Device structure and physical operation

The active switching element is a zigzag GNR field-effect transistor with a constant gate voltage and two CNT control wires, as illustrated in Fig. 1. The gate voltage is held constant, and the GNR conductivity is therefore modulated solely by the magnetic fields generated by the CNTs. These magnetic fields can flip the orientation of the strong on-site magnetization at the GNR edges, which display local antiferromagnetic (AFM) ordering due to Hubbard interactions36 (see Methods). As shown in Fig. 2, the magnetization at each edge is controlled by its neighbouring CNT, with magnetization decaying towards the centre of the GNR. In the absence of an external magnetic field or with edge magnetizations of opposite polarities, the GNR exhibits global AFM ordering in the ground state. Significantly, GNRs with edge magnetizations of the same polarity exhibit global ferromagnetic (FM) ordering in the ground state.

Figure 1: All-carbon spin logic gate. Magnetoresistive GNR unzipped from carbon nanotube and controlled by two parallel CNTs on an insulating material above a metallic gate. As all voltages are held constant, all currents are unidirectional. The magnitudes and relative directions of the input CNT control currents I CTRL determine the magnetic fields B and GNR edge magnetization, and thus the magnitude of the output current I GNR . Full size image

Figure 2: Graphene nanoribbon edge magnetization. (a) On-site magnetization profile of a zigzag graphene edge. The magnetic field created by an adjacent CNT current causes strong on-site magnetization at the GNR edge. The colour of each circle represents the spin species, while the radius corresponds to the magnitude of the magnetization. (b) The on-site magnetization of each site in a unit cell as a function of distance from the edge. (c) Graphene nanoribbon edge magnetization in the absence and presence of an externally applied magnetic field. In the absence of a magnetic field, the GNR exhibits global AFM ordering with edges of opposite polarities. The application of a magnetic field aligns the edge polarities, achieving global FM ordering. Full size image

Mean-field tight-binding calculations show that the GNR global magnetic ordering determines the band structure, and therefore the conductivity. The Zeeman interaction can switch the magnetic ground state, causing spin-dependent band splitting. There are conduction modes in the FM state for all energies, but no conduction modes in the AFM state for Fermi energy E F within the AFM state bandgap. By tuning E F into the AFM bandgap through control of the gate voltage, the application of magnetic fields at the GNR edges causes a colossal change in conductivity, switching the GNR from the resistive AFM state to a conductive FM state. Importantly, if E F is outside the AFM bandgap, conduction modes are always available, and switching of the magnetic ordering does not cause a change in conductivity. This is one possible explanation for the lack of magnetoresistance observed by Bai et al.28 when applying an in-plane magnetic field to a GNR. It can be further noted that given the proximity between the CNTs and GNR, the attractive van der Waals and repulsive Casimir forces may alter the electronic wavefunctions and energy dispersion. However, these effects do not change the nature of the highly conductive CNT transport, nor the electron–electron repulsion among lattice sites. As a result, the spontaneous AFM ordering and edge magnetization are not sufficiently affected to alter the GNR magnetoresistance.

Edge effects and operation temperature

The spin-dependent band splitting is strongest with pristine zigzag edges37 as achieved in ref. 35, enabling a spin-polarized current38 and closing the energy gap for the GNR in the FM state as shown in Fig. 3. Local edge defects in quasi-pristine GNRs cause local perturbation in the magnetic ordering around these defects37. However, the magnetic state is quickly regained within two unit cells (<1 nm) from the defect. As a result, the switching mechanism persists with defect spacing >3 nm, increasing the magnitude of the critical magnetic field for large defect density. As the magnetic ordering originates from the GNR edges, it is not affected significantly by defects present away from the edges. In the case of very rough edges, a lack of sufficient contiguous zigzag portions to compensate for the presence of armchair edges may result in large switching fields.

Figure 3: Magnetoresistive behaviour of GNR controlled by adjacent CNTs. (a,b) Band diagrams for the AFM and FM global ordering of a 12-atom-wide zigzag GNR with zero current in the CNTs and Hubbard parameter U=2.7 eV, as in equation (1) of Methods. In the global AFM state (a), there is a large gap between the valence and conduction bands, within which lies the Fermi energy, E F . Therefore, there are no available conduction modes, and the conductance is zero. In the FM state (b), there is no bandgap and there is at least one conduction mode at all energies. (c,d) The magnetic instability energy in μeV for zigzag GNRs with widths of (c) 20 nm and (d) 35 nm. The blue region designates a positive instability energy (the insulating AFM state), while the red region indicates negative instability energies (the conductive FM state). In the narrower GNR transistor, the axes of the CNTs are 10 nm from the GNR edge, while the wider GNR has CNTs placed 1 nm away. The critical switching current, which depends on U, is denoted with a dashed line. (e) The transmission function of the AFM state defines the number of available conduction modes as well as the probability for an electron to travel across the device. Thus, for E F values within the bandgap, the GNR conductance switches when the global ordering switches between the FM and AFM states. (f) A typical switching event, where the GNR conductance increases by G 0 when the CNT current overcomes the critical switching current I C . Full size image

Smooth GNRs with long contiguous stretches of pristine zigzag edges have been experimentally demonstrated35. As defects affect the magnetization on the order of 1 nm around the defect location37, this abundance of zigzag edges of 5 nm or larger elicits strong magnetic ordering. Sufficient contiguous zigzag edges between defects thus enable a persistence of the magnetic order.

Yazyev39 indicated a GNR Curie temperature near 10 K, below which the spin correlation length grows exponentially. At temperatures around 70 K, correlation lengths are on the order of 10 nm, presenting a limitation for device operation. The correlation length approaches 1 nm at room temperature, making observation of the magnetization difficult in disordered systems. Therefore, low temperatures are desirable to minimize the required magnetic field and to ensure the manifestation of this effect in large samples. This concern may have been resolved, with magnetic order recently demonstrated in zigzag GNRs at room temperature40.

Switching behaviour

We performed simulations of the proposed all-carbon spintronic switching device to determine the system and material parameters required to ensure feasibility. The magnetic instability energy is dependent on the GNR width (Supplementary Note 1), and determines the edge magnetic field required to switch the global ground state from AFM to FM ordering. As shown in Fig. 3c,d, the CNT current sufficient to overcome the magnetic instability energy is strongly affected by the proximity of the CNT control wires to the GNR edges. The current requirement can be tuned through control of the Hubbard U parameter. The required current ranges from exceptionally small magnitudes to significant fractions of an Ampere, and can be minimized with a wide GNR positioned close to the CNT control wires. As the GNR width is increased, the magnetic instability energy decreases as nearly the inverse square of the width25. For many U values and GNR/CNT geometries, the 20 μA that can be passed through a single-walled CNT is sufficient to maintain the required switching current41,42,43.

When the GNR switches from the AFM to the FM state, there is a massive change in conductance, as shown in Fig. 3f. The magnitude of the current through the GNR functions as the binary gate output, with binary 1 representing the large current of the conductive FM state and binary 0 representing the resistive AFM state. The GNR current flows through the CNT from which it was unzipped, and this binary CNT current is the input to cascaded GNR gates. It should be noted that unlike other spintronic logic proposals, logic gates can be cascaded directly through the carbon materials without requiring intermediate control or amplification circuitry.

Logic gates and system integration

The various combinations of input magnitudes and directions permit the computation of the logical OR and XOR operations. When there is no difference in magnetization between the edges of the GNR, the GNR is in the resistive AFM state and outputs a binary 0. Application of current through the CNTs can cause the GNR to switch into the FM state and output a binary 1. The OR logic function of Table 1 is computed by CNT currents oriented in opposite directions that create aligned on-site magnetization at the GNR edges. This OR gate thus enables a highly conductive FM state in the presence of current in at least one input CNT. In the XOR logic function of Table 2, the input currents are oriented in the same direction. Therefore, large currents flowing through both CNTs cause AFM ordering in the XOR gate, resulting in a small output current. This GNR switching device provides the functionality necessary for general-purpose computing, as the OR and XOR gates form a sufficient basis set to generate all binary functions.

Table 1 GNR OR gate truth table for input CNT control currents in opposite directions. Full size table

Table 2 GNR XOR gate truth table for input CNT control currents in the same direction. Full size table

Nanofabrication trends suggest potential techniques for efficiently constructing cascaded all-carbon spin logic integrated circuits scaled up to perform complex computing tasks. Parallel and perpendicular CNTs can be laid out on an insulating surface44 above a metallic material used as a constant universal gate voltage for the entire circuit. As shown in Fig. 4, a complex circuit composed of the logic gates of Fig. 1 can be created through selective CNT unzipping to form GNRs24,30,32,33,34,35. Electrical connectivity between overlapping CNTs34,45,46 can be determined by the placement of an insulating material. The only external connections are to the supply voltage and user input/output ports (for example, keyboard, monitor and so on), possibly with vertical covalent contacts of the type described by Tour47. All computing functionality is performed by the carbon materials alone, without the aid of external circuitry. As in other large-scale integrated circuits, fabrication imprecision (for example, misaligned CNTs, imperfect CNT junctions, edge defects and so on) can be tolerated provided that the GNR logic gates function properly and the electrical connectivity between CNTs is correct. Though the possibility of miniaturization is an important figure of merit for conventional computing structures, the atomic dimensions of CNTs and GNRs make the concept of down-scaling irrelevant for all-carbon spin logic.

Figure 4: All-carbon spin logic one-bit full adder. (a) The physical structure of a spintronic one-bit full adder with magnetoresistive GNR FETs (yellow) partially unzipped from CNTs (green), some of which are insulated (brown) to prevent electrical connection. The all-carbon circuit is placed on an insulator above a metallic gate with constant voltage V G . Binary CNT input currents A and B control the state of the unzipped GNR labelled XOR1, which outputs a current with binary magnitude ⊕B. The output of XOR1 flows through a CNT that functions as an input to XOR2 and XOR3 before reaching the wired-OR gate OR2, which merges currents to compute C IN V(A⊕B). This current controls XOR4 and terminates at V − . The other currents operate similarly, computing the one-bit addition function with output current signals S and C OUT . (b) In the symbolic circuit diagram shown here with conventional symbols, the output of XOR1 is used as an input to OR2 and XOR3 along with C IN . The full adder S output is computed as S=C IN V⊕(A⊕B). OR2 outputs C IN V(A⊕B), which is used along with S as an input to XOR4 to compute (C IN V(A⊕B))⊕(C IN ⊕(A⊕B)). This output of XOR4 is equivalent to (A∧C IN )V(B∧C IN ). OR3 takes this signal as an input along with the output of XOR2, which is equal to A∧B, to compute C OUT =(A∧B)V(A∧C IN )V(B∧C IN ). As the wired-OR gates simply sum the currents and have no significant delay, the total propagation time is that of three XOR gates, determined by the XOR1–XOR3–XOR4 worst-case path. Full size image