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Graphene-based spin logic gates
Minggang Zeng,1,2 Lei Shen (沈雷兲,1,a兲Haibin Su,3Chun Zhang,1,4 and Yuanping Feng1,b兲
1Department of Physics, 2 Science drive 3, National University of Singapore, Singapore 117542
2NanoCore, 5A Engineering Drive 4, National University of Singapore, Singapore 117576
3Division of Materials Science, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798
and Institute of High Performance Computing, 1 Fusionopolis Way, Connexis, Singapore 138632
4Department of Chemistry, 3 Science Drive 3, National University of Singapore, Singapore 117543
共Received 6 January 2011; accepted 12 February 2011; published online 1 March 2011兲
Logic operation is the key of digital electronics and spintronics. Based on spin-dependent transport
property of zigzag graphene nanoribbons studied using nonequilibrium Green’s function method
and density functional theory, we propose a complete set of all-carbon spin logic gates, in which the
spin-polarized current can be manipulated by the source-drain voltage and magnetic configuration of
the electrodes. These logic gates allow further designs of complex spin logic operations and pave the
way for full implementation of spintronics computing devices. © 2011 American Institute of
Physics.关doi:10.1063/1.3562320兴
Graphene, a single layer of graphite, is considered a
promising material for spintronics since spin injection and
detection in graphene at room temperature have been
demonstrated.1,2Zigzag graphene nanoribbons 共ZGNRs兲can
be patterned from graphene sheets or unzipped from carbon
nanotubes.3–5In addition to its interesting spin properties of
graphene, ZGNRs have unique spin polarized edge states.6
These edge states may be tuned by applying electrical field
or choosing edge functional groups, giving rise to half-
metallic properties.7–10 Moreover, ZGNR-based giant mag-
netoresistance devices has been theoretically proposed and
experimentally realized, indicating possible application of
ZGNRs in digital storage.3,11 However, there have not been
any implementation for the ZGNR-based logic gates, which
is crucial for building a complete digital spin-based electron-
ics. In this letter, we propose theoretical design of a complete
set of spin logic gates based on an intrinsic selective rule of
spin-polarized current in ZGNRs. We also present a half
adder as an example of spin calculators.
Our calculations were carried out within the framework
of density functional theory 共DFT兲combined with nonequi-
librium Green’s function method 共NEGF兲as implemented in
ATK package.12,13 The local spin density approximation with
the Perdew–Zunger exchange-correlation functional was
adopted, and the single-
共SZ兲basis set was used for electron
wave function as that in Ref. 11. A cutoff energy of 150 Ry
and a Monkhorst–Pack k-mesh of 1⫻1⫻100 yielded a good
balance between computational time and accuracy in the re-
sults. The predefined norm-conserving pseudopotential was
used for modeling interatomic potential. The NEGF-DFT
self-consistency was controlled by a numerical tolerance of
10−5 eV. Contour integration was carried out in the imagi-
nary plane to obtain the density matrix from the Green’s
function. We used 30 contour points, with a lower energy
bound of 3 Ry in the contour diagram in the case of zero bias
and additional contour points spaced at 0.02 eV along the
real energy axis in the case of nonzero bias. The electron
temperature was set to 300 K in the transport calculation. In
all the calculations, dangling bonds at the edges of GNRs
were saturated with pseudohydrogen atoms. A 15 Å vacuum
slab was used to eliminate interaction between ZGNRs in
neighboring cells.
A ZGNR with Nzigzag chains is denoted by N-ZGNR.14
In our calculation, we focus on 8-ZGNR since previous
study has concluded that only ZGNR with an even number
of zigzag chain shows the transmission selection rule, which
is related to the symmetry of ZGNRs.16 Magnetization of the
ZGNR electrodes can be controlled by an external magnetic
field,2,11,15 and can be set to 1 共spin up polarization, i.e., spin
up electron dominates spin down electron兲,0共nonmagnetic兲,
or –1 共spin down polarization兲. As shown in Fig. 1共a兲,we
denote the magnetization configuration of the left and right
electrode by 关ML,MR兴共ML,MR=1,0, or –1兲. The calculated
spin-polarized current for the 8-ZGNR are shown in Fig.
1共b兲. The ZGNR shows metallic behavior for both positive
and negative bias in the 关1,1兴configuration. In the 关1,–1兴
configuration, the spin transport property under a negative
bias is completely different from that under the positive bias.
a兲Electronic mail: shenlei@nus.edu.sg.
b兲Electronic mail: phyfyp@nus.edu.sg.
0.5 1.0 1.5 2.0 2.5 3.0 3.5
0.20
0.22
0.24
0.26
0.28
0.30
Vth (V)
width (nm)
(a)
(b) (c)
FIG. 1. 共Color online兲共a兲The schematic illustration of ZGNRs based two
terminal devices. The magnetization configuration of the left and right elec-
trode are denoted by 关ML,MR兴共ML,MR= 1 , 0, or –1兲. A positive bias drives
current from source to drain. 共b兲I-Vcurves of 关1,1兴and 关1,–1兴magnetic
configurations of the 8-ZGNR. The width dependent threshold voltage in the
关1,–1兴configuration is shown in the inset. 共c兲I-Vcurves for the 8-ZGNR
with the magnetic configuration of 关1,0兴and 关–1,0兴.
APPLIED PHYSICS LETTERS 98, 092110 共2011兲
0003-6951/2011/98共9兲/092110/3/$30.00 © 2011 American Institute of Physics98, 092110-1
Under a positive bias, only the spin-down current passes
through the device while under a negative bias, only the
spin-up current is allowed. This selective spin current
through the device is attributed to the orbital symmetry of
spin subbands.16 As shown in the inset of Fig. 1共b兲, the
threshold voltage for 关1,–1兴configuration decreases with the
increase in ribbon width. Therefore, when the ribbon is suf-
ficiently wide, the threshold voltage is zero. Besides the
共关1,1兴兲 and 共关1,–1兴兲 magnetic configurations of the elec-
trodes, we also considered the spin dependent transport in
the magnetic configurations 关1,0兴and 关–1,0兴. The calculated
I-Vcurves are shown in Fig. 1共c兲, which are similar to those
in the 关1,–1兴configuration, with the exception of a zero
threshold voltage in the 关1,0兴and 关–1,0兴configurations.
The above results indicate that the spin channel of the
two-terminal device is controllable in all three magnetic con-
figurations, 关1,–1兴,关1,0兴,关–1,0兴. The conducting spin channel
can be selected by setting proper bias direction 共+or–兲
and/or magnetic configuration 共1,0 and –1兲of the left and
right electrodes. This flexible control over spin current
makes it possible to use the two-terminal device as a basic
component for building spin logic devices. In the following,
we label the input terminals of the devices by Aand/or B,
and the output terminal by Y. In all designs, the logic inputs
are encoded by the magnetization of the terminals, with posi-
tive magnetization of the ZGNR electrode representing the
logic input 1 and negative magnetization representing logic
0. The result of the logic operation, however, is expressed in
terms of the output current. For convenience of discussion,
we assume that only the spin-up current is detected by set-
ting the proper magnetization of ferromagnetic electrode in
nonlocal measurement,1,17,18 so that we can encode the logic
output to be 1 共0兲if the output current include 共exclude兲the
spin up current.
Figure 2共a兲shows the schematic of a design for the NOT
logic gate. The device consists of two terminals, and the
magnetization of the right ZNGR electrode is set to zero
共nonmagnetic兲. The voltage of the left electrode is higher
than that of the right electrode, so that the spin polarized
current flows from left to right. If the magnetization of the
left electrode is set to –1 共logic input 0兲, the spin-up channel
is conducting, corresponding to a logic output 1. On other
hand, the spin-down channel is conducting 共logic output 0兲
when the magnetization of the left electrode is set to 1 共logic
input 1兲. The NOT logic operation is thus realized. The truth
table and circuit symbol are shown in Fig. 2共a兲. Similarly, an
AND gate can be designed but it requires three terminals, as
shown in Fig. 2共b兲. The magnetization of the left electrode is
pinned to 1, and inputs are represented by the magnetizations
of the center and right terminals. The electric potential de-
creases from left to right. Based on the I-Vcurve given in
Fig. 1, it can be easily seen that only when the magnetiza-
tions of both the center and right terminal correspond to
logic 1, the output includes the spin up current 共logic output
1兲. In all other cases, either the spin polarized currents are
completely blocked or only the spin-down current reaches
the output terminal, corresponding to logic output 0. The
logic operations are summarized in Fig. 2共b兲, along with the
truth table and circuit symbol of this AND gate. The logic
OR operation can also be realized similarly as shown in Fig.
2共c兲. Here, the left and right electrodes are used as the input
terminals, and the middle electrode is used as the output
terminal and its magnetization is pinned to 0. The spin-up
current passes through the output terminal when magnetiza-
tion of either or both input terminals is 1. Only when both of
the input terminals are set to –1 共logic input 0兲, the output
current consists of spin-down electrons, corresponding to
logic output 0. Other logic operations, such as NAND and
NOR gates, can also be realized based on the above design
concepts.
Using the logic gates as building blocks, a graphene-
based circuit architecture with spin as the operation variable
for logic operation can be expected. As an example, we
present a possible design of a nanoscale spin calculator using
a half adder. The half adder is a logical circuit that performs
an addition operation on two one-bit binary numbers, de-
noted by Aand B, respectively. The output of the half adder
is a sum of the two inputs, expressed in terms of a sum 共S兲
and a carry 共C兲, i.e., sum=2⫻C+S. Figure 3shows the
schematic diagram, the circuit symbol and the truth table for
a half adder. As can be seen, the half adder is composed of a
XOR and AND logic gates, both of them can be created
based on the ZGNR-based spintronic logic gates discussed
above.
YA
YAB
YAB
(b)
(c)
(a)
FIG. 2. 共Color online兲Schematic illustrations of the spin logic gates: 共a兲
logic NOT gate, 共b兲logic AND gate, and 共c兲logic OR gate. The input
terminals are labeled by Aand B, the output terminal is labeled by Y.Mref
represents the pinned magnetization of the terminal. The logic input 1 共0兲is
encoded by the magnetization 1 共–1兲of the input terminals. The logic output
1共0兲is encoded if the output current includes 共excludes兲the spin up current.
The truth table and circuit symbol are shown in the right side of each panel.
092110-2 Zeng et al. Appl. Phys. Lett. 98, 092110 共2011兲
Although several devices have been proposed for the
spin logic operation,19–21 the one proposed here has distinct
features and advantages. First, graphene is an excellent spin
conductor due to its long spin diffusion length. Second,
ZGNRs-based spin logic gates can be patterned from
graphene, which makes the integration of the spin logic gates
with other powerful and abundant graphene-based compo-
nents much easier. Furthermore, graphene is a half-metallic
material and can be used for as conducting wire for ZGNRs-
based spin logic circuits. In addition, owing to the fact that
magnetization can be controlled by a current-carrying wire,
the problem related to different types of input 共magnetiza-
tion兲and output 共spin current兲signals can be easily over-
come in the proposed devices.
In summary, our first-principles studies show that a com-
plete set of spin logic gates can be realized in ZGNRs due to
the intrinsic selective rule of spin-polarized current. More-
over, a nanoscale spin calculator is used to demonstrate how
these logic gates can be put together to perform calculations.
Our work demonstrate that ZGNR can be a potential candi-
dature for integrating logic operations and digital storage for
digital spin-based electronics.
This work is supported by the National Research
Foundation 共Singapore兲Competitive Research Program
共Grant No. NRF-G-CRP 2007-05兲.
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(b)
(a)
FIG. 3. 共Color online兲Schematic diagram of a ZGNR-based half-adder and
its true table.
092110-3 Zeng et al. Appl. Phys. Lett. 98, 092110 共2011兲