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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.
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Graphene-based spin logic gates
Minggang Zeng,1,2 Lei Shen (沈雷,1,aHaibin Su,3Chun Zhang,1,4 and Yuanping Feng1,b
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
Received 6 January 2011; accepted 12 February 2011; published online 1 March 2011
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.doi:10.1063/1.3562320
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 ZGNRscan
be patterned from graphene sheets or unzipped from carbon
nanotubes.35In 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.710 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 DFTcombined with nonequi-
librium Green’s function method NEGFas implemented in
ATK package.12,13 The local spin density approximation with
the Perdew–Zunger exchange-correlation functional was
adopted, and the single-
SZbasis 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 11100 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 spin up polarization, i.e., spin
up electron dominates spin down electron,0nonmagnetic,
or –1 spin down polarization. As shown in Fig. 1a,we
denote the magnetization configuration of the left and right
electrode by ML,MR兴共ML,MR=1,0, or –1. The calculated
spin-polarized current for the 8-ZGNR are shown in Fig.
1b. The ZGNR shows metallic behavior for both positive
and negative bias in the 1,1configuration. In the 1,–1
configuration, the spin transport property under a negative
bias is completely different from that under the positive bias.
aElectronic mail: shenlei@nus.edu.sg.
bElectronic 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. Color online兲共aThe schematic illustration of ZGNRs based two
terminal devices. The magnetization configuration of the left and right elec-
trode are denoted by ML,MR兴共ML,MR= 1 , 0, or –1. A positive bias drives
current from source to drain. bI-Vcurves of 1,1and 1,–1magnetic
configurations of the 8-ZGNR. The width dependent threshold voltage in the
1,–1configuration is shown in the inset. cI-Vcurves for the 8-ZGNR
with the magnetic configuration of 1,0and –1,0.
APPLIED PHYSICS LETTERS 98, 092110 2011
0003-6951/2011/989/092110/3/$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. 1b, the
threshold voltage for 1,–1configuration 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 1,0and –1,0. The calculated
I-Vcurves are shown in Fig. 1c, which are similar to those
in the 1,–1configuration, with the exception of a zero
threshold voltage in the 1,0and –1,0configurations.
The above results indicate that the spin channel of the
two-terminal device is controllable in all three magnetic con-
figurations, 1,–1,1,0,–1,0. The conducting spin channel
can be selected by setting proper bias direction +or–
and/or magnetic configuration 1,0 and –1of 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 0if the output current include excludethe
spin up current.
Figure 2ashows 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
nonmagnetic. 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 logic input 0, the spin-up channel
is conducting, corresponding to a logic output 1. On other
hand, the spin-down channel is conducting logic output 0
when the magnetization of the left electrode is set to 1 logic
input 1. The NOT logic operation is thus realized. The truth
table and circuit symbol are shown in Fig. 2a. Similarly, an
AND gate can be designed but it requires three terminals, as
shown in Fig. 2b. 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 logic output
1. 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. 2b, 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.
2c. 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 logic input 0, 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 S
and a carry C, i.e., sum=2C+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. Color onlineSchematic illustrations of the spin logic gates: a
logic NOT gate, blogic AND gate, and clogic 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 0is
encoded by the magnetization 1 –1of the input terminals. The logic output
10is encoded if the output current includes excludesthe 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 2011
Although several devices have been proposed for the
spin logic operation,1921 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 magnetiza-
tionand output spin currentsignals 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 SingaporeCompetitive Research Program
Grant No. NRF-G-CRP 2007-05.
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(b)
(a)
FIG. 3. Color onlineSchematic diagram of a ZGNR-based half-adder and
its true table.
092110-3 Zeng et al. Appl. Phys. Lett. 98, 092110 2011
... Here, the spin transport properties of molecular devices comprised of a transition metal-dibenzotetraaza [14]annulene complex (TM-DBTAA, TM=Co, Cu, Ni) connected to two single-walled carbon nanotube (SWCNT) electrodes have been theoretically investigated by using the first-principles method. In addition, the effect of O 2 adsorption on the TM atom on the spin transport properties of the investigated devices is inspected. ...
... Molecular spintronic devices, using molecular materials as one of the working components, have been attracting more and more attention due to their promise to improve device performance or offer new functionalities compared with the traditional analogues [1,2]. So far, a wide variety of functional molecular spintronic devices have been theoretically designed and experimentally fabricated, including molecular spin filters [3][4][5][6], molecular spin sensors [7][8][9], molecular spin switches [10,11], molecular spin valves [12,13], molecular spin logic gates [14][15][16][17] and so on. Among these molecular spintronic devices, molecular spin filters are of paramount importance in the spin circuit because they can generate spin-polarized current that is mainly composed of electrons with a specific spin. ...
... Besides metal porphyrin or metal phthalocyanine complexes, the dibenzotetraaza [14]annulene (DBTAA) has been shown to be another promising candidate for designing molecular spintronic devices [25][26][27][28]. For example, Wu et al. found the magnetic property of transition metal (TM) embedded DBTAA molecules (TM-DBTAA) was closely related to the embedded TM atom, of which Ni-DBTAA was nonmagnetic while others were magnetic [26]. ...
... [22] show the correlation between the electronic and magnetic properties of ZGNs. (b) Zeng [23] and colleagues determined the spin-dependent electron transport properties of 8-ZGNR. (c) Yun et al. [24] propose a diagrammatic representation of the magnetic moment of the MoS 2 monolayer induced by tensile strain. ...
... Further improvements in ferromagnetism behavior were observed when different research groups have conducted density functional theory calculations to investigate the strain-induced electronic and magnetic properties of single-layer MoS2 with vacancy defects [22][23][24][25][26][27]. It has been observed that the application of tensile strain induces ferromagnetic behavior and transforms the material into a metallic state [24]. ...
... Furthermore the spin polarized edge states, in principle also enable us to gain access to the spin degree of freedom in such ribbons. It has already been shown that the magnetic configuration of ZGNRs can be tuned by using an external magnetic field 22,23,24,25 or ferromagnetic electrodes 26,27,28,29 , which can be exploited in various device applications such as spin valves, spin diodes, spin transistor and GMR devices. ...
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... On the other hand, molecular spintronics, which combines molecular electronics and spintronics, is an emerging research field that takes full advantage of the spin degree of freedom of electrons and is expected to break through bottlenecks in areas including information storage, data process, and power consumption [25−28]. Till now, a great number of molecular spintronic devices have been designed, such as molecular spin valves [29,30], molecular spin filters [31−34], and molecular spin diodes [35]. ...
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