known as maximal matching. (b) Bow-tie graphene nanoflake, or Clar's goblet. Note that the topological frustrations can exist on the interior or the edge atoms (as long as they belong to the given sublattice, for the structures presented here), and there are many more arrangements of the Kekulé structure possible. (c) If we connect the TZGNF from (a) with its mirror image, we arrive at structure (c) which has no topological frustration. The free radicals were able to recombine and form stable double bonds.

Figure 2. Example spintronic logic gate devices constructed from carbon.

A demonstration calculation for finding the magnetic coupling of each is presented in Table 1. The regions labeled A and B are the inputs, while D is the output, and C is a programmable bit. Devices (a) and (b) each can function as NOR or NAND gates, depending on the value of the programmable bit. Both devices also have valid Kekulé structures (no topological frustrations or free radicals), and both have the highest magnetic coupling values of their respective families (demonstrated in Figure 3).

Figure 3. Structure and magnetic couplings vs. structure index for (a) TZGNF-based NOT gate (b) RGNF-based NOT gate (c) TZGNF-based NOR/NAND gate and (d) armchair-less TZGNF-based NOR/NAND gate.

In the example structure images the structure index n is three. Up spin on-site occupation is in blue, down spin occupation in red, and half/half up/down occupation in white. It is apparent that the majority of the spin polarization occurs on the zigzag edges. Note that the axis scaling is different between the NOT and NOR/NAND gates. The best performing device for each structure family have magnetic couplings of: (a) 135 meV (b) 179 meV (c) 93 meV and (d) 113 meV, well above the 18 meV bare minimum threshold imposed by thermal fluctuations at room temperature (denoted as an orange horizontal line).

Figure 4

Left: the two classes of graphene nanoflakes considered for benchmarking purposes. The indices n and m correspond to the shape of the points on each line in the energy plots. Right: magnetic couplings computed using TB + U and VASP as a function of index n. In these plots, the different symbols correspond to m = 1 (), m = 2 (), m = 3 (), m = 4 (). Colors used for data on the right correspond to the colored structures on the left.